E2ec85e027d51288f9becf17b31c3e1ad02c [617465]

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E2ec85e027d51288f9becf17b31c3e1ad02c [617465]

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Individual Blade Pitch and Disturbance
Accommodating Control of Floating
Offshore Wind T urbines
Hazim Namik
A thesis submitted in fulﬁlment of the requirements for the degree of Doctor of Philosophy in
Mechanical Engineering, The University of Auckland.
February 2012

ii

Abstract
Floating wind turbines offer a feasible solution for going further offshore into deep waters.
However, using a ﬂoating platform introduces additional motions that must be taken into ac-
count actively or passively. Therefore, the control system becomes an important component in
controlling these motions.
In this work, the development, implementation, and simulation of multi-objective state feed-
back and disturbance accommodating controllers applied on the three main ﬂoating concepts
are described. The three concepts are the barge, tension leg, and spar-buoy ﬂoating platforms.
These controllers utilise individual blade pitching to create asymmetric aerodynamic loads in
addition to the symmetric loads created by collective blade pitching to increase the platform
restoring moments.
Simulation results, according to design load case 1.2 of the IEC 61400-3 standard for offshore
wind turbines, show that state feedback controllers improve the performance relative to a col-
lective blade pitch gain scheduled proportional-integral controller in terms of power and rotor
speed regulation as well as reducing tower fore-aft and side-side bending loads. However, the
magnitude of the improvements depends on the dynamics of each platform, its responsiveness
to individual blade pitching and sensitivities to external wind and wave disturbances. Further-
more, interesting physical phenomena, such as the platform roll to pitch coupling caused by
the controller, are identiﬁed.
Disturbance accommodating controllers for rejecting wind speed perturbations further im-
prove rotor speed regulation and reduce tower fore-aft bending loads except on the barge
platform; the barge platform motion is dominated by incident waves and therefore rejecting
wind speed perturbations has no noticeable impact. Wave moment disturbance rejection is
also investigated but in a limited case study. While the approach taken can theoretically cancel
the effects of incident wave moments, practically, the required actuation force cannot be gen-
erated by the wind turbine blades. Furthermore, using the blades for rejecting wave moments
increases the tower bending due to the load path of the restoring moment through the tower.
Out of the three investigated platforms, the tension leg platform with a disturbance accom-
modating controller has the best overall performance with fatigue loads close or less than that
of an onshore wind turbine. The other two platforms, in their current design form, experience
large tower fore-aft bending loads that would prevent them from being deployed in rough sea
conditions.
iii

iv

To my loving parents
v

vi

Acknowledgements
First and foremost, I would like to thank my main supervisor Dr. Karl Stol for his guidance,
support, patience, and encouragement. Karl’s excellent supervision style has deﬁnitely made
the journey enjoyable for the most parts.
A special thanks for Dr. Jason Jonkman at the National Renewable Energy Laboratory for provid-
ing the simulation models and continued support over the years. Without his support, I
wouldn’t have been able to do all the work that is in this thesis.
Thanks to Edith Willson ,Lesley Darby , and Anu Sunkari for helping me out with the many bur-
eaucratic processes of the university and for making things happen in the department.
I would like to thank the Tertiary Education Commission of New Zealand for funding the ﬁrst
three years through the Top Achiever Doctoral Scholarship and The University of Auckland
for extending the scholarship for another six months. The scholarship has allowed me to focus
on my research and attend important conferences and meetings.
Thanks to my good friends Andrew, Avi, Claudio, Ehad, Nasser, Ramin, and Rav for their com-
panionship, support, and the unusually long lunch hours and afternoon “tea breaks”!
Finally, I would like to thank my parents Ban and Said, brother Salim , and sister Hana for their
support, understanding, patience, and constant encouragement to ﬁnish as soon as possible .
vii

viii

Contents
1 Introduction 1
1.1 Introduction to Offshore Wind Turbines . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Overview of Wind Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Offshore Wind Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.3 Historical Development of Floating Offshore Wind Turbine Concepts . . . 5
1.2 Introduction to Wind Turbine Control . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.1 Operating Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2.2 Overall Controller Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.3 Control of Floating Wind Turbines . . . . . . . . . . . . . . . . . . . . . . . 13
1.3 Research Objectives and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2 Review of Floating Wind T urbine Controllers 17
2.1 Gain Scheduled PI Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.1 Barge Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1.2 Tension Leg and Spar-Buoy Platforms . . . . . . . . . . . . . . . . . . . . . 22
2.2 Variable Power Pitch Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Estimator Based Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4 Active Structural Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 Other Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.6 Onshore Wind Turbine Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.7 Controller Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 State Feedback Control 29
3.1 State-Space Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 Collective vs. Individual Blade Pitching . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.1 Collective Blade Pitching . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.2 Individual Blade Pitching . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
ix

Contents
3.3 Multi-Blade Coordinate Transformation . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.4.1 Generator Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4.2 Azimuth Angle Correction due to Platform Rolling . . . . . . . . . . . . . 39
3.4.3 Actuator Saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4.4 Azimuth State Anti-windup . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.5 Stability Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4 Disturbance Accommodating Control 43
4.1 Introduction to DAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 DAC Theory Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2.1 Disturbance Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3 DAC After MBC Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.4.1 DAC Limitations and Challenges . . . . . . . . . . . . . . . . . . . . . . . . 49
4.5 Wind Speed Disturbance Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.5.1 Collective Blade Pitch Drift . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5 Modelling, Simulation, and Analysis Tools 55
5.1 Wind Turbine Modelling and Simulation Tools . . . . . . . . . . . . . . . . . . . . 55
5.1.1 FAST Simulation Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.2 5MW Wind Turbine Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3 The IEC 61400-3 Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.4 Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.5 Simulation and Comparison Set Up . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.6 Weibull Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6 The Barge Platform 69
6.1 The Barge Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.2 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2.1 Collective Blade Pitch State Feedback Control . . . . . . . . . . . . . . . . 71
6.2.2 Platform Roll-Pitch Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2.3 Final Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.3 Offshore DLC Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
x

Contents
6.3.1 Averaged Normalised Results . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.3.2 Time Series Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
7 The Tension Leg Platform 81
7.1 The Tension Leg Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.2 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
7.3 Offshore DLC Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
7.3.1 Averaged Normalised Results . . . . . . . . . . . . . . . . . . . . . . . . . . 83
7.3.2 Time Series Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
7.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
8 The Spar-Buoy Platform 89
8.1 The Spar-Buoy Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
8.2 Effects of Lowering the Platform’s Pitch Natural Frequency in Control Design . . 91
8.2.1 Platform Surge DOF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
8.2.2 Effectiveness of Individual Blade Pitching . . . . . . . . . . . . . . . . . . . 92
8.2.3 Final Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
8.3 Offshore DLC Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
8.3.1 Averaged Normalised Results . . . . . . . . . . . . . . . . . . . . . . . . . . 95
8.3.2 Times Series Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
8.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
9 Platform Comparisons 103
9.1 Comparison Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
9.2 Platform Pitch Input and Disturbance Sensitivities . . . . . . . . . . . . . . . . . . 104
9.3 DLC Results Relative to an Onshore Wind Turbine . . . . . . . . . . . . . . . . . . 108
9.3.1 The Barge Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
9.3.2 The Tension Leg Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
9.3.3 The Spar-buoy Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
9.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
10 Wave Disturbance Rejection: A Case Study 113
10.1 Wave Disturbance Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
10.1.1 Simpliﬁed Modelling Approach . . . . . . . . . . . . . . . . . . . . . . . . 114
10.2 Case Study: Wave Disturbance Rejection on Floating Wind Turbines . . . . . . . . 116
10.2.1 Linear Time-varying Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
10.2.2 Nonlinear Periodic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
xi

Contents
10.2.3 Case Study Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
10.3 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
11 Conclusions and Recommendations 125
Appendices 131
A MBC Transformation of Linear State-Space Models 133
A.1 Overview of Approach and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 133
A.2 The State Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
A.3 The Output Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
A.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
B Implementation Options for DAC After MBC Transformation 139
C Design Load Cases 143
D Relative Performance Trends for Controllers on Floating Platforms 147
E Adaptive Disturbance Estimator 155
E.1 Dealing with Periodic Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
E.1.1 Case Study: Simple Linear System with Periodic Disturbances . . . . . . . 156
E.2 ADE for Disturbances with Variable Frequency . . . . . . . . . . . . . . . . . . . 157
E.2.1 Frequency Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
E.2.2 On-line Estimator Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
E.2.3 Case Study: ADE Performance with Mismatched Frequency . . . . . . . . 159
E.2.4 Case Study: ADE Performance on a Linear Floating Wind Turbine Model 160
E.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
References 165
xii

List of Figures
1.1 Offshore wind energy growth history . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 The ﬂoating platform’s 6 DOFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 The three main ﬂoating concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 The Tri-ﬂoater concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Hywind and SWAY concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.6 Main components of a wind turbine . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.7 Wind turbine operating regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1 Baseline controller implementation in above rated wind speed region . . . . . . 20
3.1 Platform pitch restoring forces with different blade pitch operation . . . . . . . 33
3.2 Collective and individual blade 1 gains as a function of rotor azimuth . . . . . . 35
3.3 Block diagram implementations of an IBP state-space controller . . . . . . . . . 38
3.4 Azimuth angle correction due to platform roll motion . . . . . . . . . . . . . . . 40
4.1 DAC with FSFB implementation for ﬂoating wind turbines . . . . . . . . . . . . 49
4.2 Wind disturbance rejection by a DAC on a simple nonlinear model . . . . . . . 52
4.3 Collective blade pitch drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.1 Baseline controller model showing Simulink/FAST interface . . . . . . . . . . . 58
5.2 Offshore FAST structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.3 The Weibull distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.4 Weibull scaling factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.1 The barge platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.2 Normalised results for 2 DOFs CBP SFC relative to the Baseline controller . . . 72
6.3 Blade 1 Bmatrix elements for platform roll and pitch of a 3 DOFs model . . . . 73
6.4 Typical platform yaw motion envelope for the barge platform . . . . . . . . . . 74
6.5 Averaged DLC results for the barge platform . . . . . . . . . . . . . . . . . . . . 76
6.6 Sample time series response of the barge platform . . . . . . . . . . . . . . . . . 79
6.7 Frequency content of the tower side-side base moment . . . . . . . . . . . . . . 80
xiii

List of Figures
7.1 The tension leg platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
7.2 Averaged DLC results for the tension leg platform . . . . . . . . . . . . . . . . . 84
7.3 Sample time series response of the tension leg platform . . . . . . . . . . . . . . 87
7.4 Frequency content of tower base moments . . . . . . . . . . . . . . . . . . . . . . 88
8.1 The spar-buoy platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
8.2 Effects of adding the surge DOFs on frequency response . . . . . . . . . . . . . 93
8.3 Platform pitch frequency response with different sets of DOFs . . . . . . . . . . 94
8.4 The three platforms’ pitch frequency response to blade 1 pitch . . . . . . . . . . 94
8.5 Averaged DLC results for the spar-buoy platform . . . . . . . . . . . . . . . . . 96
8.6 Rotor speed and power errors trends with increasing wind mean speed . . . . . 98
8.7 Effect of platform roll on tower SS bending trend . . . . . . . . . . . . . . . . . . 98
8.8 Sample time series response of the spar-buoy platform . . . . . . . . . . . . . . 100
8.9 Frequency content of tower base moments . . . . . . . . . . . . . . . . . . . . . . 101
9.1 Platform pitch frequency response to blade 1 pitch input . . . . . . . . . . . . . 105
9.2 Blade pitch frequency content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
9.3 Platform pitch frequency response to disturbance inputs . . . . . . . . . . . . . 107
9.4 Averaged DLC results relative to an onshore wind turbine . . . . . . . . . . . . 109
10.1 Wave disturbance rejection on a linear 2 DOFs model . . . . . . . . . . . . . . . 118
10.2 Wave disturbance rejection on a nonlinear 2 DOFs model . . . . . . . . . . . . . 119
10.3 Blade 1 pitch rates with different a. . . . . . . . . . . . . . . . . . . . . . . . . . 120
10.4 Wave DACs with different asimulated with a nonlinear 2 DOFs model . . . . 121
10.5 Wave minimisation moment load path . . . . . . . . . . . . . . . . . . . . . . . . 122
B.1 General DAC implementation options . . . . . . . . . . . . . . . . . . . . . . . . 141
D.1 Performance trends for the SFC on the barge platform . . . . . . . . . . . . . . . 148
D.2 Performance trends for the DAC on the barge platform . . . . . . . . . . . . . . 149
D.3 Performance trends for the SFC on the TLP . . . . . . . . . . . . . . . . . . . . . 150
D.4 Performance trends for the DAC on the TLP . . . . . . . . . . . . . . . . . . . . . 151
D.5 Performance trends for the SFC on the spar-buoy platform . . . . . . . . . . . . 152
D.6 Performance trends for the DAC on the spar-buoy platform . . . . . . . . . . . . 153
E.1 Periodic disturbance cancellation with matched estimator frequency . . . . . . 156
E.2 Mismatched frequency disturbance estimate and state regulation . . . . . . . . 157
E.3 Quantised response of the estimated frequency . . . . . . . . . . . . . . . . . . . 159
E.4 Adaptive disturbance estimator implementation block diagram . . . . . . . . . 160
xiv

List of Figures
E.5 Variable frequency disturbance estimates and state regulation . . . . . . . . . . 161
E.6 Constant mismatched frequency case . . . . . . . . . . . . . . . . . . . . . . . . . 162
E.7 Continuously changing wave disturbance frequency case . . . . . . . . . . . . . 163
xv

List of Figures
xvi

List of Tables
1.1 Total installed wind energy capacity for the top 10 countries in 2010 . . . . . . . 2
1.2 Water depth distribution for different regions up to 100km offshore . . . . . . . . 4
1.3 Differences between single or multiple turbine ﬂoaters . . . . . . . . . . . . . . . 7
1.4 Comparison between different ﬂoating platform designs . . . . . . . . . . . . . . 7
1.5 Relative comparison between the major ﬂoating platform concepts . . . . . . . . 9
2.1 Overview of most important controllers applied on ﬂoating wind turbines . . . . 18
2.2 Types of controllers implemented on onshore wind turbines . . . . . . . . . . . . 27
5.1 Floating wind turbine simulation codes . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2 NREL 5MW wind turbine properties . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3 DLC 1.2 conditions summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.4 Relative importance of performance metrics . . . . . . . . . . . . . . . . . . . . . 63
5.5 Types of observed performance trends . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.6 Simulated controllers’ comparison summary . . . . . . . . . . . . . . . . . . . . . 65
5.7 Wind speed region limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.1 Barge platform properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2 Performance trends of the barge platform controllers relative to Baseline controller 77
7.1 Tension leg platform properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
7.2 Performance trends of the TLP controllers with increasing mean wind speed . . 85
8.1 Spar-buoy platform properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
8.2 DOFs list for Figure 8.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
8.3 Performance trends of the spar-buoy platform controllers . . . . . . . . . . . . . 97
9.1 Platform controllers to be compared to the onshore wind turbine . . . . . . . . . 104
10.1 Effect of DAC gain scaling factor aonkBaGd+BdQk. . . . . . . . . . . . . . . . 117
11.1 Summary of most important controllers applied on ﬂoating wind turbines . . . . 127
xvii

List of Tables
C.1 Stochastic wind and wave parameters used for DLC analysis . . . . . . . . . . . 143
xviii

Nomenclature
Abbreviations
ADE Adaptive Disturbance Estimator
CBP collective blade pitch or pitching
DAC Disturbance Accommodating Control or Controller
DLC Design Load Case
DOF degree(s) of freedom
FA fore-aft
FAST Fatigue, Aerodynamics, Structures, and Turbulence
FSFB Full State Feedback
GSPI Gain Scheduled Proportional-Integral
IBP individual blade pitch or pitching
IEC International Electrotechnical Commission
LQR Linear Quadratic Regulator
LSS low speed shaft
LTI linear time-invariant
MBC multi-blade coordinate
MIMO multi-input multi-output
OC3 Offshore Code Comparison Collaboration
PID Proportional-Integral-Derivative
RMS root mean square
RNA Roto-Nacelle Assembly
xix

Nomenclature
SFC State Feedback Control or Controller
SISO single-input single-output
SS side-side
TLP Tension Leg Platform
TMD Tuned Mass Damper
Alphabetical Symbols
A state matrix
A augmented A matrix
B actuators gain matrix
Bd disturbances gain matrix
B augmented B matrix
C matrix that relates the states, x, to the measurements, y
c Weibull distribution scaling parameter
Cd damping matrix
C augmented C matrix
CP,max maximum power coefﬁcient of the wind turbine
D matrix that relates the controlled inputs, u, to the measurements, y
Dd matrix that relates the disturbance inputs, ud, to the measurements, y
F actuators gain matrix for second order system
Fd disturbance inputs matrix for second order system
g acceleration due to gravity
Gd disturbance minimising gain matrix
H signiﬁcant wave height
II drivetrain inertia from the low speed shaft end
K state feedback control gain matrix
k Weibull distribution shape parameter
Ke state estimator gain matrix
KP,KI proportional and integral gains
xx

Nomenclature
Ks stiffness matrix
KT optimum generator torque gain in below rated wind speed region
M mass/inertia matrix
N gearbox ratio
PRated rated generator power
q degreees of freedom vector
RRotor rotor radius
T boolean transition matrix
TGen applied generator torque
Tc(y) control input utransformation matrix
Td(y) transformation matrix for augmented states vector w
To(y) output measurements ytransformation matrix
Ts(y) state xtransformation matrix
Tw wave period
u actuators inputs vector
U ten–minute mean wind speed
ud disturbance inputs vector
v augmented estimator inputs ( uand y) in the mixed frame of reference
w augmented state vector xwith disturbance states z
x states vector
y measurements vector
z disturbance states vector
Greek Symbols
a DAC gain scaling factor
hGen generator efﬁciency
G disturbance state matrix
lo optimum tip speed ration that yields maximum power
W rotor speed
xxi

Nomenclature
wn natural frequency
Wr rated rotor speed in revolutions per second
y azimuth angle
ya actual azimuth angle of the rotor
r air density
Q matrix that relates disturbance states, z, to disturbance inputs, ud
q blade pitch angle
x platform roll angle
z damping ratio
Notation
Dx perturbation about an operating or linearisation point
˙x rate of change with respect to time
ˆx estimate
xNR an entity transformed to the non-rotating frame of reference
xopoperating point
xcommanded or desired signal
x vector
xxii

1
Introduction
Contents
1.1 Introduction to Offshore Wind Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Introduction to Wind Turbine Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Research Objectives and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Growing demand for more renewable energy sources to reduce the emission of green-
house gases is one of the main drivers for the substantial growth of the global wind
energy sector. Part of that growth is to deploy wind turbines further offshore into
deep water. This chapter gives a brief introduction to offshore wind energy, especially ﬂoating
wind turbines, and wind turbine control. Research objectives and scope are also outlined.
1.1 Introduction to Offshore Wind T urbines
1.1.1 Overview of Wind Energy
Wind energy is a clean, renewable, and sustainable source of energy. According to the Inter-
national Energy Agency, as of May 2011, wind energy along with solar, geothermal and other
renewable sources (excluding hydro) produce around 4% of the global energy supply [1]. Wind
energy is the fastest growing harvested energy source in the world and continues to grow ex-
ponentially [2, 3].
In 2010, China surpassed the United States to become world leader in installed wind energy
capacity with 44.7 GW of total installed capacity [4]; Table 1.1 lists the top 10 countries that
account for 86% of the global installed capacity as of December 2010. Also in 2010, China
1

Chapter 1: Introduction
Table 1.1: Total installed wind energy capacity for the top 10 countries in 2010 (adapted from
[4])
# Country Installed Capacity (MW) % of Global Total
1 China 44,733 22.7
2 USA 40,180 20.4
3 Germany 27,214 13.8
4 Spain 20,676 10.5
5 India 13,065 6.6
6 Italy 5,797 2.9
7 France 5,660 2.9
8 UK 5,204 2.6
9 Canada 4,009 2.0
10 Denmark 3,752 1.9
installed 18,928 MW of wind energy accounting for 49.5% of the new installed capacity globally
followed by USA and India with installed capacities of 5,115 MW and 2,139 MW respectively.
In terms of wind energy penetration, Denmark is the world leader with 26% of its energy
generated from wind [5].
With global warming caused by green house gases and drive for sustainability, some govern-
ments have set goals by which a certain percentage of their power supply is generated from
renewable energy sources (mainly wind) [3]. Two examples are given: Australia has set a
goal of 20% energy generation from renewable sources by 2020, and France has set the goal of
25 GW of wind power with 6 GW of offshore installations by 2020 to meet the EU directive of
23% renewable energy generation [4].
According to the Global Wind Energy Council [4], New Zealand’s onshore wind energy re-
source is sufﬁcient to meet its annual demand several times. In 2010, the total installed wind
energy capacity reached 506 MW accounting for 4% of the energy supply. There is no expli-
cit target for wind energy set by the New Zealand government but it is planned that by 2025,
90% of power supply sourced from renewable sources; to date, 70% of the energy supply is
generated using hydroelectric and geothermal sources and only 26% is generated using non-
renewable sources such as natural gas and coal [4, 6]. Unlike other countries, such as Ger-
many for example, New Zealand does not have an incentive programme to promote investing
in wind energy. However, New Zealand’s wind energy sector is competing successfully with
other energy sources; this globally unique achievement demonstrates the cost-effectiveness and
competitiveness of wind energy without any form of government subsidy [4].
1.1.2 Offshore Wind Energy
The ﬁrst commercial offshore wind farm is Vindeby wind farm located 2.5 km off the Danish
coast which became operational in 1991 [2, 7]. It is still operational, has eleven 450 kW wind
2

1.1 Introduction to Offshore Wind Turbines
Figure 1.1: Offshore wind energy growth history in the European Union [5]
turbines with total capacity of 4.95 MW, and is installed in water depths ranging from 2.5 m to
5 m. Since then, the growth in the offshore wind industry has been exponential (Figure 1.1).
In 2010, the offshore wind energy market grew by 51% while the onshore market decreased by
13% [4].
The majority of offshore wind farms are located around Europe (North, Baltic, and Irish seas)
with some offshore wind farms in USA, Japan, and China [2]. Historically, Denmark has been
the world leader in offshore wind energy, but in 2010, the UK became the world leader with
total installed capacity of 1,341 MW compared to Denmark’s 854 MW [4, 5]. To date, all com-
mercial offshore wind farms are located in shallow water (less than 30 m deep) and use ﬁxed
foundations such as mono-piles or lattice structures.
The main reason for going offshore is due to better wind resource attributes when compared
to onshore wind; these include [8–10]: stronger and steadier wind; less turbulence resulting in
longer turbine life; less vertical shear (i.e. higher wind speeds at lower altitudes) and higher
annual mean wind speed. On average, offshore winds are 20% faster. However, offshore winds
also have greater extremes, interact with surface waves, and are harder to measure.
In addition to having better offshore wind resource attributes, placing wind turbines offshore
has several design and location advantages; these include [8, 11]:
• Turbines operate closer to maximum efﬁciency since no restrictions are imposed due to
noise and other operational regulations.
• Proximity to load centres (large cities) thus requiring less transmission distance and ac-
cess the less heavily used transmission lines.
3

Chapter 1: Introduction
• Reduced visual impact.
• Energy balance: An offshore wind turbine can recover the energy cost used during man-
ufacture, transport, installation, operation, maintenance, and decommissioning in three
months. Over its lifetime, the turbine can generate over 100 times that energy.
Placing the turbines offshore has the following challenges [12]: increased capital cost due to
foundations, integration with the electrical network, and installation, operation and mainten-
ance being subject to weather conditions.
The offshore wind energy potential is very large. For example, the UK’s offshore energy po-
tential is estimated to be 986 TWh/year while demand is estimated to be 321 TWh/year (based
on 2003 estimates); i.e. more than three times the demand [8]. The US wind energy potential
between 10 km and 100 km offshore is estimated to be more than 900 GW which is more than
the currently installed electricity generation capacity in the US; however, much of this potential
is located in deep water that is deeper than 30 m [13]. Table 1.2 shows the percentage of water
depths for different regions up to 100 km offshore. It shows that in Northern Europe 47% of
water depth is below 50 m while in Southern Europe 72% is deeper than 50 m [14]. Similarly in
Japan, 69% is deeper than 50 m. However, in the USA 76% is below 50 m deep.
Floating Wind T urbines
Currently, the deepest installed ﬁxed-bottom offshore wind turbine is the Beatrice wind farm
off the coast of Scotland [15]; it is constructed in 44 m deep water. However, for water deeper
than 60 m the most feasible option is to deploy ﬂoating wind turbines [10, 16].
Due to the lack of rigid foundations, ﬂoating wind turbines have 6 additional degrees of free-
dom (DOFs); 3 linear (surge, sway, and heave) and 3 rotational (roll, pitch, and yaw) DOFs as
shown by Figure 1.2. A main challenge of ﬂoating wind turbines is that the motions induced
by wind and wave conditions are almost impossible to eliminate. Therefore, the design of these
turbines must take into account the added degrees of freedom due to platform motions.
Figure 1.3 illustrates the three main ﬂoating platform concepts. Each concept uses a different
principle to achieve hydrostatic stability. The three ﬂoating concepts shown in Figure 1.3 are: a
Table 1.2: Water depth distribution for different regions up to 100km offshore [14]
Water Depth (m)
Region <25 25-50 50-100 100-300
North Europe 21% 26% 32% 20%
South Europe 16% 11% 23% 49%
Japan 22% 9% 18% 51%
USA 50% 26% 13% 11%
North West USA 27% 29% 25% 19%
4

1.1 Introduction to Offshore Wind Turbines
Surge Heave
Sway
RollPitch Yaw
Figure 1.2: The ﬂoating platform’s 6 DOFs
buoyancy stabilised barge platform, a mooring line stabilised Tension Leg Platform (TLP), and
a ballast stabilised spar-buoy platform. Of course, each concept has its advantages and lim-
itations. Early comparisons of all three platforms used simple static or dynamic models that
usually excluded the effect of the control system [10, 17–20]. Note that the three ﬂoating prin-
ciples (buoyancy, mooring lines, and ballast) are not mutually exclusive. That is, a combination
of these principles into a single platform is possible; for example, semi-submersible platforms,
not shown in Figure 1.3, use a combination of ballast and buoyancy for stability.
1.1.3 Historical Development of Floating Offshore Wind T urbine Concepts
The concept of ﬂoating offshore wind turbines was originally introduced in 1972 [18]. Only
until the 1990’s, when wind turbines were successful commercially, that ﬂoating offshore wind
turbines became a topic for research. Initial studies conducted in the early 1990’s showed that
a ﬂoating wind turbine is technically possible but not feasible [17]. It was estimated that the
5

Chapter 1: Introduction
Barge TLP Spar-Buoy Mooring lines not to scale
Figure 1.3: The three main ﬂoating concepts
cost of energy would be three times the cost of an onshore wind turbine. However, at the time
of these studies, shallow water offshore wind turbines were also considered uneconomical and
cost twice as much as an onshore turbine. Clearly, today’s shallow water offshore turbines are
used on a utility scale for power production.
In 1998, Tong [21] designed a 1.4 MW ﬂoating turbine utilising the spar-buoy concept with
catenary mooring lines. The turbine was downwind1to have a free yawing system because
it was believed that the platform could not support the moment reaction for an active yaw
system. This was proven to be incorrect in later analyses. Tong found that wave loadings were
prominent mainly on the tower but were not severe such that it became a main design driver
for the tower. Furthermore, gyroscopic yaw motion caused by platform pitch was found to be
small and of no serious concern.
Bulder et al. [17] considered several design options in 2003; these include: single or multiple tur-
bines per ﬂoating platform; and single or multi-rotor turbines. First, they concluded based on
qualitative analysis that a single turbine per ﬂoating platform (or ﬂoater) with spread mooring
was the best technical and economic solution. This was conﬁrmed by Musial et al [18] in 2004;
Table 1.3 lists the advantages and disadvantages of both concepts. Second, Bulder et al. [17] also
compared several single platform concepts listed in Table 1.4 and concluded that the Tri-ﬂoater,
1When the rotor is downwind of the tower (i.e. the wind hits the tower before the blades) it is attributed as a
downwind wind turbine. Similarly, an upwind wind turbine has the rotor is upwind of the tower.
6

1.1 Introduction to Offshore Wind Turbines
Table 1.3: Differences between single or multiple turbine ﬂoaters [18]
Advantages Disadvantages
Multiple
Turbine
Floaters– Wave stability
– Shared anchors
– Mass optimisation possibilities– High cost support structure
– Wave loading
– Complex yaw control
Single
Turbine
Floaters– Simplicity
– Modularity for manufacture
– Lower structural requirements
– Standard yaw control– Individual anchors cost
Table 1.4: Comparison between different ﬂoating platform designs
Concept Description Advantages Disadvantages
Single
Cylindrical
FloaterSimple cylinder plat-
form held by spread
mooringsGood static stability Motion behaviour was not
acceptable in terms of mo-
tion periods coinciding with
wave periods (high energy
region of wave spectrum)
Cylindrical
with Tension
LegsReduced cylinder
size but held by
tensioned mooring
linesGood vertical stiff-
ness (heave)Not suitable for water
depths considered because
gains in stability from
adding the tensioned line
were marginal
Tri-ﬂoater Single column car-
rying the turbine
connected to three
ﬂoating cylinders via
trussesRequires less steel
than the rest. Good
stability with modi-
ﬁcation of ﬂoater
cylindersInitially the heave motion
was still in the high energy
region but this was solved
through increasing the hy-
drodynamic mass by adding
circular plates to the 3 ﬂoat-
ers
Jack-up Floating legs but the
platform is above
waterSimple installation
and convenient for
transportation
Minimises wave in-
duced motionCost. It is estimated to cost
12 million Euros to carry an
estimated 4-5 MW turbine
shown in Figure 1.4, was the best design. However, their analysis was not comprehensive and
several issues need to be addressed; among these:
• The need to consider and evaluate barge platforms.
• Use of simple equations of motion to describe heave and roll.
• Effects of mooring lines and waves were not included in analysis.
Musial et al. [18] have conducted a similar study to Bulder et al. [17], however, they found that
a Tension Leg Platform (TLP), having vertical moorings, has excellent stability due to mul-
tiple tension legs that are spread out. With a tension leg platform, the majority of the platform
7

Chapter 1: Introduction
Figure 1.4: The Tri-ﬂoater concept [17]
is submerged thus experiencing lower wave loading. However, the vertical anchors have to
withstand larger forces than anchors used with catenary mooring lines. A cost analysis was
carried out to compare their TLP concept with the Tri-ﬂoater concept; results showed that the
TLP would cost less mainly due to its smaller structure size. However, both concepts are es-
timated to be able to bring energy cost down to US$0.05/kWh which is required for large scale
development as identiﬁed by the US Department of Energy.
In 2004, Ushiyama et al. [19] considered several ﬂoating turbine concepts to be deployed in
Japanese waters. Vertical axis wind turbines were also considered to be placed on top of the
ﬂoating structure because they have a low centre of gravity and can receive the wind from
any direction without the need for a yawing system. However, their preliminary study did
not ﬁnd a clear winning concept which is the case for most ﬂoating structures. Each type had
certain advantages and disadvantages, thus the choice of the platform concept would be site
and application dependent. This was further illustrated by the study carried out by Butterﬁeld
et al. [20] where they compared the relative advantages and disadvantages of the three main
ﬂoating concepts. The comparison in shown in Table 1.5; for further details please refer to [20].
In 2006, Nielsen et al. [10] carried out scale model testing for a spar-buoy type platform known
as the Hywind concept being developed by a Norwegian company Norsk Hydro in cooperation
with Siemens Power Generation [22]. The 1:47 scale model was tested in an 80 m×50 m basin at
the Ocean Basin Laboratory at Marintek in Trondheim [10,23]. Their scale model testing results
agree with their simulation results which tested a new control algorithm to add active damping
of tower motions; the controller was effective in reducing induced tower motions [10].
Also in 2006, Vijfhuizen [24] developed a wind and wave power barge platform. This barge
8

1.1 Introduction to Offshore Wind Turbines
Table 1.5: Relative comparison between the major ﬂoating platform concepts (reproduced from
[20])
Platform Stability Classiﬁcations
Platform Design Challenge Buoyancy
(Barge)Mooring Line
(TLP)Ballast
(Spar-Buoy)
Design tools and methods – + –
Buoyancy tank cost/complexity – + –
Mooring line system cost/complexity – + –
Anchors cost/complexity + – +
Load out cost/complexity (potential) + –
On-site installation simplicity (potential) + – +
Decommissioning and maintainability + – +
Corrosion resistance – + +
Depth independence + – –
Sensitivity to bottom condition + – +
Minimum footprint – + –
Wave sensitivity – + +
Impact of Stability Class on Turbine Design
Turbine weight + – –
Tower top motion – + –
Controls complexity – + –
Maximum healing angle – + –
Key
+ relative advantage
– relative disadvantage
blank neutral advantage
platform has a wind turbine to extract energy from the wind and an oscillating water column
to extract energy from the waves. The barge platform was chosen because it was assumed to
cost the least among other concepts; this was conﬁrmed by Wayman in 2006 [25] where she
showed that a shallow drafted barge would have the least capital cost and estimated cost of
energy (excluding operation and maintenance costs) of US$ 0.0129/kWh and US$ 0.0089/kWh
for mean wind speeds of 5.8 m/s and 8 m/s respectively. Vijfhuizen’s main conclusions were
[24]:
• The barge’s motions and stability were acceptable even under severe conditions.
• With the wind turbine operating the motions were reduced while the oscillating water
column operation had no effect.
• The barge’s design can withstand at least 25 years of fatigue life.
9

Chapter 1: Introduction
(a) Hywind (Photo: Øyvind Ha-
gen/Statoil)
(b) SWAY [27]
Figure 1.5: Hywind and SWAY concepts
In June of 2009, the world’s ﬁrst full scale ﬂoating wind turbine prototype, the spar-buoy Hy-
wind concept with a 2.3 MW wind turbine, was installed off the coast of Norway in 220 m deep
water [26] (Figure 1.5a). In March 2011 another Norwegian company, SWAY, deployed a small
scale ﬂoating wind turbine prototype for testing [27]; the full scale prototype with a 2.6 MW
downwind turbine (Figure 1.5b) is scheduled for deployment in 2013. The tower is moored by
a single tension leg cable that allows the tower to yaw freely with the wind; the concept is a
hybrid between and a tension leg and a spar-buoy concept.
1.2 Introduction to Wind T urbine Control
Large wind turbines (utility scale) generally have an active control system that is used to regu-
late the operation of the turbine [28]. As wind turbines get larger in size and power capacity, the
role of the control system in reducing loads becomes more important as the turbine structure
becomes more ﬂexible.
There are two types of wind turbine control: supervisory and closed-loop control [29]. Su-
pervisory control determines the high level operation of the wind turbines such as when to
start-up and when to shut-down. Closed-loop control operates between these two states and
10

1.2 Introduction to Wind Turbine Control
Figure 1.6: Main components of a horizontal axis wind turbine [31]
is responsible for the power production objectives such as minimising turbine yaw error and
regulating rotor speed to maximise or limit power capture.
Horizontal axis wind turbines are generally under-actuated systems where the number of actu-
ators or control inputs is signiﬁcantly less than the controlled degrees of freedom. On a typical
large wind turbine, there are three types of control inputs [30]: commanded generator torque,
blade pitch angle, and the yaw drive giving a total of ﬁve available actuators (for a three-
bladed wind turbine) as shown in Figure 1.6. Depending on the control algorithm, the blades
can either be operated collectively or individually; differences between the two are discussed
in Chapter 3. The yaw drive is only used to correct the turbine’s yaw error2due to a change in
mean wind direction. It is normally a slow actuator and ineffective for power production and
regulation.
1.2.1 Operating Regions
Wind turbines have three regions of operation. In each region the turbine has a different oper-
ational objective according to the mean wind speed [30, 32, 33]. These are summarised below
and the ideal power captured in each region is shown in Figure 1.7.
Region 1 The wind speed is too low for operation.
2Yaw error is the angle between the mean wind direction and the turbine yaw angle.
11

Chapter 1: Introduction
Region 2 This is where the turbine will spend most of its operational life in the designed wind
speed region. Therefore, the main objective is to maximise power capture in this region.
This region is also known as the below rated wind speed region.
Region 3 This is the above rated wind speed region where the extracted power of the wind must
be limited to the rated power to avoid damaging the turbine components. Hence, the
turbine is reducing its aerodynamic efﬁciency to limit power capture to the rated power
of the generator.
PRated Power
VWind VRated VCut in Region 1 Region 2 Region 3VCut off
Spar
TLP Barge Mooring
System Ballast
Buoyancy
Moment
Figure 1.7: Wind turbine operating regionsAn upper limit for region 3 exists
where the wind speed is too fast
for safe operation of the wind tur-
bine. Therefore, the wind turbine
goes into shut-down mode for wind
speeds higher than the cut-off wind
speed. The blades are feathered into
the wind to minimise the lift gen-
erated and the shaft brakes are ap-
plied. The control logic that de-
termines the operational state of the
wind turbine and controls start-up
and shut-down is the supervisory
control. This higher control layer is
not considered in this work.
1.2.2 Overall Controller Objectives
The main purpose of a wind turbine is to generate power with a competitive cost of energy.
There are many factors that affect the cost of energy such as the location and wind speed dis-
tribution, turbine efﬁciency, etc. From a control system point of view, there are two factors that
the controller can inﬂuence to reduce the cost of energy: power capture and component fatigue
life. To reduce the cost of energy, the control system must
1. maximise power capture subject to
(a) limits on the captured power according to the operating regions (i.e. limit power
capture in regions 1 and 3);
(b) actuation constraints for each region.
i. To maximise power in region 2, the blade pitch is set to the ﬁxed optimum angle
that maximises the aerodynamic torque and the generator torque is used to con-
trol the rotor speed to achieve a desired tip speed ratio3[33, 34].
3Tip speed ratio is dimensionless number deﬁned as the ratio of the blade’s tip velocity to the upstream wind
velocity [28, 29].
12

1.2 Introduction to Wind Turbine Control
ii. In region 3, generator torque is not allowed to vary greatly (e.g. within 5% of
rated torque) to limit power ﬂuctuations.
2. prolong the operational life of the wind turbine. Apart from regular maintenance, the
life of the wind turbine can be increased by reducing fatigue loads on its components4
(blades, drivetrain, and tower).
To reduce the cost of energy utilising both approaches of maximising power and reducing fa-
tigue loads, ideally one would require a single multi-objective controller implementation. Due
to the abovementioned actuation needs for each region and the nonlinearity of wind turbines,
a single multi-objective controller for all operating regions is very difﬁcult to design and imple-
ment. The standard approach is to use a separate controller for each region and switch between
them using certain rules [29, 30, 35].
1.2.3 Control of Floating Wind T urbines
Floating wind turbines experience additional motion due to the lack of rigid foundations.
These additional motions, especially the platform pitch motion, can signiﬁcantly affect power
regulation and turbine loads. Therefore, reducing these motions becomes an important part
of the design of the ﬂoating system. Several methods can be used separately or collectively to
reduce these motions; these include:
• the design of the platform itself and the way it interacts with the waves,
• additional passive modiﬁcations to the system such as modifying the wind turbine to
include a Tuned Mass Damper, and/or
• using the control system to actively reduce the platform motions using available or addi-
tional actuators.
The latter is the main focus of this research. Studies on the control of ﬂoating wind turbines
have been conducted prior to this work; these are discussed in Chapter 2. These studies primar-
ily use a single objective controller for rotor speed regulation utilising collective blade pitching.
Structural control using active and passive Tuned Mass Dampers have also been investigated
on ﬂoating wind turbines to reduce platform pitching. However, the controller set-up consisted
of two separate single objective control loops: one for rotor speed regulation using collective
blade pitch and the other for platform pitch regulation using the Tuned Mass Damper. Of all
the reviewed works on ﬂoating wind turbine control , none used a single multi-objective control-
ler to regulate rotor speed and reduce platform pitch motion. Furthermore, the effectiveness of
individual blade pitching has not been investigated on ﬂoating wind turbines.
4A control system may also be capable of reducing the peak/maximum load on turbine components. However,
peak loads are not usually design drivers from a control system point of view.
13

Chapter 1: Introduction
1.3 Research Objectives and Scope
The main research objective is to quantify the performance of multi-objective and Disturbance
Accommodating Controllers applied to the three main ﬂoating platform concepts: the barge,
tension leg, and spar-buoy platforms. The results and conclusions in this work are intended to
be used by designers and developers of ﬂoating turbines to aid and guide the development of
their ﬂoating concepts, such as in a multi-disciplinary optimisation.
The research undertaken uses model-based control theory to design and implement multi-
objective controllers to reduce the induced motions by the ﬂoating platforms while maintaining
rotor speed and power regulation under normal operating conditions . Time domain control design
using linear state-space models for State Feedback Control is utilised.
The results presented in this thesis are based entirely on hi-ﬁdelity simulations and, therefore,
the results are bound by the limitations of the simulation tools used and their associated as-
sumptions. However, the results are presented in a relative sense such that the absolute values
of the simulation results are not used. Furthermore, the relative results are used to draw conclu-
sions based on physical interpretations of the the ﬂoating systems. Design Load Case (DLC) 1.2
in the IEC 61400-3 standard for offshore wind turbines is used to analyse the fatigue load per-
formance of the ﬂoating wind turbines under normal operating conditions. Simulations are
carried out using FAST (Fatigue, Aerodynamics, Structures, and Turbulence) [36], a well estab-
lished wind turbine design and simulation tool, in conjunction with MATLAB®Simulink®for
control design and implementation; more details are given in Chapter 5.
Finally, the research undertaken in this thesis answers the following research questions (in no
particular order of importance):
1. Does using individual blade pitching help improve the performance over collective blade
pitching on a ﬂoating wind turbine?
2. Similarly, does using a multi-objective controller help improve the performance relative
to a single-objective Gain Scheduled Proportional-Integral controller on ﬂoating wind
turbines, consistent with ﬁndings for onshore wind turbines?
3. Can a Disturbance Accommodating Controller designed to reject wind and wave disturb-
ances help improve the performance?
4. How will the three ﬂoating platforms perform when compared to each other under nor-
mal operating conditions especially when controlled by multi-objective controllers?
5. Is it possible to maintain fatigue loads to a level comparable to an onshore wind turbine
of similar size?
6. With the addition of the platform’s 6 DOFs, are the current actuators capable of address-
ing the control needs of the system?
In addition to the above objective and research questions, it is important to deﬁne what is out
of scope of this research. Below are several items that are not part of the research undertaken
in this thesis.
14

1.3 Research Objectives and Scope
• No below rated wind speed region analysis: All controllers are simulated in the above
rated wind speed region since it is in this region where the platform motions are affected
the most due to high wind speeds as well as large incident waves. Furthermore, region
transition methods/algorithms between the regions are not implemented.
• No stress analysis: Stress analysis is not part of this research; only structural loads are
calculated and analysed. Performing stress analysis is usually performed at the ﬁnal
stages of the design whereas the aim of this research is to compare between different
concepts rather than produce a solution ready for testing/implementation.
• No turbine/platform design changes or optimisations: Design changes such as adding
extra actuators is not considered here as the objective is to assess the limitations of avail-
able actuators on the ﬂoating wind turbine. Optimisation of ﬂoating concepts is usually
carried out to ﬁnalise a concept for prototyping or manufacture. Again, this is deviating
from the objectives of this research.
• No meteorological modelling: Interaction between the wind and water surface where
the wind inﬂuences the incident wave height and direction is beyond the scope of this
research. However, realistic wind and wave conditions are used in the simulations but
they are not coupled.
• No nacelle yaw control: The yaw control loop for correcting wind direction errors is
separate from the main power and speed regulation control loop. Furthermore, DLC 1.2
does not specify a change in wind direction or a misalignment error.
• No state estimator design for state regulation: This work is of an exploratory nature and
will not focus on implementation issues such as cost of sensors, effects of noise, sensor
failure, etcetera. Therefore, the State Feedback Controllers are implemented using Full
State Feedback where all the necessary measurements are assumed to be available.
• No actuator dynamics: A static actuator model with saturation limits is used due to the
lack of a blade pitch time constant of a 5 MW or similar sized wind turbine in the liter-
ature. In the static model, the actuators are assumed to be fast enough such that their
dynamics can be neglected. However, absolute and rate saturations are implemented in
the simulation model to represent the operating limits of real actuators. These limits,
deﬁned in [37] and listed in Chapter 5, are based on data collected from several similar
sized wind turbines.
• No ultimate load or extreme operating cases: This work only focuses on fatigue loads
under normal operating conditions as this is where the major contribution of the multi-
objective controllers is expected. Generally, ultimate loads occur under extreme operating
conditions where the controller is in shut-down mode (e.g. during a fault). These cases
are well documented for ﬂoating wind turbines [32, 38].
• No experimental testing: Scale model testing of such concepts requires substantial fund-
ing and a large facility that are not available.
15

Chapter 1: Introduction
1.4 Thesis Outline
Chapter 2 reviews the state of the art in the control of ﬂoating wind turbines thereby answering
the ﬁrst research question. Of particular interest is the Gain Scheduled Proportional-Integral
controller. This controller is used as a reference controller for comparing the performance of
the developed multi-objective controllers and is referred to as the Baseline controller.
Chapter 3 brieﬂy describes the theory for State Feedback Control using linear time-invariant
state-space models, implementation and stability assessment for ﬂoating wind turbines. Wind
turbines are periodic systems, therefore, multi-blade coordinate (MBC) transformation (also
known as the Coleman or Fourier transformation) is used to transform the system to a non-
rotating frame of reference. The resultant transformed model becomes time-invariant allowing
for linear time-invariant control design. Differences between the mechanisms of individual
and collective blade pitching at regulating platform pitch are discussed since State Feedback
Control theory can accommodate multi-input multi-output systems.
Chapter 4 presents the background theory for Disturbance Accommodating Control, its imple-
mentation and limitations on ﬂoating wind turbines after MBC transformation is applied. The
design of a Disturbance Accommodating Controller for rejecting wind speed perturbations on
ﬂoating wind turbines is outlined as well.
In Chapter 5, the selected simulation tool (FAST) is brieﬂy described along with the assump-
tions used to model wind turbines with ﬂoating platforms. The chapter also describes the sim-
ulation set-up according to DLC 1.2 of the IEC 61400-3 standard and the performance metrics
used to analyse the simulation results.
Simulation results for the barge, tension leg, and spar-buoy platforms are analysed and dis-
cussed in Chapters 6, 7, and 8 respectively. The analysis is based on overall averaged perform-
ance metrics to compare the performance of the State Feedback and Disturbance Accommodat-
ing Controllers relative to the Baseline controller on each ﬂoating platform. Performance trends
across the above rated wind speed region and time series results are also used in the analysis.
The platforms’ simulation results are then compared relative to an onshore wind turbine in
Chapter 9. Normalising the results relative to an onshore wind turbine allows for comparison
between the ﬂoating platforms. It also allows for the evaluation of the required strength of tur-
bine components (tower, blades, and drive-shafts) in relative terms to well established onshore
wind turbine designs.
Chapter 10 presents results for simple case studies used to implement wave disturbance rejec-
tion on ﬂoating wind turbines.
Finally, conclusions and recommendations for future work are presented in Chapter 11.
16

2
Review of Floating Wind Turbine Controllers
Contents
2.1 Gain Scheduled PI Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Variable Power Pitch Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Estimator Based Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4 Active Structural Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 Other Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.6 Onshore Wind Turbine Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.7 Controller Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Areview of the most important contributions made towards designing and testing con-
trollers for ﬂoating wind turbines is presented in this chapter. These controllers range
in complexity, description detail, simulation results and testing styles, and ﬂoating
platform structure. Furthermore, they have not yet been compared against each other quantit-
atively using the same simulation conditions. However, the attributes of each control approach
documented in the literature are listed in this chapter. The main attributes of these controllers
are given in Table 2.1. In the table, the platform types barge, TLP , and spar-buoy refer to the ITI
Energy barge, MIT/NREL TLP , and OC3-Hywind spar-buoy respectively whose properties are
listed in Chapters 6, 7, and 8 respectively; The Hywind spar-buoy is a slightly different model
than the OC3 spar-buoy where it has a different wind turbine mounted from the NREL 5MW
baseline wind turbine. Description of each controller follows.
17

Chapter 2: Review of Floating Wind Turbine ControllersTable 2.1: Overview of most important controllers applied on ﬂoating wind turbines
Controller
NameBlade Pitch
ControlTorque
ControlAdditional Control Features Simulation
CodeNumber of
SimulationsModel
FidelitySimulation
RegionsPlatform
GSPI CBP GSPI Constant
powerTTF loop, pitch to stall, or
detuned gainsFAST Extensive High 2, 3 Barge, TLP ,
Spar-buoy
GSPI
HywindCBP GSPI Constant
torqueConstant speed region just
below rated with PI torque
control loopHAWC2 /
SIMO-RIFLEXLimited High 2, 3 Hywind
spar-buoy
VPPC CBP GSPI Constant
torqueVariable rotor speed
set-point. IBP for blade load
reductionFAST Limited High 3 Barge
EBC Unknown Unknown Wind turbine estimator to
hide tower dynamicsHywindSim /
SIMO-RIFLEXLimited Low 3 Hywind
spar-buoy
ASC Unknown Unknown Tuned mass damper with
active controlFAST-SC Moderate High 3 Barge
Legend:
ASC Active Structural Control Number of Simulations Guide:
CBP Collective Blade Pitch Limited <10
EBC Estimator Based Control Moderate <100
GSPI Gain Scheduled Proportional-Integral control Extensive >100
IBP Individual Blade Pitch
TTF Tower-Top Feedback
VPPC Variable Power Pitch Control
18

2.1 Gain Scheduled PI Control
2.1 Gain Scheduled PI Control
A Collective Blade Pitch (CBP) Gain Scheduled Proportional-Integral (GSPI) controller was
implemented on a ﬂoating wind turbine by Jonkman to assess the dynamic performance of
the barge ﬂoating platform [32]. The GSPI control loop only operates in the above rated wind
speed region (region 3) to regulate the rotor speed to the rated speed by pitching the blades
collectively to reduce their aerodynamic efﬁciency.
The GSPI control law is given by equation (2.1) where q(t)is the commanded collective blade
pitch angle, KP(q)and KI(q)are the proportional and integral gains respectively. The error
signal is denoted e(t)with wRated andwGenas the rated and actual generator speed respectively.
The GSPI controller is a single-input single-output (SISO) controller with a single objective of
rotor speed regulation.
The gains are scheduled as a function of blade pitch angle at the previous time step qsuch
that the controlled rotor DOF has the same prescribed closed-loop natural frequency, wn, and
damping ratio, z, for all above rated wind speeds. qis given by equation (2.2) where Dtis the
simulation time-step. The scheduled gains are given by equations (2.3) and (2.4) where IDis the
drivetrain inertia from the low speed shaft end, Wris the rated rotor speed in revolutions per
minute (rpm), Nis the gearbox ratio, anddP
dqis the sensitivity of the rotor aerodynamic power
to collective blade pitch angle. For more details on the power sensitivity and controller gains
derivation, please refer to [32].
q(t) =KP(q)e(t) +KI(q)t
0e(t)dt (2.1)
where
e(t) =wGenwRated
q=q(tDt) (2.2)
KP(q)=2IDWrzwn
N
dP
dq! (2.3)
KI(q)=IDWrw2
n
N
dP
dq! (2.4)
In addition to the blade pitch control loop, a separate generator torque control loop was used
to maximise power capture in below rated wind speeds and regulate power in above rated
wind speeds. The torque controller varies the applied generator torque as a function of ﬁltered
generator speed. In below rated wind speed (region 2), the relationship that maximises power
capture is given by equation (2.5) where r,RRotor,CP,max, and loare air density, rotor radius,
maximum power coefﬁcient and tip speed ratio that yields CP,maxrespectively [33]. In above
19

Chapter 2: Review of Floating Wind Turbine Controllers
Nonlinear Wind
Turbine Model +-
Collective Blade Pitch Controller Saturation Unit delay
Saturation Torque Controller
Figure 2.1: Baseline controller implementation in above rated wind speed region
rated wind speed region where the objective is to regulate power to the rated, the relationship
is given by equation (2.6) where PRated is the rated generator power and hGenis the generator
efﬁciency.
TGen =prR5
RotorCP,max
2l2oN3w2
Gen=KTw2
Gen (2.5)
TGen =PRated
hGenwGen(2.6)
The generator speed, used by both CBP GSPI and generator torque controllers, was ﬁltered
using a low pass ﬁlter with a cut-off frequency of 0.25 Hz. This frequency was chosen to be a
quarter of the blades edgewise natural frequency to prevent the controller from exciting these
modes [32]; this behaviour was also observed by Wright [35] where he found that a PI controller
with a fast actuator can destabilise certain modes due to the actuation frequency.
Since the GSPI controller was one of the ﬁrst well documented controllers implemented on
ﬂoating wind turbines, it became the reference or baseline controller for other researchers
to compare more advanced control strategies. In this work, the GSPI controller with Jonk-
man’s [32] detuned gains (see next section) will be referred to as the Baseline controller. Block
diagram implementation of the Baseline controller in the above rated wind speed region is
shown in Figure 2.1 where qand T
Genare the commanded actuator inputs and udincludes all
disturbance inputs to the ﬂoating system, namely wind and waves. Not shown in the ﬁgure is
the integrator anti-windup modules. Integrator anti-windup is used to prevent blade satura-
tion from signiﬁcantly affecting the performance by holding the integrator value during blade
saturation. Blade saturation can occur from having aggressive gains or from operation close to
region transition conditions.
20

2.1 Gain Scheduled PI Control
2.1.1 Barge Platform
Jonkman, using his newly developed FAST simulator with the HydroDyn module [32] (de-
scribed in Chapter 5), conducted an extensive set of simulations using the CBP GSPI controller
on the ITI Energy barge ﬂoating platform in accordance with the IEC 61400-3 standard for ul-
timate loads [39]. The IEC 61400-3 is a standard for offshore wind turbines with ﬁxed founda-
tions developed by the International Electrotechnical Commission (IEC). To date, no standards
for ﬂoating wind turbines have been released.
The barge platform exhibited large platform oscillations especially in the pitch direction (fore-
aft rocking motion) resulting in large tower loads and power ﬂuctuations. To mitigate these
effects, Jonkman implemented three modiﬁcations to the controller ; these were:
Tower-Top Feedback Loop
An additional proportional control loop that designed to reduce tower fore-aft motion based
on the measurement of the tower top acceleration was implemented. However, the addition
of a tower top feedback control loop did not improve platform damping due to conﬂicting
blade pitch commands issued by the separate control loops; the mechanics of issuing conﬂict-
ing blade pitch commands are discussed in §3.2.
Active Pitch to Stall Control
The purpose of using pitch to stall was to get extra restoring thrust force once the blades are
stalled when the turbine pitches forward. The active pitch to stall controller had excellent
power regulation, however, platform motions were not reduced but were increased instead.
This contradictory result was explained by examining the open and ideal closed loop damping
ratios. Jonkman concluded that the pitch to stall damping was actually positive. And, since
the pitch to feather controller had better damped response, he concluded that the actual closed
loop damping of the pitch to feather controller is greater than that of the pitch to stall; i.e. the
system has positive damping.
Reduced Controller Gains
Lowering the controller gains reduced the use of the blades and possibly reduced the negative
damping effect. These gains, referred to by Jonkman as detuned gains, produced the best
results out of the four controllers. Reducing the controller gains made the response of the
system closer to that of the open loop response hence increasing the damping. This produced
reasonable power regulation and slightly reduced the platform oscillations.
Barge Platform Summary
The increase in the main turbine loads is staggering. For example, the tower base loads are 6
times that of an onshore wind turbine. Jonkman concludes in his PhD dissertation that further
21

Chapter 2: Review of Floating Wind Turbine Controllers
reductions in platform motions is necessary and suggests many possibilities to improve plat-
form pitch damping such as the use of a constant torque algorithm, use of MIMO state-space
controllers to avoid conﬂicting blade pitch commands, and implementing individual blade
pitching control strategies.
2.1.2 Tension Leg and Spar-Buoy Platforms
Larsen and Hanson [40], working on the Hywind spar-buoy (slightly different from the OC3-
Hywind model that has a different mounted wind turbine), also implemented a GSPI pitch
control strategy in above rated wind speed region. However, to avoid the platform pitch
damping issue, they used a constant torque algorithm in the above rate wind speed region
and introduced a constant speed region just below rated wind speed. A variable speed control
below rated region was used to maximise power capture. In the constant speed region, a PI
torque control was used to regulate the rotor speed. Switching between regions was handled
by a set of variable min/max operations in addition to low pass ﬁlters to ensure smooth trans-
ition. Simulation results using HAWC2 coupled with SIMO-RIFLEX from MARINTEK showed
a 30% increase in rotor speed and power ﬂuctuations. The motion response of the ﬂoating sys-
tem was acceptable and tower loads were “reasonable” but were not compared to an onshore
system. Larsen and Hanson accidentally simulated the ﬂoating system with an active pitch
to stall controller and achieved surprisingly good results and recommended further investig-
ations. However, this contradicts with what Jonkman [32] found when he investigated pitch
to stall on the ITI Energy barge. The difference in behaviour is most likely due to different
platform dynamics, simulation tool, and/or model complexity used.
Matha [38], continuing on Jonkman’s work, extended the simulations on the Barge platform to
include fatigue loads analysis. He also carried out a series of extensive simulations in accord-
ance with the IEC 61400-3 standard on the TLP and Spar-Buoy platforms. Comparisons were
made relative to an onshore wind turbine with the same controller. The Baseline controller was
used on all three platforms, however, some modiﬁcations were made to the controller on the
Spar-Buoy platform. A constant torque instead of constant power algorithm was used in the
above rated wind speed region to improve platform pitch damping. Furthermore, the control-
ler bandwidth was limited to avoid resonance issues due to lower natural frequencies of the
system than the other platforms. Below is a brief summary of results obtained by Matha on
each platform.
ITI Energy Barge
The barge concept has some advantages such as cost effective construction, ability to be as-
sembled in any port due to its shallow draft, and relatively inexpensive slack anchoring sys-
tem. However, fatigue loads analysis results were no different to the ultimate results found by
Jonkman [32] in terms of their relative increase to an onshore system; e.g. tower fatigue loads
were approximately 8 times that of an onshore wind turbine. Matha concluded that the barge
22

2.2 Variable Power Pitch Control
may not be suitable for sites with severe sea states but could provide a cost effective solution
to more sheltered sites such as the Great Lakes in the USA.
OC3-Hywind Spar-Buoy
Results from the extensive simulations showed that the spar-buoy experienced signiﬁcantly
less loading on the turbine structure when compared to the barge. However, fatigue loads
relative to an onshore wind turbine were still approximately 1.5 to 2.5 times more than an
onshore system. Furthermore, the deep draft of the spar-buoy limits the number of ports where
the hull can be fabricated and assembled. It is important to note that the ﬁrst full-scale ﬂoating
wind turbine prototype is the Hywind project which is a spar-buoy ﬂoating system. To date,
the outcome of this project, which the offshore wind turbine community is very interested in,
are yet to be published.
MIT/NREL TLP
The performance of the TLP relative to the onshore wind turbine is excellent. Almost all of the
turbine loads are close to parity with the exception of tower Fore-Aft (FA) loads which are on
average 1.5 times that of an onshore system. Therefore, the TLP probably has the best potential,
with more advanced controllers, to achieve similar loading to that of an onshore wind turbine.
However, the TLP may not be always the most economical choice due to the relatively high
cost of the taut anchoring system.
Platform Instabilities
Jonkman [32] and Matha [38] have identiﬁed certain instabilities for each platform. These arise
from a unique Design Load Case speciﬁed by the IEC 61400-3 standard such as operating with a
faulty blade or in extreme conditions. For example, all three platforms experience yaw instabil-
ity in a certain DLC where the turbine is idling with two of its blades fully feathered and one
stuck at the maximum lift position (blade pitch angle of 0 degrees). Most of these instabilities
are due to the design of the system rather than being caused by the controller.
2.2 Variable Power Pitch Control
A simple, empirical, yet effective solution to avoid the reduced or negative damping in the
pitch motion was developed by Lackner [41]. A standard rotor speed controller exacerbates
platform pitching motion as it attempts to regulate rotor speed to the rated speed in above
rated wind speed region (see §3.2 for more details). Lackner’s solution was to change the
speed set-point for the collective blade pitch GSPI controller from a constant to a linear function
of platform pitching velocity and implemented a constant torque algorithm in above rated
wind speed region. The idea is to increase the rotor speed as the turbine is pitching forward
23

Chapter 2: Review of Floating Wind Turbine Controllers
(negative pitching velocity according to the coordinate system) forcing the rotor to increase the
aerodynamic torque to accelerate the rotor and hence create a pitch restoring moment due to
increased rotor thrust force. Also, when the wind turbine is pitching backwards, the desired
rotor speed is less than the nominal rated speed forcing the speed controller to feather the
blades to reduce the rotor speed and thereby reducing the rotor thrust allowing the turbine
to pitch forward. By holding the generator torque constant, turbine power becomes a linear
function of platform pitch velocity. Furthermore, rotor speed ﬂuctuations are reduced resulting
in reduced blade pitching which limit the changes in rotor thrust that causes the reduction in
platform pitch damping. This simple control strategy essentially trades power ﬂuctuations for
reduced pitching motion.
The rated rotor speed is given by equation (2.7) where wRand woare the reference and the
nominal rated rotor speeds respectively, ˙jis the platform pitch velocity and kis the gradient
of the linear relationship – a design parameter. It can be seen from equation (2.7) that if the
platform pitch velocity is zero, the desired rotor speed is the nominal rated speed. When the
turbine is pitching forward (negative ˙j), the desired rotor speed is increased and vice versa.
wR=wo(1k˙j) (2.7)
Lackner applied this control strategy on the ITI Energy barge using FAST. Results were ob-
tained after running two 600 second simulations with turbulent wind and irregular waves for
three different slopes, k, of equation (2.7). Results show that platform pitch and pitch rates
were, on average, reduced by 8-20% under different kvalues but power and rotor speed ﬂuctu-
ations, on average, only increased by 3-11% and 1.5-5% respectively. Of course, the higher the
slope, the bigger the reductions in platform motions and increased power ﬂuctuations.
In addition to the variable power pitch control method, Lackner also implemented individual
blade pitch control to reduce blade loads in a similar way to Bossanyi’s method [42] of using
MBC (or Coleman) transformation (described in Chapter 3) with PID control for the cosine-
cyclic and sine-cyclic components. However, Lackner found that the individual blade pitch
controller was not as effective at reducing blade loads when compared to an equivalent on-
shore wind turbine. Blade load reductions were small (0.6-1.6% reduction) despite a signiﬁcant
increase in blade pitch usage. Furthermore, the IBP controller increased platform rolling and
hence tower side-side fatigue loads. This effect was also observed during the controller design
stage in this work on the barge platform and later resolved; see Chapter 6 for more details
2.3 Estimator Based Control
Because the Hywind concept was designed with much lower tower resonance frequencies to
avoid the wave energy spectrum [40, 43], Skaare et al. [43] implemented an estimator based
control strategy in the above rated wind speed region to “hide the tower motions for the wind
turbine control system and thereby avoid the negative damping effect of the tower motion”.
The wind turbine estimator contains a simpliﬁed SISO model of the wind turbine with the
24

2.4 Active Structural Control
wind speed as an input and the rotor speed as an output. The wind speed is assumed to be
either directly measured or estimated via a wind speed estimator.
In below rated wind speed region, the control system takes the measured rotor speed and com-
mands the generator torque to maximise power capture. In above rated wind speed region, the
controller commands the blade pitch based on the estimated rotor speed from the wind turbine
estimator whose output is based on the estimated wind speed. Seven simulations were carried
out using HAWC2 coupled with SIMO-RIFLEX using the same wind and wave conditions but
with different turbulence intensities. Results show noticeable reductions in nacelle motions
and hence large reductions in tower and rotor loads were observed along with increased rotor
speed ﬂuctuations and a maximum of 3.81% reduction in the average power output.
Under these limited cases, the controller seems to be regulating the ﬂoating turbine well with
promising results. However, since the controller in above rated wind speed region depends
on the estimated rotor speed and not the actual which is calculated/estimated based on wind
speed estimates, the robustness of such controller will heavily depend on the quality of estim-
ates.
2.4 Active Structural Control
An active structural control of ﬂoating wind turbines using a Tuned Mass Damper (TMD) was
developed by Rotea et al. [44]. The idea is to add a Tuned Mass Damper with an active com-
ponent in the nacelle to inﬂuence the platform pitching motion of the ﬂoating wind turbine.
Rotea et al. derived the general equations of motion of the newly added TMDs (one along each
of the pitching and rolling directions) and incorporated these changes into FAST resulting in a
special version called FAST-SC (for structural control).
In their work in [44], only the TMD along the platform pitching direction is activated and
analysed. The TMD parameters (mass, spring stiffness, and damping) were chosen such that
they reduce the platform pitching motion on the ITI Energy barge passively (i.e. without a
controller input). This is followed by designing a family of H¥controllers to actively introduce
additional damping by driving the TMD.
Simulation results show that the passive TMD system achieves 10% reduction in the tower fore-
aft fatigue damage equivalent load (DEL)5relative to a “baseline system” without structural
control. However, no details were provided about the baseline system/controller. With active
structural control, the tower loads are reduced by an average of 15-20% relative to the passive
TMD system at the cost of 3-4% energy consumption of the rated power of the 5MW wind
turbine. However, the stroke of the TMD (passive or active) is large when the dimensions of
the nacelle are considered. Rotea et al. recommend the use to nonlinear control to implement
an active TMD with stroke stop limits.
A major beneﬁt from using a TMD (active or passive) is achieved when the turbine is operating
in extreme conditions. In these conditions the blade pitch controller is normally switched off
5Fatigue DELs are used as a metric to replace the stochastic loads on a component by a periodic load with a
calculated magnitude at a known frequency.
25

Chapter 2: Review of Floating Wind Turbine Controllers
and the blades are feathered. Having a passive TMD will help improve the pitching (and rolling
when implemented) motion(s) in these situations. The performance in these conditions are yet
to be analysed.
2.5 Other Controllers
In this section, the remaining works, to the author’s best knowledge, that have been carried
out on control of ﬂoating wind turbines are brieﬂy discussed. These works either have limited
information available and/or limited conclusions can be drawn.
In 2006, Nielsen et al. [10] implemented a blade pitch control algorithm for active damping
of the platform pitching motion in above rated wind speed region on the Hywind ﬂoating
concept. Simulation results using HywindSim (a tool used to model a simple ﬂoating wind
turbine) coupled with SIMO-RIFLEX agree to some degree with scale model testing. The pitch
control algorithm seems to improve the platform pitching response. Scale model testing was
carried out at the Ocean Basin Laboratory at Marintek in Trondheim, Norway with a scale of
1:47 [23].
Henriksen [45] implemented a model predictive controller primarily on an onshore wind tur-
bine but a simple model for a ﬂoating wind turbine was also used. However, little insight into
the performance of the ﬂoating system can be offered due to limited ﬂoating model ﬁdelity.
2.6 Onshore Wind T urbine Control
More advanced controllers than previously discussed have been applied on onshore wind tur-
bines for many reasons including but not limited to reducing fatigue loads, dealing with tur-
bine nonlinearities and model uncertainties. These techniques can be applied to ﬂoating wind
turbines to address the additional induced motions. Table 2.2 gives a non-exhaustive list of the
types of controller that have been applied on onshore wind turbines; the entries are listed in
perceived increasing complexity.
Obviously, as controller complexity increases the computational requirement also increases. In
some cases, this limits the ﬁdelity of the controller used to ensure real-time control. It’s import-
ant to note that a more advanced controller does not necessarily guarantee better performance.
For example, some form of nonlinear control requires the system model to be represented in
a certain format. This format may not be possible to obtain or can only be obtained for low
ﬁdelity models.
2.7 Controller Objectives
The current range of controllers applied on ﬂoating wind turbines have the following limita-
tions:
26

2.7 Controller Objectives
Table 2.2: Types of controllers implemented on onshore wind turbines
Type Feature(s)
LQR/LQG Multi-objective, optimal for linear systems [35, 46]
DAC Minimises/cancels effects of persistent disturbances [35, 47]
Periodic Accounts for turbine periodicity [48–50]
MPC Predictive control, allows for setting saturation limits [45, 51]
Adaptive Adapts to model changes uncertainties to guarantee performance [52, 53]
Nonlinear Accounts for turbine nonlinearities including saturation [54, 55]
Legend:
LQR/LQG Linear quadratic regulator/Gaussian
DAC Disturbance accommodating control
MPC Model predictive control
• Most had a single control objective of rotor speed control. Where an additional objective
was included, it was implemented as a separate control loop; coupling between con-
trolled DOFs is ignored.
• Fatigue load reduction was not an explicit control objective despite high tower loads.
• Used collective blade pitching. Collective blade pitching has limited actuation when mul-
tiple control objectives are considered (discussed in the next chapter).
• Not all of these controllers were simulated on all three main ﬂoating platforms.
To recap and expand on the research objectives discussed in Chapter 1, this work aims to im-
plement multi-objective controllers that utilise individual blade pitching on the three main ﬂoating
wind turbines using a state space approach.
For reducing tower fatigue loads on the wind turbine, the approach taken is to reduce tower
base load variations via reducing tower-top motion relative to the platform coordinate system.
Tower-top displacement relative to the platform coordinate system corresponds to the actual
tower bending due to the applied forces and moments.
The controllers implemented in this work have the following objectives in the above rated wind
speed region (region 3):
• Regulate the captured power to the rated (5 MW) via regulating rotor speed and varying
generator torque.
• Reduce tower-top motion in order to reduce tower fatigue loads.
• Reduce platform motions (especially platform pitch) to:
–improve rotor speed regulation via reducing the induced relative velocity caused by
platform pitching; and
–reduce loading on the tower base by reducing the deviations of the centre of mass
due to platform rolling and pitching.
27

Chapter 2: Review of Floating Wind Turbine Controllers
2.8 Chapter Summary
A recurring issue with ﬂoating wind turbines in terms of control is reduced or negative plat-
form pitch damping in the above rated wind speed region. Several ways of dealing with this
issue were proposed and below is a summary of the most important ﬁndings (in no particular
order):
• Using constant torque instead of constant power algorithm for the generator torque con-
trol in above rated wind speed region helps to improve the platform pitching response
by reducing the use of the blade pitch actuator responsible for the reduction in damping.
This is not a complete solution but it can help when used with other controllers.
• The addition of Tuned Mass Dampers (TMDs) can noticeably improve the pitching mo-
tion on certain ﬂoating platform designs. Active TMDs further improve performance,
however, based on current studies to date, the stroke length required to achieve these re-
ductions cannot be used inside the nacelle of the wind turbine. A major beneﬁt of using
TMDs (active or passive) is that it has the potential to reduce pitching motion in extreme
conditions where the blade pitch controller is not active.
28

3
State Feedback Control
Contents
3.1 State-Space Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 Collective vs. Individual Blade Pitching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Multi-Blade Coordinate Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5 Stability Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Multi-objective control of ﬂoating wind turbines is the next logical step to address the
limitations of current controllers implemented on ﬂoating wind turbines as previ-
ously discussed. State feedback control is a model based approach that uses a linear
state-space model to regulate multiple states. For brevity, the term state-space control or control-
lerrefers to a State Feedback Control (SFC) or Controller designed based on a linear state-space
model. This approach allows the control of MIMO systems such as a ﬂoating wind turbine. As
discussed in Chapter 2, this approach has not yet been applied to ﬂoating wind turbines.
This chapter describes the approach used to design, implement and assess the stability of such
controllers on ﬂoating wind turbines. Furthermore, because state feedback control allows for
the use of multiple actuators, the merits of individual over collective blade pitching and how
each one operates are also described. A description of the selected approach to achieve indi-
vidual blade pitching using a multi-blade coordinate transformation is given.
29

Chapter 3: State Feedback Control
3.1 State-Space Approach
Linear state feedback control is one of the preferred types of controllers when dealing with
MIMO systems with multiple objectives. This approach requires a linearised state-space model
of the nonlinear ﬂoating system. As a result, the system states xbecome perturbations, Dx,
about a selected operating point xopsuch that x=Dx+xop. This notation also applies for
the measurements vector y, actuators vector uand disturbance inputs vector ud. A generic
linearised state-space model is given by equations (3.1) and (3.2) where Ais the state matrix,
Bis the actuator gain matrix, Bdis the disturbance gain matrix, Crelates the measurements to
the states, Drelates the measurements to the control inputs, and Ddrelates the measurements
to the disturbance inputs.
D˙x=ADx+BDu+BdDud (3.1)
Dy=CDx+DDu+DdDud (3.2)
The state feedback control law is given by equation (3.3) where Kis the state feedback control
gain matrix. In this work, the state matrix is deﬁned as x=h
q˙qiT
where qis a vector that
contains the motions of the linearised degrees of freedom. The order or number of states of the
linearised state space model chosen for control design is platform dependant and is discussed
in relevant chapters.
Du=KDx (3.3)
The control law requires allthe states information to be available through measurement or es-
timation. In this work, the state-space controllers are implemented with Full State Feedback
(FSFB); that is, all the states are directly being measured. The selected design states for all
the state-space controllers designed in this work can be easily measured by readily available
sensors. In practice, it is desirable to reduce the number of sensors required by implementing
a state estimator; however, this work is of an exploratory nature and will not focus on imple-
mentation issues such as cost of sensors, effects of noise, sensor failure, etcetera. Furthermore,
from a stability point of view of linear systems, the separation principle allows the design of
the controller to be independent of the state estimator. Since a state estimator can be designed
separately, it is considered outside the scope of this work. Adding a state estimator only de-
grades the performance. Therefore, the state estimator is excluded from the system design be-
cause one of the objectives of this research is to assess the effectiveness/potential of advanced
control strategies on ﬂoating platforms under ideal estimation conditions. The performance is
assessed based on metrics deﬁned in Chapter (5) that measure power regulation, fatigue loads,
and platform motions.
It may be possible to express the cost of energy using a mathematical cost function for con-
troller optimisation. However, that function will be nonlinear and maybe difﬁcult to solve.
Instead, Linear Quadratic Regulator (LQR) theory is used to obtain an optimal controller gain
matrix given a set of weighting matrices that correspond to a quadratic cost function given by
30

3.1 State-Space Approach
equation (3.4) where Qand Rare the state and actuator weighting matrices. These weight-
ing matrices are manually chosen to emphasise the regulation of certain states over others to
improve performance. This method is used for all the controllers that had a state regulation
component including the disturbance accommodating controllers discussed in Chapter 4.
J=¥
0(xTQx+uTRu)dt (3.4)
So far, all of the above approach and equations only apply if the system is time-invariant.
However, wind turbines are time-varying system that are governed by the period of the rotor;
they are periodic systems. Therefore, when linearising such systems, the results is a linear
periodic state-space model given by equations (3.5) and (3.6) where yis the azimuth angle of
the rotor.
D˙x=A(y)Dx+B(y)Du+Bd(y)Dud (3.5)
Dy=C(y)Dx+D(y)Du+Dd(y)Dud (3.6)
Due to the periodic nature of the wind turbine, standard time-invariant control techniques
cannot be applied directly. However, there are three ways to address the periodicity of the
system; they are: averaging, Multi-Blade Coordinate (MBC) transformation, and direct periodic
technique.
Averaging
Averaging the periodicity of each matrix across the azimuth angle resulting in a time-invariant
state-space model. Direct averaging allows Linear Time-Invariant (LTI) control techniques to
be applied. However, some information is lost by averaging and Individual Blade Pitching
(IBP) cannot be used to control the rotor speed. Individual blade pitching may still be achieved
for other control objectives if they are driven by a periodically changing error signal such as
regulating blade ﬂapwise load.
Multi-blade Coordinate Transformation
Multi-blade coordinate transformation can be used to facilitate individual blade pitching [48,
50, 56]. MBC transformation captures periodic properties of a system in a linear time-invariant
model – useful for control design; see §3.3 for more details. Although MBC transformation
does not capture all the periodic effects, it has been shown that the residual periodic effects are
negligible for analysis and control design for three bladed wind turbines [50]. Bossanyi [57]
implemented IBP control using PI controllers to mitigate blade loads. He used a direct and
quadrature (d-q) axis representation (a form of MBC) to be able to allow for MIMO control
using PI controllers.
31

Chapter 3: State Feedback Control
Direct Periodic Technique
Direct periodic control allows the controller gains to change depending on the rotor azimuth
position and control objectives [46, 58]. Periodic control captures all the periodicity of the sys-
tem. However, it is more complicated and computationally more demanding than the previous
two methods. Stol et al. [50] showed that there were no noticeable differences between the per-
formance of controllers designed after MBC transformation and controllers with direct periodic
control.
Both MBC transformation and direct periodic technique facilitate the use of IBP . However, the
MBC transformation method allows for the utilisation of IBP control via LTI control design
without the computational complexity of direct periodic control method.
3.2 Collective vs. Individual Blade Pitching
There are several actuators available for use by a control system on wind turbines in general.
These include: blade pitch, generator torque, turbine yaw drive, smart blades with distributed
actuators such as trailing edge ﬂaps [59], and passive devices such as tuned mass dampers.
For ﬂoating systems, passive devices such as oscillating water column can also be used to
absorb energy from the waves. For active control, the most commonly used actuators for an
onshore turbine are the blade pitch angle (operated either collectively or individually) and the
commanded generator torque.
In this section, the physical mechanism behind Collective Blade Pitching (CBP) and individual
blade pitching are described. The objective is to illustrate the differences between the two pitch-
ing schemes in terms of implementation, effectiveness at regulating multiple control objectives,
and limitations with an emphasis on their impact on ﬂoating wind turbines.
3.2.1 Collective Blade Pitching
Collective blade pitch control is widely used in wind turbine control simply because it provides
the necessary actuation required for rotor speed control. CBP changes the symmetric thrust and
torque loads on the rotor. It is also easy to implement since all three blades are commanding
the same pitch angle hence combining the actuation of the three blades into one single rotor ac-
tuator, which is useful for SISO control. However, when multiple objectives are to be regulated,
collective blade pitching may not always provide the necessary actuation without sacriﬁcing
the regulation of other objectives or affecting other uncontrolled and/or un-modelled turbine
DOFs.
With regards to ﬂoating offshore wind turbines, a major limitation of CBP is conﬂicting blade
pitch commands issued by the control system with multiple objectives (whether implemented
as separate SISO loops or a single MIMO controller) [60]. The objectives that conﬂict with
each other in terms of actuator demand are rotor speed regulation and platform pitch motion
regulation This type of conﬂict also exists but to a lesser degree in onshore turbines between
32

3.2 Collective vs. Individual Blade Pitching
Surge Heave
Sway
Roll Pitch Yaw
Pitching
Velocity Restoring
Thrust
(a) Collective blade pitching
Surge Heave
Sway
Roll Pitch Yaw
Pitching
Velocity Increased
Thrust
Reduced
ThrustReduced
ThrustResulting
Restoring
Moment (b) Individual blade pitching
Figure 3.1: Platform pitch restoring forces with different blade pitch operation
rotor speed regulation and tower fore-aft motion. Below is a description using a hypothetical
example of how these conﬂicting blade pitch commands are issued based on physical insight
into the ﬂoating system.
For simplicity, assume there are two separate control loops: rotor speed controller and plat-
form pitch controller. For regulating platform pitch, the most useful force generated by the
blades is rotor thrust. Since the blades cannot inﬂuence the platform pitch angle directly but
only through the thrust force, let the platform pitch controller regulate the pitching velocity
which, ideally, must be reduced to zero. Now consider a forward pitching velocity shown in
Figure 3.1a (negative pitch velocity according to the coordinate system). To keep the turbine in
its equilibrium position (not necessarily upright due to the effect of constant wind), the plat-
form pitch controller must generate a positive restoring pitch moment. This restoring moment
can be achieved by increasing the aerodynamic thrust of each blade collectively where it will
create a positive pitching moment about the pitch axis as shown in Figure 3.1a. Therefore, the
blade pitch angles will have to be decreased to increase the torque and thrust loads generated by
the blades.
Now, consider the effect of the same pitching velocity on the rotor speed. As the platform pitch
33

Chapter 3: State Feedback Control
controller decreases the blade pitch to restore platform pitch, it is also accelerating the rotor
by generating additional aerodynamic torque. This is coupled by the fact that as the turbine
pitches forward, the wind speed relative to the blade increases thus further accelerating the
rotor. Observing an increase in rotor speed, the rotor speed controller commands the blades to
reduce the generated torque by increasing the collective blade pitch angle to reduce the aero-
dynamic efﬁciency of the blades. Therefore, the two objectives of speed and platform pitch
regulation are competing for commanded blade pitch.
Multi-objective control using SFC with collective blade pitching can improve the performance
with the abovementioned objectives but the conﬂict in objectives is present as it is still using
CBP [61]; more details are given in Chapter 6. Therefore, SFC with CBP is not considered as
one of the main controllers presented in this work.
3.2.2 Individual Blade Pitching
Individual blade pitch control where each blade is commanded independently uses a differ-
ent mechanism from CBP control. It creates asymmetric aerodynamic loads in addition to the
symmetric loads created by collective pitching thus enhancing the platform pitch restoring
moment [60]. Due to the periodic nature of wind turbines, implementing IBP control results
in time-varying gains that vary periodically with the rotor azimuth. That is, the controller
“knows” how the effectiveness of the blade changes as it rotates and acts accordingly to create
the necessary restoring forces/moments to achieve its control objectives.
There are many ways to achieve individual blade pitch control depending on the control ob-
jectives. MBC transformation and direct periodic techniques (discussed in §3.1) are the main
methods to implement IBP for general purpose control objectives (rotor speed control, load
mitigation, etc.). Wright [35] achieved IBP control using a disturbance accommodating control-
ler. He used an internal model for the wind disturbance and the effect of vertical wind shear6
to drive the individual blade pitching. This method uses IBP to only reject wind disturbance;
the turbine states are regulated using a collective blade pitch controller.
As an example to illustrate the difference between individual and collective blade pitching,
consider two controllers designed to regulate platform pitch DOF. The ﬁrst is a CBP SFC and
the second is an IBP SFC. Both controller gains are obtained using the same LQR cost function
and weightings. The difference is that the IBP SFC is designed in the non-rotating frame after
MBC transformation; this results in a periodic gain when it is transformed back. Figure 3.2 il-
lustrates the variations with the rotor azimuth angle of both controller gains (or commanded
blade pitch angle in radians) for blade 1 acting on platform pitch velocity error. The zero azi-
muth position is at the 12 o’clock position on the rotor with angle increasing clockwise when
looking downwind; initially blade 1 is at the 0 azimuth position. The periodic gain changes
sign twice as the blade goes through a full rotor revolution. The ﬁgure does not show the gains
for the other two blades as the gains are the same but shifted 120and 240out of phase for
blades 2 and 3 respectively. The signiﬁcance of the sign change will be explained next.
6Vertical wind shear describes the increasing horizontal wind speed with height/elevation known as the bound-
ary layer.
34

3.2 Collective vs. Individual Blade Pitching
0 60 120 180 240 300 360−2−1.5−1−0.500.511.52
Azimuth, degGains

Constant
Periodic
Figure 3.2: Collective and individual blade 1 gains as a function of rotor azimuth
The mechanism can be explained by looking at the periodic gain matrix (Figure 3.2). The gain
for blade 1 is negative for azimuth angles approximately between 90and 270; these angles
correspond to the blade lying in the lower half section of the rotor. Therefore, given a negat-
ive platform pitch velocity, shown in Figure 3.1b, blades at the top with a positive controller
gain are commanded to reduce blade pitch thus increasing thrust. Blades at the bottom with
a negative controller gain are commanded to increase blade pitch and hence reducing thrust.
This asymmetric aerodynamic loading generates a positive restoring pitching moment in ad-
dition to the restoring moment generated by the mean thrust load (as with collective pitch) as
illustrated in Figure 3.1b.
Looking further at the periodic gain shown in Figure 3.2, it can be seen that the maximum posit-
ive peak is when the blade is at the top (12 o’clock) position. A more positive gain value means
increased blade pitching, which indicates that the controller is making use of the combined
effect of increased moment arm of the blades and wind shear.
Wind turbines are under-actuated systems where the number of controller degrees of freedom
is more than the number of actuators available. Furthermore, having the wind turbine moun-
ted on a ﬂoating platform makes it even more difﬁcult to regulate the control objectives than
turbines with ﬁxed foundations by introducing six additional DOFs (surge, sway, heave, roll,
pitch, and yaw). The use of IBP increases the number of available actuators from 2 to 4 (for a
three bladed wind turbine and including the generator torque) which gives the controller more
authority to better regulate multiple objectives. However, there are some issues that arise when
implementing IBP that one must be aware of:
• Increased blade pitch actuation which may result in blade pitch saturation and/or in-
creased blade loads (depending on the control objectives).
• Increased computational requirements by the control system.
• The possibility of exciting or destabilising other turbine modes due to coupling with un-
modelled and/or unregulated DOFs.
35

Chapter 3: State Feedback Control
In this work, state feedback controllers utilising individual blade pitching are implemented
using MBC transformation as it utilises well established LTI control design methods without
the computational complexity of direct periodic control.
3.3 Multi-Blade Coordinate Transformation
Wind turbine systems are usually modelled with degrees of freedom in the ﬁxed and rotating
frames of reference. Therefore, the effects of the DOFs in the rotating frame of reference (e.g.
blades) on those in the ﬁxed frame of reference (such as the tower) are periodic. MBC trans-
formation is used to transform the DOFs that are in the rotating frame of reference to the ﬁxed
frame of reference [48]. For a three bladed wind turbine, transforming any three DOFs in the
rotating frame of reference results in three DOFs in the ﬁxed frame of reference that describe the
effect of the whole rotor on the turbine system. These three transformed DOFs are often termed
collective, cosine-cyclic, and sine-cyclic components. MBC transformation is also known as the
Coleman transformation or Fourier coordinate transformation [48, 62, 63].
The state, input and output vectors of equations (3.5) and (3.6) contain entities that are deﬁned
in both frames of reference (ﬁxed and rotating); this combination is referred to as the mixed
frame of reference. MBC transformation of these equations yields a state-space model whose
states are all in the non-rotating/ﬁxed frame of reference given by equations (3.7) and (3.8)
where the subscript NRindicates the transformed entity into the non-rotating frame of refer-
ence; the Dsymbol that indicates perturbation about an operating point is omitted for brevity
and clarity. For more information on MBC transformation, please refer to Appendix A.
˙xNR=ANRxNR+BNRuNR+Bd,NRud (3.7)
y
NR=CNRxNR+DNRuNR+Dd,NRud (3.8)
This transformation is achieved by applying the transformation equations (3.9) to (3.11). Note
that the disturbance vector udis assumed to have no inputs in the rotating frame of reference
and hence the vector itself is not transformed. The transformation matrices are deﬁned in
Appendix A.
x=Ts(y)xNR (3.9)
u=Tc(y)uNR (3.10)
y=To(y)y
NR(3.11)
The transformed system in equations (3.7) and (3.8) is not time-invariant; it is still slightly
periodic [48]. Strictly speaking, periodic analysis should follow the transformation but Stol et
al.[50] found that by averaging the transformed matrices ( ANR,BNR,Bd,NR,CNR,DNR, and Dd,NR),
little or no information is lost and hence time-invariant control design can be used without af-
fecting the controller performance. Therefore, with a controller designed by averaging the sys-
36

3.4 Implementation
tem matrices after applying MBC transformation, the commanded actuator effort, uNR, is time-
invariant. However, individual blade pitching is achieved when this command is transformed
back to the rotating frame of reference by expanding equation (3.10) into equation (3.12) where
TGenis the applied generator torque, and qnis the commanded blade pitch angle for blade
n. Equation (3.12) clearly shows that even if the controller commands are time-invariant in the
non-rotating frame of reference, the actual blade commands are periodic resulting in individual
blade pitching. Equation (3.12) is applicable for a three bladed wind turbine with uNRgiven by
equation (3.13) where qo,qc, and qsare the collective, cosine-cyclic, and sine-cyclic terms of the
blade pitch angles respectively.
u=2
66664TGen
q1
q2
q33
77775=2
666641 0 0 0
0 1 cos (y) sin(y)
0 1 cos
y+2p
3
sin
y+2p
3
0 1 cos
y+4p
3
sin
y+4p
33
77775uNR (3.12)
where
uNR=h
TGen qoqcqsiT
(3.13)
3.4 Implementation
MBC transformation allows the design of time-invariant controllers in the non-rotating frame
of reference that are actually periodic in nature. Therefore, equation (3.3) still applies in the
non-rotating frame (i.e. DuNR=KNRDxNR). The block diagram implementation of this equation
is shown in Figure 3.3a [64]. This implementation, obviously has two transformations: to and
from the non-rotating frame. From an implementation point of view, each transformation re-
quires periodic matrix extraction and multiplication. Periodic matrices are 3D arrays/matrices
where each layer in the “third dimension” contains the matrix data for a speciﬁed azimuth
angle. Hence, at each simulation step, the 2D matrix data has to be extracted and interpolated
according to the simulation azimuth angle before multiplication with DxNR.
A simpler implementation that does not require transformation to and from the non-rotating
frame is possible by simple manipulation of the control law. By substituting DuNR=KNRDxNR
andDxNR=T1
s(y)Dxinto equation (3.10), we obtain equation (3.14) which only contains a
single periodic controller gain matrix. This simpler approach (Figure 3.3b) is more computa-
tionally efﬁcient and only requires the periodic controller gain matrix to be computed ofﬂine
(equation (3.15)).
Du=Tc(y)KNRT1
s(y)Dx
)Du=K(y)Dx (3.14)
37

Chapter 3: State Feedback Control
where
K(y)=Tc(y)KNRT1
s(y) (3.15)
Note that the control gain K(y)depends on the azimuth angle. In this implementation, the ac-
tual azimuth angle is used instead of the desired angle ( wRatedt) for better accuracy. However,
because azimuth angle is a system state, the controller becomes nonlinear. If speed regulation
is maintained close to the rated rotor speed, then the effects of this nonlinearity are negligible.
From this point forward, the controller is considered linear.
+-++Nonlinear Wind
Turbine Model
Controller +-++Nonlinear Wind
Turbine Model
Controller Saturation
Saturation
(a) Standard
+-++Nonlinear Wind
Turbine Model
Controller +-++Nonlinear Wind
Turbine Model
Controller Saturation
Saturation
(b) Simpliﬁed
Figure 3.3: Standard and simpliﬁed block diagram implementations of an IBP state-space con-
troller
38

3.4 Implementation
3.4.1 Generator Torque
Wright [35] showed that generator torque can be used directly to inﬂuence some turbine states
such as tower side-side motion and low speed shaft loads. Therefore, the generator torque is
included in the design of the SFC as an additional actuator to help in regulating turbine states.
When the generator torque is included in the model as an actuator, the controls input vector be-
comes Du=h
DTGenDq1Dq2Dq3iT
where DTGenis the commanded torque perturbations
andDqnis blade ncommanded perturbations about the linearisation point.
For the state feedback controller, direct power regulation via state regulation is not possible as
generator power is not a state in the linearised models of the wind turbine obtained from FAST.
One approach to regulate power is to vary the generator torque operating point according to
equation (3.16) such that TGen =DTGen+Top
Genwhere wGen,fis the ﬁltered generator speed
(as discussed in §2.1). This set-up, known as constant power algorithm , maintains the constant
power objective by the Baseline torque control in addition to regulating turbine states through
the commanded torque perturbations.
Top
Gen=PRated
hGenwGen,f(3.16)
Normally, the actuators’ operating point vector is constant and based on the linearised state-
space model. For the generator torque, the constant operating point is termed constant torque
algorithm . Using the constant power algorithm improves power regulation but results in in-
creased rotor speed ﬂuctuations and slightly reduces the platform pitch damping when com-
pared to the constant torque control algorithm [61]. Constant power algorithm is implemented
on all the state feedback controllers used in this work.
3.4.2 Azimuth Angle Correction due to Platform Rolling
Due to the application of MBC transformation, any controller designed based on that trans-
formation will require periodic matrix or matrices in its implementation which can be calcu-
lated ofﬂine for improved computational efﬁciency. These periodic matrices require the current
rotor azimuth angle to be known at that time step. Since FSFB is used for the SFC, the current
azimuth angle is available.
For ﬂoating wind turbines, the roll motion changes the effective azimuth angle yaas the blades
are rotated the additional roll angle xand therefore placing the blades in a different rotor ori-
entation with respect to the incident wind ﬁeld. The effect of the roll motion on the azimuth
angle is illustrated in Figure 3.4 where the platform roll and rotor DOFs rotate about the posit-
ivex-axis [36]. If the effect of platform rolling is not taken into account, the data extracted from
the periodic matrices become inaccurate and do not represent the system at that state.
The actual azimuth angle can be calculated using equation (3.17). This angle can then be used
to extract data from the periodic matrices. However, equation (3.17) requires the roll angle to
be measured. For the controllers implemented in Chapters 6, 7, and 8, the roll DOF is part of
the controller design which allows the compensation of the azimuth angle due to roll motion.
39

Chapter 3: State Feedback Control
Figure 3.4: Azimuth angle correction due to platform roll motion
ya=y+x 0<ya<2p (3.17)
The effect of rolling and pitching motion on changing the hub height is negligible. To cause a
5 m change in hub-height for a wind turbine with 90 m hub-height, it would require a roll/pitch
angle of approximately 19; this is an extreme angle which, with an on–board active controller,
should never be reached. Furthermore, a 5m change in hub height would only cause the wind
speed to change by 1% with a power law coefﬁcient of 0.2 for the vertical wind shear.
3.4.3 Actuator Saturation
An important factor to consider when designing controllers is actuator limits. From a simula-
tion point of view, these limits must be enforced to reﬂect the limits of the real actuator. For the
the ﬂoating wind turbines considered, saturation and rate limits for the generator torque and
blade pitch angles are enforced. The rate limits are used to limit how fast the control effort can
40

3.5 Stability Assessment
change in the absence of an actuator model (as deﬁned in the scope of this work in §1.3). From
a control design point of view, these limits must be avoided as reaching them may signiﬁcantly
affect the controller performance.
With individual blade pitching, the blade actions can be thought of as a collective blade pitch
with periodic perturbations such that q=qo+Dqi(y)where qois the collective pitch angle that
creates symmetric loads on the rotor and Dqi(y)is the individual periodic perturbation that is
responsible for creating the asymmetric loads on the rotor. Therefore, during blade saturation,
Dqi(y)is allowed to pass through and continue regulating certain objectives while limiting
the collective term. MBC transformation facilitates this type of selective saturation because uNR
(equation (3.13)) has the three components already separated out. Therefore, by only saturating
the collective term the selective saturation can be achieved.
3.4.4 Azimuth State Anti-windup
Integrator windup becomes a concern when actuator saturation is possible. With state feed-
back control, there are no explicit integrators present but windup is possible through certain
states. Recall that the states vector of a ﬁrst order state-space model contains the state and its
derivative (i.e. x=h
q˙qiT
). Therefore, qcan be thought of as integrals of ˙q.
For a ﬂoating wind turbine, the only state the can grow when the blades are saturated is the
azimuth state. Therefore, an anti-windup scheme is used to stop that state from growing when
the blades are saturated. Instead of directly feeding the change in azimuth state, Dy, to the lin-
ear state-space controller, the change in rotor speed, D˙y, is passed through a special integrator
that stops integrating when the blades are saturated and holds its value. That way, Dywill not
grow to dominate the control effort when the blades are saturated.
3.5 Stability Assessment
LQR control design guarantees the closed-loop stability of the linear system it is designed to
control. However, because wind turbines in general and especially ﬂoating wind turbines have
many ﬂexibilities and degrees of freedom, the linear model used for controller design is usu-
ally of a much lower order than the actual system. Therefore, the closed-loop stability of the
controller with the full DOFs system must be assessed.
The stability of the closed-loop system can be assessed by ﬁnding the location of the closed-
loop poles. For a system given in state-space form, the closed-loop poles can be found by
evaluating the eigenvalues of the (ANRBNRKNR)matrix. Stol et al. [50] showed that there are
no differences between the closed-loop poles calculated from using MBC transformed matrices
compared to the poles found by doing a Floquet analysis on the full periodic system.
To assess the closed-loop stability of the controller with all the model ﬂexibilities enabled, we
need to introduce a boolean transition matrix Tto account for the larger full degrees of freedom
(DOFs) state-space matrices ANR,f ulland BNR,f ull. The stability of the full DOFs system is given
41

Chapter 3: State Feedback Control
by equation (3.18) where all the eigenvalues lmust lie in the left half of the complex plane (i.e.
the real part must be negative).
Re
l
ANR,f ullBNR,f ullKNRT<0 (3.18)
The boolean transition matrix T, given by equation (3.19), has dimensions of ndn fwhere
ndis the number of design states (i.e. the number of states the controller was designed with)
and n fis the number of the full system states. The elements of the matrix are either 1 or 0. The
element Ti,jis set to 1 to indicate that the ithdesign state is the jthstate in the full DOFs system.
A simple program is executed to automatically create the boolean matrix based on information
contained within the FAST linearisation ﬁles of the controller and the full DOFs system.
T=2
664T1,1 . . . T1,n f
………
Tnd,1 Tnd,n f3
775(3.19)
When one or more poles are unstable it is possible to identify which bending mode or DOF the
pole corresponds to. By looking at the associated eigenvector, one can identify which state has
the most contribution in that eigenvector and therefore is most likely the state that is unstable.
However, with complex ﬂexible structures such as wind turbines, the unstable DOF may not
be that easy to identify due to the number of DOFs and their associated coupling.
It is important to note that this approach can only assess the closed-loop stability of the linearised
system which is a close approximation of the nonlinear system around the operating point.
Therefore, away from the linearisation point, nothing can be inferred about the stability of the
nonlinear system. This approach with its limitation is sufﬁcient for the purposes of this work
since it is only used to identify any instability caused by the controller that can arise from using
individual blade pitching or using a low ﬁdelity linear model.
3.6 Chapter Summary
State feedback control using individual blade pitching is one of the main controllers that are
implemented on the three ﬂoating platforms. The state Feedback controller is designed using a
linearised periodic state-space model of a ﬂoating wind turbine, can handle multiple objectives,
and utilise all of the available actuators. The periodicity of the linear model is dealt with by
using multi-blade coordinate system transformation to transform the model to a non-rotating
frame of reference. By averaging the transformed system, a linear time-invariant model is
created without loss of information which can then be used for controller design.
MBC transformation also facilitates the use of individual blade pitching. Individual blade
pitching allows the controller to create asymmetric loads on the rotor in addition to symmet-
ric ones created by collective blade pitching. These asymmetric loads help in better regulating
certain objective/states than collective blade pitching.
42

4
Disturbance Accommodating Control
Contents
4.1 Introduction to DAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 DAC Theory Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.3 DAC After MBC Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.5 Wind Speed Disturbance Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Disturbance Accommodating Control (DAC) is a type of feed-forward control used to
minimise or cancel the effects of persistent disturbances [35, 47, 65]. In the case of
ﬂoating wind turbines, the disturbances include the incident wind and waves. If
the effects of wind and, more importantly, waves can be cancelled or reduced, then platform
motions will be signiﬁcantly reduced thus reducing the additionally induced loads on the wind
turbine and improve power regulation.
In this chapter, the general approach of applying DAC to ﬂoating wind turbines is described
where the effects of wind speed perturbations are considered. A disturbance estimator is de-
rived to estimate the system disturbances, whose effects are to be minimised, since direct meas-
urement of the disturbances is assumed to be unavailable. MBC transformation is used to deal
with the periodicity of the wind turbine.
4.1 Introduction to DAC
Disturbance accommodating controllers have been designed and implemented, at least in sim-
ulations, on large scale wind turbines in the past; two examples are described next.
43

Chapter 4: Disturbance Accommodating Control
Wright [35] has designed and implemented a DAC on a 600 kW, two bladed, wind turbine. The
wind disturbance was modelled as a superposition of a step change in horizontal hub-height
wind speed and a periodically varying term to represent the changes in wind speed at the blade
tip due to vertical wind shear as the blade completes a full revolution. The latter term facilitated
IBP control without the need to resort to periodic control theory. Results were then compared to
a standard PI controller under two distinct conditions: slow and fast actuator dynamics. With
slow actuator dynamics, both controllers performed similarly but the PI controller behaved
more robustly when the wind speed drifted away from the linearisation point. However, with
fast actuator dynamics, DAC performance was signiﬁcantly better than that of the PI controller.
Under these conditions, the PI controller could not guarantee system stability (since it was a
single-objective controller thus could not regulate/control other DOFs); in fact, certain DOFs
were destabilised when the PI controller was used with an actuator with fast dynamics.
Stol and Balas [49] performed a study to evaluate the load mitigation capability (for blade
ﬂap) of three different control strategies: time-invariant PI, time-invariant DAC, and periodic
DAC (utilising IBP control). The disturbance was modelled as a step change in hub-height
wind speed. First, they tested these controllers under full state feedback conditions. Results
showed that while all controllers gave similar speed regulation, loads were best mitigated by
the periodic DAC, then the time-invariant DAC, while the PI controller had the highest loads.
However, when state estimators were included in the design, the load mitigation capability of
DACs were severely reduced. The time-invariant controllers had similar performance while
the periodic DAC was able to reduce the loads further relative to the time-invariant controllers.
4.2 DAC Theory Overview
Disturbance accommodating controllers are implemented by modelling the disturbances using
an assumed waveform model [35, 65], similar to the use of an exo-system in reference tracking
control theory. A generic linear system is given by equations (4.1) and (4.2). The objective is to
modify the control law such that it cancels out the effects of the persistent disturbances udon
system states.
˙x=Ax+Bu+Bdud (4.1)
y=Cx+Du+Ddud (4.2)
To cancel the effects of disturbances, we must ﬁrst assume that the persistent disturbances can
be represented by a waveform model. The disturbance waveform model is given by equations
(4.3) and (4.4) where zis the disturbance states vector, GandQare assumed to be known but
with unknown initial conditions z(0)[47,65]. The choice of matrices G,Q, and initial conditions
z(0)determines the nature of the assumed waveform (step, ramp, periodic, etc.).
ud=Qz (4.3)
˙z=Gz (4.4)
44

4.2 DAC Theory Overview
The modiﬁed feedback control law that minimises or cancels the effects of disturbances is given
by equation (4.5) where Kis the state feedback controller gain matrix, and Gdis the disturbance
minimisation gain matrix. The second term in equation (4.5) exhibits feed-forward action as it
commands the blades based on an assumed disturbance model.
u=Kx+Gdz (4.5)
Substituting equations (4.3) and (4.5) into equation (4.1), we obtain equation (4.6) which clearly
shows that in order to cancel the effects of persistent disturbances, equation (4.7) must hold
true.
˙x=AxBKx +BGdz+BdQz
=(ABK)x+(BGd+BdQ)z (4.6)
BGd+BdQ=0 (4.7)
Note that the disturbance accommodating controller is simply a state feedback controller with
an additional feed-forward term that minimises the effects of persistent disturbances on the
modelled system states. This additional feed-forward term has no impact on the closed-loop
stability of the system. This is evident by examining equation (4.6) where the disturbance
minimisation gain, Gd, does not affect state regulation.
Applying the Disturbance Accommodating Control law and equations in practice gives rise to
two issues:
1. With a relatively complicated model, it is almost always impossible to completely cancel
out the disturbances (unless these disturbances enter the system through the same chan-
nels such that B=Bd) [47, 65]. Therefore, to minimise the effect of disturbances on the
system, Gdmust be chosen to minimise kBGd+BdQk. This can be achieved by applying
the Moore-Penrose pseudoinverse (indicated by+) such that Gdis calculated using equa-
tion (4.8).
Gd=B+BdQ (4.8)
2. Equation (4.5) assumes FSFB – meaning the controller has access to all states including
the disturbance states. Practically, this is very hard to implement especially with the
modelled disturbance states where they do not necessarily represent real physical entit-
ies. Therefore, a disturbance estimator has to be designed to reconstruct the system and
disturbance states based on sensor measurements, y.
4.2.1 Disturbance Estimator
In this work, it is assumed that the disturbance inputs cannot be measured, therefore, a dis-
turbance state estimator is required. It is possible to use turbine measurements to estimate the
45

Chapter 4: Disturbance Accommodating Control
disturbance states thereby utilising the turbine as an instrument that measures the effects of the
disturbances.
A disturbance state estimator can be designed by augmenting the turbine states with the dis-
turbance states forming win equation (4.9). By differentiating the new state vector with respect
to time and utilising equations (4.1) to (4.4) a new and augmented state-space model is created
and given by equations (4.10) and (4.11).
w=h
xziT
(4.9)
˙w=Aw+Bu (4.10)
y=Cw+Du (4.11)
where
A="
A B dQ
0G#
(4.12)
B="
B
0#
C=h
C D dQi
The state estimator dynamics for the augmented state-space model are given by equations
(4.13) and (4.14) [66] where Keis the state estimator gain matrix; the ˆsymbol indicates an
estimate.
ˆ˙w=Aˆw+Bu+Ke
yˆy
(4.13)
ˆy=Cˆw+Du (4.14)
Forming the error vector esuch that e=wˆwand differentiating with respect to time results
in equation (4.15). Therefore, if the pair
A,C
is observable, then the augmented vector wcan
be fully estimated [66].
˙e=˙wˆ˙w
=A(wˆw)KeC(wˆw)
)˙e=
AKeC
e (4.15)
It is important to remember that although the above description involved simple linear state-
space models for simplicity, the linear models used to describe the wind turbine are periodic
46

4.3 DAC After MBC Transformation
and are only perturbations about the linearisation point. Similar to state feedback control de-
scribed in Chapter 3, MBC transformation is used to deal with turbine periodicity.
4.3 DAC After MBC Transformation
In this work, the disturbance states, z, are modelled in the non–rotating frame of reference and
therefore do not require a transformation matrix from the rotating frame of reference. After
applying MBC transformation on a periodic system, DAC design becomes time-invariant. The
DAC law in the non-rotating frame is given by equation (4.16) and the time-invariant DAC
gain matrix is found by solving equation (4.17).
uNR =KNRˆxNR+Gd,NRˆz (4.16)
Gd,NR =B+
NRBd,NRQ (4.17)
The DAC law is now in the non-rotating frame and therefore blade pitch commands have to
be transformed back to the mixed frame using equation (3.10). Equation (4.18) shows the DAC
law transformed into the mixed frame of reference. The result is periodic gain matrices where
KMBC(y)and Gd,MBC(y)are the periodic state regulation and periodic disturbance minimisa-
tion gain matrices respectively.
u=Tc(y)KNRT1
s(y)ˆx+Tc(y)Gd,NRˆz
=KMBC(y)ˆx+Gd,MBC(y)ˆz (4.18)
Similar to the time-invariant DAC design, we form a new augmented states vector wNRgiven
by equation (4.19). Equation (4.20) can then be used to transform between wNRand wwhere I
is an identity matrix and ndis the number of disturbance states.
wNR ="
xNR
z#
(4.19)
w="
Ts(y) 0
0 Indnd#
wNR=Td(y)wNR (4.20)
Given the deﬁnition of wNRabove, we form a new disturbance estimator for the MBC trans-
formed system (equations (3.7) and (3.8)). The disturbance estimator in the non-rotating frame
is given by equation (4.21). This equation does notrepresent the MBC transformation of equa-
tion (4.13).
47

Chapter 4: Disturbance Accommodating Control
ˆ˙wNR=
ANRKe,NRCNRˆwNR+BNRuNR+Ke,NRy
NR(4.21)
where
ANR="
ANR Bd,NRQ
0 F#
BNR="
BNR
0#
CNR=h
CNR Dd,NRQi
Since the actuator commands and the measurements are in the mixed frame of reference, we
transform the input and measurement vectors into the non-rotating frame and combine the two
vectors into one for easier implementation. The result is given by equation (4.22) where vis the
augmented estimator inputs in the mixed frame of reference.
ˆ˙wNR =
ANRKe,NRCNRˆwNR+BNRT1
c(y)u+Ke,NRT1
o(y)y
| {z }
Inputs
=
ANRKe,NRCNRˆwNR+h
BNRT1
c(y)Ke,NRT1
o(y)i"
u
y#
=
ANRKe,NRCNRˆwNR+E(y)v (4.22)
4.4 Implementation
In the case of ﬂoating wind turbines, FSFB is used for the SFC part of the DAC which means
the state estimates ˆxNRare not used. Therefore, the implemented control law is given by equa-
tion (4.23) where xNRis obtained by equation (4.24).
uNR =KNRxNR+Gd,NRˆz (4.23)
xNR =T1
s(y)x (4.24)
For the disturbance estimator, FSFB implementation and the availability of xNRrequires re-
arranging equation (4.21) into equation (4.25). Equation (4.25) differs from equation (4.22) by
having the disturbance estimator inputs in the nonrotating frame of reference.
48

4.4 Implementation
++
+-Controller
Disturbance Estimator Nonlinear Wind
Turbine Model
+-Controller
Disturbance Estimator Nonlinear
Wind Turbine
Model
Saturation
+-++
Figure 4.1: DAC with FSFB implementation for ﬂoating wind turbines
ˆ˙wNR=
ANRKe,NRCNRˆwNR+h
BNR Ke,NRi"
uNR
xNR#
=
ANRKe,NRCNRˆwNR+ENRvNR (4.25)
Block diagram implementation of DAC after MBC transformation for ﬂoating wind turbines is
shown in Figure 4.1. The implementation accounts for the controller being designed based on
a linearised state-space model and actuator saturation.
Other implementation conﬁgurations, discussed in Appendix B, were considered. However,
these implementation options cannot be applied for systems with slow actuator dynamics or
when actuator saturation is possible.
4.4.1 DAC Limitations and Challenges
Since the DAC gain matrix is the result of a minimisation process (equation (4.8)) with no para-
meters to tune, the resultant gain matrix may cause severe actuator saturation if the actuators
do not have enough control authority to reduce the effects of modelled disturbances on all or
some of the system states. Therefore, one must be careful when applying DAC to a system with
relatively low saturation limits.
One way to limit the effects of the minimisation process is to exclude certain states from the
DAC design where the actuators have little control authority. That way, the DAC will not
assign large gains in an attempt to limit the effect of disturbances on those states. To exclude
49

Chapter 4: Disturbance Accommodating Control
certain states from DAC design, the elements in the Bd,NRmatrix that correspond to the selected
states must be set to zero (example given in §4.5.1).
Another challenge when implementing a DAC is the choice of disturbance waveform model.
Choosing a simple model may not accurately represent the actual disturbance but is computa-
tionally simple and only adds a few disturbance states z. Conversely, using a complex wave-
form model will increase the number of disturbance states which may render the disturbance
estimator unobservable. In such cases, increasing the turbine model ﬁdelity or directly meas-
uring some of the input disturbances (if possible) may resolve this issue.
4.5 Wind Speed Disturbance Rejection
For ﬂoating wind turbines, two types of disturbances are considered: change in horizontal
hub-height wind speed and change in resultant pitching moment due to incident waves. Min-
imising the effects of wind speed ﬂuctuations is discussed in this section. Wave disturbance
rejection is discussed in Chapter 10.
Recall that the DAC design is based on a linearised state-space model about a chosen operating
point. Linearisation also means that the disturbance input is wind speed perturbation about
that operating point. Therefore, in an ideal case, the DAC cancels the effects of any wind speed
ﬂuctuations about the designed wind speed (operating point). For simplicity, a step change
waveform model ( ˙ud=0) is used for wind speed perturbations whose parameters are given
by equation (4.26).
step input8
<
:G=0
Q=1(4.26)
Because the disturbance estimator in this case uses state measurements to estimate the wind
disturbances, the overall effect of a step waveform model with the disturbance estimator is
essentially similar to an additional integral term to the SFC. However, the DAC formulation
used in this chapter allows for more complicated waveform models to be used for disturbance
rejection; e.g. Wright [35] used a periodic waveform model to reject the effects of wind shear.
To demonstrate that the DAC is able to reject wind speed perturbations, the DAC is compared
to the SFC in a simple test case similar to what Wright [35] uses to prove that his DAC imple-
mentation cancels the effects of wind speed perturbations. The simulation set up and paramet-
ers are as follows:
• Single DOF nonlinear simulation. Only the generator/rotor DOF is enabled thereby re-
moving all bias that can come from coupling between turbine modes.
• Step incident wind with no wind shear or turbulence. The wind speed is varied between
15 m/s to 22 m/s (well into the above rated wind speed region) in a step-like manner
every 40 seconds.
50

4.5 Wind Speed Disturbance Rejection
• The DAC and SFC are designed based on a state-space model linearised at 18 m/s wind
speed. The SFC and state feedback part of the DAC are identical.
• The system is simulated with FSFB for system and disturbance states – without a disturb-
ance estimator (i.e. with measured hub-height wind speed).
• The SFC part is designed without the integrator effect. A state-space controller has no
explicit integrator term. However, integral action can be achieved by including the in-
tegral of the state to be regulated as an additional system state. For example, to have an
integral action to regulate the rotor speed, the rotor azimuth is included in the control-
ler design since the azimuth angle is the integral of the rotor speed. Therefore, driving
that state (change in azimuth angle Dy) to zero is similar to driving the integral error to
zero. Integral action forces the system states to be driven to zero, even in the presence of
disturbances, which is desirable. However, the purpose is to show that the disturbance
accommodating part is rejecting the disturbances and not the integral action. The dis-
turbance accommodating action is similar to the integral action to disturbances only but
without the delay.
Figure 4.2 shows the rotor speed regulation (the only objective) for the two simulated control-
lers (SFC and DAC) under changing external disturbances – wind speed perturbations. Results
clearly show that the DAC successfully rejected the effects of external disturbances by main-
taining a relatively constant rotor speed. The SFC is unable to regulate the rotor speed to the
rated without the integral action as the wind speed deviates away from the linearisation point.
This clearly shows that the DAC implementation is correct and successful at minimising the
effects of wind speed disturbances.
4.5.1 Collective Blade Pitch Drift
One issue exists when implementing a DAC to reject wind speed perturbation on wind tur-
bines; collective blade pitch drifting [67]. Assuming a linear wind turbine system, the collect-
ive blade pitch commanded by the feed-forward action of the DAC to reject wind disturbances
and maintain steady state is a linear function of the wind speed described by equation (4.27)
where uopis the actuators’ collective pitch operating point. However, the collective blade pitch
angle required to keep the ﬂoating wind turbine in steady state as the wind speed varies is
a nonlinear function of wind speed as shown in Figure 4.3. With steady state conditions, the
DAC forces the collective blade pitch away from the optimum angle as the turbine operates
away from the linearisation point. The blade pitch is eventually driven back to the optimum
angle by the state feedback part of the controller but after some delay due to the integral action.
u=GDx+GdDz+uop(4.27)
A solution is to split the DAC into two components: a scheduled collective blade pitching com-
ponent that follows the nonlinear optimum trajectory for rotor speed regulation and a state-
51

Chapter 4: Disturbance Accommodating Control
50 100 150 200 250 3001416182022Wind Speed (m/s)

50 100 150 200 250 30011.912.012.112.2
Time (sec)Rotor Speed (rpm)

SFC
DAC
Figure 4.2: Single DOF nonlinear simulation results showing disturbance rejection by the DAC
8 10 12 14 16 18 20 22 240510152025
Wind speed (m/s)θ (deg)

Steady−state pitch angle
DAC collective pitch command
Linearisation point
Figure 4.3: Collective blade pitch drift
52

4.6 Chapter Summary
space component that is designed to minimise the residual periodic effects on the remaining
turbine states by only using cyclic blade pitch commands.
For MBC transformed systems, the solution can be easily implemented by just zeroing the
elements in the BNRmatrix that corresponds to collective blade pitch qosince uNRis given by
equation (4.28). This results in zero gains in elements of the disturbance minimisation gain
Gd,NRthat correspond to collective blade pitching. However, removing collective blade pitch-
ing results in the state-space component of the disturbance accommodating controller trying to
compensate for that by increasing the gains on the remaining actuators (cosine- and sine-cyclic
pitch) in an attempt to regulate all states including the rotor speed. To force the state-space
part of the DAC to only remove residual periodic effects, the elements in the Bd,NRmatrix that
correspond to the drivetrain states must be set to zero in addition to any other state that peri-
odic blade pitching has limited control authority over. This method is used in this work for
disturbance accommodating controllers that reject wind speed perturbations.
uNR=h
TGen qoqcqsiT
(4.28)
An alternative approach was implemented successfully in [68] where the elements in the dis-
turbance minimisation gain, Gd,NR, that correspond to collective pitch were set to zero after the
controller was designed. This method produced a sub-optimal set of disturbance minimisation
gain matrix as it will no longer minimised kBGd+BdQk.
4.6 Chapter Summary
Disturbance accommodating control is a linear feed-forward add-on to the state feedback con-
troller (described in Chapter 3) that minimises the effects of persistent disturbances. DAC
requires knowledge of the disturbance inputs through direct measurements and how the dis-
turbance inputs affect system states through the disturbance gain matrix. Where direct meas-
urement of the disturbances is not possible, a disturbance estimator can be used to generate an
estimate based measured system states and on an assumed disturbance waveform model. For
wind turbines whose response is periodic, MBC transformation is utilised for time-invariant
controller design in the non-rotating frame of reference.
Persistent disturbances that act on ﬂoating wind turbines include wind speed perturbations
and waves. For wind speed disturbances, a step waveform model is used and is shown to be
able to mitigate the effects of changes in the wind speed away from the linearisation point.
However, due to the nonlinear nature of the wind turbine, DAC for wind tends to cause the
collective blade pitch angle to drift away from the optimum pitch angle when the turbine is
operating away from the linearisation point. This limitation is resolved by splitting the DAC
into two components: a scheduled collective blade pitch angle for rotor speed regulation and
cyclic actuation to remove residual effects of the wind speed on other turbine states via state-
space implementation.
53

Chapter 4: Disturbance Accommodating Control
54

5
Modelling, Simulation, and Analysis Tools
Contents
5.1 Wind Turbine Modelling and Simulation Tools . . . . . . . . . . . . . . . . . . . . . . . . 55
5.2 5MW Wind Turbine Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3 The IEC 61400-3 Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.4 Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.5 Simulation and Comparison Set Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.6 Weibull Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
With ﬂoating wind turbines the simulation tool and its model must take into account
the additional 6 DOFs (platform surge, way, heave, roll, pitch, and yaw) brought
by the lack of rigid foundations. These 6 DOFs cannot be approximated by exist-
ing ﬂexibilities in the modelled onshore wind turbines as they exhibit larger motion envelope,
last for longer periods, and are independent of each other. Therefore, special offshore models
and simulators are required. Many new simulation tools and modiﬁed existing ones are begin-
ning to accommodate these additional 6 DOFs. This chapter mainly deals with the simulation
tools, simulation conditions, and performance metrics used to obtain the results described in
subsequent chapters.
5.1 Wind T urbine Modelling and Simulation Tools
As mentioned in Chapter 1, results presented in this work depend on computer simulations.
Therefore, suitable simulation tools must be chosen to allow for reasonable high-ﬁdelity simu-
lations on ﬂoating offshore wind turbines.
55

Chapter 5: Modelling, Simulation, and Analysis Tools
Modelling the ﬂexibilities of the wind turbine components becomes more critical as the size
of the wind turbine increases. Furthermore, the interactions between the aerodynamics, hy-
drodynamics and structural dynamics for such large machines need to be modelled and taken
into account. Several wind turbine simulation tools exist and they vary in their modelling
approach, model ﬁdelity, user customisation, interfacing capability with other software, etc.;
Table 5.1 summarises the simulation tools that can accommodate additional DOFs of ﬂoating
wind turbines.
The Offshore Code Comparison Collaboration (OC3) project [75] compared the simulation res-
ults of several simulation codes across four different phases. Phase IV of the OC3 project dealt
with comparing simulation codes for ﬂoating wind turbines (Table 5.1) [69]. To summarise,
the design codes compared quite well with minor differences attributed to modelling approach
and ﬁdelity.
FAST (Fatigue, Aerodynamics, Structures and Turbulence) was chosen as the simulation tool
for this study for two simple reasons. First, at the start of this work, it was readily available and
the ﬁrst ﬂoating model of the barge in FAST format was kindly provided by Dr. Jason Jonkman
at the National Renewable Energy Laboratory (NREL). Second, it was the only readily available
simulation code out of those listed in Table 5.1 that allowed for interfacing with MATLAB®
Simulink®(referred to hereafter as Simulink) for controller implementation.
5.1.1 FAST Simulation Code
FAST is a freely available design code developed by NREL [36]. It is of moderate complexity
developed to analyse the structural dynamics of horizontal axis wind turbines. FAST models
the tower, blades and the drivetrain as ﬂexible elements and uses bending modeshapes for the
analysis [13,36]. Each blade has two ﬂapwise and one edgewise bending modes. The tower has
two fore-aft and two side-side bending modes. The drivetrain ﬂexibility is modelled through
a linear spring and a damper for the low speed shaft. The remaining elements of the wind
turbine (nacelle and hub) are modelled as rigid bodies. The ﬁdelity of the model can be set by
selecting which degrees of freedom are to be enabled in the nonlinear model.
FAST can also provide a linearised representation of the turbine’s nonlinear model at speciﬁed
trim conditions. The linearised periodic (i.e. time-varying) state space model is given by equa-
tions (5.1) and (5.2). Dealing with periodic models is discussed in § 3.1 on page 30.
D˙x=A(y)Dx+B(y)Du+Bd(y)Dud (5.1)
Dy=C(y)Dx+D(y)Du+Dd(y)Dud (5.2)
In addition to simulating a wind turbine, FAST allows for a control system to be integrated with
the simulation environment. The wind turbine actuators (blade pitch, generator torque, and
yaw drive) can be controlled either via a user speciﬁed control algorithm through a dynamic
link library (DLL) ﬁle or through interfacing with Simulnik. The Simulink/FAST interface
option is selected to allow for custom and complex controllers to be developed quickly and
56

5.1 Wind Turbine Modelling and Simulation Tools
Table 5.1: Floating wind turbine simulation codes (adapted from [69])
Code
NameCode
DeveloperOC3 Participant Aerodynamics Hydrodynamics Control
System
(Servo)Structural
Dynamics (Elastic)
FAST
[36]NREL NREL +
POSTECH(BEM or
GDW) + DSAiry++ ME,
Airy + PF + MEDLL, UD,
SMTurbine: FEMP+
(Modal / MBS),
Moorings: QSCE
Bladed
[70]GH GH (BEM or
GDW) + DS(Airy+or
Stream) + MEDLL Turbine: FEMP+
(Modal / MBS),
Moorings: UDFD
ADAMS
[71]MSC + NREL +
LUHNREL + LUH (BEM or
GDW) + DSAiry++ ME,
Airy + PF + MEDLL, UD Turbine: MBS
Moorings: QSCE,
UDFD
HAWC2
[72]Risø – DTU Risø – DTU (BEM or
GDW) + DSAiry + ME DLL, UD,
SMTurbine: MBS /
FEM, Moorings:
UDFD
3Dﬂoat IFE – UMB IFE – UMB (BEM or
GDW)Airy + ME UD Turbine: FEM,
Moorings: FEM,
UDFD
SIMO
[73]MARINTEK MARINTEK BEM Airy + PF + ME DLL Turbine: MBS,
Moorings: QSCE,
MSB
SESAM /
DeepC
[74]DNV Acciona
Energia +
NTNUNone Airy++ ME,
Airy + PF + MENone Turbine: MBS,
Moorings: QSCE,
FEM
Legend:
Airy+Airy wave theory, MBS multibody-dynamics formulation
+with free surface corrections ME Morison’s equation
BEM blade-element / momentum MSC MSC Software Corporation
DLL external dynamic link library NREL National Renewable Energy Laboratory
DNV Det Norsk Veritas NTNU the Norwegian University of Science and Technology
DS dynamic stall PF linear potential ﬂow with radiation and diffraction
DTU Technical University of Denmark POSTECH Pohang University of Science and Technology
FEMPﬁnite-element method QSCE quasi-static catenary equations
Pfor mode processing only SM interface to Simulink® with MATLAB®
GDW generalised dynamic wake UD user-deﬁned subroutines available
GH Garrad Hassan & Partners Ltd. UDFD implementation through user-deﬁned force-
IFE Institute for Energy Technology displacement relationships
LUH Leibniz University of Hannover UMB the Norwegian University of Life Sciences
57

Chapter 5: Modelling, Simulation, and Analysis Tools
speed filter1.5708
s+1.5708
gen eff−K−extract HSS speedf(u)
Yaw Controlleryaw and yaw rateUnit Delay
z1
Torque controller
selectorswitchTorque ControllerHSSspeed
Pitch (deg )
SwitchTg
To rad /s−K−
To deg−K−Tgen 1[TGen ]Product
Pitch ControllerW_HSS (rpm ) Pitch (rad)Go to 2[wHSS_raw]
Go to[Pitch ]Generator Torque
[TGen ]
General
OverviewFrom 2[wHSS_raw]
From 1[Pitch ]From[Pitch ]
FAST Nonlinear Wind TurbineGen . Torque (Nm ) and Power (W)
Yaw Position (rad) and Rate (rad/s)
Blade Pitch Angles (rad)OutData
q
qdot
Data Extraction
and PlottingData
PitchIn
T_gWind and Wave
Rotor Speed
Platform Pitch
Power
Blade Pitch
Torque pitchW_HSS
Filtered w _HSS (rpm )Filtered w _HSS (rpm )
Figure 5.1: Baseline controller model showing Simulink/FAST interface
utilise MATLAB tools for control design. Figure 5.1 shows an example Simulink model where
a Gain Scheduled Proportional-Integral (GSPI) controller (described in § 2.1 on page 19) is
implemented using the Simulink/ FAST interface.
FAST and Floating Wind T urbines
Since 2006, Jonkman et al. [13, 76] have modiﬁed the standard version of FAST to include a
hydrodynamics module to account for ﬂoating platform dynamics. The modiﬁed FAST now
includes a hydrodynamics and a quasi-static mooring modules; the structure is shown in Fig-
ure 5.2. The hydrodynamics module, HydroDyn , uses linear/Airy wave theory to simplify the
hydrodynamics problem into three separate components: hydrostatics, radiation, and diffrac-
tion. The quasi-static mooring module treats the system in equilibrium at every computation
time to calculate the forces in the mooring lines. The mooring line module accounts for “the ap-
parent weight in ﬂuid, elastic stretching, and seabed friction of each line” [76]. It also accounts
for the nonlinear geometric restoring force of the complete mooring system on the ﬂoating
platform.
Hydrodynamics Module Assumptions
The onshore version of FAST coupled with AeroDyn have been certiﬁed by Germanischer
Lloyd WindEnergie GmbH for use by the industry for wind turbine certiﬁcation [78]. Since
testing of full scale prototypes of ﬂoating wind turbines have just started, certiﬁcation of FAST
with HydroDyn and other similar codes is not yet possible. However, the OC3 project gives
an indication that the models developed are acceptable. Therefore, it is important to know the
limitations and assumptions of the simulation tool and keep it in mind when interpreting the
simulation results. The newly developed offshore module has the following assumptions [13]:
58

5.1 Wind Turbine Modelling and Simulation Tools
Hydro-
dynamics Aero-
dynamics
Waves &
Currents Wind-
Inflow Power
Generation Rotor
Dynamics
Platform Dynamics
Mooring Dynamics Drivetrain
Dynamics Control System
Nacelle Dynamics
Tower Dynamics
Figure 5.2: Offshore FAST structure (adapted from [77])
• The platform has 6 DOFs (surge, sway, heave, roll, pitch, and yaw) but the three rotational
DOFs (roll, pitch, and yaw) have small angles. The effects of this assumption are not
considered critical for angles smaller than 20°.
• The ﬂoating platform is modelled as a rigid body.
• The tower is perpendicular to the platform and is cantilevered.
• The inertia (excluding the wind turbine) and the centre of buoyancy lie on the centreline
of the undeﬂected tower.
• Mooring lines do not have bending stiffness.
• The hydrodynamic forces are calculated based on linearisation of the hydrodynamic prob-
lem. Linearisation has the following consequences:
–Wave heights are much smaller than wave lengths; a reasonable assumption in deep
water. This allows the use of very simple wave kinematics equations and does not
require the modelling of breaking or steep waves.
–Translational displacements of the platform are small compared to the platform
size (characteristic body length); however, this does not mean that the character-
istic length of the body has to be small when compared to the wavelength. This
allows the hydrodynamic problem to be split into 3 separate problems: radiation,
scattering, and hydrostatics.
59

Chapter 5: Modelling, Simulation, and Analysis Tools
–The linearisation of the hydrodynamics ignores:
*the nonlinear and high order effects that are used to calculate the loads on the
instantaneous wetted area; this is important for bodies with large displacements
relative to their characteristic length.
*second order mean- and slow-drift forces caused by multiple incident waves of
varying frequencies. In some situations, these second order effects are important
for platforms with small draft, large waterplane area, and a mooring system that
does not resist motions in the surge and sway directions. This is relevant to a
barge platform concept.
*second order frequency effects on the platform caused by multiple incident
waves of varying frequencies. In some situations, this second order effect can
cause ringing in platforms with mooring lines that have high resistance to heave
motion. This is relevant to a TLP concept.
• Loading from sea ice or ﬂoating debris is ignored.
5.2 5MW Wind T urbine Model
For this work, a single 5 MW wind turbine will be used for simulation on each of the three
ﬂoating platforms. This wind turbine, commonly known as the “NREL 5 MW wind turbine”,
is a ﬁctitious turbine whose properties are derived from a collection of publicly available in-
formation of similar sized wind turbines [37]. It is a three bladed upwind wind turbine with
126 m diameter rotor and 90 m hub height. Table 5.2 list all the main details about the wind
turbine.
Since FAST models the system ﬂexibilities through assumed modeshapes, the tower’s mode-
shapes change when mounted on different platforms. This is the only change that occurs in the
wind turbine properties when changing to another platform.
Table 5.2: NREL 5MW wind turbine properties
Power Rating 5 MW
Rotor orientation Upwind
Control Variable speed, variable pitch, active yaw
Rotor, hub diameter 126 m, 3 m
Hub height 90 m
Rated rotor, generator speed 12.1 rpm, 1173.7 rpm
Blade operation Pitch to feather
Maximum blade pitch rate 8 deg/s
Rated generator torque 43,093 Nm
Maximum generator torque 47,402 Nm
60

5.3 The IEC 61400-3 Standard
5.3 The IEC 61400-3 Standard
The simulations are carried out in accordance with IEC 61400-3 standard [39] for DLC 1.2 – fa-
tigue loads under normal operating conditions; these conditions are summarised in Table 5.3.
The IEC 61400-3 standard is for offshore wind turbines with ﬁxed foundations. Since no stand-
ards for ﬂoating turbines exist to date, the simulations will be carried out according to DLC 1.2
of this standard.
DLC 1.2 requires the wind and waves to be co-directional and multi-directional. However,
because the platforms are axisymmetric, only one wind and wave direction is considered. Mis-
aligned situations are covered by DLC 1.4, however, DLC 1.4 is used for ultimate load analysis
and is outside the scope of this work. The IEC standard speciﬁes for DLC 1.2 that a joint
probability distribution for the wind speed, signiﬁcant wave height, and wave period must be
used. However, due to the unavailability of full site speciﬁc data, DLC 1.1 condition of using
the expected signiﬁcant wave height at given wind speed range is implemented.
Because the above rated wind speed region is the main focus of this study, the range of wind
speed bins for DLC analysis is limited between 15 m/s and 24 m/s in 1 m/s speed increments.
The IEC standard requires six 600-second turbulent wind and irregular waves with different
random seeds to be used for each wind speed bin [79].
The wave conditions are selected based on the same reference site used by Jonkman [32] located
north-east of Scotland. In the data for that site, there exists a single signiﬁcant wave height and
a range of wave periods for a corresponding average wind speed. In this work, the wave
periods in each wind speed bin linearly range from the minimum to the maximum range of
periods for that site that do not violate the assumptions of linear wave theory used by FAST;
the use of linear wave theory is a reasonable assumption in deep water [39]. According to the
IEC 61400-3 standard, for the linear wave theory to be applied in deep water, equation (5.3)
must be satisﬁed where His the wave height, Twis the wave period, and gis the acceleration
due to gravity.
H
gT2w0.002 (5.3)
Full ﬁeld stochastic wind conditions are generated using TurbSim [80] while the irregular
stochastic waves are generated using HydroDyn. Appendix C lists the parameters used to
generate these stochastic conditions for each DLC.
Table 5.3: DLC 1.2 conditions summary
DLC Wind Condition Waves Wind and Wave
DirectionalitySea
Currents
1.2 Normal turbulence model
Vin<Vhub<VoutNormal sea
stateCo-directional and
multi-directionalNo
currents
Vin=cut-in wind speed; Vhub=hub-height wind speed; Vout=cut-out wind speed
61

Chapter 5: Modelling, Simulation, and Analysis Tools
5.4 Performance Metrics
To perform a DLC analysis, each controller is simulated in 60 different ten-minute simulations
that span the above rated wind speed region. To quantify the performance of the controllers, 14
performance metrics are used to monitor key wind turbine components. Some of these metrics
involve the calculation of a root mean square (RMS) or a fatigue damage equivalent load (DEL).
Fatigue DELs are used as a metric to replace the stochastic loads on a component by a periodic
load with a calculated magnitude at a given frequency (1 Hz in this work).
The performance metrics/indices are then averaged across their corresponding wind speed
bin as well as averaged across all the simulations. However, a real wind turbine does not
spend an equal amount of time in each wind speed bin. Hence, weighted averaging using a
Weibull distribution (discussed in §5.6) for the weighting/scaling factors is used for the overall
averaged performance metrics.
The performance metrics can broadly be grouped into three categories. The categories and a
brief description of each performance index are given below:
Power and speed regulation, and actuator usage
1. RMS of the generator power error (from rated power) in kW. The smaller the error the
better the power regulation and hence increased power quality.
2. RMS of the rotor speed error (from rated rotor speed) in rpm. The lower the value the
better the rotor speed regulation.
3. Maximum RMS of the blade pitch rates in degrees per second (deg/s). This is used to
indicate the level of actuator usage. A high value means high blade pitch actuator usage.
Fatigue damage equivalent loads of key components
4. Blade root ﬂapwise bending fatigue DEL in kNm.
5. Blade root edgewise bending fatigue DEL in kNm.
6. Tower base Fore-Aft (FA) bending fatigue DEL in kNm.
7. Tower base Side-Side (SS) bending fatigue DEL in kNm.
8. Low Speed Shaft (LSS) torsion fatigue DEL in kNm.
Platform motions
9. Floating platform RMS roll in degrees. This is used as a measure for the platform rotation
about its roll axis; this should be kept as low as possible to reduce tower side-to-side
bending loads.
62

5.4 Performance Metrics
10. Floating platform RMS pitch in degrees. This is used as a measure for the platform rota-
tion about its pitch axis; this should be kept as low as possible to reduce tower fore-aft
bending loads.
11. Floating platform RMS yaw in degrees. This is used as a measure for the platform rota-
tion about its yaw axis; this should be kept as low as possible to reduce rotor yaw error
that will result in reducing the amount of captured power and increase asymmetric aero-
dynamic loading.
12. Floating platform RMS roll rate in deg/s. Reducing platform rolling, pitching, and yaw-
ing velocities will reduce their respective motion envelope thus reducing the loads asso-
ciated with each motion direction.
13. Floating platform RMS pitch rate in deg/s.
14. Floating platform RMS yaw rate in deg/s.
With the fatigue load metrics (items 4 – 8), it is assumed that the turbine is designed such that
all the main components fail roughly at the same time placing equal importance on each fatigue
load metric. However, from the control objective point of view, the 14 metrics listed above are
not considered equal when assessing the overall performance of each controller. Table 5.4 lists
the metrics according to their relative importance.
Table 5.4: Relative importance of metrics in determining the overall performance of a controller
Level of Importance Metrics
Primary 1, 2, 6, and 7
Secondary 3, 8, 10, and 13
Tertiary 4, 5, 9, 11, 12, 14
The results presented in subsequent chapters are normalised relative to a baseline controller.
One might argue that this is an unfair comparison between the multi-objective and the Baseline
controllers. However, in a noise-free environment, the baseline controller is essentially a single
state feedback controller since the output/measurement of the baseline controller is a system
state. Furthermore, the purpose of this comparison is not to compare these controllers against
the Baseline controller. Instead, the comparison is used as a yardstick for measuring the level
of improvement SFC and DAC bring to each of the ﬂoating platforms.
With all the performance metrics except for RMS blade pitch rate, the objective is to have a value
of 1 or smaller indicating better or improved performance relative to the baseline controller. At
this stage, dealing with the absolute values of these performance metrics in terms of detailed
design or to assess whether the blades or tower are strong enough is outside the scope of this
work.
Due to the range of simulated wind speeds, a single weighted average for each metric is not
adequate to represent the full behaviour of the ﬂoating wind turbine. Therefore, trends of the
63

Chapter 5: Modelling, Simulation, and Analysis Tools
Table 5.5: Types of observed performance trends
Short Name Description
Constant A relatively constant level of performance across all wind speed bins indic-
ating the robustness of the controller to maintain the same relative perform-
ance to the Gain Scheduled Baseline controller as the turbine operates away
from the linearisation point.
Increasing An upward or positive sloping trend with increasing wind speed. Taking
the performance at 18 m/s as the starting point, a metric is better regulated
at lower wind speeds and worse otherwise.
Decreasing A downward or negative sloping trend with increasing wind speed. Taking
the performance at 18 m/s as the starting point, a metric is better regulated
at higher wind speeds and worse otherwise.
Parabolic A parabolic-type function with the minimum located around the linearisa-
tion point. The parabolic-type trend indicates a metrics is best regulated
around the linearisation point but is worse off away in either direction.
averaged and normalised performance metrics across wind speed bins are also discussed in
subsequent chapters. Table 5.5 lists the types of trends observed; these are referred to using
their short name.
In addition to the performance metrics, other metrics (such as maximum blade pitch rate) and
the time series response of each simulation are inspected for unusual or undesirable behaviour
such as prolonged or frequent actuator saturation.
5.5 Simulation and Comparison Set Up
Design load case simulations are carried out on 10 different controllers on four different plat-
forms; a total of 600 DLC simulations. The simulations are carried out using FAST with Hydro-
Dyn with all 22 DOFs enabled using turbulent full ﬁeld wind and irregular waves. The turbine
yaw DOF is locked since no active yaw control is needed as the mean wind direction remains
unchanged. Yaw error correction is not part of DLC 1.2 and is outside the scope of this work.
The performance metrics described above are used to evaluate the performance of the SFC and
DAC relative to the Baseline controller. Two types of comparisons (summarised in Table 5.6)
are made:
1. Comparing the performance of the SFC and DAC relative to the Baseline controller on
the same ﬂoating platform ; this type of comparison is made on the three platforms and
discussed in chapters 6 – 8. The purpose of this comparison is to evaluate whether adding
the disturbance minimisation component to the SFC has a measurable impact. This type
of comparison also allows for identifying the beneﬁts of individual over collective blade
pitching and multi-objective over single-objective control on ﬂoating wind turbines.
2. Comparing the performance of the Baseline controller and the best performing multi-
objective controller (SFC or DAC) on each platform relative to a Baseline controller on an
64

5.6 Weibull Scaling
onshore wind turbine (5MW NREL onshore wind turbine). The purpose of this comparison
is to allow for comparing the dynamic performance between the ﬂoating platforms in
terms of power regulation and fatigue damage equivalent loads. These comparisons are
made in Chapter 9.
Table 5.6: Simulated controllers’ comparison summary
Chapter Baseline Controllers to be
comparedPlatform(s)
Platform Controller
6 Barge GSPI SFC, DAC Barge
7 TLP GSPI SFC, DAC TLP
8 Spar–buoy GSPI SFC, DAC Spar–buoy
9 Onshore GSPI GSPI, SFC, DAC Barge, TLP , Spar–buoy
5.6 Weibull Scaling
As discussed in the previous section, a weighted average is used to obtain the overall aver-
aged performance metrics such that it accounts for the wind speed probability distribution at
a speciﬁc site. The overall average for performance metric pis given by equation (5.4) where
siand piare the scaling factor and averaged performance metric for the ith wind speed bin
respectively and nbinsis the number of wind speed bins.
p=nbins
å
i=1sipi
nbins
å
i=1si(5.4)
The Weibull distribution is considered a good ﬁt for annual mean wind speed distribution [29].
However, using data collected from 178 ocean buoys distributed around North America over
several years, Morgan et. al. [81] show that the widely accepted 2-parameter Weibull distribu-
tion provides a poor ﬁt for these offshore sites when compared to other, higher order distribu-
tions. However, for the purposes of providing weighted averages for the performance metrics,
the 2-parameter Weibull distribution is considered adequate. What follows is a description of
the approach used to obtain the scaling factors for each wind speed bin.
Using the same notation in [29], the Weibull distribution takes the form given by equation (5.5)
where F(U)is the fraction of time for which the hourly mean wind speed exceeds U,cis
the scaling parameter, and kis the shape factor. The Weibull distribution’s shape resembles
the shape shown in Figure 5.3 for certain values of c, and ktypical for annual wind speed
distribution.
F(U)=exp
(U/c)k
(5.5)
65

Chapter 5: Modelling, Simulation, and Analysis Tools
1
Wind speed bin
Figure 5.3: The Weibull distribution
Given a wind speed bin Uwhose wind speeds range from U0.5 m/s to U+0.5 m/s, the
percentage time of the year the wind turbine spends in that wind speed bin TUis given by
equation (5.6).
TU=(F(U0.5)F(U+0.5))100 (5.6)
The Weibull scaling factors sifrom equation (5.4) are obtained by normalising TUvalues by
its maximum value giving the most weight (of 1) to the dominant wind speed bin. Figure 5.4
shows how values of TUand the scaling factors change for each wind speed bin for selected
Weibull distribution parameters.
The above approach requires knowledge of the site speciﬁc Weibull parameters c, and kat the
turbine’s hub height. However, site measurements are often given at the measurement mast
height and not the wind turbine’s hub height. Therefore, given c, and kat a reference height
hre f, the mean annual wind speed Uis given by equation (5.7) [29].
U=¥
0U f(U)dU (5.7)
where
f(U)=kUk1
ckexp
(U/c)k
Equation (5.7) can be used to calculate the annual mean wind speed at the reference height Ure f
if the measured mean wind speed is not given. That reference wind speed can then be scaled to
any height haccording to the vertical shear law given by equation (5.8) where ais the vertical
shear exponent; for offshore sites ais 0.14 [39].
U(h)=Ure fh
hre fa
(5.8)
Assuming the Weibull shape factor kremains roughly the same between the measurement
66

5.6 Weibull Scaling
0 5 10 15 20 25024681012% Time of the Year
Wind Speed Bin (m/s)
% Time
Scaling Factor
Scale Factor (−)Region Allocation:
Region 1 4.10%
Region 2 70.9%
Region 3 25.0%
Shut Down 0.0%
00.20.40.60.811.2
Figure 5.4: Weibull scaling factors
height and the hub height, the Weibull shape factor ccan be calculated using the newly calcu-
lated mean hub height wind speed and equation (5.9) [29] where G()is the gamma function
and not to be confused with Gwhich is the disturbance states matrix (equation (4.4)). The
gamma function can be calculated using equation (5.10) [82].
U=cG
1+1
k
(5.9)
G(a)=¥
0ta1exp(t)dt (5.10)
The Weibull parameters in this work are selected based on real data from Vindeby offshore
wind farm in Denmark from 1993 to 1997 [83] because Weibull parameters for the chosen site
in Scotland are not available. the selected Weibull parameters are k=2.3,c=9.1, and U=
8.1 m/s at a reference height of 48 m. These are then scaled to a hub height of 90 m where the
resultant Weibull distribution is shown in Figure 5.4. The wind speed region calculations in
Figure 5.4 are based on the wind speed ranges deﬁned by Jonkman [32] and given by Table 5.7;
these wind speed ranges are only used to calculate the time a wind turbine spends in each
region.
67

Chapter 5: Modelling, Simulation, and Analysis Tools
Table 5.7: Wind speed region limits
Region Wind Speed Range (m/s)
1 0 6U<3
2 3 6U<11.4
3 11.4 6U<25
Shutdown U>25
5.7 Chapter Summary
For ﬂoating wind turbine simulation and design codes, they must take into account the ad-
ditional 6 DOFs brought by the lack of rigid foundations as well as the nonlinear interaction
with the waves. Several simulation tools have been developed and compared to each other
in the Offshore Code Collaboration (OC3) project. However, none have been veriﬁed against
real ﬁeld data as the ﬁrst full scale prototypes are still being tested. FAST with HydroDyn is
selected to be the simulation tool in conjunction with MATLAB and Simulink.
The controllers described in previous chapters are simulated according to DLC 1.2 of the IEC–
61400–3 standard for ﬁxed offshore wind turbines since no standards for ﬂoating wind turbines
are available to date. DLC 1.2 is designed to test for fatigue loads under normal operating con-
ditions. To perform DLC analysis, each controller must be simulated in 60 different simulations
across 10 different wind speed bins chosen to span the operational range of the above rated
wind speed region.
To analyse the large volume of simulation results, 14 performance metrics are used to quantify
the performance of the ﬂoating wind turbines in terms power and rotor speed regulation, fa-
tigue damage equivalent loads of key turbine components, and platform motions. These met-
rics are averaged over each wind speed bin as well as over the entire range selected of wind
speeds. The overall average is calculated using a weighted average whose weights are calcu-
lated based on a Weibull distribution of a selected offshore site. The Weibull scaling factors are
used to weigh each wind speed bin according to the time the turbine is expected to operate in
that wind speed in a year.
DLC simulations are carried out for 10 different controllers on four different platforms. The
simulations are carried out using FAST with HydroDyn with all 22 DOFs enabled using turbu-
lent full ﬁeld wind and irregular waves. The turbine yaw DOF is locked since no active yaw
control is needed because the mean wind direction remains unchanged.
Simulation results comparing the developed controllers on each ﬂoating platforms are presen-
ted in chapters 6 – 8. The platforms are compared to each other using results relative to an
onshore wind turbine in Chapter 9.
68

6
The Barge Platform
Contents
6.1 The Barge Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.2 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.3 Offshore DLC Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Results from quantitative analyses using the state feedback and disturbance accommod-
ating controllers described in chapters 3 and 4 on the barge platform are described in
this chapter. The results obtained from running an extensive set of simulations de-
scribed in Chapter 5 are normalised relative to a gain scheduled collective pitch PI controller.
The normalised results are used to compare the impact of controller features such as multiple
objectives, individual blade pitching, and disturbance accommodation on the barge platform.
In addition to the simulation results, the order of the state-space model required for control
design on ﬂoating platforms is speciﬁed based on physical insight into the ﬂoating system.
Although detailed and high-ﬁdelity simulation results for the ﬂoating platforms have been
published [32,38], the controllers used were single objective and utilised collective blade pitch-
ing. Therefore, the results presented in this chapter and chapters 7 and 8 are rather unique
in terms of assessing how multi-objective controllers utilising individual blade pitching will
behave on these ﬂoating platforms.
69

Chapter 6: The Barge Platform
6.1 The Barge Platform
The barge platform (Figure 6.1) is originally designed by Willem Vijfhuizen at the universities
of Glasgow and Strathclyde [24] and later modiﬁed by Jason Jonkman at the National Renew-
able Energy Laboratory (NREL) [32]. It is a simple rectangular platform that utilises buoyancy
due to its large water-plane area to maintain stability. Its shallow draft design makes it inde-
pendent of the minimum water depth required for installation. It is designed to be cost effective
and easy to install on site. However, the barge is very sensitive to incident waves since most of
the structure is above the water; that is, it rides the waves rather than pass through them. The
main properties of the barge platform studied in this work are listed in Table 6.1.
The original design of the barge platform had an oscillating water column incorporated into
the platform design to capture energy from the waves and perhaps add more damping to the
system [24]. However, this feature was not modelled in FAST and therefore excluded from
the barge model. For more details on the development of the barge model, please refer to
[24, 25, 32, 84].
Mooring lines not to scale
Figure 6.1: The barge platform
70

6.2 Controller Design
Table 6.1: Barge platform properties
Width 40 m
Length 40 m
Height 10 m
Draft 4 m
Water depth 150 m
Platform mass 5,452,330 kg
6.2 Controller Design
In this section, two issues are discussed that lead to the ﬁnal controller designs on the barge
platform but more importantly they deﬁne the approach used to design controllers on the other
two platforms. First, the effectiveness of collective blade pitching on a multi-objective control-
ler is evaluated. Second, coupling between platform rolling and pitching is identiﬁed that could
destabilise the system.
6.2.1 Collective Blade Pitch State Feedback Control
A simple case study is used to demonstrate the effectiveness of a multi-objective controller
using collective blade pitching [61]. The SFC is designed based on a 2 DOFs azimuth averaged
linearised state-space model; DOFs include rotor and platform pitch. This form of the SFC is
similar to the tower-top feedback loop implemented by Jonkman [32] (see § 2.1.1 on page 21
for a brief description). However, unlike the tower-top feedback controller, the SFC is able
to reduce platform pitching without severely affecting rotor speed regulation (see Figure 6.2).
Recall that a value of less than 1 indicates improvement relative to the Baseline controller. The
results presented in Figure 6.2 are based on a single nonlinear full DOFs simulation case used
to test the implementation of the CBP SFC.
Since both controllers use collective blade pitching, the physical principles used to achieve
their control objectives remain the same. The difference in performance is attributed to better
controller tuning and the use of constant torque control algorithm by the SFC to increase rotor
speed damping in the above rated wind speed region. The SFC combines the two control
objectives into a single optimal controller implementation.
A major drawback of using collective blade pitching with SFC is the issue of conﬂicting blade
pitch commands. Adding more objectives to the control design only exacerbates the problem.
Therefore, individual blade pitching is used in the ﬁnal implementations of the SFC and DAC.
6.2.2 Platform Roll-Pitch Coupling
For the previous case study, Figure 6.2 shows that tower base side-side bending fatigue DEL is
increased by 19%. Also, upgrading the SFC to use individual blade pitching further increases
71

Chapter 6: The Barge Platform
0.79 1.61 0.98 0.81 1.19 0.58 0.78 0.82 0.97 0.77 01
Speed
Error Blade
Pitch
Rate Blade
Root
Flapwise
Bending Tower
Base
Fore-aft
Bending Tower
Base
Side-side
Bending Low
Speed
Shaft
Torsion Roll Pitch Yaw Pitch Rate
RMS Fatigue DEL RMS of Platform Motions Normalised Performance Index
Figure 6.2: Normalised results for 2 DOFs CBP SFC relative to the Baseline controller
the tower side-side loads and platform rolling on a 2 DOFs nonlinear simulation model [61].
A similar behaviour is observed by Lackner [41] when he implemented IBP control to reduce
blade loads on a ﬂoating platform (see § 2.2 on page 23).
The increase in tower base side-side bending loads is caused by a net sideways load due to
an increase rotor torque load induced by the increased thrust of the rotor when regulating
platform pitch motion. For a three bladed wind turbine, the aerodynamic torque generated by
each blade is balanced given a uniform wind due to the blades’ spatial symmetry. However,
due to wind shear, rotor pre-cone, and shaft up-tilt this symmetry is broken and a net sideways
load is generated.
In addition to affecting tower base side-side loading, this induced sideways load interacts with
platform rolling motion which may lead to roll instability. This interaction is illustrated by
examining some of the linearised turbine properties. In particular, the coupling relationship
between platform roll and pitch is determined by looking at the periodic B(y)matrix of equa-
tion (3.5); the relevant elements of that matrix are shown in Figure 6.3.
Figure 6.3 shows the effects of blade 1 pitch perturbations on the roll and pitch accelerations of
the platform7; the zero azimuth position is when blade 1 is at the 12 o’clock position. Several
interesting features can be inferred from the ﬁgure:
• The blades are most effective (most negative) at the top due to the effects of wind shear
and the increased moment arm about the platform. An IBP controller utilises this effect
to generate the maximum pitch restoring moment as described in §3.2.2.
• The mean effect of the blades on the rolling motion is not zero (small negative number)
indicating that the collective effect of all three blades creates a rolling moment. Normally
7Blades 2 and 3 are 120and 240out of phase respectively.
72

6.2 Controller Design
0306090120150180210240270300330360−0.04−0.03−0.02−0.0100.01Actuator Gain (s−2)
Azimuth (deg)
Roll
Pitch
Figure 6.3: Blade 1 Bmatrix elements that correspond to platform roll and pitch acceleration
for a 3 DOFs linearised state–space model
for a 3 bladed wind turbine the lateral loads on the rotor are balanced due to the 120°
blade separation. However, wind shear, rotor pre-cone and shaft tilt angle create an im-
balance and hence the net sideways force.
• The blades affect the platform roll the same way they affect platform pitch (with much
less control authority) and the effect is almost in phase. Therefore, when the controller
generates the restoring pitch moment it also induces a rolling moment.
All of the above observations coupled with the fact that there is little aerodynamic damping
in the roll direction (compared to the pitch direction) explains the increase in rolling motion
and tower side-side fatigue load. The second and third observations indicate that even a CBP
controller designed to reduce platform pitch motion will generate a rolling moment (as shown
in Figure 6.2); the IBP controller only ampliﬁes the effect.
Roll Instability
Closed-loop stability analysis of the IBP SFC (designed based on a 2 DOFs linear model) on
the ﬂoating platform with all the DOFs enabled results in two unstable poles. The unstable
poles are determined to be those of the platform roll states using a three-step approach. First,
the eigenvectors associated with the unstable poles give an indication of which states are most
likely to contribute to that bending mode. With all 22 DOFs enabled and due to coupling, it is
unclear if a single state is actually unstable or a coupled bending mode. For example, coupling
between blade edgewise, tower side-side, and platform rolling motions allows for 10 possible
states to have contributions to the eigenvector of the unstable vibrating mode. Second, the
most likely unstable DOF is then included in a 3 DOFs model8including the rotor and platform
8The order of this model in subsequent stability analyses is equal to the order of the model used for controller
design plus the additional unstable DOF.
73

Chapter 6: The Barge Platform
0 100 200 300 400 500 600−10−8−6−4−20246810
Time (sec) Platform Yaw (deg)

Baseline
SFC
Figure 6.4: Typical platform yaw motion envelope for the barge platform
pitch DOFs where stability is assessed. The ﬁnal step involves linearising the system with all
the DOFs enabled except the unstable DOF from the second step and analysing the closed loop
stability to make sure that no other coupled mode is being destabilised by the controller.
Of course, one could argue that by lowering the controller gains the system can be stabilised.
However, lowering the gains to a stabilisable level makes the actual controller ineffective in
terms of performance. Therefore, the roll DOF is added to the control design9to ensure closed
loop stability for that model order around the linearisation point; full system stability is not
guaranteed, however, and it has to be checked. Similarly, adding the roll DOF destabilises
the ﬁrst tower side-side bending mode and hence it is added to the control design. Adding a
DOF that is strongly coupled to other existing DOFs in the linearised model for control design
ensures that the correct coupling and natural frequencies are accounted for by the controller.
6.2.3 Final Controller Design
The ﬁnal SFC is designed based on a 6 DOFs linearised model. The model includes the platform
roll, pitch and yaw, ﬁrst tower side-side bending mode, rotor and drivetrain twist DOFs. The
drivetrain twist DOF is added to maintain or reduce the fatigue loads of the drivetrain. Due
to large yaw motion experienced by the barge platform, the platform yaw DOF is added to
improve overall performance [85]. Figure 6.4 shows a typical yaw motion envelope for the
Baseline and State Feedback Controllers.
Controller tuning is carried out via careful selection of weighting matrices that emphasise the
regulation of certain states more than others. Platform motions and velocities have the highest
weighting to reduce motion and have a positive secondary effect on tower loads and power
9The roll DOF is added to the linearised state-space model used for control design.
74

6.3 Offshore DLC Results
regulation. The generator torque is part of the actuators used by the SFC and has a variable op-
erating point for power regulation (§3.4.1). Of course, the tuned controller is by no means the
optimum controller but its performance is deemed satisfactory during the tuning phase. Tun-
ing is carried out using two design load cases in the 18 m/s wind speed bin (at the linearisation
point).
Recall that the DAC consists of a SFC with an additional disturbance minimisation term (§4.2).
Therefore, the DAC uses the same model order and weighting matrices as the SFC. To resolve
the collective blade pitch drift issue discussed in §4.5.1, the column in the BNRmatrix that
corresponds to the collective blade pitch is set to zeros and elements in the Bd,NRmatrix that
correspond to the drivetrain states are also set to zero.
6.3 Offshore DLC Results
In this section, simulation results from performing DLC analysis on the State Feedback and Dis-
turbance Accommodating Controllers are compared and normalised to the Baseline controller
(GSPI controller described in §2.1) on the barge platform.
6.3.1 Averaged Normalised Results
The overall averaged and normalised simulation results for both controllers relative to the
Baseline controller on the barge platform are shown in Figure 6.5.
Looking at the performance of the State Feedback Controller relative to the Baseline, it can be
seen that power and rotor speed regulation, and blade ﬂapwise and edgewise bending, and low
speed shaft torsion fatigue DELs are similar to that of the Baseline controller. However, tower
fore-aft and side-side fatigue DELs are reduced by 33% and 51% respectively. Furthermore,
platform roll, pitch, and yaw motions are reduced by 41%, 31% and 51% respectively. Platform
roll, pitch, and yaw rates are reduced by 48%, 37%, and 60% respectively. These large and
impressive reductions can be attributed to the multi-objective nature of the controller and most
importantly to the use of individual blade pitching. Even though the tower fore-aft load is not
an explicit control objective, it is noticeably reduced; this reduction is believed to be the result of
the large reduction in platform pitching motion. The cost of this load reduction is the increased
use of the blade pitch actuators. Blade pitching rate is increased by 103%; however, this increase
does not result in blade saturation longer than 1 second at a time and, more importantly, does
not increase the blade ﬂapwise and edgewise fatigue DELs.
The Disturbance Accommodating Controller performance is almost identical to that of SFC
despite an increase in blade pitch actuation. The reason for such a result is because the barge
platform loads are dominated by incident waves rather than wind speed ﬂuctuations which the
DAC was designed to mitigate. Therefore, reducing the effects of wind speed perturbations has
a minimal effect on overall platform behaviour.
75

Chapter 6: The Barge Platform
1.04 1.06 2.03 1.02 1.06 2.19 01
Power Error Speed Error Blade Pitch Rate Normalised Performance Index SFC
DAC
0.97 0.99 0.67 0.49 0.96 0.99 0.99 0.66 0.50 0.97 01
Blade Root
Flapwise
Bending Blade Root
Edgewise
Bending Tower Base
Fore-aft
Bending Tower Base
Side-side
Bending Low Speed
Shaft
Torsion Normalised Performance Index SFC
DAC Normalised Performance Index SFC
Normalised Performance Index SFC
DAC Normalised Performance Index SFC DAC 0.59 0.69 0.49 0.60 0.69 0.50 01
Roll Pitch Yaw Normalised Performance Index SFC
DAC
0.52 0.63 0.40 0.52 0.62 0.39 01
Roll Rate Pitch Rate Yaw Rate Normalised Performance Index SFC
DAC 1.04 1.06 2.03 0.97 0.99 0.67 0.49 0.96 0.59 0.69 0.49 0.52 0.63 0.40 1.02 1.06 2.19 0.99 0.99 0.66 0.50 0.97 0.60 0.69 0.50 0.52 0.62 0.39 01
Power
Error Speed
Error Blade
Pitch Rate Blade Root
Flapwise
Bending Blade Root
Edgewise
Bending Tower
Base
Fore-aft
Bending Tower
Base
Side-side
Bending Low Speed
Shaft
Torsion Roll Pitch Yaw Roll Rate Pitch Rate Yaw Rate
RMS of Power, Speed, and
Actuator Usage Fatigue DEL RMS of Platform Motions RMS of Platform V elocities Normalised Performance Index SFC DAC
RMS of Power, Speed, and
Actuator Usage Fatigue DEL RMS of Platform Motions RMS of Platform Velocities Figure 6.5: Averaged DLC results for the barge platform relative to the Baseline controller on the barge platform
76

6.3 Offshore DLC Results
Table 6.2: Performance trends of the barge platform controllers relative to Baseline controller
Trend SFC DAC
Constant – Power and rotor speed errors
– LSS fatigue DEL
– Blade root ﬂapwise fatigue DEL
– Platform yaw and yaw rate- Power and rotor speed errors
– LSS fatigue DEL
– Platform yaw and yaw rate
Increasing – None – None
Decreasing – Blade root edgewise fatigue DEL
– Tower FA and SS fatigue DELs
– Platform roll and pitch motions- Blade root ﬂapwise and edgewise fa-
tigue DELs
– Tower FA and SS fatigue DELs
– Platform roll and pitch motions
Parabolic – None – None
Table 6.2 summarises the average performance trends across wind speed bins for the SFC and
DAC. These trends are categorised according to the 4 types of trends deﬁned in Table 5.5. Plots
of the trends are shown in ﬁgures D.1 and D.2 in Appendix D for the SFC and DAC respectively.
Both controllers have roughly the same trends with one noticeable difference. The DAC has
lower blade ﬂapwise bending DEL at high wind speeds but slightly worse at low wind speeds
than the SFC. Despite having a lower blade ﬂapwise DEL at high wind speeds, the overall
average ﬂapwise DEL for the SFC is lower than the DAC’s due to the Weibull scaling putting
more emphasis on lower, more dominant wind speeds.
The performance metrics that fall into the constant trend category demonstrate some degree of
robustness of these controllers as they operate away from their linearisation point of 18 m/s.
This relative robustness for these metrics does not mean that gain scheduling of state-space
controllers is not needed, it only shows that these controllers are robust enough to maintain
consistent performance improvement relative to the gain scheduled Baseline controller across
a wide range of wind speeds. Gain scheduling may be beneﬁcial in improving the performance
in an absolute sense rather than in a relative sense.
Performance metrics with a decreasing trend, where they are better regulated at higher wind
speed, are under-represented in the weighted average due to Weibull scaling. This variation
in performance is due to to the nonlinearity of the system sensitivities with changing wind
speeds.
Since the performance of the Disturbance Accommodating Controller is almost identical to that
of the State Feedback Controller, the State Feedback Controller is deemed better suited on the
barge platform as it is simpler and easier to implement than the DAC.
6.3.2 Time Series Results
A sample time series plot of a representative case is shown in Figure 6.610where the SFC is
compared to the Baseline controller on the barge platform. The ﬁgure shows the incident wind
10The ﬁgure starts at 100 s as this is the time period where differences in performance can be clearly identiﬁed.
77

Chapter 6: The Barge Platform
and wave conditions, rotor speed, commanded blade 1 pitch angle, platform pitch angle, tower
fore-aft and side-side base moments for the Baseline and State Feedback Controllers.
The improvement brought by individual blade pitching can be seen by the large reductions in
platform pitching especially during the time between 140 and 180 seconds. During this period,
the inﬂuence of platform pitch on tower fore-aft moment loads can also be seen coinciding with
increased wave activity. In terms of rotor speed regulation, the SFC and Baseline have roughly
the same performance; recall that the rated rotor speed is 12.1 rpm.
The “high frequency” content of the tower FA and SS moments shown in Figure 6.6 are those
of the tower’s FA and SS ﬁrst bending mode natural frequencies. The “low frequency” vari-
ation of the tower moments is caused by the platform pitch and roll motions affecting the tower
FA and SS loads respectively; platform roll motion is not shown in Figure 6.6. Since the tower
side-side bending mode is part of the SFC, the controller is able to signiﬁcantly reduce the amp-
litudes of the main frequency components of the tower side-side bending moment as shown in
Figure 6.7. Adding the tower fore-aft DOFs to the SFC is expected to further reduce the tower
loads; however, the tower loads relative to an onshore wind turbine (discussed in Chapter 9)
remain, despite the massive reductions by the SFC, infeasibly high for practical deployment of
the barge platform. Hence, the tower fore-aft DOFs are not added to the SFC design.
Interestingly, the platform pitch response for both controllers seems to be in phase. Such beha-
viour is caused by the dominance of the waves driving the platform pitch rather than observing
the free decay of the platform pitch according to the open- and closed-loop damping ratios for
the Baseline and State Feedback Controllers respectively.
The increase in blade pitching by the SFC is noticeable. This increased actuation has a higher
frequency content than that of the Baseline controller mainly due to two reasons: First, using
individual blade pitching adds a once-per-revolution (1p) frequency content that depends on
the rotor speed. Second, blade pitching by the SFC contains the structural natural frequencies
that the controller is designed to regulate and act upon.
It is important to note that for some of the DLC simulations, the platform pitch angle exceeds
10; in some extreme cases such as DLC 55 (see Table C.1 for DLC parameters) the platform
pitch angle is as high as 18for the baseline controller. In such cases, the assumptions of the
hydrodynamics module used by FAST (§5.1.1) no longer apply and the simulation results may
no longer be an accurate representation of the true ﬂoating system.
6.4 Chapter Summary
The barge platform offers a simple and cost effective solution for a ﬂoating system that is easy to
manufacture, transport and assemble. However, it suffers from being sensitive to the incident
waves and thus experiences large platform motions that increase loading on the turbine.
When implementing multi-objective controllers on the barge platform, platform pitch to roll
coupling due to blade pitch actuation is found to be present and applies for all ﬂoating plat-
forms as it is a property of the wind turbine rather than the platform’s. Due to this coupling,
78

6.4 Chapter Summary
100 120 140 160 180 200 220 240 260 280 300 -10 010 20 30 Wind and Wave Wind and Wave Conditions

Wind speed (m/s) Wave height (m)
100 120 140 160 180 200 220 240 260 280 300 6810 12 14 16 ω (rpm) Rotor Speed

Baseline SFC
100 120 140 160 180 200 220 240 260 280 300 10 15 20 25 θ (deg) Blade 1 Pitch

100 120 140 160 180 200 220 240 260 280 300 -10 -5 0510 Angle (deg) Platform Pitch

100 120 140 160 180 200 220 240 260 280 300 -2 024x 10 5Moment (Nm) Tower Fore-aft

100 120 140 160 180 200 220 240 260 280 300 -8 -4 048x 10 4
Time (sec) Moment (Nm) Tower Side-side

Figure 6.6: Sample time series response of Baseline and State Feedback Controllers on the barge
platform
79

Chapter 6: The Barge Platform
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 100.511.522.5x 104Amplitude (Nm)
Frequency (Hz)
Baseline
SFC
Figure 6.7: Frequency content of the tower side-side base moment
when a controller commands the blades to create a platform pitch restoring moment, it also
induces a rolling moment. This coupling causes the SFC to destabilise the roll DOF and sub-
sequently the ﬁrst tower side-side bending mode. These DOFs are included in the state-space
model used for control design to ensure the stability in a linear sense around the linearisation
point.
For ﬂoating wind turbines, the recommended state-space model order for control design on
ﬂoating platforms should include the following 6 DOFs: platform roll, pitch and yaw; ﬁrst
tower side-side bending mode; rotor and drivetrain twist DOFs. These DOFs are included to
improve performance and maintain closed loop stability of the ﬂoating system.
Simulation results show that when compared to the Baseline controller, there is no difference
in performance between the Disturbance Accommodating and State Feedback Controllers. The
reason the DAC for wind speed perturbations is not able to improve the performance further
than the SFC is because the barge platform is dominated by the waves rather than wind speed
perturbations. However, both controllers manage to signiﬁcantly reduce platform motions and
tower fatigue damage equivalent loads without negatively affecting any monitored aspect of
the wind turbine apart from an increase in blade pitch actuator usage. Since the DAC does not
offer a noticeable improvement despite an increase in blade pitch usage, the SFC is deemed
more suitable for the barge platform.
80

7
The Tension Leg Platform
Contents
7.1 The Tension Leg Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.2 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
7.3 Offshore DLC Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
7.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
The tension leg platform uses taught mooring lines to maintain hydrostatic stability. This
chapter gives a brief description of the tension leg platform and presents the analysed
simulation results of the implemented State Feedback and Disturbance Accommodat-
ing Controllers when compared to the Baseline controller on the tension leg platform.
7.1 The Tension Leg Platform
The tension leg platform has a cylindrical hull with four spokes where the tensioned mooring
lines are attached as shown in Figure 7.1. The TLP used in this work was originally designed
at the Massachusetts Institute of Technology (MIT) [25] and was later modiﬁed by NREL to
correct the platform roll and pitch inertias [38]; this TLP is also known as the MIT/NREL TLP .
The main properties of the TLP are listed in Table 7.1.
The TLP concept has most of its hull underwater thus minimising the interaction with incident
waves and therefore is not as sensitive to the waves as the barge platform. Furthermore, having
taught mooring lines increases the stiffness of the platform in the roll, pitch, and heave motions.
The major drawbacks of this design include the cost of anchors and dependency on seabed soil
conditions to support large tensile forces.
81

Chapter 7: The Tension Leg Platform
Mean Sea
Level
Figure 7.1: The tension leg platform
Table 7.1: Tension leg platform properties
Diameter 18 m
Number of spokes 4
Spoke length 18 m
Draft 47.89 m
Water depth 200 m
Platform mass 8,600,410 kg
82

7.2 Controller Design
7.2 Controller Design
The individual blade pitch State Feedback and Disturbance Accommodating Controllers on the
TLP are designed based on a seven DOFs state-space model. The ﬁrst six DOFs are the same
used in designing the barge controllers (see §6.2.3), the seventh DOF is the tower fore-aft ﬁrst
bending mode. Although the TLP does not experience similar resonance issues as the barge
platform, the physical mechanism behind these excitations still exists due to the individual
blade pitch controller.
The addition of the tower fore-aft DOF is aimed at reducing the associated fatigue DEL. Design
Load Case simulation results not shown here indicate that adding the tower fore-aft DOF does
indeed reduce tower fore-aft fatigue DEL when compared to a State Feedback Controller de-
signed without that additional DOF on the TLP . This DOF is not added to the barge controllers
simply because the tower loads remain very high (when compared to an onshore wind turbine
in Chapter 9) even after the large reductions from the State Feedback and Disturbance Accom-
modating Controllers. It is also believed that the reductions from adding this DOF to the barge
controllers will not be signiﬁcant due to the dominance of the waves. The 7 DOFs SFC for
the TLP is by no means the optimum controller for the TLP but its performance is deemed
satisfactory during the tuning phase.
For the Disturbance Accommodating Controller, the disturbance minimisation gain Gd,NRis
obtained after modifying the BNRand Bd,NRmatrices to avoid the collective blade pitch drift
discussed in §4.5.1. The column in the BNRmatrix that corresponds to the collective blade pitch
is set to zeros and elements in the Bd,NRmatrix that correspond to the drivetrain and ﬁrst tower
fore-aft bending states are also set to zero. The ﬁrst tower FA states are removed from the Bd,NR
matrix because the cosine- and sine-cyclic effects of the rotor have limited control authority
over the tower FA states.
7.3 Offshore DLC Results
In this section, simulation results from performing a DLC analysis on the State Feedback and
Disturbance Accommodating Controllers are compared and normalised to the Baseline con-
troller on the TLP .
7.3.1 Averaged Normalised Results
The overall averaged and normalised results are shown in Figure 7.2. Both controllers improve
power and rotor speed regulation considerably. The effect of adding wind speed disturbance
rejection to the State Feedback Controller is more prominent than on the barge platform because
the TLP is less inﬂuenced by the incident waves. The result is a noticeable improvement in rotor
speed and hence power regulation by the DAC. The DAC is also able to further reduce tower
base FA fatigue DEL.
83

Chapter 7: The Tension Leg Platform
1Normalised Performance Index SFC DAC 0.80 0.75 2.91 0.69 0.61 4.03 01
Power Error Speed Error Blade Pitch Rate Normalised Performance Index SFC
DAC
0.95 1.00 0.91 0.73 1.05 1.00 1.02 0.83 0.75 1.03 01
Blade Root
Flapwise
Bending Blade Root
Edgewise
Bending Tower Base
Fore-aft
Bending Tower Base
Side-side
Bending Low Speed
Shaft
Torsion Normalised Performance Index SFC
DAC 0.92 0.99 0.93 1.10 1.00 1.22 01
Roll Pitch Yaw Normalised Performance Index SFC
DAC
0.62 0.88 0.82 0.62 0.89 0.99 01
Roll Rate Pitch Rate Yaw Rate Normalised Performance Index SFC
DAC 0.80 0.75 2.91 0.95 1.00 0.91 0.73 1.05 0.92 0.99 0.93 0.62 0.88 0.82 0.69 0.61 4.03 1.00 1.02 0.83 0.75 1.03 1.10 1.00 1.22 0.62 0.89 0.99 01
Power
Error Speed
Error Blade
Pitch Rate Blade Root
Flapwise
Bending Blade Root
Edgewise
Bending Tower
Base
Fore-aft
Bending Tower
Base
Side-side
Bending Low Speed
Shaft
Torsion Roll Pitch Yaw Roll Rate Pitch
Rate Yaw Rate
RMS of Power, Speed, and
Actuator Usage Fatigue DEL RMS of Platform Motions RMS of Platform Velocities Normalised Performance Index SFC DAC 0.80 0.75 2.91 0.69 0.61 4.03 01
Power Error Speed Error Blade Pitch Rate Normalised Performance Index SFC
DAC
0.95 1.00 0.91 0.73 1.05 1.00 1.02 0.83 0.75 1.03 01
Blade Root
Flapwise
Bending Blade Root
Edgewise
Bending Tower Base
Fore-aft
Bending Tower Base
Side-side
Bending Low Speed
Shaft
Torsion Normalised Performance Index SFC
DAC 0.92 0.99 0.93 1.10 1.00 1.22 01
Roll Pitch Yaw Normalised Performance Index SFC
DAC
0.62 0.88 0.82 0.62 0.89 0.99 01
Roll Rate Pitch Rate Yaw Rate Normalised Performance Index SFC
DAC Figure 7.2: Averaged DLC results for the TLP relative to the Baseline controller on the TLP
84

7.3 Offshore DLC Results
The SFC is able to reduce platform roll, pitch, and yaw rates by an average of 38%, 12%, and
18% respectively while only managing to reduce the roll, pitch, and yaw angles by an average
of 8%, 1%, and 7% respectively. The reason for such performance is due to two factors: ﬁrst is
the emphasis by the controller, through tuning, to primarily focus at regulating the platform
velocities. The second is the TLP’s stiffness in the roll and pitch directions where the angles
remain very small (roll and pitch angles do not exceed 1 degree). Therefore, very little im-
provement can be achieved in these motions. The large increase in blade pitch actuation by
the DAC is responsible for the increase in rolling and yawing motions. However, these angles
remain small (less than 5 degrees) and do not result in a signiﬁcant increase in fatigue DEL on
any of the major turbine components.
Blade ﬂapwise and edgewise bending and low speed shaft torsion fatigue DELs remain close
to parity for both SFC and DAC indicating a similar performance to the Baseline controller.
Whether the Baseline performance is adequate will be discussed in Chapter 9. Tower fore-aft
DEL can be reduced by a maximum of 17% due to the addition of hub-height wind speed
disturbance rejection. Tower side-side fatigue load is better reduced than fore-aft load due to
better roll rate regulation and the availability of the generator torque to inﬂuence side-side
loading. Tower side-side fatigue DEL can be reduced by up to 27% by the SFC relative to the
Baseline controller.
Blade pitch actuation is increased, as expected, by at least 291%. However, like the barge con-
trollers, this increase in actuation has no extensive saturation periods and does not result in an
increase in blade fatigue damage equivalent loads.
In terms of performance trends across the simulation wind speed bins, Table 7.2 summarises
the trends for the SFC and DAC according to the 4 types of trends deﬁned in Table 5.5. For a
plot of the trends, please refer to ﬁgures D.3 and D.4 in Appendix D.
For the metrics that fall into the decreasing trend category, the improvement in performance
as wind speed increases is due to the nonlinearity of the system sensitivities with changing
wind speed. Such a performance trend is under-represented in the weighted average results
shown in Figure 7.2 due to the Weibull scaling factors placing more emphasis on performance
Table 7.2: Performance trends of the TLP controllers with increasing mean wind speed
Trend SFC DAC
Constant – All except power and rotor speed er-
rors- Tower FA and SS fatigue DELs
– LSS fatigue DEL
– Platform pitch
– Platform rotational velocities
Increasing – None – None
Decreasing – Power and speed errors – Power and rotor speed errors
– Platform roll
– Blade root edgewise fatigue DEL
Parabolic – None – Blade root ﬂapwise fatigue DEL
– Platform yaw
85

Chapter 7: The Tension Leg Platform
in lower wind speeds. The performance metrics that exhibit a parabolic trend are affected
by the linearity of the DAC law; these metrics would beneﬁt from gain scheduling. Gains
scheduling of SFCs or DACs is outside the scope of this work.
Since the performance of the Disturbance Accommodating Controller is generally better than
that of the State Feedback Controller, the Disturbance Accommodating Controller is deemed
better suited for the TLP .
7.3.2 Time Series Results
A sample time series plot of the TLP using the same representative case for the barge platform
is shown in Figure 7.3 for the Baseline and Disturbance Accommodating Controllers. The im-
provement in rotor speed regulation is reﬂected in the 200 second window where the DAC
regulates the rotor speed closer to the rated speed of 12.1 rpm.
Noticeable reductions in tower side-side moment loads can be observed especially during the
ﬁrst 20 seconds shown in Figure 7.3. Figure 7.4 shows the reduction in the amplitudes of certain
frequencies by the DAC for the tower fore-aft and side-side base moments. The difference in
magnitude of the moments for the tower fore-aft and side-side moments (also in Figure 7.3) is
mainly because the main rotor thrust and wave loads act in the fore-aft direction when no yaw
errors are present.
It is important to note that platform pitch angle during the 200 second window shown does
not exceed 0.3 degrees in magnitude. Consequently, further reducing platform pitching mo-
tion becomes difﬁcult. This limited improvement is reﬂected by the almost identical pitching
motion for both controllers on the TLP and, as shown by Figure 7.2, only moderate reductions
in platform pitching velocity and tower fore-aft fatigue DEL are achieved when compared to
the large reductions achieved by the SFC controller on the barge platform.
Finally, note that the mean blade pitch of the DAC closely follows the collective blade pitch of
the Baseline controller. This suggests that most of the performance improvements brought by
the DAC on the TLP are due to individual blade pitching.
7.4 Chapter Summary
The tension leg platform uses taught mooring lines to achieve hydrostatic stability in the wa-
ter. The tensioned mooring lines increase the stiffness of the platform’s roll, pitch, and heave
motions. Furthermore, the design of the hull to have minimal water-plane area reduces the
interaction with incident waves thus reducing the magnitude of induced motions. This design
produces the smallest motion envelope out of the three platforms considered in this work.
The State Feedback Controller is designed based on a 7 DOFs linearised state-space model; the
ﬁrst six are the same DOFs used for control design on the barge platform in addition to the ﬁrst
bending mode of the tower fore-aft DOF. This DOF is added to further reduce the tower base
fore-aft fatigue DEL.
86

7.4 Chapter Summary
100 120 140 160 180 200 220 240 260 280 300 -10 010 20 30 Wind and Wave Conditions Wind and Wave

Wind speed (m/s) Wave height (m)
100 120 140 160 180 200 220 240 260 280 300 10 12 14 Rotor Speed ω (rpm)

Baseline DAC
100 120 140 160 180 200 220 240 260 280 300 10 15 20 25 Blade 1 Pitch θ (deg)
100 120 140 160 180 200 220 240 260 280 300 -0.5 00.5 Platform Pitch Angle (deg)
100 120 140 160 180 200 220 240 260 280 300 0246x 10 4 Tower Fore-aft Moment (Nm)
100 120 140 160 180 200 220 240 260 280 300 -1 012x 10 4 Tower Side-side Moment (Nm)
Time (sec)
Figure 7.3: Sample time series response of Baseline and Disturbance Accommodating Control-
lers on the TLP
87

Chapter 7: The Tension Leg Platform
00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1010002000300040005000
Frequency (Hz)Amplitude (Nm)

Baseline
DAC
(a) Tower fore-aft
00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10500100015002000
Frequency (Hz)Amplitude (Nm)

Baseline
DAC
(b) Tower side-side
Figure 7.4: Frequency content of tower base moments
Simulation results show that the SFC manages to improve most of the performance metric,
although, the magnitude of the reductions in platform motions is not as signiﬁcant as the re-
ductions achieved by the SFC on the barge platform. The reason for such limited improvement
is because the platform roll and pitch motions are very small (typically less than 1 degree)
leaving little room for improvement.
The DAC further improves power and rotor speed regulation and further reduces tower fore-
aft fatigue DEL by rejecting wind speed ﬂuctuations. However, the DAC increases the use of
the blade pitch actuators which in turn increases the platform’s rolling and yawing motions via
coupling. The DAC is able to reject the effects of the wind speed perturbations with noticeable
results due to the fact that the TLP motions are not very sensitive to incident waves compared
to the barge platform. Since the performance of the Disturbance Accommodating Controller
is generally better than that of the State Feedback Controller, the Disturbance Accommodating
Controller is deemed better suited for the tension leg platform.
88

8
The Spar-Buoy Platform
Contents
8.1 The Spar-Buoy Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
8.2 Effects of Lowering the Platform’s Pitch Natural Frequency in Control Design . . . . . . 91
8.3 Offshore DLC Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
8.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Spar-buoy platform concepts use ballast tanks to achieve hydrostatic stability and usually
have deep drafts. This chapter presents the averaged DLC results for the State Feedback
and Disturbance Accommodating Controllers relative to the Baseline controller on the
OC3-Hywind Spar-buoy platform. The effects of the spar-buoy’s low natural frequency and its
implications on control design and individual blade pitching are also discussed.
8.1 The Spar-Buoy Platform
The spar-buoy platform utilises a deep-draft ballast to maintain hydrostatic stability and caten-
ary mooring lines for station-keeping (Figure 8.1). The spar-buoy platform model used in this
work is known as the “OC3-Hywind Spar-buoy”. It is developed for Phase IV of the OC3 pro-
ject and based on the Hywind Spar-buoy model [69, 86]. The main difference between the two
models is that the Hywind Spar-buoy has a 2.3 MW wind turbine whereas the OC3-Hywind
has a 5 MW wind turbine mounted on the platform. Recall that a full-scale prototype of the
Hywind spar-buoy is currently being tested in Norway, therefore, assessing the potential and
limitations of State Feedback and Disturbance Accommodating Control on a spar-buoy-type
platform is important. Table 8.1 lists the main properties of the OC3-Hywind spar-buoy. More
details on the OC3-Hywind spar-buoy can be found in [86].
89

Chapter 8: The Spar-Buoy Platform
Figure 8.1: The spar-buoy platform
Table 8.1: Spar-buoy platform properties
Diameter above taper 6.5 m
Diameter below taper 9.4 m
Freeboard 10 m
Draft 120 m
Water depth 320 m
Platform mass 7,466,330 kg
90

8.2 Effects of Lowering the Platform’s Pitch Natural Frequency in Control Design
Like the TLP , the spar-buoy has most of its hull underwater thus minimising the interaction
with surface waves. However, for cost effectiveness, the spar-buoy uses catenary mooring
lines which results in a larger motion envelope than the TLP . Due to the large ballast, the Spar-
buoy is designed such that the platform’s roll and pitch natural frequencies are below the wave
excitation frequency of most sea states [86]. The spar-buoy’s deep draft limits the locations
where it can be deployed whereas the barge and tension leg platforms can be deployed in
shallower sites.
8.2 Effects of Lowering the Platform’s Pitch Natural Frequency in
Control Design
A low platform pitch natural frequency (of about 0.21 rad/s or 0.03 Hz [86]) has a direct im-
pact on control design and performance. Starting with the Baseline controller, the controller’s
design natural frequency is reduced from 0.6 rad/s to 0.2 rad/s to avoid the reduced or neg-
ative damping in the pitch direction and wave excitation frequency of most sea states [40, 86].
Furthermore, the torque control strategy in the above rated wind speed region is changed from
constant power to constant torque to prevent a reduction in platform pitch damping; this has a
direct impact on power regulation quality.
For the State Feedback Controller, recall that it is designed based on a linearised state-space
model of the nonlinear system with only certain DOFs enabled. Having a low platform pitch
natural frequency means that other low frequency DOFs, such as the platform surge, can in-
teract with the platform pitch therefore altering its peak resonant frequency. Furthermore, the
low platform pitch natural frequency reduces the effectiveness of important high-frequency in-
dividual blade pitch commands at regulating platform pitch. These two effects are discussed
next.
8.2.1 Platform Surge DOF
For State Feedback Controllers designed for the barge and tension leg platforms, the surge
DOF is not included in the controller design as it has little or no effect on the controller per-
formance. However, because the spar-buoy’s pitch frequency is now reduced, the surge DOF
does have an impact on the model, changing the ﬁrst pitch peak resonant frequency11by 68%.
Figure 8.2a shows the change in the peak resonant frequency of the platform pitch when the
platform surge is added to the linearised model. Compare that with the barge platform (Fig-
ure 8.2b) where adding the surge DOF does not change the main peak resonant frequency. The
frequency responses shown in Figure 8.2 are based on 2 and 3 DOFs linearised (at 18 m/s)
models transformed into the nonrotating frame of reference; note the actuator inputs are now
collective, cosine- and sine-cyclic pitch. The DOFs include the rotor and platform pitch DOFs
with the addition of the platform surge DOF. Therefore, if the SFC is designed based on a linear
11The peak resonant frequency is a function of the natural frequency wnand damping ratio z. It should not be
confused with the damped natural frequency.
91

Chapter 8: The Spar-Buoy Platform
Table 8.2: DOFs list for Figure 8.3
# of DOFs Description
6 Platform roll, pitch, and yaw, 1sttower SS bending mode, rotor and drivetrain
7 6 DOFs + platform surge
8 7 DOFs + 1sttower FA bending mode
21 All DOFs except nacelle yaw
model that does not include the surge DOF, then the controller will be trying to actuate the
blades at the wrong frequency to have maximum impact on the platform pitch.
The frequency responses in Figure 8.2 use simple models to demonstrate the effect of including
the surge DOF on the linearised model and compare with the barge platform. The effects of
adding certain DOFs to the linearised state-space model (for control design) on the platform
pitch frequency response are shown in Figure 8.3; the list of DOFs is given in Table 8.2. In the
ﬁgure, only the collective blade pitch input is shown as the other two (cosine- and sine-cyclic
pitch) display the same trends.
Figure 8.3 shows that by including the platform surge DOF, the correct peak frequency is at-
tained and the low frequency gain is closer to the actual system (21 DOFs). Adding the ﬁrst
tower fore-aft bending mode to the linearised model (8 DOFs model) accounts for the second
resonant peak which is in close proximity to the ﬁrst resonant frequency. Adding more DOFs
such as the second tower FA bending mode or the blade ﬂap bending modes makes the fre-
quency response of the model used for control design approach the real system. However, it is
deemed that an 8 DOFs linear state-space model is adequate to account for the platform pitch
dynamics.
8.2.2 Effectiveness of Individual Blade Pitching
The spar-buoy’s platform pitch frequency is lower than the other two platforms mainly due to
the signiﬁcantly larger pitch inertia. Having a lower platform pitch natural frequency than the
other two platforms means that high frequency blade pitch inputs are more attenuated thus
reducing their effectiveness (Figure 8.4). For now, assume that the main frequency components
of individual blade pitching occur at frequencies higher than 0.2 Hz (this is demonstrated in
Chapter 9). Therefore, individual blade pitching on the spar-buoy platform is not as effective
at regulating the platform pitch as on the other ﬂoating platforms when actuator saturation is
taken into account. Explaining the differences in the frequency response of the three platforms
(Figure 8.4) is discussed further in Chapter 9.
8.2.3 Final Controller Design
The ﬁnal form of the State Feedback Controller used for DLC analysis is based on an 8 DOFs
linearised state-space model that includes the DOFs listed in Table 8.2. However, the plat-
92

8.2 Effects of Lowering the Platform’s Pitch Natural Frequency in Control Design
10−410−310−210−1100−120−100−80−60−40−200From: θo
Frequency (Hz)Magnitude (dB)
To: Pitch
10−410−310−210−1100−120−100−80−60−40−200From: θc
Frequency (Hz)10−410−310−210−1100−120−100−80−60−40−200From: θs
Frequency (Hz)
wihtout surge DOF
with surge DOF
(a) Spar-buoy platform
10−410−310−210−1100−90−80−70−60−50−40−30−20−10010From: θo
Frequency (Hz)Magnitude (dB)
To: Pitch
10−410−310−210−1100−90−80−70−60−50−40−30−20−10010From: θc
Frequency (Hz)10−410−310−210−1100−90−80−70−60−50−40−30−20−10010From: θs
Frequency (Hz)
wihtout surge DOF
with surge DOF
(b) Barge platform
Figure 8.2: Effects of adding the surge DOFs on frequency response
93

Chapter 8: The Spar-Buoy Platform
0.0001 0.001 0.01 0.1 1 10−160−140−120−100−80−60−40−200
Frequency (Hz)Magnitude (dB)

21 DOFs
6 DOFs
7 DOFs
8 DOFs
Figure 8.3: Spar-buoy platform pitch frequency response to collective blade pitch with different
sets of DOFs
0.001 0.01 0.1 1 10−120−100−80−60−40−200
Frequency (Hz)Magnitude (dB)

Barge
TLP
Spar−buoy
Figure 8.4: The three platforms’ pitch frequency response to blade 1 pitch on a 3 DOFs model
that includes the platform surge, platform pitch, and rotor DOFs
94

8.3 Offshore DLC Results
form surge state (position) is removed from the linear state-space model before the controller is
designed; platform surge velocity is still part of the model. Regulating the platform surge po-
sition is not considered critical to normal operation, and by removing it as a control objective,
an unnecessary increase in blade pitch actuation is avoided.
Recall that the Baseline controller’s torque algorithm is changed from constant power to con-
stant torque to improve the platform’s pitch damping [38, 86]; using the constant torque al-
gorithm and reducing the desired closed-loop natural frequency produces the best results for
the Baseline controller. When tuning the 8 DOFs SFC, little or no difference is observed between
the two torque algorithms in terms of platform pitch response. However, with the constant
power algorithm, power regulation is signiﬁcantly improved. Therefore, the constant power
algorithm is used as the generator torque operating point for the SFC. Being a multi-objective
controller gives the SFC an obvious advantage allowing it to use the constant power algorithm
without suffering the negative or reduced platform pitch damping whereas the single-objective
Baseline controller has to compensate by using the constant torque algorithm.
Tuning the SFC to achieve somewhat satisfactory performance involves sacriﬁcing rotor speed
regulation in favour of improved platform pitch regulation. Relaxing rotor speed control allows
the controller to use the blade pitch to regulate the platform pitch but increases rotor speed
ﬂuctuations. However, since the constant power torque algorithm is used, power regulation is
not signiﬁcantly affected.
The wind speed perturbation Disturbance Accommodating Controller on the spar-buoy is con-
ﬁgured using the same set-up used for the DAC on the TLP – discussed in §7.2.
8.3 Offshore DLC Results
In this section, simulation results from performing DLC analysis on the State Feedback and Dis-
turbance Accommodating Controllers are compared and normalised to the Baseline controller
on the spar-buoy platform.
8.3.1 Averaged Normalised Results
The overall averaged and normalised results are shown in Figure 8.5. The SFC manages to
reduce the tower fatigue DELs by 9%. All other metrics remain close to parity except for RMS
power error, blade pitch rate and low speed shaft torsion fatigue DEL. Since rotor speed regu-
lation performance is essentially similar to the Baseline controller, the massive 64% reduction
in power error is simply due to the use of the constant power algorithm for the torque operat-
ing point. The massive relative increase in blade pitch usage is thought to be having a negative
impact on low speed shaft fatigue load.
There are two main reasons as to why most of the SFC’s relative performance metrics are close
to parity. First, unlike the barge platform, the Baseline controller’s performance is good in the
sense that rotor speed is closely regulated and platform motions remain below 5°. Second and
95

Chapter 8: The Spar-Buoy Platform
0.36 1.01 7.74 0.30 0.88 12.09 01
Power Error Speed Error Blade Pitch Rate Normalised Performance Index SFC
DAC
0.99 1.01 0.91 0.91 1.18 1.06 1.03 0.88 1.09 1.20 01
Blade Root
Flapwise
Bending Blade Root
Edgewise
Bending Tower Base
Fore-aft
Bending Tower Base
Side-side
Bending Low Speed
Shaft
Torsion Normalised Performance Index SFC
DAC Normalised Performance Index SFC
Normalised Performance Index SFC
DAC Normalised Performance Index SFC DAC 0.98 0.98 1.01 1.33 0.98 1.28 01
Roll Pitch Yaw Normalised Performance Index SFC
DAC
0.97 0.99 0.98 1.64 1.01 1.18 01
Roll Rate Pitch Rate Yaw Rate Normalised Performance Index SFC
DAC 0.36 1.01 7.74 0.99 1.01 0.91 0.91 1.18 0.98 0.98 1.01 0.97 0.99 0.98 0.30 0.88 12.09 1.06 1.03 0.88 1.09 1.20 1.33 0.98 1.28 1.64 1.01 1.18 01
Power
Error Speed
Error Blade
Pitch Rate Blade Root
Flapwise
Bending Blade Root
Edgewise
Bending Tower
Base
Fore-aft
Bending Tower
Base
Side-side
Bending Low Speed
Shaft
Torsion Roll Pitch Yaw Roll Rate Pitch Rate Yaw Rate
RMS of Power, Speed, and
Actuator Usage Fatigue DEL RMS of Platform Motions RMS of Platform V elocities Normalised Performance Index SFC DAC
RMS of Power, Speed, and
Actuator Usage Fatigue DEL RMS of Platform Motions RMS of Platform Velocities Figure 8.5: Averaged DLC results for the spar-buoy platform relative to the Baseline controller on the spar-buoy platform
96

8.3 Offshore DLC Results
as discussed earlier, the effectiveness of individual blade pitching is limited and therefore the
controller requires to actuate the blades further to achieve the required actuation force. How-
ever, due to the presence of actuator saturation, individual blade pitching becomes of limited
effect on the ﬂoating wind turbine. Therefore, the SFC can only have limited improvement on
the spar-buoy relative to the Baseline controller.
The DAC manages to improve rotor speed regulation by reducing the effects of wind speed
perturbations through increased blade pitch usage; power regulation is improved as a con-
sequence. However, the increased blade pitch actuation does have a negative impact on plat-
form roll and yaw motions, and as a result, tower side-side loads are increased by an average of
9%. The DAC’s feed-forward term operates linearly away from the linearisation point; the fur-
ther away from the linearisation point the turbine is operating, the more and further the blades
are actuated. System nonlinearities mean that the DAC is either under- or over-actuating the
blades to minimise the effects of wind speed perturbations away from the linearisation point.
To be able to utilise the DAC’s rejection of wind speed perturbations, tuning of the SFC can
allow for the expected impact of the DAC by further relaxing rotor speed regulation. Further
tuning is not considered here as the objective is to assess the performance of just adding the
feed-forward term to the SFC.
In terms of performance trends across the simulation wind speed bins, Table 8.3 summarises
the trends for the SFC and DAC according the 4 types of trends deﬁned in Table 5.5. For a plot
of the trends, please refer to ﬁgures D.5 and D.6 in Appendix D.
Interestingly, certain performance metrics for both controllers on the spar-buoy platform ex-
hibit an increasing trend with increasing wind speed. Since both controllers have these spe-
ciﬁc metrics fall into this category, this indicates the actuators’ limited inﬂuence on these met-
rics/control objectives. Such limitation is possibly due to the limited effectiveness of IBP and
the presence of actuator saturation limiting the controller design from increasing the gain. The
increasing trend over-represents the improvement of metric due to the Weibull scaling placing
more emphasis on the lower wind speed range where it is better regulated.
Table 8.3: Performance trends of the spar-buoy platform controllers relative to the Baseline
controller with increasing mean wind speed
Trend SFC DAC
Constant – Blade root edgewise fatigue DEL
– Tower FA and SS fatigue DELs
– Platform velocities- Tower FA fatigue DEL
– LSS fatigue DEL
– Platform pitch and yaw velocities
Increasing – Blade root ﬂapwise fatigue DEL
– Platform motions- Platform roll and pitch motions
– Platform roll velocity
Decreasing – Rotor speed error
– LSS fatigue DEL- Rotor speed error
– LSS fatigue DEL
– Blade root edgewise fatigue DEL
Parabolic – Power error – Power error
– Platform yaw
– Blade root ﬂapwise fatigue DEL
97

Chapter 8: The Spar-Buoy Platform
16 18 20 22 240.20.40.60.811.2Performance Metric (−)
Wind Speed (m/s)
Power
Rotor speed
(a) SFC
16 18 20 22 240.20.40.60.811.2Performance Metric (−)
Wind Speed (m/s)
Power
Rotor speed (b) DAC
Figure 8.6: Rotor speed and power regulation errors trends with increasing wind mean speed
relative to the Baseline controller
The parabolic power error trend for the SFC (Figure 8.6a) and DAC (Figure 8.6b) may seem
counter-intuitive as the rotor speed error improves with increasing wind speed suggesting that
power error should follow suit. However, because both controllers have relaxed rotor speed
control, the generator torque usage is increased to compensate, thus reaching its maximum
saturation limit. As the wind speed increases, rotor speed ﬂuctuations increase as well (recall
that the trends are relative to the Baseline controller). This in turn increases the periods where
generator torque is saturated resulting in worse power regulation than at lower wind speeds.
151617181920212223240.811.21.41.61.822.2Normalised Metric (−)
Wind Speed (m/s)
Tower side−side DEL
Platform roll
Platform roll rate
Figure 8.7: Effect of platform roll on tower SS bending trendThe tower side-side bending
fatigue DEL for the DAC trend
is not included in Table 8.3 as
it does not belong to any of
the four trend types convin-
cingly. The metric ﬂuctuates
wildly following the effects of
the platform rolling motion as
shown in Figure 8.7.
Since the performance of the
State Feedback Controller is
generally better than that of
the Disturbance Accommodat-
ing Controller, the State Feed-
back Controller is deemed bet-
ter suited for the spar-buoy platform given the current actuators’ limitations.
98

8.4 Chapter Summary
8.3.2 Times Series Results
Figure 8.8 shows the time series response of the Baseline and State Feedback Controllers for
the same representative case used for the barge and tension leg platforms. Since rotor speed
regulation performance of the two controllers is almost identical, the generator power is shown
instead. The SFC’s power regulation is signiﬁcantly better than the Baseline’s due to the use of
the constant power algorithm for the torque operating point as discussed earlier.
The reductions in tower fore-aft and side-side base bending loads are clearly noticeable in Fig-
ure 8.8. For the tower fore-aft base bending load, Figure 8.9a shows the reduction in the amp-
litudes of certain frequencies and especially at the platform pitch resonant frequency of 0.03 Hz.
However, for the tower side-side base moment, there is an increase in the amplitude at the plat-
form roll natural frequency of 0.03 Hz (Figure 8.9b). This increase is caused by the change in
the platform roll resonant frequency due to excluding the platform sway from the linearised
model based on the same principles discussed in §8.2.1. The platform sway DOF is not ad-
ded to the control design as the blade pitch actuators are already reaching the limits of their
effectiveness. Furthermore, the reduction in tower side-side loads due to the inclusion of the
platform sway DOF is not expected to change the overall feasibility of the spar-buoy platform
as tower side-side is not a main design driver; tower fore-aft is (see Chapter 9).
Note how the SFC’s blade 1 pitch angle closely follows the Baseline’s collective blade pitch
trajectory. Since both controllers have similar rotor speed regulation performance, this suggests
that most of the improvements brought by the SFC are achieved via individual blade pitching
despite its limited effectiveness at high frequencies.
8.4 Chapter Summary
The spar-buoy platform achieves hydrostatic stability using a deep drafted ballast with caten-
ary mooring lines for station-keeping. The deep draft of the spar-buoy increases the platform’s
rolling and pitching inertias signiﬁcantly thus reducing their respective natural frequencies.
This design feature puts the platform’s roll and pitch frequencies below the wave excitation
frequency of most sea states.
The platform’s lower pitch frequency affects the choice of which DOFs to include in the control
design of the State Feedback Controller. Adding the platform surge DOF and the ﬁrst tower
fore-aft bending mode to the linearised model captures all the essential features of the plat-
form pitch dynamics. Not including these two DOFs (especially the platform surge) causes the
model used for control design to incorrectly represent the nonlinear system.
Another effect caused by the platform’s lower pitch frequency is the limited effectiveness of
individual blade pitching to regulate the platform pitch. A lower natural frequency than the
other platforms means that high frequency blade pitch inputs are further attenuated. There-
fore, individual blade pitching on the spar-buoy is not as effective as on other platforms at high
frequencies requiring the controller to increase actuation to get the same desired impact. How-
99

Chapter 8: The Spar-Buoy Platform
100 120 140 160 180 200 220 240 260 280 300 -10 010 20 30 Wind and Wave Conditions Wind and Wave
Wind speed (m/s) Wave height (m)
100 120 140 160 180 200 220 240 260 280 300 4000 5000 6000 Generator Power Power (kW)

Baseline SFC
100 120 140 160 180 200 220 240 260 280 300 10 15 20 25 Blade 1 Pitch θ (deg)
100 120 140 160 180 200 220 240 260 280 300 024Platform Pitch Angle (deg)
100 120 140 160 180 200 220 240 260 280 300 0510 x 10 4 Tower Fore-aft Moment (Nm)
100 120 140 160 180 200 220 240 260 280 300 -2 024x 10 4 Tower Side-side Moment (Nm)
Time (sec)
Figure 8.8: Sample time series response of Baseline and State Feedback Controllers on the spar-
buoy platform
100

8.4 Chapter Summary
0.030.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10200040006000800010000
Frequency (Hz)Amplitude (Nm)

Baseline
SFC
(a) Tower fore-aft
0.030.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1050010001500200025003000
Frequency (Hz)Amplitude (Nm)

Baseline
SFC
(b) Tower side-side
Figure 8.9: Frequency content of tower base moments
ever, blade pitch saturation limits impose an upper limit to the controller gains thus reducing
the effectiveness of IBP on the spar-buoy platform.
Both controllers (SFC and DAC) use constant power for the torque control algorithm thus signi-
ﬁcantly improving power regulation over the Baseline controller which uses constant torque to
improve platform pitch damping. The SFC is able to reduce tower fatigue damage equivalent
loads by an average of 9% relative to the Baseline controller. All other metrics remain close to
unity except for low speed shaft torsion DEL where it is increased by an average of 18%. This
increase is thought to be due to the signiﬁcant relative increase in blade pitch actuation.
The DAC is able to improve rotor speed regulation by rejecting wind speed perturbations
through increased blade pitch actuation. This signiﬁcant increase in blade pitch actuation has
a negative impact on platform rolling and yawing motions. Therefore, the State Feedback Con-
troller is deemed better suited for the spar-buoy platform given the current actuators’ limita-
tions.
101

Chapter 8: The Spar-Buoy Platform
102

9
Platform Comparisons
Contents
9.1 Comparison Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
9.2 Platform Pitch Input and Disturbance Sensitivities . . . . . . . . . . . . . . . . . . . . . . 104
9.3 DLC Results Relative to an Onshore Wind Turbine . . . . . . . . . . . . . . . . . . . . . . 108
9.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Early comparisons between the three ﬂoating platforms involved qualitative analysis;
see Table 1.5 for an example. Then, numerical comparisons using hi-ﬁdelity simulation
models used results relative to an onshore wind turbine for comparing turbine loads
when simulated with a Gain Scheduled PI controller.
In this chapter, the platforms’ simulation results for the Baseline and multi-objective control-
lers from previous chapters are compared to each other using an onshore wind turbine as a
reference to establish whether fatigue loads can be reduced to a level comparable to an onshore
wind turbine. The differences in performance based on numerical results are then explained
using physical insight into their properties through the frequency response of the platform
pitch motion.
9.1 Comparison Approach
The platforms are compared in two different ways: The ﬁrst is by examining certain properties
of the frequency response of the platform pitch motion to establish certain differences that affect
their dynamic behaviour. The second is by comparing their simulation results from previous
chapters.
103

Chapter 9: Platform Comparisons
Table 9.1: Platform controllers to be compared to the onshore wind turbine
Platform Controller Blade Pitching Torque Control Other
Barge Baseline Collective Const. Power wn=0.6 rad/s and z=0.7
SFC Individual Const. Power 6 DOFs linear state-space model
TLP Baseline Collective Const. Power wn=0.6 rad/s and z=0.7
DAC Individual Const. Power 7 DOFs linear state-space model
Spar-buoy Baseline Collective Const. Torque wn=0.2 rad/s and z=0.7
SFC Individual Const. Power 8 DOFs linear state-space model
Since all the ﬂoating platforms use the same 5 MW wind turbine, the main differences arise in
the behaviour of their ﬂoating platform. Of most interest is the dynamics of the platform’s pitch
motion since both wind and wave conditions directly affect it. Furthermore, the platform pitch
motion can have direct impact on power output and tower fore-aft and blade loads. Therefore,
the frequency responses of the platform pitch motion to blade pitch, wind and wave inputs are
analysed for each platform.
In previous chapters, the performance of the controllers are compared to the Baseline controller
on their respective platform. To allow for a fair comparison between the platforms, the simula-
tion results are normalised relative to the Baseline controller on a 5 MW onshore wind turbine.
Comparing to an equivalent onshore system allows for:
• comparison between different ﬂoating platforms in terms of power and speed regula-
tion as well as fatigue loads on the main wind turbine components (tower, blades, and
drivetrain), and
• evaluation of the required turbine strength in relative terms to well established onshore
wind turbine designs.
The comparisons are carried out between the baseline controllers on each platform as well as
the best controller on each platform; these are summarised in Table 9.1. For more details on
each controller, please refer to the corresponding platform chapter; the Baseline controller is
described in Chapter 2.
9.2 Platform Pitch Input and Disturbance Sensitivities
Each of the three ﬂoating platforms uses a different principle to achieve hydrostatic stability
and as a consequence have different dynamic properties. Compared to the barge platform,
the TLP has higher stiffness while the spar-buoy has larger pitch inertia. These differences
determine how the blades are able to inﬂuence the platform pitch for regulation as well as how
the disturbances affect the platform pitch.
The platform pitch frequency responses to blade 1 pitch perturbations for each platform are
shown in Figure 9.1. Each frequency response is based on a 21 DOFs state-space model linear-
104

9.2 Platform Pitch Input and Disturbance Sensitivities
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−90−80−70−60−50−40−30−20−100
Frequency (Hz)Magnitude (dB)

Barge
TLP
Spar−buoy1st Tower FA bending Platform Pitch
Figure 9.1: Platform pitch frequency response to blade 1 pitch input
ised at 18 m/s wind speed. The two major resonant frequencies are those of the platform pitch
and ﬁrst tower fore-aft bending mode respectively according to frequency.
To simplify the comparison, consider the frequency response of the barge platform as the me-
dian response. The TLP’s low frequency gain is noticeably lower than the other two platforms.
This difference is due to the high platform pitch stiffness brought by having taught moor-
ing lines. Although the TLP is not as responsive to blade pitch commands as the other two
platforms at low frequencies, it is as responsive as the barge platform at higher frequencies.
Furthermore, since the TLP experiences little pitch motion, blade pitch demand is not as big as
on the other platforms, therefore, the effect of TLP’s stiffness on blade pitch sensitivity at low
frequencies is not considered critical. The TLP’s high stiffness also increases the peak frequency
of the platform pitch.
As discussed in Chapter 8, the spar-buoy platform’s lower pitch natural frequency is due to the
large platform pitch inertia. The lower natural frequency attenuates high frequency blade pitch
commands more than the other two platforms. This effect, coupled with blade pitch saturation,
limits the effectiveness of individual blade pitching on the spar-buoy. Figure 9.2 shows the
frequency content of blade 1 pitch commands for the representative case used for the time
series response of the ﬂoating platforms (Figures 6.6, 7.3 and 8.8); note the logarithmic scale
of the amplitudes in Figure 9.2 and the linear frequency range matches that of Figure 9.1. For
the spar-buoy platform (Figure 9.2c), the SFC and DAC have noticeably more high frequency
blade pitch actuation (higher than 0.2 Hz) than the Baseline controller. At frequencies higher
than 0.2 Hz, the effectiveness of the blade pitch is almost consistently lower than the other
two platforms (Figure 9.1) thus limiting the effectiveness of individual blade pitching because
increasing the controller gain would results in actuator saturation.
The frequency content of the Disturbance Accommodating Controllers on the tension leg (Fig-
ure 9.2b) and spar-buoy (Figure 9.2c) platforms shows an increase in actuation over the other
controllers around the rotor frequency of 0.2 Hz. This increase in once-per-revolution (1p) ac-
105

Chapter 9: Platform Comparisons
00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110−410−310−210−1100101Amplitude
Frequency (Hz)
DAC
SFC
Baseline
(a) Barge platform
00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110−410−310−210−1100101
Frequency (Hz)Amplitude

DAC
SFC
Baseline
(b) TLP platform
00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110−410−310−210−1100101
Frequency (Hz)Amplitude

DAC
SFC
Baseline
(c) Spar-buoy platform
Figure 9.2: Blade pitch frequency content
106

9.2 Platform Pitch Input and Disturbance Sensitivities
10−310−210−1100101−280−260−240−220−200−180−160−140−120−100−80−60−40−20From: Wind
Frequency (Hz)Magnitude (dB)
10−310−210−1100101−280−260−240−220−200−180−160−140−120−100−80−60−40−20From: Waves
Frequency (Hz)
Barge
TLP
Spar−buoy
Figure 9.3: Platform pitch frequency response to disturbance inputs
tuation frequency is due to the DACs actively reducing asymmetric loads on the rotor caused
by wind shear. The DACs reduce the ﬂuctuations in rotor torque and thrust loads thus improv-
ing rotor speed regulation and tower fore-aft bending loads; this is reﬂected in the averaged
DLC results from previous chapters. For the barge platform (Figure 9.2a), there is a moder-
ate increase in actuation around the rotor frequency and thus limited impact on rotor speed
regulation; recall that the barge platform is dominated by incident wave disturbances.
The platforms’ pitch frequency responses to wind speed perturbation and wave moment dis-
turbance inputs are shown in Figure 9.3. The frequency responses are based on the same lin-
earised models used in Figure 9.1.
For wind speed perturbations, the spar-buoy platform’s pitch is most sensitive at low frequen-
cies while TLP is the least sensitive due to its high stiffness. At high frequencies, all the plat-
forms have similar sensitivities to wind speed perturbations. Since wind speed perturbations
affect the platform pitch through the blades, the low frequency magnitude of the pitch response
to wind speed perturbations is similar to that of blade pitch perturbation (Figure 9.1). How-
ever, the magnitude itself is small (around 40 dB for the spar-buoy platform) thus requiring a
large blade pitch or wind speed perturbations to noticeably affect the platform pitch.
The frequency response of a wave disturbance input represents a perturbation in the resultant
wave moment on the platform pitch; it does not include the hydrodynamic interaction between
the incident waves and the platform or the mooring lines. Due to the platform properties, the
behaviour is similar to wind speed perturbations with one exception. Since the wave disturb-
ance enters the system through the platform pitch dynamics, the low frequency response is
constant and does not depend on the dynamics of the load path (blades and drivetrain ﬂexibil-
ities). The frequency response shown is for 1 Nm perturbation of the resultant wave moment,
hence the considerably lower gain. However, the wave moment perturbations are in the or-
107

Chapter 9: Platform Comparisons
der of 108Nm ( +160 dB) or higher, depending on sea conditions and platform hydrodynamics,
thus having a noticeable impact on platform pitch response. Note that the frequency response
to wave moment disturbances shown in Figure 9.3 does not represent the sensitivity of the
platform to incident wave conditions as the latter depends on the platform’s hydrodynamic
properties. That is, a 1 m incident wave, for example, creates a larger resultant wave moment
on the barge platform than on the TLP and spar-buoy platform.
9.3 DLC Results Relative to an Onshore Wind T urbine
In this section the DLC simulation results of the three platforms are compared relative to the
Baseline controller on an equivalent 5 MW onshore wind turbine. The results are normalised
across each individual wind speed bin and then averaged according to the Weibull distribution
to obtain the overall averaged results shown in Figure 9.4. Here, a value of less than 1 indicates
better performance than the onshore system. The direct averaged simulation results of the
Baseline controller (not shown here) agree with DLC 1.2 results presented by Matha [38] for
the three ﬂoating platforms.
Recall that these results are based on simulations only and therefore are bound by the limitation
of the simulation tools used and their associated assumptions. Furthermore, these results are
for the above rated wind speed region only. Below rated wind speed region operation and
region transition on ﬂoating wind turbines are outside the scope of this work.
An interesting result shown in Figure 9.4 is the independence of blade root edgewise bending
fatigue DEL from the ﬂoating platform type, controller, or whether the turbine is mounted
onshore or offshore. The same trend applies for the blade root ﬂapwise bending fatigue DEL
except on the barge platform where excessive platform pitching increases the fatigue DEL.
9.3.1 The Barge Platform
The barge platform experiences large motions due to its sensitivity to incident waves. These
large motions directly affect power and rotor speed regulation and tower loads. For the Baseline
controller on the barge platform, tower FA and SS fatigue loads are 6.9 and 4.48 times that of
an onshore wind turbine respectively. Despite the impressive reductions by the SFC reported
in Chapter 6, tower FA and SS fatigue DELs remain 4.6 and 2.18 times larger than the onshore
wind turbine. Low speed shaft fatigue DEL is also increased by at least 56%. Power ﬂuctu-
ations are almost 4 times larger than the onshore wind turbine, however, the power regulation
of the onshore wind turbine is excellent. In terms of percentage of rated power, the barge plat-
form’s average power ﬂuctuation is around 5.8% of the rated power of 5 MW; slightly higher
than the acceptable 5% error.
The large increase in the fatigue DEL on the main turbine components suggest that, unless
the effects of incident waves on the barge are reduced, the barge platform is not suitable for
deployment in such harsh sea conditions. Perhaps, as Matha suggested [38], the barge platform
can offer a cost-effective solution to sheltered sites such as the Great Lakes in the USA.
108

9.3 DLC Results Relative to an Onshore Wind Turbine
3.97 1.87 2.63 4.03 1.97 5.27 01
Power Error Speed Error Blade Pitch Rate Normalised Performance Index Barge
Baseline
1.74 1.03 6.90 4.48 1.62 1.69 1.03 4.60 2.18 1.56 01
Blade Root
Flapwise
Bending Blade Root
Edgewise
Bending Tower Base
Fore-aft
Bending Tower Base
Side-side
Bending Low Speed
Shaft
Torsion Normalised Performance Index Barge
Baseline Normalised Performance Index Barge
Baseline
Normalised Performance Index Barge
Baseline
5Barge Baseline
Barge SFC 01
Roll Pitch Yaw Normalised Performance Index Barge
Baseline
01
Roll Rate Pitch Rate Yaw Rate Normalised Performance Index Barge
Baseline 3.97 1.87 2.63 1.74 1.03 6.90 4.48 1.62 4.03 1.97 5.27 1.69 1.03 4.60 2.18 1.56 0.99 0.94 0.91 0.97 1.01 1.42 1.01 1.07 0.68 0.57 3.71 0.96 1.03 1.17 0.75 1.11
8.88 1.61 0.45 0.93 0.99 2.12 1.22 0.98
3.22 1.63 3.52 0.93 1.00 1.92 1.11 1.15 012345
Power Error Speed Error Blade Pitch Rate Blade Root
Flapwise Bending Blade Root
Edgewise Bending Tower Base Fore-
aft Bending Tower Base Side-
side Bending Low Speed Shaft
Torsion
RMS of Power, Speed, and Actuator Usage Fatigue DEL Normalised Performance Index Barge Baseline
Barge SFC
TLP Baseline
TLP DAC
Spar Baseline
Spar SFC
RMS of Power, Speed, and Actuator Usage Fatigue DEL
Figure 9.4: Averaged DLC results for all ﬂoating platforms relative to the Baseline controller on an onshore wind turbine
109

Chapter 9: Platform Comparisons
9.3.2 The Tension Leg Platform
For the tension leg platform, it is worthy to note that the performance of the Baseline control-
ler relative to the onshore system is almost at parity across most metrics with the exception
of RMS power and speed errors, RMS blade pitch rate, and tower fore-aft fatigue DEL. As a
result of this parity, the performance of the Disturbance Accommodating Controller relative to
the onshore system almost mirrors that of the offshore case in Chapter 7 with the exception of
the tower fore-aft fatigue DEL. The Disturbance Accommodating Controller manages to have
better power and speed regulation and reduce tower side-side fatigue DEL relative to the on-
shore system. It may be argued that this is an unfair comparison but recall that the Baseline
controller is gain scheduled to account for the nonlinearities present in the system that affect
rotor speed regulation. However, tower fore-aft fatigue DEL remains 17% more than that of
an onshore wind turbine. The almost parity performance of the TLP controllers relative to the
onshore turbine demonstrates the effectiveness of the TLP concept. That is, because platform
motions and rotations are kept small, turbine fatigue loads were of a comparable level to an
onshore wind turbine with the same controller.
From these results, the TLP demonstrates that with slight strengthening of the turbine tower
and when coupled with the improvement in performance brought by using the DAC, it is
possible to deploy wind turbines on a ﬂoating platform without having to redesign the well
established onshore wind turbines.
9.3.3 The Spar-buoy Platform
The dynamic performance of the spar-buoy platform is somewhere between that of the barge
platform and the TLP; platforms motions are not as small as the TLP but not as large as the
barge platform. As a result, its performance in terms of the tower and low speed shaft fatigue
DELs lies between the two platforms. Tower FA and SS fatigue DELs are 2.12 and 1.22 times
the onshore loads respectively with the Baseline controller on the spar-buoy platform; the SFC
reduces these loads to 1.92 and 1.11 times the onshore wind turbine respectively. Power ﬂuc-
tuations for the Baseline controller, that uses constant torque control algorithm, is 8.88 times
that of the onshore wind turbine power variations. These ﬂuctuations are noticeably reduced
by the SFC to a factor of 3.22 through the use of constant power control algorithm. In terms
of percentage of the turbine’s rated power, the Baseline and State Feedback Controllers have
average power ﬂuctuations of 11.52% and 4.6% of rated power respectively.
The increase in loading on the tower would require some degree of strengthening of the tur-
bine tower to withstand these loads. Although no information/properties of the deployed
2.3 MW Hywind prototype are publicly available, it is likely that the turbine tower has been
strengthened and/or the offshore site where the prototype is deployed is relatively “calmer”
than the site used for simulations in this work.
110

9.4 Chapter Summary
9.4 Chapter Summary
Comparing the simulation results obtained in previous chapters and comparing them relative
to an onshore wind turbine allows for direct comparison between the platforms as well as
evaluation of the required turbine strength in relative terms to well established onshore wind
turbine designs.
Simulation results for the Baseline controller on each ﬂoating platform relative to the onshore
wind turbine agree with previously published results. The main beneﬁt of using individual
blade pitching with the State Feedback and Disturbance Accommodating Controllers is the
large reduction in tower fatigue bending loads.
The barge platform experiences large motions due to its sensitivity to incident waves. These
motions induce tower loads that are at least 2.18 times that of the onshore wind turbine. There-
fore, the current design of the barge platform is not suitable for open sea deployment, however,
it may offer a cost effective solution for sheltered sites.
Due to the TLP’s extra stiffness from the taught mooring lines, platform motions are kept to a
minimum resulting in loads that are comparable to the onshore wind turbine. The additional
stiffness reduces the platform’s sensitivity to incident wind and wave disturbances. The DAC
on the TLP is able to improve power and rotor speed errors and tower base side-side DEL
over the onshore wind turbine. Only the tower base fore-aft DEL remains 17% more than
the onshore wind turbine. Therefore, with minor strengthening of the tower and using the
DAC, the TLP makes an excellent candidate for open sea deployment. However, the economic
feasibility of the TLP concept could be a limiting factor.
The spar-buoy platform’s large inertia limits the effectiveness of individual blade pitching with
the current actuator’s saturation limits; this limits the potential of the SFC to improve the plat-
form pitch performance. The spar-buoy platform experiences large enough motions to more
than double the tower fore-aft fatigue loads of an onshore wind turbine. Therefore, strength-
ening or redesign of the tower is required for open sea deployment.
111

Chapter 9: Platform Comparisons
112

10
Wave Disturbance Rejection: A Case Study
Contents
10.1 Wave Disturbance Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
10.2 Case Study: Wave Disturbance Rejection on Floating Wind Turbines . . . . . . . . . . . . 116
10.3 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Floating wind turbines are subject to an additional disturbance input over onshore wind
turbines: waves. These waves can have a large impact on the dynamic performance of
the ﬂoating wind turbines and can induce large loads. Therefore, if a Disturbance Ac-
commodating Controller can minimise the effects of incident waves on turbine motion (espe-
cially roll and pitch motions), then further load reductions are possible to those achieved by the
State Feedback and Disturbance Accommodating Controllers described in previous chapters.
This chapter describes the formulation and implementation of a disturbance accommodating
controller designed to minimise the effects of the resultant wave moment on the platform.
Wave disturbance rejection is unique to this work where a simpliﬁed approach is used to in-
clude the effects of waves on system dynamics for disturbance rejection.
10.1 Wave Disturbance Rejection
Implementing wave disturbance rejection on a ﬂoating wind turbine requires a slightly differ-
ent approach to the general DAC formulation described in Chapter 4. To be able to design a
DAC for wave disturbance rejection (referred to hereafter as DAC for waves ), the effects of the
input disturbances on system states must be known in the form of the Bdmatrix; recall that
DAC formulation requires the linearised system to be in the form given by equation (10.1). For
113

Chapter 10: Wave Disturbance Rejection: A Case Study
wind disturbances, the effect is readily available from FAST linearisation. However, FAST lin-
earisation does not include waves as a disturbance input. Therefore, to be able to implement
wave disturbance rejection, a new Bdmatrix must be evaluated.
D˙xNR =ANRDxNR+BNRDuNR+Bd,NRDud (10.1)
There are many factors that add complexity to this issue. Incident waves are periodic with
a spectrum of frequencies whereas FAST linearises the wind turbine based on a fundamental
frequency that is a multiple of rotor period. Therefore, it will be extremely difﬁcult to correctly
linearise the interaction of incident waves with the periodic wind turbine states. Furthermore,
what parameters can be used to describe the incident waves that can be perturbed during
linearisation? Irregular waves are described by a wave spectrum, signiﬁcant wave height, peak
spectral period, and random seed numbers, none of which are suitable for linearisation. A
simpliﬁed approach is used in this work to allow for wave disturbance rejection.
10.1.1 Simpliﬁed Modelling Approach
Instead of considering some wave parameters as disturbance inputs, their resultant effect on
the platform in terms of moments is considered as the disturbance input. This approach by-
passes all the complexity of the nonlinearity and randomness of the waves and their nonlinear
interaction with the platform.
The set of nonlinear equations of motion for the ﬂoating system, equation (10.2), is in the same
format used by FAST [32] where qis a vector of the DOFs modelled, and Mis the mass matrix.
M
q,u,t
¨q=f
˙q,q,u,ud,wind,t
(10.2)
Given an incident wave with an arbitrary direction, the resultant moment vector is expressed
along the global inertial axes (roll, pitch, and yaw). This additional moment vector results in
a term appended to equation (10.2) giving equation (10.3), where ud,wave is a 31 moment
vector (moments long the inertial axes) and Fd,waveis ando f3 matrix that applies the resultant
moments to the correct differential equations. The term Fd,waveud,wave is a nonlinear function of
wave height, wave period, current, platform yaw angle, and wave direction.
M
q,u,t
¨q=f
˙q,q,u,ud,wind,t
+Fd,waveud,wave (10.3)
Equation (10.3) is in a generic form that can accommodate incident waves with changing dir-
ection. For simplicity, it is assumed that platform yaw angles remain small such that the wave
moment components only act on their respective axis. For example, if waves are modelled to
act only in the pitch direction for DAC implementation, then the resultant pitch moment only
acts on the pitch DOF and has no components in the roll or yaw directions. This assumption
reduces Fd,waves to a known time-invariant boolean matrix.
Linearisation of equation (10.3) assuming still water (no waves) and without underwater cur-
rents results in equation (10.4) where Cdis the damping matrix, Ksis the stiffness matrix, and F
114

10.1 Wave Disturbance Rejection
is the actuators gain matrix for a 2ndorder system. All the terms in equation (10.4) except for the
last term on the right side of the equation can be obtained numerically from FAST linearisation.
M(y)D¨q+Cd(y)D˙q+Ks(y)Dq=F(y)Du+Fd,wind (y)Dud,wind +Fd,waveDud,wave (10.4)
where
ud,wave =Dud,wave +uop
d,wave
The moment vector operating point uop
d,wavecontains the hydrostatic and mooring line moments
that keep the system in equilibrium at the operating point. Now, let
Dud=h
Dud,windDud,waveiT
and
Fd(y)=h
Fd,wind (y)Fd,wavei
(10.5)
such that
M(y)D¨q+Cd(y)D˙q+Ks(y)Dq=F(y)Du+Fd(y)Dud (10.6)
Equation (10.6) is a standard linearised second order state-space equation. All FAST linearisa-
tions used in this work are in the second order form (to give access to the mass, damping, and
stiffness matrices) which are then converted to ﬁrst order state-space models for control design.
The ﬁrst order representation of equation (10.6) is given by equation (10.7) where the A(y),
B(y), and Bd(y)matrices can be calculated using equations (10.8) to (10.10) respectively where
n,m, and ndare the number of states, control inputs, and disturbance inputs respectively.
D˙x=A(y)Dx+B(y)Du+Bd(y)Dud (10.7)
where
A(y)="
0 Indo fndo f
M(y)1Ks(y)M(y)1Cd(y)#
nn(10.8)
B(y)="
0
M(y)1F(y)#
nm(10.9)
Bd(y)="
0
M(y)1Fd(y)#
n(nd,wind +nd,wave )(10.10)
Since the new disturbance inputs vector contains wind and wave disturbance inputs, the Bd
matrix is partitioned accordingly in equation (10.11). The ﬁrst element Bd,wind is readily avail-
able from FAST linearisation. By substituting equation (10.5) into equation (10.10), the second
115

Chapter 10: Wave Disturbance Rejection: A Case Study
element Bd,wavecan be calculated using equation (10.12).
Bd(y)=h
Bd,wind (y)Bd,wave (y)i
(10.11)
="
0 0
M(y)1Fd,wind (y)M(y)1Fd,wave (y)#
)Bd,wave (y)="
0
M(y)1Fd,wave (y)#
nnd,wave(10.12)
The above derivation allows for a DAC design that rejects wind speed perturbations only, res-
ultant wave moment perturbations only, or both depending on which Bdmatrix is used. Once
the ﬁnal form of the Bdmatrix is obtained, MBC transformation is used to facilitate the time-
invariant DAC design discussed in Chapter 4.
10.2 Case Study: Wave Disturbance Rejection on Floating Wind T ur-
bines
To verify that the aforementioned approach minimises the effects of the wave moment on a
ﬂoating wind turbine, it is implemented on a low-order linearised model of the spar-buoy plat-
form. The spar-buoy platform is chosen as a test case because it is less sensitive to incident
waves than the barge at high frequencies (see Figure 9.3) and not as stiff as the TLP . Nonlin-
ear simulations are then used to evaluate the performance of DAC for waves where actuator
saturation and system nonlinearities have an impact on performance. Similar to wind speed
disturbance rejection, it is assumed that the wave moment cannot be measured and therefore a
disturbance estimator is used.
10.2.1 Linear Time-varying Model
The linear model is based on a 2 DOFs model (rotor and platform pitch DOFs) transformed in
the non-rotating frame of reference; MBC transformation is used to account for the periodicity
of the wind turbine. The linear model is implemented without actuator saturation to test the
full potential of the Disturbance Accommodating Controller.
The ﬂoating wind turbine is subjected to constant periodic wave moments of a similar mag-
nitude observed in nonlinear simulations of the spar-buoy platform. Wind speed is held con-
stant at 18 m/s – the linearisation point – thereby having no impact on the turbine dynam-
ics. The DAC is implemented with a gain scaling factor ato “tune” the controller such that
uNR=KNRxNR+aGd,NRˆz;aranges from 0 to 1.
The disturbance estimator is designed with an assumed waveform of a periodic input with
an offset such that ˆud=asin(wt)+bcos(wt)+c. The waveform model is given by equa-
tions (10.13) – (10.15). For simplicity, the assumed waveform frequency wused to design the
116

10.2 Case Study: Wave Disturbance Rejection on Floating Wind Turbines
disturbance estimator matches the incident wave moment period in the linear simulation.
G=2
640 0 0
0 0 1
0w203
75 (10.13)
Q=h
1 1 0i
(10.14)
z(0)=h
c b a wiT
(10.15)
The simulation starts with a=0 (i.e. the DAC becomes a State Feedback Controller) and the
DAC is fully activated ( a=1) at t=50 seconds. Figure 10.1 shows the output of the linear
simulation. When the DAC is activated, there is a large increase in blade pitch actuation. This
increased actuation is generating the required moment to resist the incident wave moment; of
course, such actuation magnitude and rate are not realistic for a ﬂoating wind turbine such as
the spar-buoy.
The estimate of the incident wave moment closely follows the actual moment (Figure 10.1).
Consequently, the restoring moment generated by the blades is in phase with the incident wave
moment and, therefore, the DAC is able to reject almost all of the wave effects on system states.
Note that complete cancellation can only occur if the disturbances enter the system through
the same channel as the actuators [47]; for ﬂoating wind turbines, the wave moment affects
the system through the ﬂoating platform while the restoring moments are generated via the
blades, hence, wave disturbance cancellation is not possible.
Table 10.1 summarises the effectiveness of the DAC for waves on a linear system with different
values of the gain scaling factor a. Recall that to minimise or cancel the effect of input disturb-
ances, the normkBaGd+BdQkmust be minimised (equation (4.6)). When the DAC is fully
activated, the norm is essentially zero when compared to the full effect of disturbance states
(a=0). Therefore, for wave disturbance rejection on a linear system, the DAC can be con-
sidered to be cancelling the effects of incident wave moments. When the DAC is operating at
10%, the norm is reduced by 10%; the reduction in the norm is linear with different values of a.
Figure 10.1 shows that after the DAC is activated and the effect of incident wave moment is
cancelled, the platform pitch angle enters a damped oscillatory response in which the perform-
ance is determined by the design of the SFC-part of the DAC. In fact, the damping ratio of this
motion is calculated, using the logarithmic decrement approach described in [87, p. 598], to
be that of the closed loop damping ratio of the system which veriﬁes the analysis. Since wind
Table 10.1: Effect of DAC gain scaling factor aonkBaGd+BdQkfor a 2 DOFs linear wind
turbine model
akBaGd+BdQkComment
0.0 1.41 Full effect of disturbance states on system states
0.1 1.27 DAC operating at 10% capacity
1.0 4.11010DAC operating at 100% capacity
117

Chapter 10: Wave Disturbance Rejection: A Case Study
0 50 100 150 200 250 300 -0.5 00.5 11.5 22.5 x 10 8Moment (Nm) Wave Moment

0 50 100 150 200 250 300 12 12.05 12.1 12.15 12.2 ω (rpm) Rotor Speed
0 50 100 150 200 250 300 00.5 11.5 22.5 3Angle (deg) Platform Pitch Angle Estimate Actual
0 50 100 150 200 250 300 -50 050 100
Time (sec) θ (deg) Blade Pitch

θ1θ2θ3
Figure 10.1: Wave disturbance rejection on a linear 2 DOFs model (DAC activated at t=
50 seconds)
118

10.2 Case Study: Wave Disturbance Rejection on Floating Wind Turbines
speed is kept constant, the ﬂuctuations in rotor speed are primarily due to platform pitching
velocity affecting the wind speed relative to the rotor.
When the disturbance waveform model only accounts for the wave moment disturbance, a
wind speed perturbation is incorrectly interpreted as an incident wave thus leading to a wrong
moment estimate. Because the rotor is generating the large wave minimising moment, an er-
ror in the estimate causes this large moment to be applied out of phase thus exacerbating the
platform pitch moment rather than minimising it. To overcome this limitation, a model of the
wind speed perturbation is included in the disturbance waveform model.
This case study demonstrates that wave disturbance rejection based on the approach described
in §10.1 is valid for linear systems.
10.2.2 Nonlinear Periodic Model
This case study is used to test the robustness of the DAC for waves when simulated using
a nonlinear 2 DOFs model of the spar-buoy with constant wind, regular waves, and actuator
saturation. To establish the limit for continuous blade saturation, ﬁve simulations are carried
out using a different value of the DAC gain scaling factor a.
Figure 10.2 shows the trends of selected performance metrics (relative to the Baseline control-
ler) with a. Note that a=0 represents a SFC without any feed-forward disturbance rejection
component. Platform pitch and pitch rate regulation are noticeably improved for a60.1 where
platform pitch error and pitch rate are reduced by 35% and 20% relative to the baseline con-
troller respectively. For simulations with a>0.15, the blade pitch rate is periodically saturated
to8 deg/s for longer periods as shown in Figure 10.3 and performance degradation is re-
ﬂected in ﬁgures 10.2 and 10.4. When the blades are frequently saturated for a>0.15, the
improvement trend in platform pitch regulation is reversed and rotor speed error is drastically
increased.
0 0.05 0.1 0.15 0.2−100−50050100150200% ChangeRotor Speed and Tower FA DEL
DAC gain scaling factor, α
RMS Rotor Speed Error
Tower FA DEL
0 0.05 0.1 0.15 0.2−35−30−25−20−15−10−50% ChangeRMS of Platform Pitch
DAC gain scaling factor, α
Platform Pitch Error
Platform Pitch Velocity
Figure 10.2: Wave disturbance rejection performance relative to the Baseline controller on a
nonlinear 2 DOFs model
119

Chapter 10: Wave Disturbance Rejection: A Case Study
0 5 10 15 20 25 30−12−10−8−6−4−2024681012
Time (sec) Pitch rate (deg/s)

α = 0.1 α = 0.15 α = 0.2
Figure 10.3: Blade 1 pitch rates with different a
The main purpose for implementing wave disturbance rejection is to reduce platform motion
such that tower loads caused by the offset gravity load of the Rotor-Nacelle Assembly (RNA)
is reduced. However, despite the DAC for waves reducing platform pitch motion and pitch-
ing velocity, tower loads suffer a signiﬁcant increase (up to 67% increase for a non-saturated
actuator). This increase in tower fore-aft load can be explained by studying the load path on
the tower when a wave moment hits the tower (Figure 10.5). When the ﬂoating wind turbine
is subjected to an incident wave moment ( MWAVE in Figure 10.5), the DAC would, ideally, gen-
erate an equal and opposite moment ( MDAC) instantly. These two moments bend the tower in
the same direction thus increasing the bending loads in the fore-aft direction. This increased
bending load is larger than the load reduction brought by reducing the moment created by the
offset gravity load of the Rotor-Nacelle Assembly ( FRNA).
Figure 10.5 illustrates a fundamental limitation to minimising the effects of wave moments on
platform motion by using the blades to generate the restoring moment. Therefore, to reject
wave disturbances and reduce tower loads, additional actuators are needed to generate the
wave minimisation moment at the platform or mooring line level such that the load is not
transferred through the tower. Adding and analysing the effectiveness of additional actuators
on ﬂoating wind turbines is beyond the scope of this work.
10.2.3 Case Study Summary
Despite the effectiveness of wave disturbance rejection on a linear wind turbine model, there
are several factors that limit the performance of DAC for waves on a nonlinear (or more real-
istic) wind turbine model.
• The incident wave moments are large in magnitude requiring large actuation forces to
minimise their effect. Therefore,
120

10.2 Case Study: Wave Disturbance Rejection on Floating Wind Turbines
0 20 40 60 80 100 120 140 160 180 2001111.51212.513ω (rpm) Rotor Speed

α = 0.1 α = 0.15 α = 0.2
0 20 40 60 80 100 120 140 160 180 200−10123Angle (deg)Platform Pitch

0 20 40 60 80 100 120 140 160 180 200051015202530
Time (sec)θ (deg) Blade Pitch

Figure 10.4: Wave DACs with different asimulated with a nonlinear 2 DOFs model
–actuator saturation becomes an important limiting factor in the successful imple-
mentation of wave disturbance rejection; and
–accuracy of the disturbance estimates becomes important as a relatively small estim-
ation error causes the large actuation force(s) to be applied out of phase which may
excite the platform motions rather than reducing them.
• The approach described in §10.1 and the underlying DAC theory are based on linear
systems. Therefore, system nonlinearities can have an impact on performance especially
if the DAC is forcing the system or the actuator far away from the linearisation point.
For example, Figure 10.1 shows the blade pitch angles range from -50° to 80°. Saturation
issues aside, the effectiveness of the blade pitch at these angles varies greatly from the
121

Chapter 10: Wave Disturbance Rejection: A Case Study
Offset
Figure 10.5: Wave minimisation moment load path
linearisation point12due to the nonlinearities associated with the blade aerodynamics
and blade pitch angle.
• Using the blades to generate the wave minimising moment increases the bending mo-
ment on the tower despite the reduction in platform motions. For reducing tower loads,
the wave minimising moment must not be transferred through the tower.
Due to the above limitations, further analysis of wave disturbance rejection using full DOFs
nonlinear simulation with stochastic wind and irregular waves is not warranted for this work.
The simpliﬁed waveform model used in the above approach assumes a constant wave fre-
quency. Irregular waves are usually modelled using a spectrum of frequencies. However, they
can also be modelled as having a dominant frequency that slowly changes with time and a ran-
domly varying amplitude depending on sea conditions. Appendix (E) describes the limitations
of this approach and introduces an empirical approach to deal with periodic disturbances with
a slowly changing frequency.
12The DAC, based on the linear model, assumes the blade pitch effectiveness is constant for all operating blade
pitch angles.
122

10.3 Chapter Summary
10.3 Chapter Summary
Implementation of wave disturbance rejection requires manipulation of the linearised state-
space model produced by FAST because FAST linearisation currently does not include waves
as disturbance inputs. By only considering the resultant moments due to incident waves as dis-
turbance inputs, the effects of these moments on system states can be calculated and thereby fa-
cilitating DAC design. This simpliﬁed approach bypasses all the nonlinear interaction between
the waves and the platform structure but it requires a disturbance estimator because direct
measurement of the resultant moments is not possible.
Implementing wave disturbance rejection on a linear model of a ﬂoating wind turbine shows
that the Disturbance Accommodating Controller can cancel the effects of input periodic wave
moments. However, due to actuator saturation and system nonlinearities most of the beneﬁts
of wave disturbance rejection are lost when applied on a nonlinear wind turbine model us-
ing FAST. Furthermore, using the turbine blades to generate the wave minimisation moment
results in increasing the tower bending loads despite reductions in platform motion.
123

Chapter 10: Wave Disturbance Rejection: A Case Study
124

11
Conclusions and Recommendations
Having no rigid foundations, ﬂoating offshore wind turbines experience additional
motions in 6 directions: platform surge, sway, heave, roll, pitch, and yaw. These ad-
ditional motions, especially the platform pitch motion, can signiﬁcantly affect power
regulation and turbine loads. Interaction with the waves adds another source of loading on
the wind turbine as well as inducing platform motions; incident waves are considered as a
disturbance input from a control system point of view.
There are several ﬂoating wind turbine designs currently being investigated with some of them
reaching a full scale prototype stage. In this work, only the three main ﬂoating wind turbine
concepts are considered. Each platform uses a different principle to achieve hydrostatic sta-
bility. The three ﬂoating concepts are: a buoyancy stabilised barge platform, a mooring line
stabilised tension leg platform (TLP), and a ballast stabilised spar-buoy platform.
The main objective of this research is to quantify the performance of multi-objective state feed-
back and disturbance accommodating controllers applied to the three main ﬂoating platform
concepts. The results presented in this thesis are based entirely on hi-ﬁdelity simulations and,
therefore, the results are bound by the limitations of the simulation tools used and their as-
sociated assumptions. However, the results are presented in a relative sense with the main
conclusions drawn based on physical insight of the ﬂoating systems.
The controllers implemented to date on ﬂoating wind turbines range from a Gain Scheduled
Proportional-Integral (GSPI) controller to account for system nonlinearities over a wide range
of wind speeds, a variable power pitch controller that changes the captured power to improve
platform pitching, to passive and active tuned mass dampers to add damping to platform pitch.
All of these controllers have mainly used collective blade pitching for their actuation. None of
the implemented controllers use multi-objective state feedback or disturbance accommodating
125

Chapter 11: Conclusions and Recommendations
controllers to improve platform pitch response andregulate rotor speed in a single controller
implementation.
Table 11.1 summarises the state of the art in ﬂoating wind turbine control. The main contri-
butions of this thesis are included in the last three rows of the table. These controllers use
individual blade pitching in a multi-objective controller implementation for state feedback reg-
ulation and disturbance rejection of wind speed and wave moment perturbations.
To help categorise the main conclusions of this thesis, this chapter answers the 6 research ques-
tions introduced in Chapter 1:
1.Does using individual blade pitching help improve the performance over collective blade
pitching on a ﬂoating wind turbine?
Individual blade pitching (IBP) allows the controller to create asymmetric loads on the
rotor in addition to the symmetric loads that can be created using collective blade pitch-
ing. These asymmetric loads help in better regulating some objective/states, such as the
platform pitch DOF, over collective blade pitching alone. Individual blade pitching also
prevents the controller from issuing blade pitch commands that conﬂict when simultan-
eously regulating rotor speed and platform pitch motion (or tower fore-aft motion, to a
lesser extent, on onshore wind turbines). IBP effectively increases the number of avail-
able actuators from 2 (generator torque and collective blade pitch angle) to 4 (generator
torque and each blade’s pitch angle). Therefore, individual blade pitching does help im-
prove the performance on ﬂoating wind turbines. For example, IBP with a state feedback
controller is able to reduce platform roll, pitch, and yaw rates on the barge platform by
48%, 37%, and 60% respectively relative to the Baseline controller while maintaining rotor
speed regulation to a similar level.
2.Similarly, does using a multi-objective controller help improve the performance relative
to a single-objective Gain Scheduled Proportional-Integral controller on ﬂoating wind
turbines, consistent with ﬁndings for onshore wind turbines?
Two types of multi-objective controllers are implemented on the three ﬂoating platforms:
State Feedback Controller (SFC) and Disturbance Accommodating Controller (DAC) for
rejecting wind speed perturbations. Simply put, the DAC consists of the SFC with a
feed-forward term for rejecting modelled persistent disturbances. The SFC is implemen-
ted with full state feedback as adding a state estimator only degrades the performance.
Therefore, the state estimator is excluded from the system design because the objective is
to assess the effectiveness/potential of advanced control strategies on ﬂoating platforms
under ideal estimation conditions.
Overall, both the SFC and DAC result in better performance in terms of better tower load
reductions and reduced platform motions relative to the Baseline controller – collective
blade pitch GSPI. The magnitude of relative improvement depends on the performance
of the Baseline controller, the dynamics of each platform, its responsiveness to individual
blade pitching and sensitivities to external wind and wave disturbances. For example,
the SFC on the barge platform reduces the platform roll angle by 41% relative to the
126

Table 11.1: Summary of most important controllers applied on ﬂoating wind turbines to date
Controller
NameBlade Pitch
ControlTorque
ControlAdditional Control Features Simulation Code Number of
SimulationsModel
FidelitySimulation
RegionsPlatform
GSPI CBP GSPI Constant
powerTTF loop, pitch to stall, or detuned
gainsFAST Extensive High 2, 3 Barge, TLP ,
Spar-buoy
GSPI
HywindCBP GSPI Constant
torqueConstant speed region just below
rated with PI torque control loopHAWC2 /
SIMO-RIFLEXLimited High 2, 3 Hywind
spar-buoy
VPPC CBP GSPI Constant
torqueVariable rotor speed set-point. IBP
for blade load reductionFAST Limited High 3 Barge
EBC Unknown Unknown Wind turbine estimator to hide
tower dynamicsHywindSim /
SIMO-RIFLEXLimited Low 3 Hywind
spar-buoy
ASC Unknown Unknown Tuned mass damper with active
controlFAST-SC Moderate High 3 Barge
IBP SFC IBP SFC Constant
Power + SFCFull State Feedback (no state
estimator)FAST Extensive High 3 Barge, TLP ,
Spar-buoy
DAC
WindIBP SFC Constant
Power + SFCWind speed disturbance rejection
onlyFAST Extensive High 3 Barge, TLP ,
Spar-buoy
DAC
WavesIBP SFC Constant
Power + SFCWave moment disturbance
rejection onlyFAST Limited Low 3 Spar-buoy
Legend:
ASC Active Structural Control TTF tower-top feedback
CBP Collective Blade Pitch VPPC variable power pitch control
DAC Disturbance Accommodating Control
EBC Estimator Based Control Number of Simulations Guide:
GSPI Gain Scheduled Proportional-Integral control Limited <10
IBP Individual Blade Pitch Moderate <100
SFC State Feedback Control Extensive >100
127

Chapter 11: Conclusions and Recommendations
platform’s Baseline controller. The SFC on the TLP only manages an 8% reduction due to
the TLP’s high stiffness in the roll direction resulting in very small rolling motion for the
Baseline and SFC.
3.Can a Disturbance Accommodating Controller designed to reject wind and wave disturb-
ances help improve the performance?
On the barge platform, there are no differences in performance between the SFC and
DAC for wind speed disturbance rejection because of the platform’s sensitivity to incident
waves thereby dominating the platform motions. However, on the tension leg and spar-
buoy platforms, the DAC better regulates rotor speed thus improving power quality and
further reduces tower fore-aft bending loads. These improvements are obtained through
signiﬁcant increase in blade pitch actuation without reaching saturation. The increase in
blade pitch actuation negatively affects platform roll and yaw motions on the spar-buoy
platform.
Rejecting the effects of incident wave moments on the ﬂoating platform using the rotor
increases the bending on the tower thus defeating one of the main reasons for implement-
ing the DAC. The increase in tower bending is caused by the load path of the restoring
moment generated at the rotor going through the tower; ideally, this restoring moment
should be generated at the platform level or lower. Furthermore, to cancel the effects
of incident wave moments, the restoring moment requires a large actuation force that,
realistically, cannot be generated using the blades.
4.How will the three ﬂoating platforms perform when compared to each other under nor-
mal operating conditions especially when controlled by multi-objective controllers?
Comparing between platforms is carried out by normalising the simulation results re-
lative to an equivalent onshore wind turbine. With a single-objective GSPI controller,
the TLP has the best overall performance, followed by the spar-buoy and then the barge
platform. Despite having a different magnitude in relative improvement in performance
brought by implementing the multi-objective controllers on each platform, the ranking of
the platforms’ performance remains unchanged. However, the resultant loads are closer
to that of the onshore wind turbine with the multi-objective controllers.
The barge platforms is the most sensitive to incident waves due to its large water-plane
area forcing it to ride the waves. As a results, it experiences the largest motions and thus
the largest tower and blade loads. Multi-objective controllers help reduce these motions
and loads, but even the massively reduced loads remain too high for practical deploy-
ment in open seas. For example, with the Baseline controller, tower fore-aft (FA) and
side-side (SS) fatigue loads are 6.9 and 4.48 times higher than the onshore wind turbine
tower loads respectively. The SFC manages to reduce these load factors to 4.6 and 2.18
for tower FA and SS loads respectively.
Due to the TLP’s extra stiffness in the roll, pitch, and heave motions brought by having
taught mooring lines, it experiences signiﬁcantly less rolling and pitching motion than
the barge platform. Furthermore, since most of the TLP’s hull is underwater, its sensitiv-
ity to incident waves is also minimised. As a result of these features and when coupled
128

with the improvement in performance brought by using the Disturbance Accommodat-
ing Controller, the TLP’s performance closely resembles that of an onshore wind turbine
with slightly higher tower fore-aft bending (17%) and low speed shaft torsion (11%) fa-
tigue loads. Compare these results to the loads of the Baseline controller on the TLP with
42% increase in tower FA load and 7% increase in low speed shaft load relative to the on-
shore wind turbine; the increase in low speed shaft load for the DAC is due to increased
blade pitch actuation.
The spar-buoy platform’s motion envelope is not as large as the barge platform but not as
good as the TLP’s. Therefore, in terms of loads, it falls between the other two platforms.
The effectiveness of individual blade pitching and hence the multi-objective controllers
is limited on the spar-buoy platform due to its large pitch inertia; performance is mar-
ginally better than the GSPI. For example, tower FA fatigue loads ratios to the onshore
wind turbine are 2.12 and 1.92 for the Baseline and state feedback controllers respectively.
The large pitch inertia results in a low natural frequency that attenuates important high
frequency individual blade pitching commands.
5.Is it possible to maintain fatigue loads to a level comparable to an onshore wind turbine
of similar size?
The TLP has the best performance in terms of fatigue loads relative to an onshore wind
turbine. Tower base fore-aft bending and low speed shaft torsion fatigue damage equi-
valent loads (DELs) are only on average 17% and 11% higher than an onshore wind tur-
bine respectively with a Disturbance Accommodating Controller. The DAC manages to
reduce tower base side-side bending fatigue DEL by 25% relative to the onshore wind
turbine with a GSPI controller.
The other two platforms experience loads that are much higher than the onshore wind
turbine loads especially for the tower base fore-aft bending loads; for example, tower
fore-aft bending loads on the barge and spar-buoy platforms are, on average, at least 4.6
and 1.92 times those of an onshore wind turbine respectively. These large loads make the
barge and spar-buoy platforms impractical in their current form for open sea deployment.
Fatigue DELs for the blade root edgewise bending on all three platforms and blade root
ﬂapwise bending on the tension leg and spar-buoy platforms are indifferent to the plat-
form and controller used; these loads remain similar to the loads on an onshore wind
turbine.
6.With the addition of the platform’s 6 degrees of freedom, are the current actuators cap-
able of addressing the control needs of the system?
The answer to this question depends on the control objectives; for example, wave disturb-
ance rejection with the current actuators is not possible. Actuator saturation especially for
the blade pitch actuator does limit the potential of the implemented multi-objective con-
trollers; however, the performance improvements obtained with the current saturation
limits are more than satisfactory. Of course, additional actuators that directly affect plat-
form motions are expected to improve the performance noticeably.
129

Chapter 11: Conclusions and Recommendations
In addition to answering the above questions, an interesting behaviour is observed for ﬂoating
wind turbines. There is coupling between platform pitch and roll in the presence of a controller
that only regulates the platform pitch motion and not both. This coupling is caused by the way
the blades affect the platform roll and pitch motions and asymmetry in the rotor due to rotor
pre-cone, shaft tilt, and wind shear. The result is that the controller induces a rolling moment
as it regulates platform pitch. This coupling applies to any controller but is exacerbated by
individual blade pitching. This coupling is resolved by including the roll degree of freedom
(DOF) in the linear state-space model used for controller design.
Finally, for ﬂoating wind turbines, the recommended state-space model order for control design
should include the following 6 DOFs: platform roll, pitch and yaw; ﬁrst tower side-side bend-
ing mode; rotor and drivetrain twist. These DOFs are included to improve performance, re-
solve coupling, and maintain closed loop stability of the ﬂoating system.
Below is a list of topics that are yet to be explored yet have the potential to improve the response
of ﬂoating systems when coupled with advancements in other wind turbine ﬁelds (such as
blade design and materials). These topics are listed below in no particular order of importance.
• Veriﬁcation of simulation and controller responses against full scale prototypes. This is
a critical issue. The veriﬁcation process may take some time, but when successful veri-
ﬁcation of simulation tools is achieved, it will increase the conﬁdence in the predicted
controllers’ performance.
• A detailed look at region transition to and from above and below rated for ﬂoating wind
turbines is yet to be investigated. There is a potential for limit cycle oscillations (continu-
ously switching between regions regardless of wind conditions) due to the lack of rigid
foundations.
• The effectiveness of passive (or active) structural dampers in extreme conditions. A re-
duction in platform motions in extreme conditions where the blades are feathered is ex-
pected. However, the extent of this reduction needs to be established.
This work showed that the implemented controllers’ performance is limited mainly due to
actuator saturation, under-actuation, and system nonlinearities. Therefore, the following is
suggested:
• Including additional active or passive actuators on the platform to help regulate the plat-
form motions and reduce the usage of the blade pitch actuators. Additional actuators
may help improve the motion response of the ﬂoating platform. An example would be
to use structural control techniques with individual blade pitching in a single controller
implementation to regulate rotor speed and reduce platform pitching.
• Applying more advanced controllers such as model predictive and nonlinear control on
such systems that take actuator and state saturation and other system nonlinearities into
account. The beneﬁts of implementing such complex controllers are yet to be evaluated
on ﬂoating wind turbines.
130

Appendices
131

A
MBC Transformation of Linear State-Space
Models
Multiblade coordinate system transformation of linear state-space systems is derived
here. The derivation of MBC transformation for second order equations of motion
is described in detail by Bir [48]. MBC transformation of state-space systems is only
brieﬂy described by Bir giving the ﬁnal transformation results, however.
A.1 Overview of Approach and Notation
In this derivation we will use the same notation used by Bir [48] where possible; some variable
names are changed as they conﬂict or don’t match with previously deﬁned variables.
The equations of motion of a 2ndorder dynamic system is given by equation (A.1). The ele-
ments in the DOFs vector qare sorted such that the ﬁxed DOFs come ﬁrst followed by those in
the rotating frame of reference.
M¨q+Cd˙q+Ksq=Fu+Fdud (A.1)
MBC transformation is a linear transformation between the non-rotating (NR) and the mixed
frames of reference. Equation (A.2) deﬁnes this transformation for the DOFs vector q.
q=T1q
NR(A.2)
133

Appendix A: MBC Transformation of Linear State-Space Models
The transformation matrix T1, given by equation (A.3), consists of block diagonal sub-matrices
where Fnis the number of states deﬁned using ﬁxed coordinates. Note that T1is a periodic
matrix since the transformation sub-matrix ˜tis a function of rotor azimuth. For brevity of de-
rivation the periodicity is implied and the notation is omitted. The transformation sub-matrix
˜t, given by equation (A.4), is the fundamental transformation matrix used to transform a set of
three rotating states between the rotating and non-rotating coordinate systems where yb, given
by equation (A.5), is the azimuth angle of blade b.
T1=2
66664IFnFn
˜t
…
˜t3
77775(A.3)
˜t=2
641 cos y1siny1
1 cos y2siny2
1 cos y3siny33
75 (A.4)
yb=Wt+(b1)2p
Nblades(A.5)
Similarly, equations (A.6) and (A.7) deﬁne the transformations for the control inputs and out-
put measurements respectively where the transformation matrices Tcand Toare deﬁned by
equations (A.8) and (A.9) respectively. Fcand Foare the number of control inputs and outputs
deﬁned using ﬁxed coordinates respectively.
u=TcuNR (A.6)
y=Toy
NR(A.7)
Tc=2
66664IFcFc
˜t
…
˜t3
77775(A.8)
To=2
66664IFoFo
˜t
…
˜t3
77775(A.9)
Similar to the derivation of MBC transformation equations for 2ndorder equations of motion,
we need to differentiate vectors and matrices with respect to time. Below, we deﬁne some
relationships that will be useful for the derivation. Let
134

A.2 The State Equation
˜t2=2
640siny1cosy1
0siny2cosy2
0siny3cosy33
75
˜t3=2
640cosy1siny1
0cosy2siny2
0cosy3siny33
75
such that
˙˜t=W˜t2 (A.10)
˙˜t2=W˜t3 (A.11)
Similarly, let
T2=2
666640FnFn
˜t2
…
˜t23
77775
T3=2
666640FnFn
˜t3
…
˜t33
77775
such that
˙T1=WT2 (A.12)
˙T2=WT3 (A.13)
Note that equations (A.12) and (A.13) utilise the relationships deﬁned by equations (A.10) and
(A.11).
A.2 The State Equation
In order to make use of the already deﬁned transformation equation (equation (A.2)) for a
second order state-space model given by equation (A.1), we must deﬁne the system in state-
space notation given by equation (A.14) by deﬁning a state vector. The state vector is deﬁned
by equation (A.15) while its non-rotating equivalent is given by equation (A.16).
135

Appendix A: MBC Transformation of Linear State-Space Models
˙x=Ax+Bu+Bdud (A.14)
x=h
q˙qiT
(A.15)
xNR =h
q
NR˙q
NRiT
(A.16)
To transform equation (A.14) to the non-rotating frame, we must ﬁrst derive the transformation
equations of the variables ˙x,x, and u; recall that we assumed the disturbance inputs udis
always in the ﬁxed frame. For the actuators vector u, the transformation equation is deﬁned by
equation (A.6).
For the states vector, we start by differentiating the equation (A.2) with respect to time and
substituting in equation (A.12). The result is given by equation (A.17).
˙q= ˙T1q
NR+T1˙q
NR
=WT2q
NR+T1˙q
NR(A.17)
Substituting equations (A.2) and (A.17) into equation (A.15) and in conjunction with equa-
tion (A.16) we arrive at equation (A.18). Note that equation (A.18) is actually equation (3.9)
that was used to deﬁne the state transformation in Chapter 3.
x="
T1q
NR
WT2q
NR+T1˙q
NR#
="
T1 0
WT2T1#
xNR
)x=TsxNR (A.18)
where
Ts="
T1 0
WT2T1#
The transformation equation for ˙xcan be derived by differentiating equation (A.18) with re-
spect to time as shown by equation (A.19). The time differential of the state transformation
matrix Tsis given by equation (A.20).
˙x= ˙TsxNR+Ts˙xNR (A.19)
˙Ts="˙T1 0
˙WT2+W˙T2˙T1#
="
WT2 0
˙WT2+W2T3WT2#
(A.20)
136

A.3 The Output Equation
Substituting equation (A.20) into equation (A.19) and collecting similar terms of ˙q
NRin the
second row of equations of ˙xresults in the transformation equation for ˙xgiven by equa-
tion (A.21).
˙x="
T1 0
WT2T1#"
˙q
NR
¨q
NR#
+"
WT2 0
˙WT2+W2T3WT2#"
q
NR
˙q
NR#
="
T10
0T1#
˙xNR+"
WT2 0
˙WT2+W2T32WT2#
xNR (A.21)
Finally, substituting equations (A.18), (A.21), and (3.10) into the state equation (equation (A.14)),
we get
"
T10
0T1#
˙xNR+"
WT2 0
˙WT2+W2T32WT2#
xNR =ATsxNR+BTcuNR+Bdud
Rearranging for ˙xNRwe get equation (A.23) which is the same as equation (3.7) and matrices
ANR,BNR, and Bd,NRcan be inferred from equation (A.22).
˙xNR ="
T1
10
0 T1
1#"
ATs"
WT2 0
˙WT2+W2T32WT2##
xNR+
"
T1
10
0 T1
1#
BTcuNR+
"
T1
10
0 T1
1#
Bdud (A.22)
˙xNR =ANRxNR+BNRuNR+Bd,NRud (A.23)
A.3 The Output Equation
The output equation for a state-space model is given by equation (A.24).
y=Cx+Du+Ddud (A.24)
To obtain the output equation transformed in the non-rotating frame, we substitute equations
(A.6), (A.7), (A.18), and (A.21) into equation (A.24). The result is equation (A.7) which is the
same as equation (3.8) and matrices CNR,DNR, and Dd,NRcan be inferred from equation (A.25).
137

Appendix A: MBC Transformation of Linear State-Space Models
Toy
NR=CTsxNR+DT cuNR+Ddud
y
NR=T1
oCTsxNR+T1
oDT cuNR+T1
oDdud (A.25)
)y
NR=CNRxNR+DNRuNR+Dd,NRud (A.26)
Note that in Bir’s derivation [48], the state transformation matrix Ts(equation (A.18)) is not
deﬁned. Hence, his deﬁnition of CNR, given by equation (A.27), is different from that given
by equation (A.36). Starting with equation (A.36), one can arrive at Bir’s expression, given in
equation (A.27), by expanding Tsand appropriately partitioning the Cmatrix.
CNR=T1
oh
C1T1+WC2T2C2T1i
where C=h
C1C2i
(A.27)
A.4 Summary
Given a linear periodic state-space model in the mixed frame of reference (given by equations
(3.5) and (3.6)) is transformed into a time-invariant model given by equations (A.28) and (A.29)
using equations (A.30) to (A.32).
˙xNR=ANRxNR+BNRuNR+Bd,NRud (A.28)
y
NR=CNRxNR+DNRuNR+Dd,NRud (A.29)
x=Ts(y)xNR (A.30)
u=Tc(y)uNR (A.31)
y=To(y)y
NR(A.32)
The deﬁnitions of the newly transformed matrices ANR,BNR,Bd,NR,CNR,DNR, and Dd,NRare
given by equations (A.33) to (A.38) respectively.
ANR="
T1
10
0 T1
1#"
ATs"
WT2 0
W2T3+˙WT22WT2##
(A.33)
BNR="
T1
10
0 T1
1#
BTc (A.34)
Bd,NR="
T1
10
0 T1
1#
Bd (A.35)
CNR=T1
oCTs (A.36)
DNR=T1
oDT c (A.37)
Dd,NR=T1
oDd (A.38)
138

B
Other Implementation Options for DAC After
MBC Transformation
Various implementation options are developed and considered for implementing dis-
turbance accommodating controllers for periodic systems after applying multi-blade
coordinate transformation. These options are described in this appendix. However,
these options are not suitable for systems with slow actuator dynamics or actuator saturation.
This appendix follows the discussion in § 4.4 on page 48.
There are two implementation options for DAC after MBC transformation. The ﬁrst option,
illustrated in Figure B.1a, uses equation (B.1) instead of equation (B.2) since the output of the
disturbance estimator is already in the nonrotating frame. The controller commands are then
transformed into the mixed frame by applying equation (B.3).
uNR =KNRˆxNR+Gd,NRˆz (B.1)
u=KMBC(y)ˆx+Gd,MBC(y)ˆz (B.2)
u=Tc(y)uNR (B.3)
In the second option, equation (B.2) is applied. For this implementation option, the disturbance
estimator output ˆwNRmust be transformed back into the mixed frame using equation (B.4)
before the control law is applied. This implementation is shown in Figure B.1b. Implementation
option 1 is preferred as it requires periodic gain calculations only for two matrices ( E(y)and
Tc(y)) whereas option 2 requires periodic gain calculations for four matrices ( E(y),KLQR(y),
Gd,MBC(y)and Td(y)).
139

Appendix B: Implementation Options for DAC After MBC Transformation
w="
Ts(y) 0
0 Indnd#
wNR=Td(y)wNR (B.4)
Another variant of implementation option 1 is used to avoid the redundant transformation of
DuNRtoDuand then back to DuNR. This is achieved by rewriting equation (B.5) into equa-
tion (B.6) where DuNRis obtained directly from the controller output and Dy
NRis the only input
that is transformed to the non-rotating frame. In block diagram, this is shown in Figure B.1c.
Note that the disturbance estimator now includes matrix ENRinstead of the identity matrix in
the previous two implementation options. This option does not require the computation of the
T1
c(y)matrix which is part of the E(y)matrix given by equation (4.22).
ˆ˙wNR =
ANRKe,NRCNRˆwNR+BNRuNR+Ke,NRy
NR(B.5)
ˆ˙wNR =
ANRKe,NRCNRˆwNR+h
BNR Ke,NRi"
uNR
y
NR#
=
ANRKe,NRCNRˆwNR+ENRvNR (B.6)
Unfortunately, option 3 cannot be implemented if actuator saturation limits exist because the
limits cannot be transformed to the non-rotating frame. Furthermore, this set up cannot be used
if the actuator dynamics are sufﬁciently slow. Otherwise, if the controller output in the non-
rotating frame is passed directly to the disturbance estimator, it could lead to wrong estimates
as the passed control inputs do not match the actual inputs to the plant.
140

Nonlinear Model +++-y y∆ u
NR u∆
v
()ψENR vu∆
NR xˆ∆
zˆzGxKuNR NR NR NR dˆˆ,+∆−=∆()ψcTop u
ControllerNR wˆop ydu
()NR NR NR NR NR NR v IwCKAwe+ −=ˆ ˆ
, &
Disturbance Estimator(a) Option 1
Nonlinear Model +++-y y∆ u
v
()ψENR vu∆
xˆ∆
zˆ()()zGxKuMBC LQR dˆˆ,ψ ψ+∆=∆op u
ControllerNR wˆ
()ψdTwˆu∆op y du
()NR NR NR NR NR NR v IwCKAwe+ −=ˆ ˆ
, &
Disturbance Estimator
(b) Option 2
Nonlinear Model +++-yop y
y∆ u
NR u∆du
()ψ1−
oTNR vu∆
NR xˆ∆
zˆ()ψcTop u
ControllerNR wˆNR u∆
NR y∆()NR NR NR NR NR NR NR vEwCKAwe+ −=ˆ ˆ
,&
Disturbance EstimatorzGxKuNR NR NR NR dˆˆ,+∆−=∆
(c) Option 3
Figure B.1: General DAC implementation options
141

Appendix B: Implementation Options for DAC After MBC Transformation
142

C
Design Load Cases
In this appendix, Table C.1 lists the parameters used to generate the stochastic wind and
wave conditions used for DLC analysis speciﬁed by the IEC 61400-3 standard [39]. The full
ﬁeld stochastic wind speed proﬁles are generated using TurbSim [80] while the irregular
waves are generated using the HydroDyn module of FAST.
Table C.1: Stochastic wind and wave parameters used for DLC analysis
Wind
Speed Bin
(m/s)Wind
Random
Seed 1Wind
Random
Seed 2Wave
Height
(m)Wave
Period
(s)Wave
Random
Seed 1Wave
Random
Seed 2DLC
#
15905792 126987
3.413.164 957506835 157613082 1
134974 988776 14.331 970592782 485375649 2
357689 98366 15.498 800280469 141886339 3
5687 12767 16.666 327229303 758402255 4
229702 848597 17.833 1773428449 1763500767 5
113949 50647 19.000 1156081573 33078631 6
Table continues on next page …
143

Appendix C: Design Load Cases
… continued from previous page.
Wind
Speed Bin
(m/s)Wind
Random
Seed 1Wind
Random
Seed 2Wave
Height
(m)Wave
Period
(s)Wave
Random
Seed 1Wave
Random
Seed 2DLC
#
16310923 466202
3.613.451 2139183008 92392911 7
800281 141887 14.361 167880670 362903324 8
651998 630206 15.271 950644343 1393964863 9
66161 230300 16.181 229035080 1571361853 10
275432 579885 17.090 2065660392 1391023859 11
281821 603157 18.000 9951921 968351283 12
17880067 599880
3.813.917 1664107546 1174692648 13
444331 448428 14.734 1755145296 636344083 14
755915 35424 15.550 1865507668 1599215621 15
603297 513815 16.367 181324597 405777804 16
783266 407731 17.183 858526699 1474839008 17
113931 108047 18.000 558067439 394087205 18
18814724 585268
4.014.278 1718133973 791314643 19
157613 957167 15.583 926454137 1343505625 20
485376 421761 16.887 1955600811 1675525653 21
459876 506795 18.191 390513519 174216262 22
450883 199926 19.496 566512448 1995841168 23
551141 427194 20.800 312542580 1665830287 24
19805405 168691
4.114.456 292205004 1045377067 25
700851 751695 15.465 1866790795 935999189 26
872236 368351 16.473 1244906118 959460793 27
52193 941818 17.482 1180815788 657880480 28
219682 17173 18.491 311288058 1092014019 29
459643 829056 19.500 1831870370 1096873578 30
Table continues on next page …
144

… continued from previous page.
Wind
Speed Bin
(m/s)Wind
Random
Seed 1Wind
Random
Seed 2Wave
Height
(m)Wave
Period
(s)Wave
Random
Seed 1Wave
Random
Seed 2DLC
#
20958534 626591
4.615.312 1335853219 1755842128 31
790046 538747 16.050 753664497 1706887465 32
451875 650508 16.787 1102194991 1383662644 33
333429 726630 17.525 862876179 813057456 34
59096 94489 18.262 163137228 1742855757 35
740906 877574 19.000 515216015 1144234235 36
21678735 757740
4.915.803 264825396 753180718 37
392227 655478 16.243 394938967 2016490493 38
97541 278499 16.682 515294124 1881072858 39
14363 796180 17.121 896074205 1181451746 40
294303 691192 17.561 106632077 1336755064 41
179915 345308 18.000 1938568078 1260668899 42
22926295 946817
5.116.123 2028915034 446123175 43
68181 520191 16.898 1054122609 646921566 44
581094 953814 17.674 1050662037 1011300187 45
637152 73596 18.449 725246908 494969554 46
651270 207032 19.225 1932850911 1813139320 47
864623 775028 20.000 792951422 418253126 48
2355953 914188
5.216.280 238806098 485163329 49
816856 782551 17.524 1675578552 366592739 50
528923 295535 18.768 836957777 488905355 51
694351 151846 20.012 519028083 935655797 52
212405 847911 21.256 867394725 668087071 53
543280 784855 22.500 207134515 1982942675 54
Table continues on next page …
145

Appendix C: Design Load Cases
… continued from previous page.
Wind
Speed Bin
(m/s)Wind
Random
Seed 1Wind
Random
Seed 2Wave
Height
(m)Wave
Period
(s)Wave
Random
Seed 1Wave
Random
Seed 2DLC
#
24702521 270832
5.817.194 283410487 923863335 55
956435 227811 17.715 2023038232 396890024 56
444543 321024 18.236 2053283283 1943217077 57
85398 829562 18.757 1235251048 2103993614 58
57341 822183 19.279 128375591 942466088 59
629451 570683 19.800 504186023 238626715 60
146

D
Relative Performance Trends for Controllers on
Floating Platforms
Performance trends of the State Feedback and Disturbance Accommodating Control-
lers on each ﬂoating platform across wind speed bins for the IEC 61400-3 standard are
presented in this appendix. The performance metrics are relative to the respective plat-
form’s Baseline controller. A summary of the performance trends is presented in each of the
platform’s respective chapter.
Figures D.1 and D.2 show the performance trends of the SFC and DAC on the barge platform
respectively. Both Controllers are designed based on a 6 DOFs linear state-space model. The
barge platform’s performance trends are discussed in § 6.3.1 on page 75.
For the tension leg platform, ﬁgures D.3 and D.4 show the performance trends of the SFC
and DAC on the barge platform respectively. Both Controllers are designed based on a 7 DOFs
linear state-space model. The tension leg platform’s performance trends are discussed in § 7.3.1
on page 83.
Finally, the performance trends of the SFC and DAC on the spar-buoy platform are shown
in ﬁgures D.5 and D.6 respectively. Both Controllers are designed based on a 8 DOFs linear
state-space model. The spar-buoy platform’s performance trends are discussed in § 8.3.1 on
page 95.
147

Appendix D: Relative Performance Trends for Controllers on Floating Platforms
1618 2022 241234Performance Metric (-)
Wind Speed (m/s)
Power
Rotor speed
BP rate
1618 2022 240.80.911.1Blade DELs (-)
Wind Speed (m/s)
Flap
Edge
1618 2022 240.40.50.60.70.8Tower DELs (-)
Wind Speed (m/s)
Fore-aft
Side-side
1618 2022 240.80.911.1LSS DEL (-)
Wind Speed (m/s)
1618 2022 240.40.50.60.70.8Platform Motions (-)
Wind Speed (m/s)
Roll
Pitch
Yaw
1618 2022 240.40.50.60.7Platform Velocities (-)
Wind Speed (m/s)
Roll
Pitch
Yaw
Figure D.1: Performance trends for the SFC on the barge platform
148

1618 2022 241234Performance Metric (-)
Wind Speed (m/s)
Power
Rotor speed
BP rate
1618 2022 240.80.911.1Blade DELs (-)
Wind Speed (m/s)
Flap
Edge
1618 2022 240.40.50.60.70.8Tower DELs (-)
Wind Speed (m/s)
Fore-aft
Side-side
1618 2022 240.80.911.1LSS DEL (-)
Wind Speed (m/s)
1618 2022 240.40.50.60.70.8Platform Motions (-)
Wind Speed (m/s)
Roll
Pitch
Yaw
1618 2022 240.40.50.60.7Platform Velocities (-)
Wind Speed (m/s)
Roll
Pitch
YawFigure D.2: Performance trends for the DAC on the barge platform
149

Appendix D: Relative Performance Trends for Controllers on Floating Platforms
16 18 20 22 240.450.50.550.60.650.70.750.80.850.9Performance Metric (-)
Wind Speed (m/s)
Power
Rotor speed
16 18 20 22 240.80.850.90.9511.051.11.15Blade DELs (-)
Wind Speed (m/s)
Flap
Edge
16 18 20 22 240.60.70.80.911.1Tower DELs (-)
Wind Speed (m/s)
Fore-aft
Side-side
16 18 20 22 240.80.850.90.9511.051.11.15LSS DEL (-)
Wind Speed (m/s)
16 18 20 22 240.80.911.11.21.31.41.51.6Platform Motions (-)
Wind Speed (m/s)
Roll
Pitch
Yaw
16 18 20 22 240.60.70.80.911.11.21.31.4Platform Velocities (-)
Wind Speed (m/s)
Roll
Pitch
Yaw
Figure D.3: Performance trends for the SFC on the TLP
150

16 18 20 22 240.450.50.550.60.650.70.750.80.850.9Performance Metric (-)
Wind Speed (m/s)
Power
Rotor speed
16 18 20 22 240.80.850.90.9511.051.11.15Blade DELs (-)
Wind Speed (m/s)
Flap
Edge
16 18 20 22 240.60.70.80.911.1Tower DELs (-)
Wind Speed (m/s)
Fore-aft
Side-side
16 18 20 22 240.80.850.90.9511.051.11.15LSS DEL (-)
Wind Speed (m/s)
16 18 20 22 240.80.911.11.21.31.41.51.6Platform Motions (-)
Wind Speed (m/s)
Roll
Pitch
Yaw
16 18 20 22 240.60.70.80.911.11.21.31.4Platform Velocities (-)
Wind Speed (m/s)
Roll
Pitch
YawFigure D.4: Performance trends for the DAC on the TLP
151

Appendix D: Relative Performance Trends for Controllers on Floating Platforms
16 18 20 22 24 0.2 0.4 0.6 0.8 11.2 Performance Metric (-)
Wind Speed (m/s)
Power
Rotor speed
16 18 20 22 24 0.9 0.95 11.05 1.1 1.15 Blade DELs (-)
Wind Speed (m/s)
Flap
Edge
16 18 20 22 24 0.8 0.85 0.9 0.95 11.05 1.1 1.15 Tower DELs (-)
Wind Speed (m/s)
Fore-aft
Side-side
16 18 20 22 24 11.05 1.1 1.15 1.2 1.25 1.3 LSS DEL (-)
Wind Speed (m/s)
16 18 20 22 24 0.9 11.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Platform Motions (-)
Wind Speed (m/s)
Roll
Pitch
Yaw
16 18 20 22 24 11.2 1.4 1.6 1.8 2Platform Velocities (-)
Wind Speed (m/s)
Roll
Pitch
Yaw
Figure D.5: Performance trends for the SFC on the spar-buoy platform
152

16 18 20 22 24 0.2 0.4 0.6 0.8 11.2 Performance Metric (-)
Wind Speed (m/s)
Power
Rotor speed
16 18 20 22 24 0.9 0.95 11.05 1.1 1.15 Blade DELs (-)
Wind Speed (m/s)
Flap
Edge
16 18 20 22 24 0.8 0.85 0.9 0.95 11.05 1.1 1.15 Tower DELs (-)
Wind Speed (m/s)
Fore-aft
Side-side
16 18 20 22 24 11.05 1.1 1.15 1.2 1.25 1.3 LSS DEL (-)
Wind Speed (m/s)
16 18 20 22 24 0.9 11.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Platform Motions (-)
Wind Speed (m/s)
Roll
Pitch
Yaw
16 18 20 22 24 11.2 1.4 1.6 1.8 2Platform Velocities (-)
Wind Speed (m/s)
Roll
Pitch
Yaw Figure D.6: Performance trends for the DAC on the spar-buoy platform
153

Appendix D: Relative Performance Trends for Controllers on Floating Platforms
154

E
Adaptive Disturbance Estimator
Irregular waves are modelled using a spectrum of frequencies. They can also be modelled
as having a dominant frequency that slowly changes with time and a randomly varying
amplitude depending on sea conditions. In this appendix, the limitations of using a peri-
odic waveform model for periodic disturbance estimation are highlighted when the assumed
design frequency is mismatched from the input disturbance frequency. An empirical method
to account for the change in period/frequency is introduced in §E.2.
E.1 Dealing with Periodic Waves
To reject periodic disturbances of the form asin(wt)+bcos(wt), the waveform model para-
meters are given by equations (E.1) – (E.3); the static offset of the waveform from the previous
implementation is removed for simplicity.
G="
0 1
w20#
(E.1)
Q=h
1 0i
(E.2)
z(0)=h
b awiT
(E.3)
This waveform model allows the DAC to minimise or cancel persistent disturbances only if
the assumed frequency wmatches the actual frequency of the persistent disturbance. Also, a
disturbance estimator based on this waveform matches the amplitude and phase of the input
disturbance provided that the assumed frequency is matched.
155

Appendix E: Adaptive Disturbance Estimator
0 2 4 6 8 10−1.5−1−0.500.511.5
Time (sec)
Actual Estimate
(a) Disturbance estimate
0 2 4 6 8 10−0.08−0.06−0.04−0.0200.020.040.060.08
Time (sec)
x1
x2 (b) States
Figure E.1: Periodic disturbance cancellation with matched estimator frequency
E.1.1 Case Study: Simple Linear System Subjected to Periodic Disturbances
In this section, the effectiveness of a DAC at cancelling periodic disturbances when the assumed
frequency matches the actual disturbance frequency is demonstrated. The effects of frequency
mismatch are also demonstrated.
The model considered here is a simple non-dimensional linear second order system with the
following matrices:
A="
1 0.5
05#
B="
0
10#
Bd="
0
1#
C="
1 0
0 1#
D="
0
0#
For simplicity, all the states are measured for state regulation. Furthermore, the disturbance is
assumed to enter the system through the same channel as the actuator ( Band Bdmatrices are
linearly dependent). This allows for disturbance cancellation rather than minimisation even
though the Bmatrix is not a square matrix.
The controller is an optimal linear quadratic regulator that is designed to drive the states to
zero. The DAC is set up to start 5 seconds after the simulation has started.
Matched Frequency
The system is subjected to periodic disturbances that match the assumed frequency of the dis-
turbance estimator. Figure E.1a shows that the disturbance estimator correctly estimates the
input disturbance. Therefore, when the DAC is activated 5 seconds after the start of the simu-
lation, the system states are driven to zero as shown in Figure E.1b. The states’ decay envelope
fort>5 seconds is governed by the SFC-part of the DAC.
Since the assumed estimator frequency matches the actual disturbance frequency, the estimates
for the disturbance states eventually match the actual disturbance and hence the DAC is able
to completely cancel the effects of the persistent periodic disturbance.
156

E.2 ADE for Disturbances with Variable Frequency
0 2 4 6 8 10−1.5−1−0.500.511.5
Time (sec)
Actual Estimate
(a) Disturbance estimate
0 2 4 6 8 10−0.1−0.08−0.06−0.04−0.0200.020.040.060.080.1
Time (sec)
x1
x2 (b) States
Figure E.2: Mismatched frequency disturbance estimate and state regulation
Mismatched Frequency
When the assumed frequency does not match that of the actual disturbance, the disturbance
estimates become out of phase and have a different amplitude as shown in Figure E.2a. The
amount of phase lag and amplitude are determined by the dynamics of the state estimator.
Slow dynamics increase the phase lag and reduce the amplitude (i.e. a low-pass ﬁltered re-
sponse).
This phase lag, regardless of how small, prevents the DAC from completely cancelling the
effects of the periodic disturbance. Whether the DAC is able to minimise the effects of the
disturbance or degrade the performance depends on the phase lag. Figure E.2b shows that
little minimisation is being achieved by the DAC after 5 seconds.
E.2 Adaptive Disturbance Estimator for Disturbances with Variable
Frequency
As demonstrated in §E.1.1, any mismatch in the assumed frequency degrades the DAC per-
formance. Furthermore, for systems with periodic disturbances that change frequency with
time, the problem is made more difﬁcult as careful selection of a design frequency is no longer
relevant as soon as the frequency changes.
One possible solution is to assume a disturbance waveform model with multiple periodic terms
with different frequencies to form a Fourier series. However, one major limitation of this ap-
proach is to ensure that the system remains observable with all the additional disturbance states
as discussed in §4.4.1.
The ﬁeld of unknown input observers [88–92] deals with cases such as changing frequency of
a periodic signal or having no knowledge of the estimated signal. However, these methods are
157

Appendix E: Adaptive Disturbance Estimator
usually demonstrated on simple abstract models that do not necessarily represent a real phys-
ical system. Below is a new empirical method that is relatively quick and easy to implement
but has not yet proven mathematically to guarantee stability.
The new approach, termed Adaptive Disturbance Estimator (ADE), consists of two modules:
the ﬁrst module dynamically estimates the frequency/period of the disturbance and the second
module updates the disturbance estimator model, similar to direct model reference adaptive
control. This involves on-line estimator design and update of variables.
E.2.1 Frequency Estimation
Starting with a hypothetical situation, assume that the input disturbance can be measured and
is a perfect sinusoidal signal with zero offset. The frequency can be extracted by detecting when
the signal crosses zero and measuring the time between the crossings (which corresponds to
half the period). The frequency can then be calculated using equation (E.4). However, the
input disturbance signal can have an offset and therefore may not cross at zero. Furthermore,
as discussed earlier, the input disturbance cannot always be measured. Therefore, the actual
disturbance signal cannot be used to detect the period.
w=p
Dt(E.4)
The same approach can be used to detect the period of the disturbance estimator. Since the
estimator is estimating the periodic disturbance input (as well as the system states), its outputs
that correspond to the disturbance states zare sinusoidal with no offset. When subjected to
periodic input, the steady-state output of the estimator matches the disturbance frequency but
with a different amplitude and with a phase lag. Therefore, the output of the estimator can be
used to detect the input frequency when the system reaches steady state.
The output of the disturbance states zare periodic with zero offset because when constructing
the disturbance waveform model (equations (E.1) and (E.2)), the deﬁned disturbance states
(given by equation (E.5)) are periodic in order to create a waveform given by equation (E.6).
Therefore, the outputs corresponding to these states can be used to measure the frequency of
the input disturbance.
z=2
4p
a2+b2sin
wt+tan1(a/b)
wp
a2+b2cos
wt+tan1(a/b)3
5 (E.5)
ud=asin(wt)+bcos(wt) (E.6)
One limitation of this approach is that it gives a discrete response. As a result, the lower the fre-
quency the longer it takes to reach the correct input frequency because the estimate is updated
every half a period of the disturbance state output. A sample response is shown in Figure E.3
where the input frequency is set to 1 Hz and the design frequency is assumed to be 0.5 Hz.
158

E.2 ADE for Disturbances with Variable Frequency
0 2 4 6 8 1000.511.522.533.54
Time (sec)Frequency (Hz)
Figure E.3: Quantised response of the estimated frequency
E.2.2 On-line Estimator Design
Once an estimate of the frequency is obtained, the disturbance estimator must be updated. The
change in frequency affects the G,A, and Kematrices as described by equations (E.1), (4.12),
and (4.13) respectively. Therefore, these matrices are updated on-line which in turn update the
dynamics of the disturbance estimator.
One important issue is how often the disturbance estimator variables are updated. The fre-
quency estimate depends on the dynamics of the state estimator and the plant. Therefore, the
update rate of the estimator variables should be longer than the time it takes for the transients
of the estimator and the plant to decay. This is because when the state estimator is updated, it
introduces new transients unless bump-less transfer [93, pp. 381–388] is implemented (not con-
sidered here). For the case study considered, the Adaptive Disturbance Estimator is updated
every 10 seconds. The ADE implementation block diagram is shown in Figure E.4.
Stability and convergence assessment of the ADE is difﬁcult as it contains continuous time,
triggered, and time-sampled modules. Stability analysis of such systems is considered beyond
the scope of this work.
E.2.3 Case Study: ADE Performance with Mismatched Frequency
In this case study the same ﬁctitious plant and controllers in §E.1.1 are used with the ADE. The
performance of the DAC with ADE are compared to the LQR controller and the DAC with a
ﬁxed frequency estimator.
The disturbance estimators start with an assumed frequency of 0.01 Hz and are subjected to a
disturbance signal that has a sinusoidally varying frequency. The estimators are designed to
have fast dynamics to accommodate a range of input frequencies. Of course, the higher the
159

Appendix E: Adaptive Disturbance Estimator
Plant
Disturbance
Estimator
, Γ,
Frequency
Estimation Estimator
Redesign
Figure E.4: Adaptive disturbance estimator implementation block diagram
disturbance frequency the faster the dynamics of the estimator need to be. The effect of noise
on the quality of the estimates is not considered here. The disturbance frequency ranges from
0.05 Hz to 0.15 Hz with a frequency of 0.05 Hz (given by equation (E.7)) .
w(t)=(0.052p)sin(0.052pt)+0.12p (E.7)
Higher frequencies have been tested (with linearly varying frequency up to 4 Hz) but since the
results are similar to those presented here, they are not included. The “low” range frequencies
are chosen to be in the range of the irregular waves expected at sea.
The time series results of the disturbance estimates and state regulation are shown in Figure E.5.
Due to fast estimator dynamics, the ﬁxed frequency disturbance estimator has relatively good
performance but the ADE has more accurate estimates especially at the low frequency range.
The effects of the accuracy of the estimates can be clearly seen in the regulation of the states.
In general, the DAC with ADE has better disturbance rejection especially at the low frequency
range as the estimate is more accurate. At higher frequencies, the DAC with ADE can still
improve performance but the transients from updating the estimator become more signiﬁcant.
E.2.4 Case Study: ADE Performance on a Linear Periodic Floating Wind T urbine
Model
This case study is used to assess the performance of an Adaptive Disturbance Estimator with a
wave Disturbance Accommodating Controller on the linear time-varying ﬂoating wind turbine
model used in §10.2.1.
Two cases are tested: the ﬁrst is with a constant frequency that does not match the assumed
waveform frequency by the disturbance estimator. The second is where the wave moment
frequency is continuously changing with time.
160

E.2 ADE for Disturbances with Variable Frequency
0 10 20 30 40 50 60 70−2−1012ud

Actual DAC estimate DAC with ADE estimate
0 10 20 30 40 50 60 70−0.04−0.0200.020.04State 1

LQR DAC DAC with ADE
0 10 20 30 40 50 60 70−0.1−0.0500.050.1
Time (sec)State 2
Figure E.5: Disturbance estimates and state regulation with a variable frequency disturbance
input
Constant Mismatched Frequency Case
The 2 DOFs ﬂoating wind turbine model is subjected to wave moments with a constant period
of 30 seconds (an extreme case for the site chosen for the ﬂoating wind turbines). The perform-
ance of the DAC with ADE at regulating the platform pitch is compared to a State Feedback
Controller and a DAC with a ﬁxed-frequency disturbance estimator that has an assumed wave
period of 15 seconds. The state regulating part of the DACs has the same gains and weightings
as the SFC.
Figure E.6 shows the platform pitch and disturbance moment estimates for the different con-
trollers and estimators. Looking at the wave moment estimates, there are no signiﬁcant dif-
ferences between the actual wave moment and both estimates of the DAC and DAC with
ADE. The phase lag for both estimators is not as prominent as the phase lag in the simple non-
dimensional model shown in Figure E.2a because the state estimators are designed to have fast
161

Appendix E: Adaptive Disturbance Estimator
0 50 100 150 200 250 300 1.3 1.35 1.4 1.45 1.5 1.55 1.6 Angle (deg) Platform Pitch

0 50 100 150 200 250 300 -1.5 -1 -0.5 00.5 11.5 x 10 8
Time (sec) Δ Moment (Nm) Wave Moment Estimates

Actual DAC with ADE DAC 0 100 200 300
-2 024 DAC with ADE
DAC
SFC
Figure E.6: Constant mismatched frequency case
dynamics. However, DAC with ADE does eventually (when the estimated frequency is close
to the actual) regulate the platform pitch angle closer to the operating point of 1.4°, therefore,
suggesting that there is a difference in wave estimate accuracy.
Putting the differences between the DAC and DAC with ADE in perspective, the difference
between them in terms of platform pitch regulation is insigniﬁcant when compared to the per-
formance of the SFC (see top right inset in Figure E.6). Both Disturbance Accommodating
Controllers have excellent platform pitch regulation.
Continuously Varying Frequency Case
For wave disturbances with continuously changing frequency, the wave period Twis made to
vary from 5 seconds to 20 seconds (values typical for the chosen site [32]) tracking a periodic
trajectory with a period of 600 seconds as deﬁned by equation (E.8).
Tw=7.5 cos2p
600t
+12.5 (E.8)
The simulation results are shown in Figure E.7; the disturbance estimates are not shown be-
162

E.3 Summary
0 50 100 150 200 250 3001.21.251.31.351.41.451.51.551.6
Time (sec)Pitch Angle (deg)

DAC
DAC with ADE using the estimated frequency
DAC with ADE using the actual disturbance frequency
Figure E.7: Platform pitch angle regulation with continuously changing wave disturbance fre-
quency
cause there are no signiﬁcant differences that can be easily identiﬁed. In addition to comparing
the performance between the DAC and DAC with ADE, another conﬁguration is included
where the ADE is designed based on the actual wave frequency rather than the estimated one
to remove the quality of the frequency estimates from the DAC performance.
In this simulation case, the performance of the DAC with ADE that uses the estimated fre-
quency has slightly larger ﬂuctuations than the other two. This is mainly due to poor estimate
of the wave frequency which is caused by slow dynamics of the ﬂoating wind turbine and the
low frequency of the waves. By the time it takes for the disturbance states to complete half a
period and trigger the system to get an estimate of the period, the actual wave frequency has
changed. Furthermore, due to the slow dynamics of the wind turbine, it takes a long time for
the system to reach steady state to match the period of the waves (recall that disturbance es-
timates are based on system states measurements). Although it may seem unlikely, however,
in this case the frequency is changing too fast for the ADE to give accurate estimates of the
frequency.
E.3 Summary
Irregular waves are modelled using a spectrum of frequencies. They can also be represented
as having a variable amplitude and a dominant frequency that slowly change with time de-
pending on sea conditions. Therefore, using a periodic disturbance waveform may actually
make the performance worse caused by wrong estimates due to frequency mismatch. A new
and empirical method (termed Adaptive Disturbance Estimator) is used to dynamically estim-
ate the input disturbance frequency and redesign the disturbance estimator on-line. Test cases
show that this approach can improve the accuracy of disturbance estimates and thereby im-
proving the DAC performance. However, in cases where the frequency is changing rapidly
163

Appendix E: Adaptive Disturbance Estimator
relative to the system dynamics and input disturbance frequencies, an accurate estimate of the
disturbance frequency may not be achieved; the speed at which the wave frequency changes
is not available for this work. Despite the limitations of the Adaptive Disturbance Estimator
method, it can be applied on a variety of systems outside the realm of Disturbance Accom-
modating Control or ﬂoating wind turbines. An example application would be on a periodic
system whose properties slowly change with time (such as a spring wearing out thus changing
the natural frequency of the system).
164

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