ScienceDirectIFAC-PapersOnLine 48-22 (2015) 020027 [600129]

Licență

ScienceDirectIFAC-PapersOnLine 48-22 (2015) 020027 [600129]

Byadmin ianuarie 1, 2024

ScienceDirectIFAC-PapersOnLine 48-22 (2015) 020–027
Available online at www.sciencedirect.com
2405-8963 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
Peer review under responsibility of International Federation of Automatic Control.
10.1016/ifacol.2015.10.301Sven Bodenburg et al. / IF AC-PapersOnLine 48-22 (2015) 020–027
© 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.Plug-and-play reconﬁguration of locally
interconnected systems with limited model
information
Sven Bodenburg∗and Jan Lunze∗
∗Ruhr-University Bochum, 44801 Bochum, Germany,
(e-mail: {bodenburg, lunze}@atp.rub.de)
Abstract: This paper proposes a novel method for reconﬁguration of decentralised controllers
after actuator failures in a locally interconnected system. If an actuator fails in a subsystem,
only the corresponding control station should be reconﬁgured, although the fault has eﬀectson other subsystems through the physical couplings. Therefore, design agents are introducedwhich store the model of the subsystem they are assigned to. Based on this local information,the design agent of the faulty subsystem procures relevant model information from other design
agents to model the faulty subsystem under the inﬂuence of the physical interactions and to
reconﬁgure the corresponding control station. The paper presents conditions to approximatethe behaviour of the physically coupled faulty subsystem in order to limit the amount of modelinformation for the design of a virtual actuator. As a consequence, the design agents have to“play” together to gather the model of the faulty subsystem before the reconﬁgured controlstation is “plugged-in” the control hardware. Plug-and-play reconﬁguration is illustrated on anelectric power network.
Keywords: Fault-tolerant control, large-scale systems, plug-and-play control, reconﬁguration
1. INTRODUCTION
1.1 Plug-and-play reconﬁguration
The paper concerns interconnected systems with Nsub-
systems Sithat are controlled by Ncontrol stations Ci. It
considers the situation in which a fault fat subsystem S1
occurs and only the control station C1should be reconﬁg-
ured to recover overall system stability, although the fault
has also eﬀects to other subsystems through the physicalinterconnections (Fig. 1).
Plug-and-play reconﬁguration states an automated solu-
tion to this problem. The controller reconﬁguration isaccomplished by the existing method of a virtual actuator.Hence, the focus is on the set-up of a model that is used todesign the virtual actuator. This model has to describe the
behaviour of the faulty subsystem S
f1under the inﬂuence
of the physical interactions. The main idea is to use Nde-
sign agents Dithat have a local view of the overall system.
Accordingly, the design agent D1of the faulty subsystem
has available only local information, i.e., exact model in-
formation of its subsystem S1, its faulty subsystem Sf1,
its control station C1and information about the physical
coupling K. First, the design agent D1has to manage the
online exchange of model information between itself andother design agents (shown as double arrows in Fig. 1) to
model the eﬀect of the physical interactions. Second, the
control station C
1is automatically reconﬁgured with a
virtual actuator based on the gathered model information,now available to design agent D
1.
In summary, the paper is devoted to the question:Which model information is needed to be communicatedamong the design agents D
iso that the model to design
the virtual actuator is available to design agent D1?
Fig. 1. Plug-and-play reconﬁguration
Motivated from the large-scale system theory, it is rea-
sonable to ignore the interaction to weakly coupled sub-
systems for the reconﬁguration process, to reduce thereconﬁguration eﬀort as well as the amount of model in-formation. This approach is referred to as reconﬁgurationwith limited model information.
The main contributions of the paper are
•the automated procurement of model information
to model the behaviour of the faulty subsystem S
f1
under the inﬂuence of strongly coupled subsystems(Sec. 5) to design the virtual actuator (Sec. 4),
•a plug-and-play reconﬁguration algorithm (Sec. 6),
•simulations on an electric power network (Sec. 7).5th IFAC Workshop on Distributed Estimation and
Control in Networked Systems
September 10-11, 2015. Philadelphia, USA,
Copyright © 2015 IFAC 20Plug-and-play reconﬁguration of locally
interconnected systems with limited model
information
Sven Bodenburg∗and Jan Lunze∗
∗Ruhr-University Bochum, 44801 Bochum, Germany,
(e-mail: {bodenburg, lunze}@atp.rub.de)
Abstract: This paper proposes a novel method for reconﬁguration of decentralised controllers
after actuator failures in a locally interconnected system. If an actuator fails in a subsystem,only the corresponding control station should be reconﬁgured, although the fault has eﬀectson other subsystems through the physical couplings. Therefore, design agents are introducedwhich store the model of the subsystem they are assigned to. Based on this local information,the design agent of the faulty subsystem procures relevant model information from other designagents to model the faulty subsystem under the inﬂuence of the physical interactions and toreconﬁgure the corresponding control station. The paper presents conditions to approximatethe behaviour of the physically coupled faulty subsystem in order to limit the amount of model
information for the design of a virtual actuator. As a consequence, the design agents have to
“play” together to gather the model of the faulty subsystem before the reconﬁgured controlstation is “plugged-in” the control hardware. Plug-and-play reconﬁguration is illustrated on anelectric power network.
Keywords: Fault-tolerant control, large-scale systems, plug-and-play control, reconﬁguration
1. INTRODUCTION
1.1 Plug-and-play reconﬁguration
The paper concerns interconnected systems with Nsub-
systems Sithat are controlled by Ncontrol stations Ci. It
considers the situation in which a fault fat subsystem S1
occurs and only the control station C1should be reconﬁg-
ured to recover overall system stability, although the fault
has also eﬀects to other subsystems through the physicalinterconnections (Fig. 1).
Plug-and-play reconﬁguration states an automated solu-
tion to this problem. The controller reconﬁguration isaccomplished by the existing method of a virtual actuator.Hence, the focus is on the set-up of a model that is used todesign the virtual actuator. This model has to describe the
behaviour of the faulty subsystem S
f1under the inﬂuence
of the physical interactions. The main idea is to use Nde-
sign agents Dithat have a local view of the overall system.
Accordingly, the design agent D1of the faulty subsystem
has available only local information, i.e., exact model in-
formation of its subsystem S1, its faulty subsystem Sf1,
its control station C1and information about the physical
coupling K. First, the design agent D1has to manage the
online exchange of model information between itself andother design agents (shown as double arrows in Fig. 1) to
model the eﬀect of the physical interactions. Second, the
control station C
1is automatically reconﬁgured with a
virtual actuator based on the gathered model information,now available to design agent D
1.
In summary, the paper is devoted to the question:Which model information is needed to be communicatedamong the design agents D
iso that the model to design
the virtual actuator is available to design agent D1?
Fig. 1. Plug-and-play reconﬁguration
Motivated from the large-scale system theory, it is rea-
sonable to ignore the interaction to weakly coupled sub-
systems for the reconﬁguration process, to reduce thereconﬁguration eﬀort as well as the amount of model in-formation. This approach is referred to as reconﬁgurationwith limited model information.
The main contributions of the paper are
•the automated procurement of model information
to model the behaviour of the faulty subsystem S
f1
under the inﬂuence of strongly coupled subsystems(Sec. 5) to design the virtual actuator (Sec. 4),
•a plug-and-play reconﬁguration algorithm (Sec. 6),
•simulations on an electric power network (Sec. 7).5th IFAC Workshop on Distributed Estimation and
Control in Networked Systems
September 10-11, 2015. Philadelphia, USA,
Copyright © 2015 IFAC 20Plug-and-play reconﬁguration of locally
interconnected systems with limited model
information
Sven Bodenburg∗and Jan Lunze∗
∗Ruhr-University Bochum, 44801 Bochum, Germany,
(e-mail: {bodenburg, lunze }@atp.rub.de)
Abstract: This paper proposes a novel method for reconﬁguration of decentralised controllers
after actuator failures in a locally interconnected system. If an actuator fails in a subsystem,only the corresponding control station should be reconﬁgured, although the fault has eﬀectson other subsystems through the physical couplings. Therefore, design agents are introducedwhich store the model of the subsystem they are assigned to. Based on this local information,the design agent of the faulty subsystem procures relevant model information from other designagents to model the faulty subsystem under the inﬂuence of the physical interactions and toreconﬁgure the corresponding control station. The paper presents conditions to approximatethe behaviour of the physically coupled faulty subsystem in order to limit the amount of model
information for the design of a virtual actuator. As a consequence, the design agents have to
“play” together to gather the model of the faulty subsystem before the reconﬁgured controlstation is “plugged-in” the control hardware. Plug-and-play reconﬁguration is illustrated on anelectric power network.
Keywords: Fault-tolerant control, large-scale systems, plug-and-play control, reconﬁguration
1. INTRODUCTION
1.1 Plug-and-play reconﬁguration
The paper concerns interconnected systems with Nsub-
systems S
ithat are controlled by Ncontrol stations Ci. It
considers the situation in which a fault fat subsystem S1
occurs and only the control station C1should be reconﬁg-
ured to recover overall system stability, although the fault
has also eﬀects to other subsystems through the physicalinterconnections (Fig. 1).
Plug-and-play reconﬁguration states an automated solu-
tion to this problem. The controller reconﬁguration isaccomplished by the existing method of a virtual actuator.Hence, the focus is on the set-up of a model that is used todesign the virtual actuator. This model has to describe the
behaviour of the faulty subsystem S
f1under the inﬂuence
of the physical interactions. The main idea is to use Nde-
sign agents Dithat have a local view of the overall system.
Accordingly, the design agent D1of the faulty subsystem
has available only local information, i.e., exact model in-
formation of its subsystem S1, its faulty subsystem Sf1,
its control station C1and information about the physical
coupling K. First, the design agent D1has to manage the
online exchange of model information between itself andother design agents (shown as double arrows in Fig. 1) to
model the eﬀect of the physical interactions. Second, the
control station C
1is automatically reconﬁgured with a
virtual actuator based on the gathered model information,now available to design agent D
1.
In summary, the paper is devoted to the question:Which model information is needed to be communicatedamong the design agents D
iso that the model to design
the virtual actuator is available to design agent D1?
Fig. 1. Plug-and-play reconﬁguration
Motivated from the large-scale system theory, it is rea-
sonable to ignore the interaction to weakly coupled sub-
systems for the reconﬁguration process, to reduce thereconﬁguration eﬀort as well as the amount of model in-formation. This approach is referred to as reconﬁgurationwith limited model information.
The main contributions of the paper are
•the automated procurement of model information
to model the behaviour of the faulty subsystem S
f1
under the inﬂuence of strongly coupled subsystems(Sec. 5) to design the virtual actuator (Sec. 4),
•a plug-and-play reconﬁguration algorithm (Sec. 6),
•simulations on an electric power network (Sec. 7).5th IFAC Workshop on Distributed Estimation and
Control in Networked Systems
September 10-11, 2015. Philadelphia, USA,
Copyright © 2015 IFAC 20Plug-and-play reconﬁguration of locally
interconnected systems with limited model
information
Sven Bodenburg∗and Jan Lunze∗
∗Ruhr-University Bochum, 44801 Bochum, Germany,
(e-mail: {bodenburg, lunze}@atp.rub.de)
Abstract: This paper proposes a novel method for reconﬁguration of decentralised controllers
after actuator failures in a locally interconnected system. If an actuator fails in a subsystem,only the corresponding control station should be reconﬁgured, although the fault has eﬀectson other subsystems through the physical couplings. Therefore, design agents are introducedwhich store the model of the subsystem they are assigned to. Based on this local information,the design agent of the faulty subsystem procures relevant model information from other design
agents to model the faulty subsystem under the inﬂuence of the physical interactions and to
reconﬁgure the corresponding control station. The paper presents conditions to approximatethe behaviour of the physically coupled faulty subsystem in order to limit the amount of modelinformation for the design of a virtual actuator. As a consequence, the design agents have to“play” together to gather the model of the faulty subsystem before the reconﬁgured controlstation is “plugged-in” the control hardware. Plug-and-play reconﬁguration is illustrated on anelectric power network.
Keywords: Fault-tolerant control, large-scale systems, plug-and-play control, reconﬁguration
1. INTRODUCTION
1.1 Plug-and-play reconﬁguration
The paper concerns interconnected systems with Nsub-
systems S
ithat are controlled by Ncontrol stations Ci. It
considers the situation in which a fault fat subsystem S1
occurs and only the control station C1should be reconﬁg-
ured to recover overall system stability, although the fault
has also eﬀects to other subsystems through the physicalinterconnections (Fig. 1).
Plug-and-play reconﬁguration states an automated solu-
tion to this problem. The controller reconﬁguration isaccomplished by the existing method of a virtual actuator.Hence, the focus is on the set-up of a model that is used todesign the virtual actuator. This model has to describe the
behaviour of the faulty subsystem S
f1under the inﬂuence
of the physical interactions. The main idea is to use Nde-
sign agents Dithat have a local view of the overall system.
Accordingly, the design agent D1of the faulty subsystem
has available only local information, i.e., exact model in-
formation of its subsystem S1, its faulty subsystem Sf1,
its control station C1and information about the physical
coupling K. First, the design agent D1has to manage the
online exchange of model information between itself andother design agents (shown as double arrows in Fig. 1) to
model the eﬀect of the physical interactions. Second, the
control station C
1is automatically reconﬁgured with a
virtual actuator based on the gathered model information,now available to design agent D
1.
In summary, the paper is devoted to the question:Which model information is needed to be communicatedamong the design agents D
iso that the model to design
the virtual actuator is available to design agent D1?
Fig. 1. Plug-and-play reconﬁguration
Motivated from the large-scale system theory, it is rea-
sonable to ignore the interaction to weakly coupled sub-
systems for the reconﬁguration process, to reduce thereconﬁguration eﬀort as well as the amount of model in-formation. This approach is referred to as reconﬁgurationwith limited model information.
The main contributions of the paper are
•the automated procurement of model information
to model the behaviour of the faulty subsystem S
f1
under the inﬂuence of strongly coupled subsystems(Sec. 5) to design the virtual actuator (Sec. 4),
•a plug-and-play reconﬁguration algorithm (Sec. 6),
•simulations on an electric power network (Sec. 7).5th IFAC Workshop on Distributed Estimation and
Control in Networked Systems
September 10-11, 2015. Philadelphia, USA,
Copyright © 2015 IFAC 20Plug-and-play reconﬁguration of locally
interconnected systems with limited model
information
Sven Bodenburg∗and Jan Lunze∗
∗Ruhr-University Bochum, 44801 Bochum, Germany,
(e-mail: {bodenburg, lunze}@atp.rub.de)
Abstract: This paper proposes a novel method for reconﬁguration of decentralised controllers
after actuator failures in a locally interconnected system. If an actuator fails in a subsystem,only the corresponding control station should be reconﬁgured, although the fault has eﬀectson other subsystems through the physical couplings. Therefore, design agents are introducedwhich store the model of the subsystem they are assigned to. Based on this local information,the design agent of the faulty subsystem procures relevant model information from other design
agents to model the faulty subsystem under the inﬂuence of the physical interactions and to
reconﬁgure the corresponding control station. The paper presents conditions to approximatethe behaviour of the physically coupled faulty subsystem in order to limit the amount of modelinformation for the design of a virtual actuator. As a consequence, the design agents have to“play” together to gather the model of the faulty subsystem before the reconﬁgured controlstation is “plugged-in” the control hardware. Plug-and-play reconﬁguration is illustrated on anelectric power network.
Keywords: Fault-tolerant control, large-scale systems, plug-and-play control, reconﬁguration
1. INTRODUCTION
1.1 Plug-and-play reconﬁguration
The paper concerns interconnected systems with Nsub-
systems S
ithat are controlled by Ncontrol stations Ci. It
considers the situation in which a fault fat subsystem S1
occurs and only the control station C1should be reconﬁg-
ured to recover overall system stability, although the fault
has also eﬀects to other subsystems through the physicalinterconnections (Fig. 1).
Plug-and-play reconﬁguration states an automated solu-
tion to this problem. The controller reconﬁguration isaccomplished by the existing method of a virtual actuator.Hence, the focus is on the set-up of a model that is used todesign the virtual actuator. This model has to describe the
behaviour of the faulty subsystem S
f1under the inﬂuence
of the physical interactions. The main idea is to use Nde-
sign agents Dithat have a local view of the overall system.
Accordingly, the design agent D1of the faulty subsystem
has available only local information, i.e., exact model in-
formation of its subsystem S1, its faulty subsystem Sf1,
its control station C1and information about the physical
coupling K. First, the design agent D1has to manage the
online exchange of model information between itself andother design agents (shown as double arrows in Fig. 1) to
model the eﬀect of the physical interactions. Second, the
control station C
1is automatically reconﬁgured with a
virtual actuator based on the gathered model information,now available to design agent D
1.
In summary, the paper is devoted to the question:Which model information is needed to be communicatedamong the design agents D
iso that the model to design
the virtual actuator is available to design agent D1?
Fig. 1. Plug-and-play reconﬁguration
Motivated from the large-scale system theory, it is rea-
sonable to ignore the interaction to weakly coupled sub-
systems for the reconﬁguration process, to reduce thereconﬁguration eﬀort as well as the amount of model in-formation. This approach is referred to as reconﬁgurationwith limited model information.
The main contributions of the paper are
•the automated procurement of model information
to model the behaviour of the faulty subsystem S
f1
under the inﬂuence of strongly coupled subsystems(Sec. 5) to design the virtual actuator (Sec. 4),
•a plug-and-play reconﬁguration algorithm (Sec. 6),
•simulations on an electric power network (Sec. 7).5th IFAC Workshop on Distributed Estimation and
Control in Networked Systems
September 10-11, 2015. Philadelphia, USA,
Copyright © 2015 IFAC 20

Sven Bodenburg et al. / IF AC-PapersOnLine 48-22 (2015) 020–027 21
Plug-and-play reconﬁguration of locally
interconnected systems with limited model
information
Sven Bodenburg∗and Jan Lunze∗
∗Ruhr-University Bochum, 44801 Bochum, Germany,
(e-mail: {bodenburg, lunze}@atp.rub.de)
Abstract: This paper proposes a novel method for reconﬁguration of decentralised controllers
after actuator failures in a locally interconnected system. If an actuator fails in a subsystem,
only the corresponding control station should be reconﬁgured, although the fault has eﬀectson other subsystems through the physical couplings. Therefore, design agents are introducedwhich store the model of the subsystem they are assigned to. Based on this local information,the design agent of the faulty subsystem procures relevant model information from other design
agents to model the faulty subsystem under the inﬂuence of the physical interactions and to
reconﬁgure the corresponding control station. The paper presents conditions to approximatethe behaviour of the physically coupled faulty subsystem in order to limit the amount of modelinformation for the design of a virtual actuator. As a consequence, the design agents have to“play” together to gather the model of the faulty subsystem before the reconﬁgured controlstation is “plugged-in” the control hardware. Plug-and-play reconﬁguration is illustrated on anelectric power network.
Keywords: Fault-tolerant control, large-scale systems, plug-and-play control, reconﬁguration
1. INTRODUCTION
1.1 Plug-and-play reconﬁguration
The paper concerns interconnected systems with Nsub-
systems S
ithat are controlled by Ncontrol stations Ci. It
considers the situation in which a fault fat subsystem S1
occurs and only the control station C1should be reconﬁg-
ured to recover overall system stability, although the fault
has also eﬀects to other subsystems through the physicalinterconnections (Fig. 1).
Plug-and-play reconﬁguration states an automated solu-
tion to this problem. The controller reconﬁguration isaccomplished by the existing method of a virtual actuator.Hence, the focus is on the set-up of a model that is used todesign the virtual actuator. This model has to describe the
behaviour of the faulty subsystem S
f1under the inﬂuence
of the physical interactions. The main idea is to use Nde-
sign agents Dithat have a local view of the overall system.
Accordingly, the design agent D1of the faulty subsystem
has available only local information, i.e., exact model in-
formation of its subsystem S1, its faulty subsystem Sf1,
its control station C1and information about the physical
coupling K. First, the design agent D1has to manage the
online exchange of model information between itself andother design agents (shown as double arrows in Fig. 1) to
model the eﬀect of the physical interactions. Second, the
control station C
1is automatically reconﬁgured with a
virtual actuator based on the gathered model information,now available to design agent D
1.
In summary, the paper is devoted to the question:Which model information is needed to be communicatedamong the design agents D
iso that the model to design
the virtual actuator is available to design agent D1?
Fig. 1. Plug-and-play reconﬁguration
Motivated from the large-scale system theory, it is rea-
sonable to ignore the interaction to weakly coupled sub-
systems for the reconﬁguration process, to reduce thereconﬁguration eﬀort as well as the amount of model in-formation. This approach is referred to as reconﬁgurationwith limited model information.
The main contributions of the paper are
•the automated procurement of model information
to model the behaviour of the faulty subsystem S
f1
under the inﬂuence of strongly coupled subsystems(Sec. 5) to design the virtual actuator (Sec. 4),
•a plug-and-play reconﬁguration algorithm (Sec. 6),
•simulations on an electric power network (Sec. 7).5th IFAC Workshop on Distributed Estimation and
Control in Networked Systems
September 10-11, 2015. Philadelphia, USA,
Copyright © 2015 IFAC 20Plug-and-play reconﬁguration of locally
interconnected systems with limited model
information
Sven Bodenburg∗and Jan Lunze∗
∗Ruhr-University Bochum, 44801 Bochum, Germany,
(e-mail: {bodenburg, lunze}@atp.rub.de)
Abstract: This paper proposes a novel method for reconﬁguration of decentralised controllers
after actuator failures in a locally interconnected system. If an actuator fails in a subsystem,
only the corresponding control station should be reconﬁgured, although the fault has eﬀectson other subsystems through the physical couplings. Therefore, design agents are introducedwhich store the model of the subsystem they are assigned to. Based on this local information,the design agent of the faulty subsystem procures relevant model information from other design
agents to model the faulty subsystem under the inﬂuence of the physical interactions and to
reconﬁgure the corresponding control station. The paper presents conditions to approximatethe behaviour of the physically coupled faulty subsystem in order to limit the amount of modelinformation for the design of a virtual actuator. As a consequence, the design agents have to“play” together to gather the model of the faulty subsystem before the reconﬁgured controlstation is “plugged-in” the control hardware. Plug-and-play reconﬁguration is illustrated on anelectric power network.
Keywords: Fault-tolerant control, large-scale systems, plug-and-play control, reconﬁguration
1. INTRODUCTION
1.1 Plug-and-play reconﬁguration
The paper concerns interconnected systems with Nsub-
systems S
ithat are controlled by Ncontrol stations Ci. It
considers the situation in which a fault fat subsystem S1
occurs and only the control station C1should be reconﬁg-
ured to recover overall system stability, although the fault
has also eﬀects to other subsystems through the physicalinterconnections (Fig. 1).
Plug-and-play reconﬁguration states an automated solu-
tion to this problem. The controller reconﬁguration isaccomplished by the existing method of a virtual actuator.Hence, the focus is on the set-up of a model that is used todesign the virtual actuator. This model has to describe the
behaviour of the faulty subsystem S
f1under the inﬂuence
of the physical interactions. The main idea is to use Nde-
sign agents Dithat have a local view of the overall system.
Accordingly, the design agent D1of the faulty subsystem
has available only local information, i.e., exact model in-
formation of its subsystem S1, its faulty subsystem Sf1,
its control station C1and information about the physical
coupling K. First, the design agent D1has to manage the
online exchange of model information between itself andother design agents (shown as double arrows in Fig. 1) to
model the eﬀect of the physical interactions. Second, the
control station C
1is automatically reconﬁgured with a
virtual actuator based on the gathered model information,now available to design agent D
1.
In summary, the paper is devoted to the question:Which model information is needed to be communicatedamong the design agents D
iso that the model to design
the virtual actuator is available to design agent D1?
Fig. 1. Plug-and-play reconﬁguration
Motivated from the large-scale system theory, it is rea-
sonable to ignore the interaction to weakly coupled sub-
systems for the reconﬁguration process, to reduce thereconﬁguration eﬀort as well as the amount of model in-formation. This approach is referred to as reconﬁgurationwith limited model information.
The main contributions of the paper are
•the automated procurement of model information
to model the behaviour of the faulty subsystem S
f1
under the inﬂuence of strongly coupled subsystems(Sec. 5) to design the virtual actuator (Sec. 4),
•a plug-and-play reconﬁguration algorithm (Sec. 6),
•simulations on an electric power network (Sec. 7).5th IFAC Workshop on Distributed Estimation and
Control in Networked Systems
September 10-11, 2015. Philadelphia, USA,
Copyright © 2015 IFAC 20Plug-and-play reconﬁguration of locally
interconnected systems with limited model
information
Sven Bodenburg∗and Jan Lunze∗
∗Ruhr-University Bochum, 44801 Bochum, Germany,
(e-mail: {bodenburg, lunze}@atp.rub.de)
Abstract: This paper proposes a novel method for reconﬁguration of decentralised controllers
after actuator failures in a locally interconnected system. If an actuator fails in a subsystem,
only the corresponding control station should be reconﬁgured, although the fault has eﬀectson other subsystems through the physical couplings. Therefore, design agents are introducedwhich store the model of the subsystem they are assigned to. Based on this local information,the design agent of the faulty subsystem procures relevant model information from other design
agents to model the faulty subsystem under the inﬂuence of the physical interactions and to
reconﬁgure the corresponding control station. The paper presents conditions to approximatethe behaviour of the physically coupled faulty subsystem in order to limit the amount of modelinformation for the design of a virtual actuator. As a consequence, the design agents have to“play” together to gather the model of the faulty subsystem before the reconﬁgured controlstation is “plugged-in” the control hardware. Plug-and-play reconﬁguration is illustrated on anelectric power network.
Keywords: Fault-tolerant control, large-scale systems, plug-and-play control, reconﬁguration
1. INTRODUCTION
1.1 Plug-and-play reconﬁguration
The paper concerns interconnected systems with Nsub-
systems S
ithat are controlled by Ncontrol stations Ci. It
considers the situation in which a fault fat subsystem S1
occurs and only the control station C1should be reconﬁg-
ured to recover overall system stability, although the fault
has also eﬀects to other subsystems through the physicalinterconnections (Fig. 1).
Plug-and-play reconﬁguration states an automated solu-
tion to this problem. The controller reconﬁguration isaccomplished by the existing method of a virtual actuator.Hence, the focus is on the set-up of a model that is used todesign the virtual actuator. This model has to describe the
behaviour of the faulty subsystem S
f1under the inﬂuence
of the physical interactions. The main idea is to use Nde-
sign agents Dithat have a local view of the overall system.
Accordingly, the design agent D1of the faulty subsystem
has available only local information, i.e., exact model in-
formation of its subsystem S1, its faulty subsystem Sf1,
its control station C1and information about the physical
coupling K. First, the design agent D1has to manage the
online exchange of model information between itself andother design agents (shown as double arrows in Fig. 1) to
model the eﬀect of the physical interactions. Second, the
control station C
1is automatically reconﬁgured with a
virtual actuator based on the gathered model information,now available to design agent D
1.
In summary, the paper is devoted to the question:Which model information is needed to be communicatedamong the design agents D
iso that the model to design
the virtual actuator is available to design agent D1?
Fig. 1. Plug-and-play reconﬁguration
Motivated from the large-scale system theory, it is rea-
sonable to ignore the interaction to weakly coupled sub-
systems for the reconﬁguration process, to reduce thereconﬁguration eﬀort as well as the amount of model in-formation. This approach is referred to as reconﬁgurationwith limited model information.
The main contributions of the paper are
•the automated procurement of model information
to model the behaviour of the faulty subsystem S
f1
under the inﬂuence of strongly coupled subsystems(Sec. 5) to design the virtual actuator (Sec. 4),
•a plug-and-play reconﬁguration algorithm (Sec. 6),
•simulations on an electric power network (Sec. 7).5th IFAC Workshop on Distributed Estimation and
Control in Networked Systems
September 10-11, 2015. Philadelphia, USA,
Copyright © 2015 IFAC 20Plug-and-play reconﬁguration of locally
interconnected systems with limited model
information
Sven Bodenburg∗and Jan Lunze∗
∗Ruhr-University Bochum, 44801 Bochum, Germany,
(e-mail: {bodenburg, lunze}@atp.rub.de)
Abstract: This paper proposes a novel method for reconﬁguration of decentralised controllers
after actuator failures in a locally interconnected system. If an actuator fails in a subsystem,
only the corresponding control station should be reconﬁgured, although the fault has eﬀectson other subsystems through the physical couplings. Therefore, design agents are introducedwhich store the model of the subsystem they are assigned to. Based on this local information,the design agent of the faulty subsystem procures relevant model information from other design
agents to model the faulty subsystem under the inﬂuence of the physical interactions and to
reconﬁgure the corresponding control station. The paper presents conditions to approximatethe behaviour of the physically coupled faulty subsystem in order to limit the amount of modelinformation for the design of a virtual actuator. As a consequence, the design agents have to“play” together to gather the model of the faulty subsystem before the reconﬁgured controlstation is “plugged-in” the control hardware. Plug-and-play reconﬁguration is illustrated on anelectric power network.
Keywords: Fault-tolerant control, large-scale systems, plug-and-play control, reconﬁguration
1. INTRODUCTION
1.1 Plug-and-play reconﬁguration
The paper concerns interconnected systems with Nsub-
systems S
ithat are controlled by Ncontrol stations Ci. It
considers the situation in which a fault fat subsystem S1
occurs and only the control station C1should be reconﬁg-
ured to recover overall system stability, although the fault
has also eﬀects to other subsystems through the physicalinterconnections (Fig. 1).
Plug-and-play reconﬁguration states an automated solu-
tion to this problem. The controller reconﬁguration isaccomplished by the existing method of a virtual actuator.Hence, the focus is on the set-up of a model that is used todesign the virtual actuator. This model has to describe the
behaviour of the faulty subsystem S
f1under the inﬂuence
of the physical interactions. The main idea is to use Nde-
sign agents Dithat have a local view of the overall system.
Accordingly, the design agent D1of the faulty subsystem
has available only local information, i.e., exact model in-
formation of its subsystem S1, its faulty subsystem Sf1,
its control station C1and information about the physical
coupling K. First, the design agent D1has to manage the
online exchange of model information between itself andother design agents (shown as double arrows in Fig. 1) to
model the eﬀect of the physical interactions. Second, the
control station C
1is automatically reconﬁgured with a
virtual actuator based on the gathered model information,now available to design agent D
1.
In summary, the paper is devoted to the question:Which model information is needed to be communicatedamong the design agents D
iso that the model to design
the virtual actuator is available to design agent D1?
Fig. 1. Plug-and-play reconﬁguration
Motivated from the large-scale system theory, it is rea-
sonable to ignore the interaction to weakly coupled sub-
systems for the reconﬁguration process, to reduce thereconﬁguration eﬀort as well as the amount of model in-formation. This approach is referred to as reconﬁgurationwith limited model information.
The main contributions of the paper are
•the automated procurement of model information
to model the behaviour of the faulty subsystem S
f1
under the inﬂuence of strongly coupled subsystems(Sec. 5) to design the virtual actuator (Sec. 4),
•a plug-and-play reconﬁguration algorithm (Sec. 6),
•simulations on an electric power network (Sec. 7).5th IFAC Workshop on Distributed Estimation and
Control in Networked Systems
September 10-11, 2015. Philadelphia, USA,
Copyright © 2015 IFAC 20Plug-and-play reconﬁguration of locally
interconnected systems with limited model
information
Sven Bodenburg∗and Jan Lunze∗
∗Ruhr-University Bochum, 44801 Bochum, Germany,
(e-mail: {bodenburg, lunze}@atp.rub.de)
Abstract: This paper proposes a novel method for reconﬁguration of decentralised controllers
after actuator failures in a locally interconnected system. If an actuator fails in a subsystem,
only the corresponding control station should be reconﬁgured, although the fault has eﬀectson other subsystems through the physical couplings. Therefore, design agents are introducedwhich store the model of the subsystem they are assigned to. Based on this local information,the design agent of the faulty subsystem procures relevant model information from other design
agents to model the faulty subsystem under the inﬂuence of the physical interactions and to
reconﬁgure the corresponding control station. The paper presents conditions to approximatethe behaviour of the physically coupled faulty subsystem in order to limit the amount of modelinformation for the design of a virtual actuator. As a consequence, the design agents have to“play” together to gather the model of the faulty subsystem before the reconﬁgured controlstation is “plugged-in” the control hardware. Plug-and-play reconﬁguration is illustrated on anelectric power network.
Keywords: Fault-tolerant control, large-scale systems, plug-and-play control, reconﬁguration
1. INTRODUCTION
1.1 Plug-and-play reconﬁguration
The paper concerns interconnected systems with Nsub-
systems S
ithat are controlled by Ncontrol stations Ci. It
considers the situation in which a fault fat subsystem S1
occurs and only the control station C1should be reconﬁg-
ured to recover overall system stability, although the fault
has also eﬀects to other subsystems through the physicalinterconnections (Fig. 1).
Plug-and-play reconﬁguration states an automated solu-
tion to this problem. The controller reconﬁguration isaccomplished by the existing method of a virtual actuator.Hence, the focus is on the set-up of a model that is used todesign the virtual actuator. This model has to describe the
behaviour of the faulty subsystem S
f1under the inﬂuence
of the physical interactions. The main idea is to use Nde-
sign agents Dithat have a local view of the overall system.
Accordingly, the design agent D1of the faulty subsystem
has available only local information, i.e., exact model in-
formation of its subsystem S1, its faulty subsystem Sf1,
its control station C1and information about the physical
coupling K. First, the design agent D1has to manage the
online exchange of model information between itself andother design agents (shown as double arrows in Fig. 1) to
model the eﬀect of the physical interactions. Second, the
control station C
1is automatically reconﬁgured with a
virtual actuator based on the gathered model information,now available to design agent D
1.
In summary, the paper is devoted to the question:Which model information is needed to be communicatedamong the design agents D
iso that the model to design
the virtual actuator is available to design agent D1?
Fig. 1. Plug-and-play reconﬁguration
Motivated from the large-scale system theory, it is rea-
sonable to ignore the interaction to weakly coupled sub-
systems for the reconﬁguration process, to reduce thereconﬁguration eﬀort as well as the amount of model in-formation. This approach is referred to as reconﬁgurationwith limited model information.
The main contributions of the paper are
•the automated procurement of model information
to model the behaviour of the faulty subsystem S
f1
under the inﬂuence of strongly coupled subsystems(Sec. 5) to design the virtual actuator (Sec. 4),
•a plug-and-play reconﬁguration algorithm (Sec. 6),
•simulations on an electric power network (Sec. 7).5th IFAC Workshop on Distributed Estimation and
Control in Networked Systems
September 10-11, 2015. Philadelphia, USA,
Copyright © 2015 IFAC 201.2 Literature survey
The notion of plug-and-play control has been introduced in
fault-tolerant control (FTC) as a framework to adapt anexisting controller to a changing number of subsystems,
see Patton et al. (2007). A plug-and-play fault tolerant
controller has been proposed in Bodenburg et al. (2014),where a diagnostic unit and a reconﬁguration unit arecombined through a network to ensure fault tolerance. InRiverso et al. (2014) a plug-and-play framework for FTChas been presented consisting of a distributed fault detec-
tion unit and a redesign unit of a distributed model predic-
tive controller with limited model information. If a faultis detected, the faulty subsystem is unplugged, repairedand re-plugged-in without jeopardising stability and stateconstraint satisfaction. Plug-and-play reconﬁguration withlocal model information has been studied in Bodenburget al. (2015), where conditions are presented to reconﬁgurethe control station of the faulty subsystem with local infor-mation only. In Teixeira et al. (2013) the reconﬁgurationof an actuator network after actuator failures has beenstudied. The actuators are reconﬁgured locally by solvinga distributed optimisation problem. The decentralisationof the reconﬁguration task has also been considered in Vey
et al. (2015) and references therein. If the faulty system is
not stabilisable in a decentralised manner, in Amani et al.(2014) a method is proposed to ﬁnd subsystems to allow
cooperative stabilisation. In addition, a survey of FTC of
network controlled systems is given in Ding (2012) withthe focus on network eﬀects such as drop-outs and delays.
Beyond FTC, plug-and-play control as proposed in Stous-
trup (2009) is a concept to adjust the controller afteradding sensors and actuators. Moreover, plug-and-playcontrol for interconnected systems with a changing num-
ber of subsystems has been presented in Riverso et al.
(2013) and Bodenburg and Lunze (2015). Further con-troller design and system analysis methods with limitedmodel information have also been elaborated in Lunze(1992); Deroo et al. (2014); Farokhi et al. (2013) for spe-ciﬁc system structures and design methods. A concept forexchanging algorithms and models for MATLAB/Simulinkis presented in Bodenburg and Lunze (2013).
In summary, all the existing concepts for reconﬁguration
of interconnected systems assume the availability of a
model of the faulty process for reconﬁguration. Plug-and-
play reconﬁguration, however, is devoted to the modellingproblem of the faulty subsystem under the inﬂuence of thephysical couplings. The modelling aim is to describe thebehaviour from the input u
f1to the output yf1as exactly
as required to design the virtual actuator presented in Veyet al. (2015) in order to maintain global system stability.
1.3 Outline
Relevant background is given in Sec. 2. In Sec. 3, the main
idea and relevant models of plug-and-play reconﬁguration
is presented. The reconﬁguration with a virtual actuator isintroduced in Sec. 4 and the analysis of the communicationamong the designs agent during the procurement of modelinformation in Sec. 5. The plug-and-play reconﬁgurationprocedure is presented in Sec. 6 and evaluated on a electric
power network in Sec. 7. The paper closes with ﬁnal a
conclusion in Section 8.2. PRELIMINARIES
In this section the used notation, basic models, graphs aswell as required assumptions are stated.
2.1 Notation
Scalars are denoted by italic font (d), vectors by boldface
letters (b ) and matrices by upper case boldface letters (L ).
Sets are written in calligraphic letters ( N).R,CandN
0
denote the ﬁelds of real, complex and natural numbers
including 0. Models are denoted by capital italic letters ( S)
and subscripts distinguish distinct parts (S i). The combi-
nation of two models S,Cis denoted by comb/parenleftbig
{S, C }/parenrightbig
,
where the input signals of the models to be combinedare connected to the equivalently named output signals.A set of models S
i,(i∈N) is denoted by {Si}i∈N, where
Nincludes all indices of Si, i.e., N:={1, 2, .., N }, with
N≥2.Syu(s) represents the transfer function from the
complex signal u(s) to y(s). The corresponding Fourier
transformation is given by Syu(jω) representing the fre-
quency response from the u(jω) toy(jω), where ω∈R. The
magnitude plot of Syu(jω) and the absolute value of y(jω)
are denoted by |Syu(jω)|∈Rand|y(jω)|∈R, respectively.
2.2 Basic Models
A subsystem is modelled as follows:
Si:

˙xi(t)=Aixi(t)+B iui(t)+e isi(t),xi(0)=0
yi(t)=cT
ixi(t)
zi(t)=cTzixi(t),i∈N
where xi∈Rniis the state vector, ui∈Rmiis the control
signal vector and yi,si,zi∈Rare the scalar measurement
signal, the scalar interconnection input signal and scalar
interconnection output signal respectively. The equivalentfrequency-domain model reads as
S
i:/braceleftbigg
yi(s)=ST
yui(s)ui(s)+S ysi(s)si(s),
zi(s)=ST
zui(s)ui(s)+S zsi(s)si(s),(1)
where
ST
yui(s)=cT
i/parenleftbig
sI−Ai/parenrightbig−1Bi,Sysi(s)=cT
i/parenleftbig
sI−Ai/parenrightbig−1ei
ST
zui(s)=cTzi/parenleftbig
sI−Ai/parenrightbig−1Bi,Szsi(s)=cTzi/parenleftbig
sI−Ai/parenrightbig−1ei.
As actuator failures are considered, a subsystem has to
provide alternative actuators. Hence, ST
yui(s) and ST
zui(s)
are row vectors. The physical interconnection is charac-
terised by the model
K:s(s)=Lz(s),
where s,z∈CNdenote vectors of all interconnection inputs
and interconnection outputs respectively and
L=
0l12··· 0
l210… 0……0 lN−1N00 lNN− 1 0
 (2)
represents the local interactions. That is subsystem Si
fori=1, .., N −1 is coupled to Si+1and vice versa. Thus,
subsystem Siis inﬂuenced by subsystem Si−1and Si+1,
denoted by the local interaction model
Ki:si(s)=/summationtext
j∈{i−1,i+1}∩Nlijzj(s).
The overall system given by S=comb/parenleftbig
{Si}i∈N∪{K}/parenrightbig
does not contain any decentralised ﬁxed modes and is
controlled by Ndecentralised controllers
Ci:/braceleftbigg
˙xCi(t)=ACixCi(t)+b Ci(wi(t)−yi(t)),xCi(0)=0
ui(t)=CCixCi(t)+d Ci(wi(t)−yi(t)),IFAC NecSys 2015
Sept 10-11, 2015. Philadelphia, USA
21

22 Sven Bodenburg et al. / IF AC-PapersOnLine 48-22 (2015) 020–027
where xCi∈RnCiis the state vector and wi∈Ris the
scalar reference signal. The equivalent frequency-domain
representation reads
Ci:ui(s)=Ci(s)(w i(s)−yi(s)), (3)
where Ci(s)=d Ci+CCi/parenleftbig
sI−ACi/parenrightbig−1bCi. Thus, the com-
bined model Fi=comb (Si,Ci) of the subsystem (1) com-
bined with the decentralised controller (3) is denoted by
Fi:

˙xFi(t)=AFixFi(t)+b Fiwi(t)+e Fisi(t),xFi(0)=0
yi(t)=cT
FixFi(t)
zi(t)=cTFzixFi(t),
where xFi∈Rni+nCiand equivalently by
Fi:/braceleftbigg
yi(s)=Fywi(s)wi(s)+F ysi(s)si(s),
zi(s)=Fzwi(s)wi(s)+F zsi(s)si(s).
It is assumed that an actuator failure foccurs at subsys-
temS1at the time instance tf≥0, where the subsystem is
in its operating point ( xf1(tf)=0). The failure is modelled
by setting the corresponding column b1,jinB1to zero.
The faulty subsystem is, therefore, denoted by
Sf1:

˙xf1(t)=A1xf1(t)+B f1uf1(t)+e isf1(t)
yf1(t)=cT
1xf1(t),xf1(tf)=0
zf1(t)=cTz1xf1(t),(4)
where xf1denotes the faulty state and yf1,uf1,sf1,zf1the
faulty signals. In the frequency domain the fault aﬀects the
transfer functions ST
yu1(s) and ST
zu1(s) which, thereafter,
are denoted by ST
yuf1(s) and ST
zuf1(s).
2.3 Design agent
Every subsystem is associated with a design agent that
manages the following tasks:
•procurement of model information for reconﬁguration
•performing the reconﬁguration
•implementation of the reconﬁgured control algorithm
Each design agents is able to communicate with all otherdesign agents D
ithrough the network. Furthermore, the
design agents Diinitially store the models Si,Ci,Kand
the local control aim Ai.
The modelling aim is to approximate the behaviour from
input uf1to the output yf1appropriately (see Sec. 5),
whereas the reconﬁguration aim is to recover overall sys-tem stability (see Sec. 4).
2.4 Further background and assumptions
Let the overall system interconnection structure be given
as directed graph G
K=/parenleftbig
VK,EK/parenrightbig
with vertex set VK=Nand
edge set EK=/braceleftbig
(i, j):lij/negationslash=0/bracerightbig
⊆VK×VK, where lijare the
elements of the interconnection matrix Land the pair (i, j )
indicates a physical coupling from SjtoSi(Fig. 2 (a)). For
later use, strong connectivity of subsystems is deﬁned:
Deﬁnition 1. (Strong connection Lunze (1992)) The sub-
system Siis strongly connected to subsystem Sj, if in the
interconnection graph GKthere exists a path from vertex
ito vertex jand vice versa.
Moreover, for locally interconnected systems with the
characteristic structure shown in Fig. 2 (a), the termneighbour-degree is introduced:Deﬁnition 2. (Neighbour-degree) Consider a local inter-
connection (2). The subsystem S
iis an l-th degree neigh-
bour of Sj, if in the interconnection graph GKvertex iis
connected to vertex jby at least ledges, where l∈N0.
Considering the interconnection graph shown in Fig. 2,subsystem S
3is the 2-nd degree neighbour of S1.
Fig. 2. Interconnection graph and communication graph
To visualise the communication among the design agents
at time instant ka directed graph GD(k)=/parenleftbig
VD,ED(k)/parenrightbig
with vertex set VD=Nfor the design agents and edge set
ED(k)=/braceleftbig
(i, j):Djcommunicates with Di/bracerightbig
⊆V D×VDis
introduced as shown in Fig. 2 (b). Moreover, the cumu-
lated communication graph yields GD=/parenleftbig
VD,ED/parenrightbig
, where
ED=/uniontext
kED(k).
The diagnostic task is assumed to be given which leads to
the following assumption:
Assumption 1. The local diagnostic unit of subsystem Si
identiﬁes the fault funiquely and forwards the model Sf1
(4) of the faulty subsystem to the design agent D1.
Moreover, a nominal controller exists stated as follows:
Assumption 2. There exist Ndecentralised control sta-
tions Cisuch that the overall controlled system is stable.
It is furthermore assumed that the models are exact and
the network is ideal, (i.e., no delays and no package losses).
3. MAIN IDEA AND MODELS OF PLUG-AND-PLAY
RECONFIGURATION
This section proposes the main idea of plug-and-playreconﬁguration and motivates to limit the amount ofmodel information used for controller reconﬁguration.
3.1 Main idea
The main idea of plug-and-play reconﬁguration is the
introduction of Ndesign agents D
iwhich equally store the
corresponding subsystem model Sito replace the presence
of a central omniscient entity. The moment an actuatorfails in subsystem S
1, the design agent D1procures model
information from the other design agents Diover the
network to model the dynamics of the physically coupledfaulty subsystem from a local view, i.e., the I/O-pair
(u
f1,yf1) as depicted in Fig. 3 (a). As a special attribute of
locally interconnected systems (Fig. 2 (a)) subsystems with
a high neighbour-degree lonly have a weak inﬂuence on the
dynamics of the faulty subsystem Sf1, whereas subsystems
with a low neighbour-degree eﬀect the dynamics of Sf1
signiﬁcantly. This fact motivates to ignore the models ofweakly coupled subsystems to limit the amount of modelinformation for reconﬁguration.
3.2 Models
From the I/O-pair (u
f1,yf1) the overall faulty process
consists of the faulty subsystem Sf1and all other intercon-IFAC NecSys 2015
Sept 10-11, 2015. Philadelphia, USA
22

Sven Bodenburg et al. / IF AC-PapersOnLine 48-22 (2015) 020–027 23
where xCi∈RnCiis the state vector and wi∈Ris the
scalar reference signal. The equivalent frequency-domain
representation reads
Ci:ui(s)=Ci(s)(w i(s)−yi(s)), (3)
where Ci(s)=d Ci+CCi/parenleftbig
sI−ACi/parenrightbig−1bCi. Thus, the com-
bined model Fi=comb (Si,Ci) of the subsystem (1) com-
bined with the decentralised controller (3) is denoted by
Fi:

˙xFi(t)=AFixFi(t)+b Fiwi(t)+e Fisi(t),xFi(0)=0
yi(t)=cT
FixFi(t)
zi(t)=cTFzixFi(t),
where xFi∈Rni+nCiand equivalently by
Fi:/braceleftbigg
yi(s)=Fywi(s)wi(s)+F ysi(s)si(s),
zi(s)=Fzwi(s)wi(s)+F zsi(s)si(s).
It is assumed that an actuator failure foccurs at subsys-
temS1at the time instance tf≥0, where the subsystem is
in its operating point ( xf1(tf)=0). The failure is modelled
by setting the corresponding column b1,jinB1to zero.
The faulty subsystem is, therefore, denoted by
Sf1:

˙xf1(t)=A1xf1(t)+B f1uf1(t)+e isf1(t)
yf1(t)=cT
1xf1(t),xf1(tf)=0
zf1(t)=cTz1xf1(t),(4)
where xf1denotes the faulty state and yf1,uf1,sf1,zf1the
faulty signals. In the frequency domain the fault aﬀects the
transfer functions ST
yu1(s) and ST
zu1(s) which, thereafter,
are denoted by ST
yuf1(s) and ST
zuf1(s).
2.3 Design agent
Every subsystem is associated with a design agent that
manages the following tasks:
•procurement of model information for reconﬁguration
•performing the reconﬁguration
•implementation of the reconﬁgured control algorithm
Each design agents is able to communicate with all otherdesign agents D
ithrough the network. Furthermore, the
design agents Diinitially store the models Si,Ci,Kand
the local control aim Ai.
The modelling aim is to approximate the behaviour from
input uf1to the output yf1appropriately (see Sec. 5),
whereas the reconﬁguration aim is to recover overall sys-tem stability (see Sec. 4).
2.4 Further background and assumptions
Let the overall system interconnection structure be given
as directed graph G
K=/parenleftbig
VK,EK/parenrightbig
with vertex set VK=Nand
edge set EK=/braceleftbig
(i, j):lij/negationslash=0/bracerightbig
⊆VK×VK, where lijare the
elements of the interconnection matrix Land the pair (i, j )
indicates a physical coupling from SjtoSi(Fig. 2 (a)). For
later use, strong connectivity of subsystems is deﬁned:
Deﬁnition 1. (Strong connection Lunze (1992)) The sub-
system Siis strongly connected to subsystem Sj, if in the
interconnection graph GKthere exists a path from vertex
ito vertex jand vice versa.
Moreover, for locally interconnected systems with the
characteristic structure shown in Fig. 2 (a), the termneighbour-degree is introduced:Deﬁnition 2. (Neighbour-degree) Consider a local inter-
connection (2). The subsystem S
iis an l-th degree neigh-
bour of Sj, if in the interconnection graph GKvertex iis
connected to vertex jby at least ledges, where l∈N0.
Considering the interconnection graph shown in Fig. 2,subsystem S
3is the 2-nd degree neighbour of S1.
Fig. 2. Interconnection graph and communication graph
To visualise the communication among the design agents
at time instant ka directed graph GD(k)=/parenleftbig
VD,ED(k)/parenrightbig
with vertex set VD=Nfor the design agents and edge set
ED(k)=/braceleftbig
(i, j):Djcommunicates with Di/bracerightbig
⊆V D×VDis
introduced as shown in Fig. 2 (b). Moreover, the cumu-
lated communication graph yields GD=/parenleftbig
VD,ED/parenrightbig
, where
ED=/uniontext
kED(k).
The diagnostic task is assumed to be given which leads to
the following assumption:
Assumption 1. The local diagnostic unit of subsystem Si
identiﬁes the fault funiquely and forwards the model Sf1
(4) of the faulty subsystem to the design agent D1.
Moreover, a nominal controller exists stated as follows:
Assumption 2. There exist Ndecentralised control sta-
tions Cisuch that the overall controlled system is stable.
It is furthermore assumed that the models are exact and
the network is ideal, (i.e., no delays and no package losses).
3. MAIN IDEA AND MODELS OF PLUG-AND-PLAY
RECONFIGURATION
This section proposes the main idea of plug-and-playreconﬁguration and motivates to limit the amount ofmodel information used for controller reconﬁguration.
3.1 Main idea
The main idea of plug-and-play reconﬁguration is the
introduction of Ndesign agents D
iwhich equally store the
corresponding subsystem model Sito replace the presence
of a central omniscient entity. The moment an actuatorfails in subsystem S
1, the design agent D1procures model
information from the other design agents Diover the
network to model the dynamics of the physically coupledfaulty subsystem from a local view, i.e., the I/O-pair
(u
f1,yf1) as depicted in Fig. 3 (a). As a special attribute of
locally interconnected systems (Fig. 2 (a)) subsystems with
a high neighbour-degree lonly have a weak inﬂuence on the
dynamics of the faulty subsystem Sf1, whereas subsystems
with a low neighbour-degree eﬀect the dynamics of Sf1
signiﬁcantly. This fact motivates to ignore the models ofweakly coupled subsystems to limit the amount of modelinformation for reconﬁguration.
3.2 Models
From the I/O-pair (u
f1,yf1) the overall faulty process
consists of the faulty subsystem Sf1and all other intercon-IFAC NecSys 2015
Sept 10-11, 2015. Philadelphia, USA
22nected controlled subsystems Ficombined in the residual
system R1=comb/parenleftbig
{Fi}i=2,..,N ∪{K}/parenrightbig
characterised by
R1:s1(s)=R1(s)z1(s),
which are also aﬀected by the fault through the physical
couplings (Fig. 3 (a)). The residual system is separated
Fig. 3. Plug-and-play reconﬁguration from a local view of
design agent D1
into two disjoint parts. First, the subsystems with a greatinﬂuence on the I/O-pair ( s
f1,zf1) are combined in the
approximate residual system ˆR1=comb/parenleftbig
{Fi,K i}i∈N S1/parenrightbig
ˆR1:/braceleftbigg
s1(s)= ˆR1(s)z1(s)+ˆRsq1(s)q1(s)
p1(s)= ˆRpz1(s)z1(s)+ˆRpq1(s)q1(s),
where/parenleftbig
i∈N S1:={2, .., w −1}/parenrightbig
. The second part cumulates
the weakly coupled subsystems Fi,/parenleftbig
i∈N W1:={w, .., N }/parenrightbig
which have a minor eﬀect w.r.t. the I/O-pair (s f1,zf1) to
yield the error system E1=comb/parenleftbig
{Fi,K i}i∈N W1/parenrightbig
E1:q1(s)=E1(s)p1(s). (5)
Consider that the system ˆR1yields an appropriate approx-
imation of the behaviour of the residual system so that it isused to reconﬁgure control station C
1, whereas the weakly
coupled subsystems are treated as model uncertainties.Thus, there is no need to model the error system exactly
but only as comparison system
¯E
1:¯q1(ω)=¯E1(ω)·|p1(jω)|, (6)
where ¯ q1(ω)∈Rshown in Fig. 3 (b), where the following
relation presented in Lunze (1988) holds:
Deﬁnition 3. (Comparison system) The model (6) is a
comparison system of the linear system (5), if
¯E1(ω)≥|¯E1(jω)|,∀ω. (7)
Then Eqn. (6) yields ¯ q1(ω)≥|q1(jω)|for the input |p1(jω)|.
As a consequence, the combination of the approximate
residual system ˆR1and the upper bound ¯E1is represented
by the comparison system ¯R1=comb ({ˆR1,¯E1}) deﬁned by
¯R1:¯s1(ω)=¯R1(ω)|z1(jω)|with
¯R1(ω)=|ˆR1(jω)|+|ˆRzq1(jω)|·¯E1(ω)
/parenleftbig
1−|ˆRpq1(jω)|·¯E1(ω)/parenrightbig−1|ˆRps1(jω)|.
That is ¯R1(ω)≥|R1(jω)|,∀ω. The residual dynamics
|R1(jω)|are approximated by |ˆR1(jω)|≈|R1(jω)|.
The model Sf1under the inﬂuence of the physical couplings
is modelled by ˆPf1=comb/parenleftbig
{Sf1,ˆR1}/parenrightbig
, where
ˆPf1:

˙ˆxPf1(t)=ˆAP1ˆxPf1(t)+ˆBPf1uf1(t)+ˆeP1qf1(t)
yf1(t)=ˆcT
P1ˆxfP1(t),ˆxPf1(0)=0
pf1(t)=ˆcT
Pp1ˆxfP1(t).(8)
For later use, the combination of ˆPf1and C1/parenleftbigˆAf1=
comb ({ˆPf1,C1)}/parenrightbig
is introduced given in time-domain by
ˆAf1:

˙ˆxAf1(t)=ˆAA1ˆxAf1(t)+ˆbAf1w1(t)+ˆeA1qf1(t)
yf1(t)=ˆcT
A1ˆxfA1(t),ˆxAf1(0)=0
pf1(t)=ˆcTAp1ˆxfA1(t),(9)
which represents the approximation model of the con-
trolled extended subsystem Af1=comb/parenleftbig
{ˆPf1,C1}/parenrightbig
.
Moreover, the notation ˆR(l)
1andE(l)
1is introduced to in-
dicate up to which neighbour degree lmodels are included
within the approximate residual system respectively ex-
cluded from the error system. In particular,
ˆR(l)
1=comb/parenleftbig
{Fi,K i}i∈N(l)
S1/parenrightbig
, (10)
where N(l)
S1:={2, .., l +1}. Similarly, E(l)
1lumps together all
subsystems not included in N(l)
S1
E(l)
1=comb/parenleftbig
{Fi,K i}i∈N(l)
W1/parenrightbig
, (11)
where N(l)
W1:=N \N(l)
S1\{1}. Note that for ˆR(0)
1it yields
ˆR(0)
sq1(s)=ˆR(0)
pz1(s)=1 and ˆR(0)
1(s)=ˆR(0)
pq1(s)=0.
For the following investigations it is essential to ensurestability of the error system (11) and the approximateresidual system (10) for arbitrary l(see Thm. 2). Fur-
thermore, it is reasonable for the locally interconnectedsystem (2) that the eﬀect w.r.t. the I/O-pair (z
f1,sf1) of
subsystem Sf1becomes weaker for increasing neighbour-
degree (Prop. 3). Thus, the following assumption is stated
Assumption 3. It exist Ndecentralised control stations Ci
such that for i=2, .., N
|Fzsi−1(jω)·li−1i·Fzsi(jω)·lii−1|<1/4,∀ω (12)
4. RECONFIGURATION WITH A VIRTUAL
ACTUATOR
In this section it is focused on the reconﬁguration C1using
a virtual actuator. Local conditions A1are derived to
guarantee global stability of the reconﬁgured closed loop
despite of the limited model information (i.e., ˆPf1).
A solution to the controller reconﬁguration problem af-
ter actuator failures is given by the fault-hiding princi-ple, introduced in Steﬀen (2005); Richter (2011). A vir-tual actuator VAis placed between the faulty subsystem
S
f1and the nominal controller C1with the goal that
the faulty plant together with the virtual actuator VA
mimics the behaviour of the fault-free process. In par-ticular, a failure is hidden from the nominal controller,
if the reconﬁgured system P
⋆
1=comb ({Sf1,R1, VA}) hasIFAC NecSys 2015
Sept 10-11, 2015. Philadelphia, USA
23

24 Sven Bodenburg et al. / IF AC-PapersOnLine 48-22 (2015) 020–027
the same I/O-behaviour w.r.t. ( uc1,yc1) as the nominal
system P1=comb ({S1,R1}). Then the nominal controller
stabilises the reconﬁgured system due to Assumption 2.
Fig. 4. Reconﬁguration with a virtual actuator
The virtual actuator VAis a model-based system which
contains the model Sf1under the inﬂuence of the physical
interaction shown in Fig. 4. As motivated in Sec. 3, the I/O
behaviour from the faulty input uf1to the faulty output
yf1is adequately described by the model ˆPf1combining all
strongly coupled controlled subsystems. The state-spacemodel of the virtual actuator reads
VA:

˙x
∆1(t)=A∆1x∆1(t)+ˆBP1uc1(t),x∆1(0)=0
uf1(t)=M1x∆1(t)
yc1(t)=yf1(t)+ ˆcT
P1x∆1(t),(13)
where x∆1=xP1−xPf1andA∆1=ˆAP1−ˆBPf1M1.
The following theorem states a condition to stabilise the
faulty system by the virtual actuator (13):
Theorem 1. (Overall system stability after an actuator
failure) The faulty overall system is stabilisable by the VA
(13), if and only if the pair/parenleftbigˆAP1,ˆBPf1/parenrightbig
is stabilisable.
The feedback gain M1of the VA(13) has to be designed
such that the matrix A∆1is Hurwitz and
|ˆA⋆
pq1(jω)|·¯E1(ω)<1,∀ω,
where ˆA⋆
pq1(s)=ˆc⋆T
Ap1(sI−ˆA⋆A1)−1ˆe⋆A1of the reconﬁgured
extended controlled system ˆA⋆
1=comb/parenleftbig
{ˆPf1,C1, VA}/parenrightbig
.
The proof is given in Appendix A. In summary, the local
conditions to guarantee overall system stability claims thatthe feedback gain M
1should be designed in order that
A1:

1.the matrix ˆAP1−ˆBPf1M1is Hurwitz
2.the following condition holds
|ˆA⋆
pq1(jω)|·¯E1(ω)<1,∀ω.(14a)
(14b)
5. PROCUREMENT OF MODEL INFORMATION
FOR RECONFIGURATION
As stated in Sec. 3.1 the model ˆPf1=comb/parenleftbig
{Sf1,ˆR1}/parenrightbig
to
design the virtual actuator is a priori unknown and not
available to D1. In this section, local conditions are derived
to ﬁnd the strongly coupled subsystems to set up the model
ˆPf1. Moreover, the exchange and combination of model
information is elaborated.
5.1 Classiﬁcation of strongly and weakly coupled subsystems
To distinguish between relevant and non-relevant model
information for reconﬁguration the subsystems coupled tothe faulty subsystem Sf1are categorised into strongly and
weakly coupled subsystems.
Deﬁnition 4. (Strong and weak coupling) Consider a local
interconnection (2). The l-th degree neighbour Siof sub-
system S1is said to be strongly coupled with subsystem
S1, if and only if for a given function γ1(ω):R→R, with
γ1(ω)≥0,∀ωthe condition
|ˆR(l)
1(jω)|−|ˆR(l−1)
1(jω)|≥γ1(ω),∃ω (15)
holds. The l-th degree neighbour Siof subsystem S1is said
to be weakly coupled with subsystem S1, if and only if
|ˆR(l)
1(jω)|−|ˆR(l−1)
1(jω)|<γ1(ω),∀ω. (16)
Note that the classiﬁcation is w.r.t. the I/O-pair ( sf1,zf1).
The function γ1(ω) is a tuning element to adjust the
accuracy of the approximation ˆR1. The smaller γ1(ω), the
more subsystems are categorised as strongly coupled. It is
emphasised that strong coupling is w.r.t. to the strength
of the physical inﬂuence, whereas strong connectivity is a
structural property deﬁned in Def. 1, although in literatureboth terms are used synonymously (e.g. Lunze (1992)).
On basis of Deﬁnition 4 the following theorem is derived:
Theorem 2. (Local condition to classify strongly and
weakly coupled subsystems) Consider the local inter-
connection (2) and Assumption 3 to be satisﬁed.
Denote the l-th degree neighbour of S1bySiand the
l−1-th degree neighbour by Si−1. Then, for a given
function γ1(ω):R→R, with γ1(ω)≥0,∀ω, the l-th
degree neighbour Siis weakly coupled with subsystem
S1according to (16), if
|Fzsi(jω)·lii−1|<γ(l)
1(ω),∀ω, (17)
where
γ(l)
1(ω)=|li−1i|−1/parenleftBig
|ˆR(l−1)
sq1(jω)|·/parenleftbig
γ1(ω)/parenrightbig−1·
|ˆR(l−1)
pz1(jω)|+|ˆR(l−1)
pq1(jω)|/parenrightBig−1
.(18)
Proof. For the original condition (16) an upper bound
can be determined
|ˆR(l)
1(jω)|−|ˆR(l−1)
1(jω)|≤| ˆR(l−1)
∆1(jω)|<γ1(ω),
where
|ˆR(l−1)
∆1(jω)|=|ˆR(l−1)
sq1(jω)li−1iFzsi(jω)lii−1ˆR(l−1)
pz1(jω)|Ψ(ω)
(19)
with
Ψ(ω)=/parenleftbig
1−|l i−1iFzsi(jω)lii−1ˆR(l−1)
pq1(jω)|/parenrightbig−1. (20)
Rearranging the letter relation yields the relation (17)with (18). Furthermore, Assumption 3 ensures that
ˆR(l−1)
∆1(jω) is stable for all l∈N0. /square
It has to be emphasised that condition (17) can be lo-cally evaluated by design agent D
iwith the local model
information (see Sec. 2.3) and function γ(l)
1(ω) which is
calculated by D1and forwarded from D1toDi. This is
subject of discussion in the Sec. 5.2.
To determine weakly coupled subsystems, condition (17)
yields a suﬃcient condition of the inequality (16). Inaddition, it can be concluded that if S
iis strongly coupled
toS1according to (15), condition (17) is violated, i.e.,
|Fzsi(jω)·lii−1|≥γ(l)
j(ω),∃ω∈R. (21)IFAC NecSys 2015
Sept 10-11, 2015. Philadelphia, USA
24

Sven Bodenburg et al. / IF AC-PapersOnLine 48-22 (2015) 020–027 25
the same I/O-behaviour w.r.t. ( uc1,yc1) as the nominal
system P1=comb ({S1,R1}). Then the nominal controller
stabilises the reconﬁgured system due to Assumption 2.
Fig. 4. Reconﬁguration with a virtual actuator
The virtual actuator VAis a model-based system which
contains the model Sf1under the inﬂuence of the physical
interaction shown in Fig. 4. As motivated in Sec. 3, the I/O
behaviour from the faulty input uf1to the faulty output
yf1is adequately described by the model ˆPf1combining all
strongly coupled controlled subsystems. The state-spacemodel of the virtual actuator reads
VA:

˙x
∆1(t)=A∆1x∆1(t)+ˆBP1uc1(t),x∆1(0)=0
uf1(t)=M1x∆1(t)
yc1(t)=yf1(t)+ ˆcT
P1x∆1(t),(13)
where x∆1=xP1−xPf1andA∆1=ˆAP1−ˆBPf1M1.
The following theorem states a condition to stabilise the
faulty system by the virtual actuator (13):
Theorem 1. (Overall system stability after an actuator
failure) The faulty overall system is stabilisable by the VA
(13), if and only if the pair/parenleftbigˆAP1,ˆBPf1/parenrightbig
is stabilisable.
The feedback gain M1of the VA(13) has to be designed
such that the matrix A∆1is Hurwitz and
|ˆA⋆
pq1(jω)|·¯E1(ω)<1,∀ω,
where ˆA⋆
pq1(s)=ˆc⋆T
Ap1(sI−ˆA⋆A1)−1ˆe⋆A1of the reconﬁgured
extended controlled system ˆA⋆
1=comb/parenleftbig
{ˆPf1,C1, VA}/parenrightbig
.
The proof is given in Appendix A. In summary, the local
conditions to guarantee overall system stability claims thatthe feedback gain M
1should be designed in order that
A1:

1.the matrix ˆAP1−ˆBPf1M1is Hurwitz
2.the following condition holds
|ˆA⋆
pq1(jω)|·¯E1(ω)<1,∀ω.(14a)
(14b)
5. PROCUREMENT OF MODEL INFORMATION
FOR RECONFIGURATION
As stated in Sec. 3.1 the model ˆPf1=comb/parenleftbig
{Sf1,ˆR1}/parenrightbig
to
design the virtual actuator is a priori unknown and not
available to D1. In this section, local conditions are derived
to ﬁnd the strongly coupled subsystems to set up the model
ˆPf1. Moreover, the exchange and combination of model
information is elaborated.
5.1 Classiﬁcation of strongly and weakly coupled subsystems
To distinguish between relevant and non-relevant model
information for reconﬁguration the subsystems coupled tothe faulty subsystem Sf1are categorised into strongly and
weakly coupled subsystems.
Deﬁnition 4. (Strong and weak coupling) Consider a local
interconnection (2). The l-th degree neighbour Siof sub-
system S1is said to be strongly coupled with subsystem
S1, if and only if for a given function γ1(ω):R→R, with
γ1(ω)≥0,∀ωthe condition
|ˆR(l)
1(jω)|−|ˆR(l−1)
1(jω)|≥γ1(ω),∃ω (15)
holds. The l-th degree neighbour Siof subsystem S1is said
to be weakly coupled with subsystem S1, if and only if
|ˆR(l)
1(jω)|−|ˆR(l−1)
1(jω)|<γ1(ω),∀ω. (16)
Note that the classiﬁcation is w.r.t. the I/O-pair ( sf1,zf1).
The function γ1(ω) is a tuning element to adjust the
accuracy of the approximation ˆR1. The smaller γ1(ω), the
more subsystems are categorised as strongly coupled. It is
emphasised that strong coupling is w.r.t. to the strength
of the physical inﬂuence, whereas strong connectivity is a
structural property deﬁned in Def. 1, although in literatureboth terms are used synonymously (e.g. Lunze (1992)).
On basis of Deﬁnition 4 the following theorem is derived:
Theorem 2. (Local condition to classify strongly and
weakly coupled subsystems) Consider the local inter-
connection (2) and Assumption 3 to be satisﬁed.
Denote the l-th degree neighbour of S
1bySiand the
l−1-th degree neighbour by Si−1. Then, for a given
function γ1(ω):R→R, with γ1(ω)≥0,∀ω, the l-th
degree neighbour Siis weakly coupled with subsystem
S1according to (16), if
|Fzsi(jω)·lii−1|<γ(l)
1(ω),∀ω, (17)
where
γ(l)
1(ω)=|li−1i|−1/parenleftBig
|ˆR(l−1)
sq1(jω)|·/parenleftbig
γ1(ω)/parenrightbig−1·
|ˆR(l−1)
pz1(jω)|+|ˆR(l−1)
pq1(jω)|/parenrightBig−1
.(18)
Proof. For the original condition (16) an upper bound
can be determined
|ˆR(l)
1(jω)|−|ˆR(l−1)
1(jω)|≤| ˆR(l−1)
∆1(jω)|<γ1(ω),
where
|ˆR(l−1)
∆1(jω)|=|ˆR(l−1)
sq1(jω)li−1iFzsi(jω)lii−1ˆR(l−1)
pz1(jω)|Ψ(ω)
(19)
with
Ψ(ω)=/parenleftbig
1−|l i−1iFzsi(jω)lii−1ˆR(l−1)
pq1(jω)|/parenrightbig−1. (20)
Rearranging the letter relation yields the relation (17)with (18). Furthermore, Assumption 3 ensures that
ˆR(l−1)
∆1(jω) is stable for all l∈N0. /square
It has to be emphasised that condition (17) can be lo-cally evaluated by design agent D
iwith the local model
information (see Sec. 2.3) and function γ(l)
1(ω) which is
calculated by D1and forwarded from D1toDi. This is
subject of discussion in the Sec. 5.2.
To determine weakly coupled subsystems, condition (17)
yields a suﬃcient condition of the inequality (16). Inaddition, it can be concluded that if S
iis strongly coupled
toS1according to (15), condition (17) is violated, i.e.,
|Fzsi(jω)·lii−1|≥γ(l)
j(ω),∃ω∈R. (21)IFAC NecSys 2015
Sept 10-11, 2015. Philadelphia, USA
24Thus, by condition (17) it is guaranteed that all subsys-
tems strongly coupled to S1in accordance to Def. 4 are
classiﬁed as strongly coupled.
As the subsystems are locally couple (see Fig. 2 (a)), the
eﬀect w.r.t. the I/O-pair ( zf1,sf1) of subsystem Sibecomes
weaker for increasing neighbour-degree (Assumption 3).The next proposition shows that if the l-th degree neigh-
bour is weakly coupled with S
1, then all subsystems of a
higher neighbour-degree are also weakly coupled with S1.
Proposition 3. (Relation between subsystems weakly cou-
pled to S1)Consider the local interconnection (2) and the
satisfaction of condition (12) of Assumption 3. Further-
more, denote the l-th degree neighbour of S1bySi, the
l−1-th degree neighbour by Si−1and the l−2-th degree
neighbour by Si−2. If the l−1-th degree neighbour Si−1is
weakly coupled with subsystem S1
|Fzsi−1(jω)·li−1i−2|<γ(l−1)
1(ω),∀ω, (22)
then the l-th degree neighbour Siis also weakly coupled
to subsystem S1
|Fzsi(jω)·lii−1|<γ(l)
1(ω),∀ω. (23)
Proof. The implication from (22) to (23) is equivalent to
|ˆR(l−1)
∆1(jω)|<γ1(ω),∀ω⇒| ˆR(l)
∆1(jω)|<γ1(ω),∀ω,(24)
where |ˆR(l−1)
∆1(jω)|and|ˆR(l)
∆1(jω)|are constructed accord-
ing to (19). The implication (24) is satisﬁed, if
|ˆR(l−1)
∆1(jω)|≥| ˆR(l)
∆1(jω)|,∀ω (25)
holds. With (19) the relation (25) can be rewritten into
|ˆR(l−1)
∆1(jω)|≥| ˆR(l−1)
∆1(jω)|·Γ(ω),∀ω
with
Γ(ω)=|li−1iFzsi(jω)lii−1ˆR(l−1)
pq1(jω)|·
/parenleftbig
1−|li−1iFzsi(jω)lii−1ˆR(l−1)
pq1(jω)|/parenrightbig−1
and
|ˆR(l)
pq1(jω)|=|Fzsi(jω)|·Ψ(ω) (26)
with Ψ(ω) from (20) such that to show (25) it is to prove
thatΓ(ω)≤1,∀ω∈R,which is equivalent to
|li−1iFzsi(jω)lii−1ˆR(l−1)
pq1(jω)|≤0.5,∀l∈N0. (27)
Inserting the relation (12) recursively into (26), it is that
|ˆR(l)
pq1(jω)|≤2·|F zsi(jω)|,∀l∈N0, where the index i
corresponds with the l-th degree neighbour. Hence, with
(12) the relation (27) holds. This proves the satisfaction
of the implication (24), if the Assumption 3 holds. The
satisfaction of (24), ﬁnally, proves the satisfaction of the
relation stated in Proposition 3. /square
5.2 Communication among the design agents
As mentioned in Sec. 2.3 each design agent Distores the
model SiandCiof the corresponding subsystem and con-
trol station respectively as well as the interaction model K.
D1additionally stores the frequency-depending threshold
γ1(ω). To have the model ˆR1and the comparison system
¯E1available to D1for controller reconﬁguration (cf. (14)),
design agent D1has to request model information from
all other design agents. The request and the combination
of model information has to follow a particular orderwhich is prescribed by the recursive composition rule of
the threshold γ(l)
1(ω) (18). Hence, D1has to request themodels iteratively beginning from the 1st degree neighbour
up to the N−1-th degree neighbour as visualised by the
communication graph GD1(k) in Fig. 5(a).
The received model information about the strongly cou-pled subsystems are combined according to (26),
|ˆR(l)
1(jω)|=|ˆR(l−1)
1(jω)|+|ˆR(l−1)
∆1(jω)|, (28)
|ˆR(l)
sq1(jω)|=|li−1iFzsi(jω)ˆR(l−1)
sq1(jω)|·Ψ(ω), (29)
|ˆR(l)
pz1(jω)|=|ˆR(l−1)
pz1(jω)Fzsi(jω)lii−1|·Ψ(ω), (30)
withΨ(ω) from (20) to yield the approximate system ˆR(l)
1.
Based on this system, the threshold (18) can be calculated.
Once the ﬁrst weakly coupled subsystem Swis detected,
all subsystems of higher neighbour degree are also weakly
coupled (Proposition 3). Since the behaviour of the weaklycoupled subsystems are described by the upper bound¯E
1,D1requests only upper bounds ¯Fszi(ω) on the actual
behaviour Fszi(jω) (i.e., ¯Fszi(ω)≥|Fszi(jω)|,∀ω) from
the remaining design agents Di,(i=w+1, .., N ). As the
threshold γ(l)
1(ω) is not longer needed to be calculated, all
upper bounds ¯Fszi(ω) are requested in one step (Fig. 5(a)).
Then, ¯E1(ω) is constructed according to
¯E1(ω)=|lT
E1|/parenleftbig
I−diag/parenleftbig¯Fzsi(ω)/parenrightbig
i∈NW1|LE1|/parenrightbig−1
diag/parenleftbig¯Fzsi(ω)/parenrightbig
i∈NW1|lE1|,(31)
where diag/parenleftbig¯Fzsi(ω)/parenrightbig
i∈NW1denotes a diagonal matrix with
¯Fzsi(ω), (i∈N W1),LE1represents the interconnection ma-
trix Lby crossing out all rows and columns which are
not in the set NW1,lT
E1is a the w-th row vector of Lby
crossing out all elements which are not in the set NW1
andlE1thew-th column of Lby crossing out all elements
which are not in the set NW1.|·|is applied element-wise.
Fig. 5. Communication graph GD(k) and GD
As it can be seen in Fig. 5 (a), the procurement of modelinformation does only take wsteps, where the sorting
of the ﬁrst weakly coupled subsystems S
wdepends on
the chosen threshold γ1(ω). It is emphasised that the
cumulated graph GD(Fig. 5 (b)) is not fully connected.
6. ALGORITHM FOR PLUG-AND-PLAY
RECONFIGURATION WITH A VA
If an actuator failure in subsystem S1occurs, then due
to the physical interaction (2), global system stabilityis jeopardised. Plug-and-play reconﬁguration guaranteesthe recovery of overall system stability by reconﬁguration
of control station C
1using a VA(Sec. 4). Due to the
absence of an omniscient global reconﬁguration unit, theIFAC NecSys 2015
Sept 10-11, 2015. Philadelphia, USA
25

26 Sven Bodenburg et al. / IF AC-PapersOnLine 48-22 (2015) 020–027
local design agent D1has to procure relevant model
information to run the reconﬁguration (Sec. 5). For this,
the required model information is limited to the models ofthose subsystems which are strongly coupled to the faultyoneS
f1.
The following algorithm summarises the automated pro-cedure of plug-and-play reconﬁguration:
Algorithm 1. (Plug-and-play reconﬁguration to actu-
ator failures)
Given: •γ1(ω),ˆR(0)
1,Sf1,S1,C1andKatD1
•Si,Ciavailable to Di
Init: l= 1, i= 2, γ(1)
1(ω)=γ1(ω)
(1)D1calculates γ(l)
1(ω) according to (18)
(2)D1sends γ(l)
1(ω) toDito request model infor-
mation
(3)Diveriﬁes condition (21). If condition (21) is sat-
isﬁed, Ditransmits SiandCitoD1, otherwise
Ditransmits ¯Fzsi(ω) toD1, setl=l+1,i=i+1
and goto step (6)
(4)D1combines the received models to result the
approximated residual system ˆR(l)
1according to
(26) and (28)–(30)
(5)setl=l+ 1, i=i+ 1. If i≤Ngoto step (1),
otherwise goto step (8)
(6)D1requests the upper bounds ¯Fzsj(ω) from Dj,
(j=i, .., N )
(7)D1constructs the comparison system ¯E1on basis
of the received upper bounds according to (31)
(8)D1combines the extended subsystem ˆPf1(8) for
the design of the VAin order to satisfy A1(14)
with information available to D1
(9)D1implements the VAinto the control hardware
Result: Reconﬁgured controller C⋆
1=comb/parenleftbig
{C1, VA}/parenrightbig
which stabilises the faulty system
7. EXAMPLE: ELECTRIC POWER NETWORK
In this section the procurement of model information to
set-up the model ˆPf1for controller reconﬁguration (cf.
Sec. 5) is illustrated on an electric power network. First,
the process is described, followed by the communication ofmodel information among the design agents.
7.1 System description
Fig. 6. Faulty electric power networkThe considered electric power network consists of four
power plants locally interconnected by tie lines (Fig. 6).Each power plant consists of a steam turbine which drivesan generator to produce electric power Saadat (1999). Thesubsystems are described by (1), where
A
1=A4=
0 1 00
−0.5−0.07 0. 10
00 −1.51.5
0−200 0 −10
,B1=B4=
00
0000
25 10
,
A
2=A3=
0 1 00
−0.5−0.035 0. 05 0
00 −1.25 1. 25
0−200 0 −10
,B2=B3=
00
0000
25 10

and for i=1, ..,4
e
i=(0 1 0 0)T,ci=(0 1 0 0)T,cT
zi=(1 0 0 0)T.
Each plant has two input signals ui=(u i,1ui,2)T, where in
the nominal case ui,1is used for control and ui,2remains
as a reserve input. The plants interact, if their mains
frequency diﬀers caused by varying loads modelled by
l21=l32=l23=l34=0.24 and l12=l43=0.48.
For reference tracking, four decentralised integral con-troller (3) are used, where
a
Ci=0,bCi=4,cCi=1,dCi=0
in order that Assumption 3 and Assumption 2 are satisﬁed.
7.2 Modelling of Sf1in an electric power network
The threshold γ1(ω) available to D1is given as γ1(ω)=
0.3|Szs1(jω)|in order to classify subsystems as strongly
coupled, if their inﬂuence w.r.t. the I/O-pair (s f1,zf1) is
greater than 30 % of the local inﬂuence |Szs1(jω)|. A failure
of the ﬁrst actuator in S1leads to make use of the second
one. This triggers the processing of Alg. 1. Next, the
procurement of model information is illustrated to build up
the model ˆPf1used for controller reconﬁguration (Fig. 7).
Fig. 7. Information ﬂow and processing diagram
D1starts with requesting D2(1st neighbour) to send its
model information (k =1). As condition (21) is satisﬁed
(Fig. 8 (a)), D2transmits S2andC2toD1which are
subsequently combined at k=3 to yield ˆR(1)
1. Thereafter,
D1sends the calculated threshold γ(2)
1toD3. Since con-
dition (21) is violated (Fig. 8 (b)) D3transmits the upper
bound ¯Fzs3(ω) to D1atk=6. As D1receives an upper
bound, D3is labelled as weakly coupled (i.e., w=3). Due to
Proposition 3, D1requests solely the upper bound ¯Fzs4(ω)
from D4(Fig. 8 (c)) and ﬁnally combines the comparison
system ¯E(1)
1at event k=9.
Figure 9 visualises the step response from input uf1to
output yf1for the isolated subsystem Sf1as well as for
the extended subsystem ˆP(1)
f1including the model F2,ˆP(2)
f1
including the models F2andF3and ﬁnally ˆP(3)
f1=P1. AsIFAC NecSys 2015
Sept 10-11, 2015. Philadelphia, USA
26

Sven Bodenburg et al. / IF AC-PapersOnLine 48-22 (2015) 020–027 27
local design agent D1has to procure relevant model
information to run the reconﬁguration (Sec. 5). For this,
the required model information is limited to the models ofthose subsystems which are strongly coupled to the faultyoneS
f1.
The following algorithm summarises the automated pro-cedure of plug-and-play reconﬁguration:
Algorithm 1. (Plug-and-play reconﬁguration to actu-
ator failures)
Given: •γ
1(ω),ˆR(0)
1,Sf1,S1,C1andKatD1
•Si,Ciavailable to Di
Init: l= 1, i= 2, γ(1)
1(ω)=γ1(ω)
(1)D1calculates γ(l)
1(ω) according to (18)
(2)D1sends γ(l)
1(ω) toDito request model infor-
mation
(3)Diveriﬁes condition (21). If condition (21) is sat-
isﬁed, Ditransmits SiandCitoD1, otherwise
Ditransmits ¯Fzsi(ω) toD1, setl=l+1,i=i+1
and goto step (6)
(4)D1combines the received models to result the
approximated residual system ˆR(l)
1according to
(26) and (28)–(30)
(5)setl=l+ 1, i=i+ 1. If i≤Ngoto step (1),
otherwise goto step (8)
(6)D1requests the upper bounds ¯Fzsj(ω) from Dj,
(j=i, .., N )
(7)D1constructs the comparison system ¯E1on basis
of the received upper bounds according to (31)
(8)D1combines the extended subsystem ˆPf1(8) for
the design of the VAin order to satisfy A1(14)
with information available to D1
(9)D1implements the VAinto the control hardware
Result: Reconﬁgured controller C⋆
1=comb/parenleftbig
{C1, VA}/parenrightbig
which stabilises the faulty system
7. EXAMPLE: ELECTRIC POWER NETWORK
In this section the procurement of model information to
set-up the model ˆPf1for controller reconﬁguration (cf.
Sec. 5) is illustrated on an electric power network. First,
the process is described, followed by the communication ofmodel information among the design agents.
7.1 System description
Fig. 6. Faulty electric power networkThe considered electric power network consists of four
power plants locally interconnected by tie lines (Fig. 6).Each power plant consists of a steam turbine which drivesan generator to produce electric power Saadat (1999). Thesubsystems are described by (1), where
A
1=A4=
0 1 00
−0.5−0.07 0. 10
00 −1.51.5
0−200 0 −10
,B1=B4=
00
0000
25 10
,
A
2=A3=
0 1 00
−0.5−0.035 0. 05 0
00 −1.25 1. 25
0−200 0 −10
,B2=B3=
00
0000
25 10

and for i=1, ..,4
e
i=(0 1 0 0)T,ci=(0 1 0 0)T,cT
zi=(1 0 0 0)T.
Each plant has two input signals ui=(u i,1ui,2)T, where in
the nominal case ui,1is used for control and ui,2remains
as a reserve input. The plants interact, if their mains
frequency diﬀers caused by varying loads modelled by
l21=l32=l23=l34=0.24 and l12=l43=0.48.
For reference tracking, four decentralised integral con-troller (3) are used, where
a
Ci=0,bCi=4,cCi=1,dCi=0
in order that Assumption 3 and Assumption 2 are satisﬁed.
7.2 Modelling of Sf1in an electric power network
The threshold γ1(ω) available to D1is given as γ1(ω)=
0.3|Szs1(jω)|in order to classify subsystems as strongly
coupled, if their inﬂuence w.r.t. the I/O-pair (s f1,zf1) is
greater than 30 % of the local inﬂuence |Szs1(jω)|. A failure
of the ﬁrst actuator in S1leads to make use of the second
one. This triggers the processing of Alg. 1. Next, the
procurement of model information is illustrated to build up
the model ˆPf1used for controller reconﬁguration (Fig. 7).
Fig. 7. Information ﬂow and processing diagram
D1starts with requesting D2(1st neighbour) to send its
model information (k =1). As condition (21) is satisﬁed
(Fig. 8 (a)), D2transmits S2andC2toD1which are
subsequently combined at k=3 to yield ˆR(1)
1. Thereafter,
D1sends the calculated threshold γ(2)
1toD3. Since con-
dition (21) is violated (Fig. 8 (b)) D3transmits the upper
bound ¯Fzs3(ω) to D1atk=6. As D1receives an upper
bound, D3is labelled as weakly coupled (i.e., w=3). Due to
Proposition 3, D1requests solely the upper bound ¯Fzs4(ω)
from D4(Fig. 8 (c)) and ﬁnally combines the comparison
system ¯E(1)
1at event k=9.
Figure 9 visualises the step response from input uf1to
output yf1for the isolated subsystem Sf1as well as for
the extended subsystem ˆP(1)
f1including the model F2,ˆP(2)
f1
including the models F2andF3and ﬁnally ˆP(3)
f1=P1. AsIFAC NecSys 2015
Sept 10-11, 2015. Philadelphia, USA
26Fig. 8. Local veriﬁcation of weak coupling
it can be seen, ˆP(1)
f1yields a reasonable approximation of
Pf1and is, therefore, used for controller reconﬁguration.
Fig. 9. Step response from uf1toyf1
8. CONCLUSION
This paper has presented a method for the plug-and-play
reconﬁguration of a single control station after an actuatorfailure to the corresponding subsystem of a locally inter-connected system. If an actuator fails, the correspondingdesign agent automatically procures relevant model infor-
mation from other design agents to model the behaviour
of the faulty subsystem under the inﬂuence of the physicalinteractions for the design of a virtual actuator in orderto recover global system stability. It has been shown thatthe required amount of model information is limited to themodels of those subsystems strongly coupled to the faultyone. The presented concept was implemented and success-fully tested by simulations on a electric power network.
REFERENCES
Amani, A., Poorjandaghi, S., Afshar, A., and Menhaj, M. (2014).
Fault tolerant control of large-scale systems subject to actuator
fault using a cooperative approach. Proceedings of the Institution
of Mechanical Engineers, Part I: Journal of Systems and Control
Engineering, 228(2), 63–77.
Bodenburg, S. and Lunze, J. (2013). Plug-and-play control –
deﬁnition and realisation in MATLAB. Automatisierungstechnik ,
61, 487–494.
Bodenburg, S. and Lunze, J. (2015). Plug-and-play control of
interconnected systems with a changing number of subsystems.
2015 European Control Conf. , 3525–3532.
Bodenburg, S., Niemann, S., and Lunze, J. (2014). Experimental
evaluations of a fault-tolerant plug-and-play controller. 2014
European Control Conf., 1945–1950.
Bodenburg, S., Vey, D., and Lunze, J. (2015). Plug-and-play recon-
ﬁguration of decentralised controllers of interconnected systems.9th Symposium on Fault Detection, Supervision and Safety ofTechnical Processes.
Deroo, F., Meinel, M., Ulbrich, M., and Hirche, S. (2014). Distributed
control design with local model information and guaranteed sta-bility. 19th IFAC World Congress, 4864–4870.
Ding, S. (2012). A survey of fault-tolerant networked control systems.
8th IFAC Symposium on Fault Detection, Supervision and Safetyof Technical Processes, 874–885.
Farokhi, F., Langbort, C., and Johansson, K. (2013). Optimal
structured static state-feedback control design with limited modelinformation for fully-actuated systems. Automatica , 49(2), 326–
337.Lunze, J. (1988). Robust Multivariable Feedback Control. Akademie-
Verlag Berlin.
Lunze, J. (1992). Feedback Control of Large-Scale Systems. Prentice
Hall.
Patton, R.J., Kambhampati, C., Casavola, A., Zhang, P., Ding, S.,
and Sauter, D. (2007). A generic strategy for fault-tolerance
in control systems distributed over a network. European J. of
Control , 13, 280–296.
Richter, J. (2011). Reconﬁgurable Control of Nonlinear Dynamical
Systems – A Fault-Hiding Approach. Springer.
Riverso, S., F. Boem, G.F.T., and Parisini, T. (2014). Fault diagnosis
and control-reconﬁguration in large-scale systems: a plug-and-play
approach. 53rd IEEE Conference on Decision and Control.
Riverso, S., Farina, M., and Ferrari-Trecate, G. (2013). Plug-and-
play decentralized model predictive control for linear systems.IEEE Trans. on Automatic Control , 58, 2608–2614.
Saadat, H. (1999). Power System Analysis. WCB/McGraw-Hill.
Steﬀen, T. (2005). Control Reconﬁguration of Dynamical Systems.
Springer.
Stoustrup, J. (2009). Plug & play control: Control technology
towards new challenges. European J. of Control , 15, 311–330.
Teixeira, A., Ara´ ujo, J., Sandberg, H., and Johansson, J. (2013). Dis-
tributed actuator reconﬁguration in networked control systems.
4th IFAC Workhop on Distributed Estimation and Control in
Networked Systems, 61–68.
Vey, D., H¨ ugging, S., Bodenburg, S., and Lunze, J. (2015). Controller
reconﬁguration of physically interconnected systems by decen-
tralized virtual actuators. 9th Symposium on Fault Detection,
Supervision and Safety of Technical Processes.
Appendix A. PROOF OF THEOREM 1
TheVA(13), the faulty extended subsystem ˆPf1(8) and
the nominal control station C1(3) are combined to the
model ˆA⋆
1=comb/parenleftbig
{ˆPf1,C1, VA}/parenrightbig
ˆA⋆
1:

/parenleftbigg˙˜x
A1
˙x∆1/parenrightbigg
=/parenleftbiggˆAA1 0/parenleftbig
−ˆBP1dC1ˆcT
P1ˆBP1CC1/parenrightbig
A∆1/parenrightbigg/parenleftbigg
˜xA1
x∆1/parenrightbigg
+/parenleftbiggˆbA1
ˆBP1dC1/parenrightbigg
w1+/parenleftbigg
ˆeA1
0/parenrightbigg
q1
yc1(t)=/parenleftbig
ˆcT
A10/parenrightbig/parenleftbigg
˜xA1
x∆1/parenrightbigg
p1(t)=/parenleftbigˆcT
Ap1−ˆcTPp1/parenrightbig/parenleftbigg
˜xA1
x∆1/parenrightbigg
,
where ˜xA1=(xPf1+x∆1xC1)T. Due to the triangular
form of the system matrix, its eigenvalues are the union
of the eigenvalues of the VA(13) and the eigenvalues
of the fault-free approximation model ˆA1(cf. (9) with
ˆbAf1=ˆbA1). Since, ˆA1is stable according to Assump-
tion 2, the reconﬁgured extended subsystem ˆA⋆
1is sta-
ble, if A∆1is Hurwitz. Due to the fact that the pair/parenleftbigˆAP1,ˆBPf1/parenrightbig
is stabilisable, there exist always a feed-
back gain M1. Furthermore, to guarantee stability of the
overall closed loop, it is required that the Nyquist plot
of 1− ˆA⋆
pq1(jω)·E1(jω),∀ωdoes not encircle the origin of
the complex plane. A suﬃcient condition is to guarantee
that Re {1− ˆA⋆
pq1(jω)·E1(jω)}>0,∀ω. Due to the relation
Re{1− ˆA⋆pq1(jω)·E1(jω)}≥1−|ˆA⋆pq1(jω)|·|E1(jω)|and (7),
it results |ˆA⋆pq1(jω)|·|E1(ω)|≤| ˆA⋆pq1(jω)|·¯E1(ω)<1 for
stability of the overall closed loop. /squareIFAC NecSys 2015
Sept 10-11, 2015. Philadelphia, USA
27

Copyright Notice

© Licențiada.org respectă drepturile de proprietate intelectuală și așteaptă ca toți utilizatorii să facă același lucru. Dacă consideri că un conținut de pe site încalcă drepturile tale de autor, te rugăm să trimiți o notificare DMCA.

Acest articol: ScienceDirectIFAC-PapersOnLine 48-22 (2015) 020027 [600129] (ID: 600129)

Dacă considerați că acest conținut vă încalcă drepturile de autor, vă rugăm să depuneți o cerere pe pagina noastră Copyright Takedown.

ScienceDirectIFAC-PapersOnLine 48-22 (2015) 020027 [600129]

Copyright Notice

1 © Curs fitoterapie – Costi Platon 1. Abcesul El reprezinta o formatie purulenta în interiorul unui tesut (conjunctiv, muscular) sau a unui organ… [610873]

TOTAL GYM ÎN DEZVOLTAREA CALITĂȚII MOTRICE FORȚA COORDONATOR ȘTIINȚIFIC : Lect. dr. Mihaela CHICOMBAN AUTOR : Mihai CUȚOIU 2019 INTRODUCERE În… [311770]

Mitrache Cristian 113 Circuite Basculante Converted [628993]

Adele B. Lynn, Eileen Klockars (cover) 50 Activities For Emotional Intelligence Hrd Press (2000) (1) [613129]

Pictura Bizantină În Locaşurile De Cult Din Nordul Moldovei [305982]

690700710720730740750760 [616355]

Copyright Notice

Similar Posts