Hybrid Petri Nets in Modeling [612580]

Hybrid Petri Nets in Modeling
the Packing Processes: Case Study

Mircea Adrian Drighiciu, Daniel Cristian Cismaru

University of Craiova / Faculty of Electrical Engineering, Craiova, 107 Decebal Blvd., Romania

[anonimizat]

Abstract — In many cases, the packing processes are
considered as hybrid systems, consisting of a set of
workstations, where various components must be processed,
and at least one flexible tran sport system used for loading
and/or unloading operations. Th is paper is focused to a
Hybrid Petri Nets approach for modeling and simulation
the behavior of such systems, considered a hybrid dynamic structure, with both continuous and discrete components
interacting. For heuristic representation of the model,
several sequences and rules were however followed. For the
case study, starting from the structure of the system, in
order to achieve a primary topology of the model, a bottom-
up synthesis technique was used, which allowed us to obtain
a basic version, consisting in several sub-models of related
physical subsystems of the packing station. Aggregation of these partial models was made in accordance with the
interactions of the physical elements of the whole system,
laid down in the operation protocol. Hence, into model
topology various elements charac teristic to generalized Petri
Nets were used, with inhibitor arcs and test arcs, mainly
aiming to reduce the complexity of the whole model. The
validation of the model was done through on-line simulation, in various scenarios, under the Visual Object
Net++ tool, which offers multip les facilities for the analysis
of behavioral properties in var ious real operating conditions
of the real physical system. Starting on the modular
structure of the whole model, consisting in several sub-
models of the same type, the authors obtained a multilevel
architecture, using Object Petri Nets paradigm for representation and exploiting their analysis potential.
Keywords — discrete event drive systems; hybrid systems;
Petri Nets; simulation
I. INTRODUCTION
In the most known approaches, packing stations are
high-speed systems, consisting in a set of workstations
for processing various (same or different) parts of
products and a flexible transport system. In order to
obtain a final product in such working process (a
sequence of operations), every part follows a route
through the set of system resources, according to a pre-
established schedule.
Traditionally, such a system is either modeled as a
continuous – state system or a discrete – state system
driven by time or asynchro nous external events. Various
artificial structures can be classified as hybrid systems, including logic – based switching control systems,
intelligent transport systems, flexible manufacturing
lines, batch processes and ma ny other electromechanical
systems (power electroni cs, robotics, flexible
manufacturing systems, control of the electrical drives, hydraulics and pneumatics systems etc.) [1], [2], [5], [6], [7], [8], [18], [19], [23], [24], [25], [26].
Hybrid Petri Nets is a powerful tool, which inherits all
the advantages of the Petri Net model such as the ability
to capture behaviors including concurrency,
synchronizations and conflicts. In this paper it was
considered a modified Hybrid Petri Net model whose
continuous part was represented by continuous Petri Nets
entities and its discrete parts were represented by a timed
Petri Net elements [5], [8], [16], [17], [22]. Our attention
was limited to build a hybrid model for an particular
automatic packing system, then to verify its behavior
properties by simulation in orde r to achieve a hierarchical
structure of the model, using the Object Petri Nets
paradigm.
II.
CASE STUDY
A.
System Structure
The analyzed packaging syst e m allows the automatic
arrangement of margarine packets into cardboard boxes, by multiple layers. Automatic packing workstation is a
complex structure containing components of an electric
drive system (ED) and elect ro-pneumatic systems (EPS),
(Fig.1), communicating with each-other via control
system (CS). It receives al l state information of the
process provided by the sensorial system, and commands the execution elements of E PS according to the proposed
schedule.
The ED contains an electric motor, which operates in
steady-state a single way conve yor – C (Fig.2.a). It was
assumed that the speed of the conveyor – for one
simulation scenario – has a constant value. The
pneumatic drive system has a basic structure, consisting
of single or double action cylinders, single or double
command valves and flow control devices (Fig.2.b).
Control System (CS)
x1 xq x2 …
We
ED
Packing
Wp
EPSpr
ocess
Fig.1. The structure of the packing system
93Annals of the University of Craiova , Electric al Engineering series , No. 39, 2015 ; ISSN 1842-4805__________________________________________ ________________________________________ _____________

An operating cycle consists in the fallowing sequences:
margarine packages are transp orted to the packing station
by the conveyor system, arra nged at a distance from each
other. At the right extremity of the conveyor, a
mechanical sensor stops the packages and allows – in the
meantime – their accumulati on, without stopping the
conveyor. At the moment in which three packets are
stored at the right extremity of the conveyor, a counter
device commands the advance of C 1. Its piston pushes
those tree packages to the mobile platform, and then returns immediately at the initial position. In the same time, another device counter is increasing (for the
counting of the package rows on the mobile platform).
When the first layer of the mobile platform was formed
(nine packages precisely), the cylinder C
2 pushes them
into the cardboard box and remains in this final state. In the same time, C
3 moves down and assures that packages
are stored into the box when the C 2 returns. Then the C 3
returns at the initial position and the mobile platform is
descended one step by cylinder C 4. Then, a new cycle
may be proceeded in the same sequence, until tree layers are formed into the cardboard box.
B.
Petri Nets – a overview
Petri Nets (PN) h
as been extensively used to model and
analyze manufacturing syst ems. One of the major
advantages of using PN models is that the same model can be used for the analysis of behavioral properties and
performance evolution, as well as for the systematic
construction of discrete event simulators and controllers
[1], [2], [3], [4], [5], [6], [7].

Known initially as an analysis tool of discrete event
drive systems PN gained – through subsequently
developments of their own formalism – unique strength in
hybrid systems representation and in study of qualitative
and quantitative their properties. Hence, Petri Nets is a
powerful tool in the modeling of hybrid systems with
autonomous commutation of the model generated by a
hysteresis phenomenon through a particular Petri Nets
structures, called M odified Hybrid Petri Nets (MHPN).
They are a formal descriptio n language for such hybrid
systems, which combines the advantages of a graphical
description with the possibility of a transparent
visualization, simulation and analysis [9], [10], [11], [12],
[13], [14], [15].
MHPN is a combination of ordinary and continuous
PN. This model can treat integer variables together with real variables and symbolic variables usually encountered
in other models of hybrid systems. It can inherit all the
modeling facilities of PN such as the ability to capture
concurrency, synchronizations and conflicts, allowing to
model systems with continuous flows and linear
evolutions in an intuitive way [5], [6], [7], [11], [12], [21].
But when a PN contains a la rge number of tokens, the
number of reachable states explodes and this is a practical
limitation of the use of this model.
An autonomous Hybrid Petri Net, [5] may be defined
as a sextuple HPN = {P, T, Pre, Post, m0, h} such that: P
is a finite, not empty, set of places: P = {P 1, P2, …P n};
T = {T 1, T 2, …, T m} is a finite, not empty, set of
transitions; P  T =  (P and T are disjointed); h, called
“hybrid function” indicates for every node whether it is a
discrete node or a continuous node; Pre : P x T  R+ or
N+, is the input incidence mapping; Post : P x T  R+
or N+, is he output incidence mapping; m0 : P  R+ or
N+, is the initial marking. Thus, there are two parts in a
hybrid Petri net, a discrete part and a continuous part ,
and these parts are interconne cted thanks to arc linking a
discrete node (pace or transition) to a continuous node
(transition or place), [4], [5], [6] (Fig.3).
The continuous places are P 1 and P 2, the continuous
transitions are T 1 and T 2, the discrete places – P 3 and P 4, R – C 4
Fig. 2. Physical struct ure of the system: a) Top vue; b) Side vue. b Lateral vue
Mechanical
stop
A – C 4 A – C 3
A – C 2 R – C 2 R – C 3
vC C3 – Cylinder
C2 – Cylinder
C4 – Cylinder One way
conveyor Mobile
platfor m R – C 2 Mechanical sto p
Cardboard box
Blade C3 – Cylinder
(top vue) A – C 2 A – C 1 R – C 1
L
MT M
vC C1 – Cylinder
C2 – Cylinder L1
a.
Continuous ne t
V2 P1
2.5 P2
0 T2
T1
V1
P3
T3 T4
P4
D
t
iscrete ne
Fig. 3. Hybrid Petri Net structure
94Annals of the University of Craiova , Electric al Engineering series , No. 39, 2015 ; ISSN 1842-4805__________________________________________ ________________________________________ _____________

and the discrete transitions – T 3 and T 4. Both continuous
transitions are enabled, and it can be fired [5], [6], [18].

Figure 4 shows a modified HPN. In this case the
continuous part represents a production system. The
transition T 1 corresponds to the working process of a
machine, continuous production or approximation by a continuous flow of a discrete production. When the output buffer reaches a certain level (10,8 on Fig. 4), production
stops (the transition T
2 id disable). This transition takes
priority over the continuous transitions.
C.
Petri Net model of the packing system
According to t
he proposed scenario, a primary model
was made, which consist in a modified discrete Petri Net (Fig.5). Beside of basic elements, this model contains
several extensions (test arcs: P
8 – T 4, P11 – T 8, P6 – T 11 and
inhibitor arc P 19 – T 1) which increases the power of
representation. The supply conveyor is a hybrid system and it has been
represented by a MHPN model (Fig. 6).
Nr.pack .

As was show
n, the main topology of the packing station
(Fig.2) emphasizes a transport system (single product conveyor), a modular manipulator (consisting in 4
separate electro-pneumatic modules) and an output buffer,
disposed around to the packing area. For this
configuration, it’s obvious that the productivity of the
packing system depends on the conveyor speed and on normal operation of all modules. The real value of the
speed is necessary to be corre lated with the operated time
of the first electro-pneumatic module, also with the cadence of the rest of entities upstream disposed.
For the model’s validation, also for analysis of its
behavioral properties, an d because of the complex
topology caused by the particularities of the Petri Net
model dynamics, it was necessary to use some specialized
and dedicated software tools. Starting from the same
topology of the net, the selected software tool allows us to
modify the values of the transition’s firing speed,
providing a greater flexibility of the entire model and
various graphical on-line representations of the number of
parts transported by the conveyor (Fig.7). [8], [11], [12].

In order to obtain an adequate and refined model, a top
– down technique can be used. Thus a transition and/or a place of the basic model are replaced with another,
detailed sub-net, and so on, until the model satisfies the
technical requirements.
The Petri Nets structures allows the user to observe
the system’s real behavior in an inadequate working situation, caused by the temporary malfunctioning of
some subassemblies, by bad implementations of the Fig .4. Modified Hybrid Petri Net structure P3
T2 2,1
7,5 P2 T1 P4
10,8 P1 START process STOP process
P2
P3
P4
P6
P7 P8
P9 T2 T3
T6 T7
T8T9 3
RM 2 – module RM 1 – module
P5 P10 P11
P12 T4
T5 T10
T11 RM 3 – module 3
P13
P14
P15 P16
P17
P18 T12 T13 T14
T15
RM 4 -module
Counter device of cardboard boxes Number of packages
at the right extremity
of the conveyor number of packages
on the blade 9 P1 T1
P19 NR
Fig. 5. The primary model of the packing systemCurrent distance
covered Distance covered Number of packages
at the right extremity
of the conve yor
Single valve command
of C1 cylinder 0
P1P2
0
P3 P4
P5 T1
vCT2
T3
vC T4 T5L
L1 NR1 P6 NR
Transport of the
first package
convey or
speed tvC = 20 cm / s Nr. pack.
10 20 305 1015 20
40[s] vC = 37 cm / s
1020
30
40
10 20 30 40 t
[s]
conveyor
speed
Fig. 6. Hybrid model of the conveyor
95Annals of the University of Craiova , Electric al Engineering series , No. 39, 2015 ; ISSN 1842-4805__________________________________________ ________________________________________ _____________

control procedure or because of wrong management of
its available resources. When a malfunction appears, the
control system must allow the user to search and find it;
in the meantime, the system remains into an intermediate
stand-by state until the fault is removed and, then it will
be restarted with or without reboot of its equipment .

P1
T1 T2

At the model synthesis should be considered that the
fault system status is caused by the occurrence of a
stochastic external event, while the whole dynamic of the
model follows general deterministic rules. Even the
events which leads the system between its states have an
asynchronous distribution, the dynamic of the whole
structure (hybrid system – in essence) is achieved in a
deterministic manner. Thus, each external event which
determines the system’s dynamics has a well-defined
position in relation with others, integrated in a structure
similar with task schedulers, found in the real-time
command systems. The model topology must allow
parallel evolutions of the marking, similar with a real
system behavior. The best results given by the
malfunction’s analysis and their impact on the control
architecture’s reorganizatio n are obtained by using
Stochastic Petri Nets models or by using a certain
stochastic temporizations, similar somewhat with
Markov’s chains.
In the deterministic models, a system’s malfunction is
represented by a configuration which makes the evolution
into complementary stat es possible, excluding
themselves, being therefore unable to be simultaneously touched (structural conflict). The system can evolve
either in one state (specific to a normal behavior) or in
another state (malfunction), (Fig. 8)

From the current state (place P 2 marked with a token)
both transitions are fireable, but only one will be executed. To select the transition that will be executed,
one doesn’t need to follow a priorities rules nor precedent
restrictions: if T 1 corresponds to a normal model
evolution, the T 2 transition is associated to the event that
leads to a malfunction.
Also, it’s important to specify that after the fault state
is eliminated, the affected equipment can be either
returned to the initial’s state (Fig. 9 a) or its dynamic can
evolve from the current stat e (the state in which it was
after the malfunction appears), (Fig 9 b).

M
oreover, each component can host a fault, leading to
a hold/stop of the system. So, each Petri Net model must
be able to reproduce the real system’s flexibility using
their inner structure. An important malfunctioning zone is
also the junction point of the modules: when a command
is issued or when they synchronize.
A situation which forces the temporary stop of
margarine packs supply conveyor is the one in which the control signal given by NR
1 does not excite the
distributor’s coil associated with cylinder C 1 and it
remains in initial’s position Fig. 10.
The structural conflict is created by P 3’s place and its
output transitions T 9 and T 3. After placing in P 3 three
tokens –corresponding to the transported packages – T 3
and T 9 are validated. It can be executed either T 9
(distributor’s command) or T 3 (the fault appearance). In
this latter case, P 4 will be marked and allows the stop
command of the conveyor supply (the T 5 transition will
be executed). Once the fault was fixed, the system returns to the state prior to the malfunction. If the system’s
dynamic continue without any fault, the T
9 transition is
executed, the P 3 becomes unmarked place, authorizing
T6’s transition (start of the conveyor). If the fault state
continues, the token from P 3 returns to P 4 and the systems
reaches a stand-by state.
All in all, by searching and finding possible fault
scenarios, the model becomes a complex Petri Net structure. Fig. 8. Explanatory for fault modeling (free-choice net). Fig. 7. Simulation’s results for the conveyor speed v c = 0,37 m/s a. working IN correcting
fault
break
s
ervice
fault P1 P3
P2
OUT fault
occuren
ce
b. workingbreak
servicefault  IN
OUTcorrecting   fault
fault occuren
ce
P1PP 3   2
Fig. 9. Modeling of failures: a) Th e system returns in initial state
after fix failure ; b) The s ystem will work from the current state .
96Annals of the University of Craiova , Electric al Engineering series , No. 39, 2015 ; ISSN 1842-4805__________________________________________ ________________________________________ _____________

In order to achieve the whole model of packing station,
several sub-models of electro-pneumatic drives were
interconnected. Usually, a pneumatic circuit contains a
directional control valve which when is turned on
switches and commands the forward stroke of an actuator
with single or double action.
Directional control valves are commutation devices
operating in pneumatic power circuits. Generally, they are used in addition with single or double acting cylinders, for
its command. The model of a directional control valve is a
synchronized PN (Fig.11): th eir places represent suitable
conditions for states evolution and its transitions are fired at the occurrence of external events (sensors outputs and
external command signals), [14], [15].

Each of pneumatic actuators can be represented as a
discrete synchronized PN (Fig.12.) in which: P 1 denotes
the initial state of the actuator (S 1 = 1), P 2 denotes the
forward stroke until S 2 is activated, P 3 shown the extreme
position of the actuator and finally, P 4 denotes its
comeback stroke. The start of forward action is given by the firing of transition T
1, after its directional control
valve has been turned on; then , after activating the sensor
S2 (end of stroke) transition T 2 is fired and P 3 in marked
with one token and so on, until the entire forward – return cycle it’s done.

Based from the above sub-models, the pneumatic
actuator with its directional control valve have been
shown as a synchronized PN (Fig.13.).
The synchronisation between the PN transitions were
indicates by test arcs (dotted-line represented). Hence, one
output transition of a test arc will be fired only the
marking of its source place becomes greater or equal with
the weight of the arc connecti ng them (Fig.13.). The test
arcs do not realize tokens transportation between the
places of the PN through the tr ansitions connected by this
[9], [10], [11], [12], [13], [14].

Fig. 11. PN models of directional control valves :
a) with 2 states ; b) with 3 states. S1
a b. S1 S2
c. P1
T1
P2 P3P4
T2T4
T3Comeback
stroke Initial state of
actuator (S 1 = 1)
Forward stroke The actuator
stops at the end
of stroke (S 2 = 1)
Fig. 12. Explanatory for the actuator PN model:
a) single acting actuator; b) double acting actuator;
c) The PN model.

P1 P2 P3 P4 P5 P6P7
T1
T2 T3
T4 T5
T6 T7 T8
4/3 directional
valve actuator
a
b S1 S2
Fig. 13. PN model of subsystem actuator, 3 states
directional control valve
P1 P2 T1
T2
a. Switch off
the coil „a” Switch on
the coil „a”
Valve in initial
state (0)
Valve switched
on (1)
P1 P2 P3T1
T2 T3
T4 a = 1
b. a = 0 b = 0 b = 1
0 1
20P1
0P2P7
P3working conveyor
Failure state T1
v
T3
v T2
T4 command single way valve
failure
occurence T4
2
T5 stoppedconveyor
T6package’s counter
LNR1
NR1 T9
authorization of conveyor’s stopT3NR1correcting
failureSTARTP5
NR1-1
L1
STOP
conveyor conv.
P6 reset
T7
T8
P4
Fig.10. Conveyor model reached in order to specify working failures
97Annals of the University of Craiova , Electric al Engineering series , No. 39, 2015 ; ISSN 1842-4805__________________________________________ ________________________________________ _____________

Using this model’s synthesis technique, all modular
sub-models of the subsystems that compose the packing
station can be rejoined in a unique and refined structure
(Fig. 14).

D.
The Object Net paradigm

The Ob
ject Net paradigm allows representation of a
system with a large and complex topology in a modular
way, replacing the sub-models synthesized by different techniques with some entities represented as interacting
object-models. Due to the object s properties, changing of
the general system model could be easier achieved, because the object-oriented concept combines the
advantages of the modular representations and hierarchies
and adds useful new concepts (such inheritance, reuse,
encapsulation, information hiding, data exchange etc.). In
this way the flexibility and the versatility of the model are
increased and the entire model becomes a hierarchical
structure [11], [12], [21]
In this manner, every object can be represented as a
hierarchical structure, which contains – generally – three
layers (Fig.15). In the lowest layer, the parent net is
represented. In the middle layer, the net inherited by the
class was enclosed in an obj ect frame. In this layer,
various net elements and objects can be added, in order to modify the behavior of the object. In the top layer, the
object frame is presented, which encapsulates the inner
net structure of the object [11], [12], [20], [21], [22]. In order to obtain the Hybrid Petri Net model’s
topology, and for its validation in various simulation scenarios, Visual Object Net ++ software tool was used.

P1 P2
P3 P4
P5 P6
P7 P8P9 P10P11P12P13 P14
P15
P16
P17
P18P19
P20
P21P22 P23
P24P25
P26 P27
P28
P29 0 P30
0
P31 P32
P33 T1 T2 T3 T4
T5
T6
T7T8T9T10
T11T12T13T14 T15T16
T17
T18
T19
T20T21
T22T23T24 T25
T26T27
v
T28
v T29
T30
2L1 L NR1 NR2
Transport subsystemModule 1 Module 2 Module 3
Module 4Failure occurence
Fix failure 2
T Failure
state Failure state
Failure
occurence Fix failure
NR1
NR1
NR1-1
Fig.14. The Hybrid Petri Net model of packin g system, enriched with failure sub-nets.
Fig. 15. Hierarchical structure 0 P1
0 P2T1P3 P4 T2
T3 parent_1
P1 P2
P4 T3 P5object_fin_1
P5
III
Object net
II
Enriched net
I
Parent net
98Annals of the University of Craiova , Electric al Engineering series , No. 39, 2015 ; ISSN 1842-4805__________________________________________ ________________________________________ _____________

For example, the initial structure of hybrid model of
the conveyor system was en capsulated into “Conveyor”
object, (Fig.16).
Only the P 1 and P 5 places (interface places) are
accessible for a possible connec tion with others modules,
similar or different, from the s uperior level (level II). In
the same way, each subsystem of the packing station can
be represented by a hybrid Petri net object, resulting at the
final a modular and flexible structure. All reached objects
can communicate one with each other by data exchange,
given by the token flow between its.

III.
CONCLUSIONS

The goal of this paper was to propose an Hybrid Petri
Net model for representation and behavioral analysis of
an automatic packing system, considered such system as
a hybrid structure. This approach is based to the fact that
a hybrid system contains in it topology discrete and
continuous subsystems which interacts. This remark has
allowed us to consider sometimes that the packing
process has a similar dynamic with a batch process, in
which the material is operated by finite quantities (the
batches); at any time, an integer number of batches are in
operation at many locations in the plant.
Used rather heuristic techniques in order to synthesize
the model, first, an autonomous PN was achieved whose the behavioral properties have been analyzed; then in
addition of delays to the transitions, the model was
converted into a T-timed PN model. Taking into account
the continuous dynamic of the transport system was achieved a MHPN model using the facilities of the
software tool. For this model the behavioral properties
was verified by on-line simulation in various scenarios.
Finally, the model is the result of the aggregation of partial sub-models. It is obvious that the general model is
not a unique structure, the MHPN formalism – in
conjunction with the facilities offered by the Visual Objet Net ++ software platform – allowing multiple solutions.
The most mathematical, textua l or graphical approaches
to describe hybrid systems are currently usable for small
examples, but models of complex systems are unwieldy. Therefore a hierarchical con cept to structure a model is
needed. Thus, using the Object Net paradigm, the authors were represented each of th e subsystem of the packing
station by a Hybrid Petri net Object, finally resulting a modular and flexible structure. Due of the properties of these modules, the objects obtained can communicate with
each other by data exchange , given by the token flow
between the objects.
Starting from this point, the next step is the
implementation of an control-command structure and a
controller set of rules based on the Petri Net model for the
real system. This will be the subject and the purpose of the
authors in a future paper.

Received on July 25, 2015
Editorial Approval on November 16, 2015
REFERENCES

[1]
P.J. Antsalkis, W. Khone, A. Nerode, S. Sastry (Coordinators),
“Hybrid Systems II”, Lecture Notes in Computer Science , 999,
Springer-Verlag, 1995.
[2]
P. J. Antsalkis, J. A. Stiver , M. D. Lemmon, “Hybrid System
Modeling and Autonomous Control Systems”, Workshop on Theory of hybrid Systems, Lecture Notes in Computer Science
736, Springer-Verlag, pp.336-392, 1993.
[3]
M. S. Branicky , “A Unified Framework for Hybrid Control”, Proc. 33rd Conference on Decision and Control , Lake Buena
Vista, Fl., USA, pp. 4228 – 4234, 1994.
[4]
B. Cébron, Commande de systèmes dynamiques hybrides – Thèse ,
Université d’Angers, France, 2000.
[5]
R. David, H. Alla, “On Hybrid Petri Nets”, Discrete Event
Dynamic Systems: Theory and Applications , 11, 2001, pp. 9 – 40.
[6]
R. David, H. Alla, “Discrete, Continuous and Hybrid Petri Nets”, Springer-Verlag 2005.Young, The Technical Writer’s Handbook.
Mill Valley, CA: University Science, 1989.
[7]
I. Demongodin, N. T. Koussoulas , “Modelling of hybrid control
systems using Petri nets”, ( Zaytoon, 1998 ), pp.330 – 337, 1998.
[8]
I. Demongodin, F. Prunet, “Batch Petri Nets”, Proceedings of 7th
Annual European Computer Conference , Paris, 1993, p.29 – 37.
[9]
R. Drath, “Objektorientierte M odellierung hybrid er Prozesse –
Vorstellung eines neuen Werkzeuges”, IWK , 42, pp. 533 – 540,
1997.
[10]
R. Drath, Tool Visual Object Net ++, Available at:
http://www.daimi.au.dk/PetriNets/tools
.
[11]
R. Drath, “
Hybrid Object Nets: An Object Oriented Concept for
Modelling Complex Hybrid Systems”, Dynamical Hybrid
Systems , ADPM98, Reims, 1998.
[12]
M. A. Drighiciu, “Petri Net formalism for a possible hierarchical
structure of complex hybrid systems”, Proceedings of 6th
International Carpathian Control Conference , Miskolc –
Lillafüred, Hungary , pp. 371- 376, 2005.
[13]
M. A. Drighiciu, Gh. Manolea, D. C. Cismaru, Anca Petri șor,
“Hybrid Petri Nets as a New Formalism for Modeling Electrical Drives”, Proceedings of Internat ional Symposium on Power
Electronics, Electrical Drives, Automation and Motion –
SPEEDAM 2008, ISBN: 978-1-4244-1664-6, IEEE Catalog Number: CFP0848A-CDR, Ischia, Italy, 11th – 13th June, pp.626-
631, 2008.
[14]
M. A. Drighiciu, Gh. Manolea, Anca Petrisor, M. C. Popescu, “On
Hybrid Systems Modeling with Petri Nets”, Recent Advances in
System Science and Simulation in Engineering, Proceedings of the 7th WSEAS International Conference on System Science and Simulation in Engineering (ICOSSSE’08), Venice , 21- 23
November, pp.73-78, 2008.
[15]
M.A. Drighiciu, Anca Petri șor, “ A Modified Petri Net Framework
for Hybrid Systems Modeling”, Analele Universităț ii din Craiova;
Seria Inginerie Electric ă, Anul 35, No.35, ISBN:1842-4805,
Editura Universitaria Craiova, pp.158-165.
[16]
E. Dubois, “Continuous Petri net with maximal speeds depending on time”, Proc.Of 15th International Conference on Application
and Theory of Petri Nets, Zaragoza, Spain, 1994. 0 P3
0 P4 P2
P5 P1 T1
v
T2
vT3
T4 L
L1 Object net
Conveyor
Parent net P5 P1
Fig. 16. The Conve yor ob ject net.
99Annals of the University of Craiova , Electric al Engineering series , No. 39, 2015 ; ISSN 1842-4805__________________________________________ ________________________________________ _____________

[17] S. Engell, G. Frehse, E. Schneider (Coordinators), “Modelling,
Analysis, and Design of Hybrid Systems”, Lecture Notes in
Control and Information Sciences 279 , Springer-Verlag, 2002,
ISBN: 3-540-43812-2, pp.3-36.
[18]
J. M. Flaus, “Hybrid flow nets for batch processes modelling and
simulation”’ Proceedings of 2nd IMACS MATHMOD Conference,
Viena, 1997, p.211 – 216.
[19]
R. L. Grosmman, “Hybrid Systems”, Lecture notes in Computer
Science , Springer, New York, Vol.736, 1993.
[20]
L. A. M. Riascos, L. A. Moscato, P.E. Miyagi, “Detection and Treatment of faults in Manufacturing Systems based on Petri Nets”, Journal of the Brazilian Soc.of Mech.Sci.&Eng .,
Vol.XXVI, No.3, July – September, 2004, p.280 – 289.
[21]
A. T. Sava, H. Alla, “Combining Hybrid Petri Nets and Hybrid Automata”, IEEE Transaction on Robotics and Automation ,
Vol.17, No.5, October 2001, p.670 – 678.
[22]
C. Valentin-Roubinet, “Hybrid Dynamic System verifica tion with
[2Mixed Petri Nets”, The 4th International Conference on
Automation of Mixed Processes: Hybrid Dynamic System ,
Dortmung, Shaker Verlag, Aachen, pp.231-236.
[23]
Emilia Villani, P. E. Miyagi, R. Valette, Modelling and Analysis
of Hybrid Supervisory Systems; a Petri Net Approach , Springer-
Verlag, 2007, ISBN 978-1-84628-650-6, pp. 1-13.
[24]
J. Zaytoon (Coordinator), Systèmes dynamiques hybrides ,
Hermes-Science, 2001.
[25]
A. Zimmermann, G. Hommel, “Modeling and evaluation of manufacturing systems using dedicated Petri nets”, International
Journal of Advanced Manufacturing Technologies
No.15(2),p.132–138.
6] W.M. Zuberek, “Timed Petri Nets in Modeling and Analysis of
Manufacturing Systems “, Emerging Technologies, Robotics and
Control Systems , Vol.1 International Society for Advanced
Researches, Palermo, Italy, 2007, ISBN 978-88-901928-1-4, p.
66-73.

100Annals of the University of Craiova , Electric al Engineering series , No. 39, 2015 ; ISSN 1842-4805__________________________________________ ________________________________________ _____________