A Model Based Approach Combining Bond Graph
and Max Plus Algebra for Hybrid System Monitoring
Nadia Zanzouri, Moncef Tagina Genevieve Dauphin - Tanguy
Laboratoire ACS, Département de Génie Electrique, LAGIS UMR 8146, Ecole Centrale de Lille,
Ecole Nationale d’Ingénieurs de Tunis, BP48, 59651 Villeneuve d’Ascq cedex France,
BP37, 1002 Tunis -Belvédère, Genevieve.Dauphin-Tanguy@ec-lille.fr
Nadia.Zanzouri@enit.rnu.tn, Moncef.Tagina@fsm.rnu.tn
Abstract - This paper deals with an original approach for
hybrid system monitoring combining bond graph modelling
and Max plus algebra. The proposed method may be
applied for systems including continuous and discrete
dynamics. Such systems cover many industrial processes
such as batch process. The continuous part of the studied
system is modelled by bond graph, the discrete evolution is
described by max plus linear equation generated from a
timed event graph. A comparison with a continuous
approach called analytical redundancy relations deduced
from bond graph modelling is realised.
I. INTRODUCTION
The complexity of industrial processes makes many
demands on Fault Detection and Isolation procedures
(FDI). For improvement of their safety and reliability,
different approaches for the design of FDI techniques are
developed [Frank, 1992][Staroswiecki, 1994]. In this
paper, we are interested in the integration of bond graph
model and max plus algebra to develop the monitoring
process for hybrid dynamic systems. In general, the
approaches used for hybrid system monitoring are based
only on one behaviour type: continuous or discrete
approach [Branicky at al., 1994]. Here, we attend to use
and to add the two approaches which are usually applied
separately.
First, the class of system model considered is shown, and
then a short introduction of the models used in FDI
process is described. Afterwards, the methods for systems
monitoring are given. And finally, a discussion and
comparison results are developed.
II. STATE OF ART OF HYBRID SYSTEM
Hybrid systems are a special class of systems where the
dynamic behaviour contains both a continuous subsystem
and a discrete event subsystem that interact together
[Grossman et al., 1993].
This type of systems includes flexible manufacturing
systems, chemical process control system, interconnected
power system and computer communication network.
The special class of hybrid systems considered here is
switching systems where the dynamic behaviour is
described by a finite number of continuous dynamic
models (differential equation, bond graph model, state
equation…) with discrete parameters (set of rules for
switching from a model to another). These switching
rules may be described by a logic expression, a discrete
system with a finite automata, a Petri Net representation
or max plus linear system…
III. MODELLING APPROACHES
In this section, a short introduction to the models used in
the monitoring procedure is presented. The continuous
dynamic of the hybrid system is modelled here by a bond
graph model (BG), the discrete one is described by a max
plus linear system generated from a timed event graph
(EG).
A.Bond Graph
The bond graph is a powerful formalism for physical
systems modelling [Karnopp and Rosenberg, 1983]
[Borne, 1992].
It supports model structure analysis and provides a good
framework for compositional modelling approaches. It
allows the deriving of other forms of system
representation such as transfer matrix, state representation
and block diagram representation (see appendice A).
B.Max Plus Algebra
The max plus algebra has been invented since the late
fifties, in relation with various fields: performance
evaluation of manufacturing systems, and discrete event
system theory [Quadrat, 1994] [Cuninghame-Green,
1979].
Recent works are participating to the development of this
tool [Plus, 1990]. Max plus algebra is a mathematic
concept, its basic operations are maximization and
addition which are represented by Å and Ä (see
appendice B).
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