Hybrid bond graphs

W. Borutzky, Bond Graph Model-based Fault Diagnosis of Hybrid Systems,... 

Beyond model development for the purpose of analysis and simulation of the dynamic or the frequency domain behaviour, bond graphs have also proven useful as a tool for model-based FDI in engineering systems represented by continuous time models. Only recently, bond graph model-based FDI has also been used for systems described by a hybrid model. Following common terminology a system will be called a hybrid system for short if its dynamic behaviour is appropriately described by a hybrid model. In Chap. 2.1 of [1] Kowalewski rightly remarks ... 

In online model-based FDI, ARRs are evaluated using measurements from the real system being subject to disturbances. The time evolution of ARR residuals serve as fault indicators. For hybrid systems, ARRs are system mode dependent. Hence, an unobserved mode change invalidates the actual set of ARRs. As a result, computed values of fault indicators may exceed current thresholds indicating faults in some system components that have not happened. ARR residuals derived from a bond graph can not only serve as fault indicators but may also be used for model-based system mode identification. 

Section 1.2 gives a literature review of various approaches to a bond graph representation of hybrid system models. In particular, the section discusses the representation of fast switching devices by means of non-ideal switches with fixed mode-independent causality and addresses the equation formulation as a DAE system. 

Clearly, for FDI it is necessary that a system is structurally observable. As switches temporarily disconnect and reconnect model parts they change the structure of a hybrid system model. Consequently, control properties, i.e. structural observability and structural controllability as well as characteristics of the mathematical model derived fl om the bond graph, i.e. the number of state variables, or the index of a DAE system become system mode dependent. Chapters briefly addresses these issues by confining to switched LTI systems and provides some small illustrating examples. 

Chapter4 presents bond graph model-based quantitative FDI for hybrid systems. As the approach uses ARRs and their residuals as fault indicators, the generation of... 

ARRs from a bond graph representing a hybrid system model and the condensation of structural information in a system mode dependent stmctural fault signature matrix are presented. The chapter concludes by addressing off-line numerical computation of ARR residuals. To that end, a model of a system subject to faults is coupled to a bond graph of the healthy system by means of so-called residual sinks. This way, faults may be deliberately introduced without any risk and their effect, detection and isolation may be studied. 

As fault indicators should be sensitive to real faults but insensitive to parameter uncertainties, adaptive system mode dependent thresholds are needed for FDI in hybrid systems robust with regard to parameter uncertainties. Chapter 5 demonstrates that incremental bond graph can serve this purpose for switched LTI systems. To that end some basics of incremental bond graphs are recalled. It is shown how parameter sensitivities of ARRs and ARR thresholds can be obtained. A small example illustrates the approach. 

In Chap. 8, fault scenarios in small switched power electronic systems are studied for illustration. The bond graph model-based approach to FDI in hybrid systems is, however, not limited to this kind of systems. 

Chapter 9 briefly consideres the use of ARRs derived from a bond graph for the purpose of failure prognosis for hybrid systems. 

The book concludes with a discussion of the presented bond graph model-based quantitative approach to FDI in hybrid systems and recommends as a possible topic for further research the use of bond graph modelling in fault tolerant control of hybrid systems. 

In this book, a quantitative ARR based approach to FDI for systems described by a hybrid model will be pursued and hybrid models are represented by bond graphs. 

Borutzky, W. (2011). Analytical redundancy relations from bond graphs of hybrid system models. In A. Bruzzone, G. Dauphin-Tanguy, S. Junco M. A. Piera (Eds.), Proceedings of the 5th International Conference on Integrated Modeling and Analysis in Applied Control and Automation (IMAACA 2011) (pp. 43-49). Rome. 

Bond Graph Representations of Hybrid System Models... 

The computation of models with variable stmcture is still a subject of ongoing research as latest publications show [4, 5]. With regard to a modelling by means of bond graphs the question arises how to represent a hybrid system model in a bond graph framework. 

Figure 2.1 depicts the well known bouncing ball problem and a bond graph representation of a hybrid model. 

Fig. 2.11 Hybrid bond graph of the bouncing ball problem and a finite state automaton associated...

In this book, the bond graph representation of a non-ideal switch proposed by Ducreux et al. as early as 1993 is used in a bond graph model-based approach to FDI in hybrid systems. This approach offers the following advantages. 

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