Linear system graph model

C.S. Lorens, Flow Graphs for the Modelling and Analysis of Linear Systems, McGraw-Hill, Monographs in Modern Engineering Sciences, 1964. 

If it is assumed that the system under consideration can be described by a linear time-invariant model for the time spans between two discrete switching events then, starting from the partitioning of a bond graph model into fields as displayed in Fig. 2.16, a DAE system in the form... 

The term direct bond graph model refers to a bond graph model in preferred integral causality that enables to compute the dynamics of the state x and the output y in terms of the input u and known parameters (see also Section 6.2.1.1). In the case of a linear time-invariant (LTI) system, the model equations are of state space form... 

Let us consider again the thermo-fluid system shown in Fig. 7.1 and its bond graph model shown in Fig. 7.2. The thermal domain cannot be converted to TCG, as it involves state-dependent nonlinearity. So we confine ourselves to the linear hydraulic domain. The corresponding TCG is shown in Fig. 7.9. Let us now consider a fault scenario, where the measured pressure of Tanki is found to be above its nominal value, i.e., in qualitative terms or e. The next step is to generate different possibilities (fault hypotheses) for this observation. Thereafter, the temporal evolutions would be used for each hypothesis and the trend observed in the temporal evolutions will be matched with the actual observations. 

The bond graph model of the hybrid system is given in Fig. 7.20. The flow through nonlinear valves is given according to (7.6). The flow through the drains (/ 3 and R4) modeled as linear resistances modulated by modes a and ax are given as... 

In the case of linear system models, the combination of CAMP-G, MATLAB, and the Symbolic Math Toolbox can generate state space matrices as well as transfer functions in symbolic form from a bond graph. MATLAB in conjunction with the Symbolic Math Toolbox can also be used for the incremental bond graph approach presented in Chapter 4. 

Chapter 2 describes the evolution in fundamental concepts of chemical kinetics (in particular, that of heterogeneous catalysis) and the "prehis-tory of the problem, i.e. the period before the construction of the formal kinetics apparatus. Data are presented concerning the ideal adsorbed layer model and the Horiuti-Temkin theory of steady-state reactions. In what follows (Chapter 3), an apparatus for the modern formal kinetics is represented. This is based on the qualitative theory of differential equations, linear algebra and graphs theory. Closed and open systems are discussed separately (as a rule, only for isothermal cases). We will draw the reader s attention to the two results of considerable importance. 

The second complexity level of chemical reaction mechanisms is the complexity level of the kinetic model corresponding to a given mechanism (or KG). Starting from the fact that ultimately the mechanism complexity will manifest itself in kinetics, it seems natural to look for a complexity index that reflects the graph complexity demonstrated in the kinetic model. Two kinds of kinetic models may be used for this purpose (a) fractional-rational equations of the rate of routes in stationary or quasistationary processes having linear mechanisms (b) systems of differential... 

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