Analytical Determination of ARR Residuals for Switched LTI Systems

The state space model of the non-faulty model reads 

If the behavioural model of the real system being subject to faults is coupled to the model of the non-faulty system, then the residual sinks force the difference y — y to zero by introducing their outputs r into the model of the non-faulty system. As a result, the model of the non-faulty system with original unmodified parameters adapts to the behaviour of the simulated faulty system. Hence, x(t) = x t), y(t) = y t) 

4 Bond Graph Model-based Quantitative FDI in Hybrid Systems 

Let ti, t2 denote the time instances of two discrete events and let t, fa) be a time interval, in which no discrete mode change and no new parametric fault takes place, i.e. the coefficients of the matrices are constant for f e [t, fa). It is assumed that some parametric faults that happened for f f i still last for f f i so that some residuals do not vanish. Laplace transformation then gives a linear system of algebraic equations for Jfr. 

The state vector x of the faulty system model differs from the state vector x of the non-faulty system model with nominal parameters due to parametric faults. The same holds for the measured outputs y, i.e. x = x + Ax and y = y -b Ay. Substituting the decomposed vectors into (4.32a and 4.32b) yields 

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Section 4.9 has addressed the analytical determination of ARR residuals for switched LTI systems. In the following, this is illustrated for the example of the boost converter. It is assumed that the diode is no longer blocking in reverse direction as of f > 13. 

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