Research On Robust Fault Detection For Singular Systems

Singular systems include dynamic constraints described by differential equations, furthermore, static constraints described by algebraic equations, so physical systems described by them are more comprehensive than by standard state space systems with dynamic constraints alone. Many control problems of linear systems have been generalized to singular systems, such as LQ problem, H2 problem, H∞problem and so on. But the fault detection problem for singular systems has not been solved effectively.This dissertation focuses on the fault detection problem for singular systems, singular time-delay systems and singular fuzzy systems. The main research results consist of the following parts.(1) The problem of H∞fault detection is studied for a kind of singular systems. An observer-based FDF is used as the residual generator and the problem is converted to H∞filtering. By using Bounded Real Lemma, sufficient conditions for the existence of the H∞-FDF are given. Solutions are obtained by solving LMIs. Then a design method of residual evaluation and threshold is given. The designed H∞-FDF guarantees the achievement of the fault detection and simultaneously the maximal robustness of residual to disturbance.(2) The problem of H∞fault detection is studied for uncertain singular systems with constant delay and for singular systems with time-varying delay respectively. An observer-based FDF is used as the residual generator and the problem is converted to H∞filtering. By using the Lyapunov-Kravoskii method, sufficient conditions for the existence of the H∞-FDF are given. Aiming at the nonlinear terms and the equality constraints about the unknown variables in the sufficient conditions, we develop the classical cone complementary linearization technique and the solving for H∞-FDF is converted to solving a sequence of convex optimization problems subject to LMIs. By using the cone complementarity linearization iterative algorithm, a linear matrix inequality method to design the H∞-FDF is obtained. Since the cone complementarity linearization iterative algorithm in this dissertation is a minor modification of the classical cone complementary linearization technique, it can be proved that the proposed algorithm converges. (3) The fault detection problem for singular TS fuzzy systems with time-delay is studied. Using an observer-based fuzzy FDF as the residual generator, the FDF design is converted to an H∞filtering problem. By using the Lyapunov-Kravoskii method, sufficient conditions are given, which guarantee the H∞-FDF exists. And by using the cone complementarity linearization iterative algorithm, the solution to H∞-FDF problem is obtained. The premise variables of the designed fuzzy filter are choosed to be the estimated premise variables of the TS fuzzy model of the plant and are not demanded to be the same as the premise variables of the plant. So the condition that the premise variables of the TS fuzzy model of the plant must be measurable is not demanded.(4) The fault detection problem for singular TS fuzzy systems with distributed delay is studied. Using an observer-based fuzzy FDF as the residual generator, the FDF design is converted to an H∞filtering problem. By using the Lyapunov-Kravoskii method, a new Lyapunov function is constructed and sufficient conditions are given which guarantee the H∞-FDF exists. And by using the cone complementarity linearization iterative algorithm, the solution to H∞-FDF problem is obtained. Then a design method of residual evaluation and threshold is given.(5) The problem of parity based fault detection is studied for discrete-time singular systems and for discrete-time singular TS fuzzy systems respectively. For discrete-time singular systems, the unified approach to obtain the parity matrix for discrete-time linear systems is generalized to discrete-time singular systems and the parameterised form of parity matrix is given. For discrete-time singular TS fuzzy systems, a reference fault model is introduced to reflect the faults'prior knowledge. Based on this, a residual generator is designed by introducing a new performance in Frobenius norm. The fault detection problem is converted to solving an optimazition problem and a linear matrix inequality method is given to obtain the parity matrix. By adjusting a parameter matrix, the given algorithm guarantees the achievement of the fault detection and simultaneously the maximal robustness of residual to disturbance.