Robust H_∞ Fault Estimation And Active Fault Tolerant Control For Linear Time-delay Systems

Time-delay is frequently encountered in various engineering systems, which usually results in unsatisfactory performances and is frequently a source of instability. With the increasing demands of safety and reliability for equipments and control systems, fault estimation and active fault tolerant control for time-delay systems have received more and more attention. On the other hand, most of the existing achievements about fault estimation and active fault tolerant control are characterized in the full frequency domain. In practice, however, the faults usually emerge in the low frequency domain, particularly in aerospace-related fields and chemical processes. Therefore, it is of considerable importance to study the fault estimation and active fault tolerant control problem for time-delay systems in finite frequency domain. The main purpose of this dissertation is to investigate observer-based robust H∞fault estimation and active fault tolerant control for some classes of time-delay systems in full frequency domain and finite frequency domain, respectively. The main works and contributions in the dissertation are given as follows:1. The problem of H∞filtering based robust H∞fault estimation for a class of time-delay systems with nonlinear perturbation is investigated. Applying an observer-based fault detection filter as the fault estimator and choosing a proper weighting function matrix, the problem of robust H∞fault estimation is formulated in the framework of H∞filtering. Then the Lyapunov-Krasovskii functional approach is used to analyze the performance of the error system. A delay dependent sufficient condition on the existence of the robust H∞fault detection filter is derived. Furthermore, an algorithm is proposed to get a feasible solution to the observer gain matrices using inequality technique and the cone complementary approach, respectively.2. Based on a generalized coordinate change, a finite frequency domain approach to H∞fault estimation for linear time-delay systems is proposed. With the aid of the Generalized Kalman-Yakubovich-Popov lemma, sufficient conditions on the existence of the H∞fault estimator are derived and a solution to the observer gain matrices is obtained by solving a set of linear matrix inequalities. Using the frequency range information of the possible fault during the fault estimator design, the finite frequency approach proposed has a better performance than the full frequency approach.3. H∞fault estimation and compensation problem for a class of linear time-delay systems is investigated by employing generalized internal model control architecture. For the possible fault whose dynamic behavior can be described by an exosystem, an observer-based fault estimator is used to estimate the fault. Based on the fault estimation, the active fault tolerant control system can implement online fault compensation. By choosing the Lyapunov-Krasovskii functional traditionally and using delay decomposition approach, respectively, delay dependent sufficient conditions on the existence of such an active fault tolerant control system are derived, and a brief design procedure is also provided. The conservatism decreases even further with the partitioning becoming thinner.4. A finite frequency domain approach to H∞fault estimation and compensation for a class of linear time-delay systems is proposed. A new H∞controller in generalized internal model control architecture with an observer-based fault estimator is presented to realize fault estimation and compensation. With the aid of the Generalized Kalman-Yakubovich-Popov lemma for time-delay systems, sufficient conditions on the existence of such an active fault tolerant control system ensuring simultaneous finite frequency estimation and control performances are derived. The calculation procedure of the parameter matrices of the fault estimator and H∞controller is also proposed. Taking the frequency range of the possible fault into consideration, the finite frequency approach proposed has a better control performance than the full frequency approach.5. A new active fault tolerant controller with residual feedback is proposed. Residual generated by a fault detection filter is used to construct the controller and compensate the influence of the fault instead of the fault estimation. With the aid of the Generalized Kalman-Yakubovich-Popov lemma for time-delay systems, sufficient conditions on the existence of such an active fault tolerant control system are derived, and iterative algorithms are employed to obtain the solutions to the fault detection filter and controller parameter matrices. Finally, a brief design procedure is provided.