| Summary: | 博士 === 國立臺灣大學 === 電機工程學研究所 === 89 === In this dissertation, we consider the application of robust control techniques to the design of fault tolerant control for linear time-invariant uncertain singular systems. The central idea of these approaches is: Make controllers insensitive to the effects of system uncertainties and failures such that the closed loop can achieve the required performance in the case of fault-free and remain regular, impulse free, and asymptotically stable in the case of malfunction occurring in sensors or actuators. Therefore, fault diagnosis and reconfiguration of the control system will not be needed during operation phases.
A multivariable singular feedback control system may loss the regularity, impulse immunity or become unstable when the feedback signals are switched off by a failure in the sensors or the actuators. We say that the system possesses integrity if it still remains regular, impulse free, and stable in the presence of such failures. This is an inherent property in multi-input multi-output control systems. The overall closed-loop system under the failure is not necessarily stable due to the interactions of the remaining feedback loops even if the open-loop system is stable. Integrity is thus a type of ‘fault-tolerance’ with respect to stability in the multivariable feedback control system. System uncertainty is an inherence of our real world. Robustness is the property of dynamic systems to tolerate variations of parts of the system with predetermined tolerance bounds in the vicinity of some nominal dynamic behaviors. Hence, an additional facility of the proposed controllers is to enable the controlled singular system to cope with uncertainties caused by varying plant structure or parameters.
Two approaches are presented for the fault-tolerant problem in this dissertation. The first approach uses the linear quadratic regulator (LQR) technique to assign the amount of rankE finite poles in a specified disk via state feedback by solving iteratively a discrete Riccati equation and a discrete Lyapunov equation. Then various sufficient criterions are derived for tolerate sensors or actuators malfunction or parameter uncertainty. In the second approach, the results of H¥ control for uncertain normal systems are extended to the singular systems. Necessary and sufficient conditions are derived for the existence of a controller solving the problem, both state feedback and dynamic output feedback cases are considered. Then we study the integrity property of the H¥ control via state feedback approach.
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