Research On Robust Fault - Tolerant Control For Several Linear Systems

When the system contains more components, it will be prone to failure in the running process. If a system can still remain stable and meet certain control requirements under some component failures, we say it is a fault-tolerant control system. The robust fault-tolerant control problems are studied in this paper for several classes of linear systems. Namely, the systems in the actuator or sensor failures in some special positions can still keep stable and meet the performance requirements. The main problems are listed as follows.Firstly, for uncertain linear system, using the Lyapunov functional method, the problem of robust fault-tolerant control is put forward. The question can be divided into two kinds of cases: to solve the state feedback gain matrix or output feedback gain matrix under actuator failures when the states of the system can be directly measured; to solve observer gain matrix and the state feedback gain matrix of the system under sensor failures when the states of the system cannot be directly measured. By establishing Lyapunov functional, the propsed problem can be changed into the question of solving a set of LMIs. Especially when the states of the system cannot be directly measured, the gains of the observer and controller can be obtained by solving the LMIs, avoiding the inconvenience of separately designing. Of the two cases, the faulted systems not only can remain stable and meet the H_∞ performance, but also have robustness to uncertain parameters and external disturbance.Secondly, using the similar method, the problem of robust fault-tolerant control for uncertain linear systems with time-delay is proposed. The problem is divided into three parts: the robust H_∞ state feedback fault-tolerant control under actuator failures, the robust non-fragile H_∞ state feedback fault-tolerant control under actuator failures and the robust H_∞ state feedback fault-tolerant control based on state observer under sensor failures in observer feedback loop. Unlike the uncertain linear system, the uncentain parameters of time-delay system have different constraint form.Finally, the problem of robust fault-tolerant control for descriptor uncertain linear systems with time-dely is discussed. The problem is also divided into three parts: the robust H_∞ state feedback fault-tolerant control under actuator failures, the robust non-fragile H_∞ state feedback fault-tolerant control under actuator failures and the robust H_∞ state feedback fault-tolerant control based on state observer under sensor failures in observer feedback loop. These methods presented in this part can avoid matrix decomposition in descriptor systems.Using of the design methods proposed in this paper can get the controller gain matrix and observer gain matrix satisfying sufficient condition so that the systems can still keep stable in the sense of Lyapunov under actuator or sensor failures and have good robustness to uncertain parameters and external disturbance.