Optimal Fault Tolerant Control Of Disturbed Singularly Perturbed Systems

Dynamic systems with different time scales often exist in aerospace,chemical,electrical and mechanical engineering fields.In control theory,systems with multi-time scales are abstracted as singular perturbation systems.The working conditions of controlled objects,controllers and sensor and actuator will affect the control performance in the actual industry.However,the aging of components and some unexpected occurrences during operation are inevitable.In addition,with the increasing scale of industrial systems and the increasingly refined and complicated control requirements,the uncertainties,time delays and external disturbances that are ubiquitous in the system can not be ignored.In this paper,the problem of fault estimation and fault-tolerant control for uncertain time-delay disturbed singularly perturbed systems with sensor and actuator faults is studied.The main contents are summarized below:(1)The optimal fault estimation for disturbed singularly perturbed systems with sensor fault is studied.The problem of fault estimation is firstly transformed into H?control problem by constructing augmented matrix.Based on Lyapunov stability theorem,the sufficient conditions for the observer to meet the design requirements are given.Then the multi-objective optimization algorithm is proposed to optimize the upper bound of stability and H? performance index of the system simultaneously.In the end,the correctness and feasibility of the conclusion is verified by a numerical example.(2)The optimal fault estimation for uncertain time-delay disturbed singularly perturbed systems with actuator and sensor faults is addressed.Firstly,the attenuation ability of finite energy disturbance is represented by H? performance index by reasonably constructing augmented system,and the design method of fault estimator is same as above.Furthermore,the maximum stability upper bound and the optimal anti-disturbance capability of the system are guaranteed based on the multi-objective optimization algorithm.Finally,different perturbation parameters are selected in numerical example,and the correctness and effectiveness of the multi-objective optimization algorithm are verified by comparing the fault estimation error with different values.(3)The optimal robust H? guaranteed cost fault-tolerant control for disturbed singularly perturbed systems with uncertain time-delay is proposed.For uncertain time-delay singularly perturbed systems with actuator and sensor faults,sufficient conditions for the existence of memorized state feedback controllers are derived by choosing Lyapunov-Krasovskii functional with time delay and perturbation parameter dependence,in this case,the closed-loop system satisfies the properties of robust H?guaranteed cost fault-tolerant control.In order to solve the problem that the state and fault vectors are not measurable in the system,the results of the fault estimator are used as the input of the fault-tolerant controller.Moreover,the minimum solution of H? performance index and upper bound of quadratic performance index in this chapter is transformed into a convex optimization problem with linear matrix inequality constraints.The optimal robust H? guaranteed cost fault-tolerant control law is solved based upon the linear matrix inequality toolbox,and the parameters same as fault estimation are selected in the numerical case analysis to verify the correctness and effectiveness of the optimal robust H? guaranteed cost fault-tolerant control law.