Fault Diagnosis And Optimal Fault-Tolerant Control For Singularly Perturbed Systems

In some practical engineering fields,there exist many state variables with greatly different orders of magnitude,these are the root of huge difference in dynamic change rate caused by the system,that is trans-scale characteristics of the system.The dynamic system which is mainly characterized by the trans-scale can be summarized as the framework of singularly perturbed systems.The research of singular perturbed systems has always been the hotspot of control theory,and many related researches mainly focus on the fields of system stability,robustness,optimization,control and so on,while the research and literature on fault diagnosis and fault-tolerant control of singularly perturbed systems are relatively few.From the perspective of research methods,previous studies use the model reduction,slow-fast decomposition,generalized system,So this paper draws a new research method and obtains meaningful conclusions for the fault diagnosis and fault-tolerant control of singularly perturbed systems from the whole point of view with using the integrated design idea.The main contents are summarized as follows:(1)The optimal disturbance rejection for a descriptor system which is the limit form of singularly perturbed systems(?=0)based on dynamic output feedback is studied.Based on the theory of generalized systems,the sufficient conditions for the existence of PI(Proportional-Integral)observers are given.Considering that not all state variables and external jamming signals can be measured directly,a new PI observer design method is proposed.All observers with full order and reduced order are designed,and design parameter of the observer can be obtained by solving the simple matrix equation.On this basis,the optimal disturbance rejection law is proposed based on the linear quadratic performance index,which can guarantee that the performance of the closed-loop system can be minimized when the system is under the worst disturbance.In the numerical example,the comparison of the original state signal,the disturbance signal,the observer state signal and the feedback control signal shows that the design of the observer is reasonable and the optimal disturbance rejection law is effective.(2)The fault diagnosis and optimal fault-tolerant control of singularly perturbed systems are studied.We consider a class of linear singularly perturbed systems with known dynamic characteristics.Firstly,the original system and the fault system are combined into an augmented system.Then,based on the theory of singularly perturbed systems,the existence condition of the full dimension PI observer is proposed.On this basis,the optimality of the closed-loop system is considered,and the state feedback controller is designed to guarantee the asymptotic stability of the system,and the linear quadratic optimal performance index reaches the minimum.Finally,a numerical example is used to illustrate the validity and correctness of the conclusion.