Application Of Preview Control Theory In Fault-tolerant Control

Preview control is a control theory and method that can significantly improve the operating efficiency of the system.It has a wide range of applications in practical problems.With the increasing demand for the safety and reliability of modern industrial systems,fault-tolerant control has become one of the hotspots in control system research.This paper studies the fault-tolerant preview control problem for several classes of linear systems by applying preview control theory to fault-tolerant control.The specific content includes the following aspects:Firstly,the design problem of fault-tolerant controllers with preview effects for a class of continuous time linear systems with actuator failures is studied.Based on the model following control method in fault-tolerant control,a reference model with ideal characteristics is introduced,and then an augmented system is constructed to convert the output tracking problem into a regulation problem.Next,the controller of the augmented system is obtained by utilizing the optimal control theory,furthermore,the fault-tolerant preview controller of the original system is obtained through integration.Applying the obtained results to the steam generator water level adjustment system,it is found that the existence of the preview can effectively eliminate the influence of the fault signal on the water level.Secondly,the fault-tolerant predictive control problem for a class of discrete time systems with multi-input delays when sensor failure occurs is considered.The original problem is transformed into an optimal regulation problem for a system without delay through the construction of an augmented system and integral transformation method.Compared with the discrete lifting technique used in the past,this method avoids the increase of the dimensionality of the augmented system with the increase of the time delay,and reduces the amount of calculation.Then a performance index function is introduced for the augmented system without time-delay,the corresponding controller is obtained by using the optimal control theory,and then the fault-tolerant preview controller of the original system is yielded according to the definition of the difference operator.The obtained result is suitable for the case of delay-free.Thirdly,impulse elimination and the design of fault-tolerant preview controller for a class of continuous time descriptor systems with sensor fault are discussed.The state pre-feedback is introduced to eliminate the impulse based on the impulsive controllability of the original system.A normal system and an algebraic equation are got via applying the restricted equivalent transform to the impulse-free descriptor system,and then an augmented system includes the normal system,reference model and error equation is constructed.The performance index function of the original system is rewritten by utilizing the variable relationships in the state pre-feedback and the process of restricted equivalent transformation,and the new augmented system and its corresponding performance index function are obtained via applying the state feedback on the constructed augmented system.By solving the optimal controller of the new augmented system and returning it to the original system,the fault-tolerant preview controller is obtained.Fourthly,the fault-tolerant preview control problem for a class of multi-input delays causal descriptor systems with actuator and sensor faults is studied.Based on the characteristics of causal descriptor system,an augmented system with multi-input delays is constructed through restricted equivalent transformation and difference.A new integral transformation is proposed to convert the constructed augmented system into a delay-free system.The relationships of stabilizability and detectability between the augmented system without delay and the original system are discussed.The results in this part are also applicable to the case without delay.Fifthly,the design of sliding mode fault-tolerant preview controller for a class of continuous time linear systems with actuator failure is studied.The original problem is transformed into a regulation problem by constructing an augmented system,and then a design method for the preview sliding surface is proposed.The required sliding mode fault-tolerant preview controller is obtained based on the exponential reaching law method.Compared with the fault-tolerant preview control method,the simulation results show that the method in this section has better suppression effect for fault.The simulation part compares the obtained controller design method with the fault-tolerant preview control,and the results show that the proposed method has better fault suppression effect and smaller overshoot.Finally,the problem of sliding mode fault-tolerant preview control for a class of discrete time linear systems with actuator failure is studied.An augmented system whose state vector does not contain previewable signals is constructed by using the difference method,and a performance index function is introduced for it.Then the gain matrices are obtained through the discrete time optimal proview control theory.Next,the previewable signal is extended to the state vector to obtain the new augmented system,and the preview sliding surface is obtained by using above gain matrices.The sliding mode controller of the new system is yielded by using the discrete exponential reaching law method,and then,the required sliding mode fault-tolerant preview controller is obtained.In addition,an extended state observer is proposed to estimate the state vector of the controlled system.All the conclusions in this paper have been proved by strict mathematical derivation,and the effectiveness of the proposed fault-tolerant preview controller has been verified by numerical simulations.