| In industrial process control such as power system,mechanical system,etc.It is often necessary to track(or reject)periodic reference(or disturbance)signals.Repetitive control is an effective method to solve this kind of problem.Based on the internal model principle,it realizes the error free tracking(or rejecting)of periodic reference(or disturbance)signals by embedding a closed-loop positive feedback time-delay link in the feedforward channel of the control system.At the same time,there are many systems with known future reference(or disturbance))and other information in the fields of electromechanical servo system,unmanned driving,vehicle active suspension and so on.Preview control is a control method that uses the known future reference(or disturbance))information to improve the dynamic quality of the system at the current time,improve the tracking accuracy of the system and reject external disturbances.Using preview compensation to design repetitive controller can undoubtedly improve the control performance of closedloop system,and has important theoretical value and broad application prospects.Based on the existing research on repetitive control and preview control,aiming at several typical continuous time systems,this paper designs repetitive controllers with preview compensation for nominal systems,time-delay systems,descriptor systems and uncertain systems with unknown external disturbances by comprehensively using the methods of linear quadratic regulation and equivalent input disturbance.The main research results and innovations are as follows:(1)Optimal preview repetitive control for linear continuous time systems.The design problem of preview repetitive control for a class of nominal systems with zero relative degree is studied.Firstly,the padé-approximation method is used to transform the basic repetitive control system into a time-delay free system.Secondly,an augmented error system including error variable,state variable and state variable derivative is constructed.Then,the differential form of the optimal state feedback controller of the augmented error system is obtained by using the optimal control theory.On this basis,through integral transformation,the optimal preview repetitive controller of the original system including state feedback,error integral,repetitive control and preview compensation is obtained.Finally,through the comparative simulation with the existing methods,the excellent characteristics of this method are verified.(2)Optimal preview repetitive control for linear continuous time impulsive free descriptor systems.The optimal preview repetitive control problem for a class of impulsive linear generalized continuous time systems is studied.Firstly,using its impulse free characteristics,the preview repetitive control problem of the controlled object is transformed into the optimal control problem of a relatively low dimensional slow subsystem through restricted equivalent transformation.On this basis,an augmented error system including error vector and state vector is constructed.Furthermore,using the lifting technique of L-order difference operator and introducing a new performance index,the preview repetitive control design problem of descriptor system is transformed into a linear quadratic regulation problem of slow subsystem.Then,the optimal preview control input of the augmented error system is obtained by using the optimal control principle.On this basis,the repetitive controller with preview compensation is obtained by integral transformation.Finally,the speed experiment of PMSM drive system proves that this method has good tracking performance.(3)Optimal preview repetitive control for linear continuous time-delay systems.The problem of preview repetitive control for a class of continuous time systems with state delay is studied.Firstly,the time-delay system is transformed into a time-delay free system with replacement variables by integral transformation.Secondly,using the lifting technique of difference operator,an augmented error system composed of replacement variables and system tracking error is obtained.On this basis,a new quadratic performance index function is introduced to transform the preview repetitive control design problem into a linear quadratic regulation problem of continuous nonautonomous systems.Further,based on the optimal control theory,the optimal preview repetitive controller including state feedback,error integration,repetitive control,time-delay compensation and preview compensation is obtained.Compared with the existing methods,the excellent characteristics of this method are verified by simulation.(4)Optimal preview repetitive control for continuous time uncertain systems.For a class of continuous time uncertain systems with unknown external disturbances,a preview repetitive control design method based on equivalent input disturbance(EID)is proposed.Firstly,the augmented error system is constructed by using the nominal system state equation of the controlled object,the improved repetitive control state equation and the error vector.Secondly,the augmented error system is transformed into a time-delay free system by state transformation.On this basis,the optimal preview repetitive control law of the nominal system is obtained by using the optimal control theory.On the other hand,in order to improve the aperiodic disturbance rejection performance of repetitive control system,firstly,the EID estimator is constructed by using the estimation error of full order state observer.On this basis,the observer and state feedback gain are designed separately.Furthermore,the stability condition of the system is derived based on the small gain theorem,and the gain of the state observer is obtained based on the duality principle.Then,a compound preview repetitive control law based on EID compensation is established by feeding back the estimated EID value to the control input.Compared with Lyapunov quadratic stable robust repetitive control method,it is proved that this method has good tracking performance and dynamic performance. |
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