Optimal Preview Repetitive Control Of Linear Discrete-time Systems

Based on the internal model principle,repetitive control constructs an internal model for describing the dynamic model of the periodic external excitation signal.The internal model contains a positive feedback time-delay link that can continuously learn the error signal to correct the tracking effect of the system and improve system tracking performance.However,there is a basic signal period delay in the repetitive control,which leads to the control system transient response slowly.Preview control introduces the known future information into the system as feedforward compensation,which can improve the response speed and tracking performance of the system.With the help of known research results of preview control and repetitive control,this thesis combines repetitive control with preview control.Taking discrete-time multi-agent systems and uncertain discrete systems as research objects,the design method of optimal preview repetitive controller is proposed to improve the tracking performance of the system on periodic preview signals.In addition,the solution method of preview repetitive controller based on information fusion estimation is also studied.The specific research work is as follows.(1)Optimal preview repetitive control for discrete-time multi-agent systems.For a class of discrete-time multi-agent systems with a directed spanning tree in information exchange topology,a design method of optimal preview repetitive controller is proposed.Firstly,the augmented error system is constructed by using the state augmentation technology,which includes the repetitive controller and the preview information of the target signal.Thus,the design problem of preview repetitive controller is transformed into the optimal regulation problem of augmented error system.Then,according to the relevant results of the discrete-time linear quadratic regulation theory,the state feedback controller of the augmented error system is obtained.In order to ensure the existence of the controller,PBH criterion is used to verify the stabilizability and detectability of the augmented error system.On this basis,reducing the order of Riccati equation to obtain the optimal preview repetitive controller of the original system。(2)Robust optimal preview repetitive control for uncertain discrete-time systems.For a class of uncertain linear discrete-time systems,a design method of robust repetitive controller with preview information compensation is proposed.Firstly,the uncertainty matrix of the original system is separated and the nominal system of theoriginal system is obtained.For the nominal system,the state translation method is used to construct the augmented error system.In order to ensure the static performance of the system,a repetitive controller is introduced.On this basis,the optimal controller of augmented error system with repetitive controller is obtained by using the results of optimal preview control theory.Then,the uncertainty is added to the augmented error system,and the robust repetitive controller with preview feedforward compensation is obtained by using the related theory of robust control and the linear matrix inequality method.(3)Optimal preview repetitive control of discrete systems based on information fusion estimation.For a class of linear discrete systems affected by disturbances,an optimal preview repetitive controller based on information fusion estimation method is proposed.It is assumed that the future information of the target trajectory and the disturbance signal is within a certain range.The L-order difference operator is defined to construct the augmented error system.Then,by using information fusion estimation method,the optimal estimation of control increment and the co-states of augmented error system are obtained.Finally,through recursive calculation,the optimal preview repetitive controller is obtained to make the closed-loop system of the original system asymptotically stable.