Preview Repetitive Control For Several Classes Of Linear Uncertain Systems

In the practice of modern control systems,repetitive control is often used to solve the tracking and disturbance rejection of periodic signals in control systems.Repetitive control uses the memory characteristics of the time-delay link to place a periodic function generator as an internal model in the closed-loop system to improve the control accuracy and achieve without steady-state error tracking.On the other hand,preview control is a method to control the system with known future information.When the reference signals value and the disturbance signals value of the system can be partially preview,these preview information can be introduced into the controller,which can improve the quality of the system and improve the control performance.Based on the research of repetitive control and predictive control,the design of a preview and repetitive controller and the stability of the controlled system are studied for the linear discrete system.The main research contents include preview and repetitive control for norm-bounded uncertain linear discrete systems,discrete two-dimensional systems and polytopic uncertain linear discrete systems.The main work and content of this paper are as follows:(1)Guaranteed cost preview and repetitive control for norm-bounded uncertain linear discrete systems.For a class of uncertain linear discrete systems with external disturbances,a design method of guaranteed cost repetitive controller is proposed.The repetitive controller is introduced in the forward channel,and the augmented error system that includes the preview information of the target signal and the disturbance signal is obtained by using the difference operator.In order to improve the tracking accuracy of the system,the integration link was introduced.On the basis of this,the guaranteed cost preview and repetitive control problem is transformed into a guaranteed cost control problem for a class of linear discrete systems.By using Lyapunov stability theory and LMI techniques,the stability conditions of discrete systems and the method of parameter solution are obtained.(2)Preview and repetitive control for norm-bounded uncertain linear discrete systems.For a class of uncertain linear discrete systems,a design method of repetitive controller based on preview compensation and observer is proposed.The preview information is introduced to the controller and the design problem of the repetitive controller is transformed into a stability problem of a class of two-dimensional linear discrete systems.Then,using LMI techniques,the stability conditions of preview repetitive control system are obtained.On the base of this,considering that the state of the system is unobservable,the observer is used to reconstruct the state of the system,and the design method of the observer-based preview repetitive controller is studied.(3)Preview repetitive control for polytopic uncertain discrete-time systems.A robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems.In order to improve the tracking performance,a repetitive controller,combined with preview compensator,is inserted in the forward channel.By using the L-order forward difference operator,an augmented dynamic system is constructed.Then,the guaranteed-cost preview repetitive control problem is transformed into a guaranteed-cost control problem for the augmented dynamic system.For a given performance index,the sufficient condition of asymptotic stability for the closed-loop system is derived by using a parameter-dependent Lyapunov function method and LMI techniques.Incorporating the controller obtained into the original system,the guaranteed-cost preview repetitive controller is derived.