Trajectory Tracking Of Linear Time-Varying Systems Based On Iterative Learning Control

Time-varying characteristics,which widely exist in engineering applications,have always been one of the challenging problems in theoretical control research.For decades,researchers in the control field have been paying attention to the problem.The trajectory tracking problem is an important research topic in the control theory,iterative learning control is a very effective method to solve the trajectory tracking problem of linear time-varying systems.In the paper,the trajectory tracking problem of repeated linear time-varying systems is analyzed based on iterative learning control.The trajectory tracking problem is studied from the following aspects:control strategy,constraint conditions(initial conditions,repeated iteration period lengths,desired trajectories),analysis method;this thesis studies the problem of robust predictive iterative learning control,the problem of iteration-varying factors and how to use the analysis method of finite-time stability to analyze the trajectory tracking problem.The performance of iterative learning trajectory tracking control is improved.Specific work is outlined in the following aspects:(1)A robust predictive iterative learning controller for trajectory tracking problem of repeated linear time-varying systems is presented,which improves the convergence speed of iterative learning algorithm and system robustness.By introducing prediction mechanism along both of iteration and time directions instead of only one direction,the control law is successively updated along two directions by learning from the predictive information,therefore,the performance of the proposed method is improved.The sufficient conditions that ensure convergence are analyzed,and the proposed method’s effectiveness is verified by simulations.(2)Iterative learning algorithms for trajectory tracking control of repeated linear time-varying systems with non-fixed-length repeated iteration are presented,which improves the convergence speed of iterative learning algorithms.First,the optimal objective functions are designed,in which the characteristics of non-fixed-length repeated iteration are considered.New iterative learning identification algorithm and optimal iterative learning control algorithm are proposed.Besides,from the perspective of iterative learning gain,the convergence of iterative learning control algorithm is analyzed based on model identification error.Then,based on the identification model obtained by the iterative learning identification algorithm,a new compensation mechanism is designed and an iterative learning control algorithm using a compensation mechanism based on the identification model is designed.The convergence condition of iterative learning control algorithm with compensation mechanism based on the identification model is obtained.Simulations verify that the proposed iterative learning identification method and the proposed compensation mechanism based on the identification model can improve identification speed and convergence speed.(3)The trajectory tracking problem for linear time-varying systems is studied by using the analysis method of finite-time stability.First,based on the sufficient conditions of finite-time stability for linear time-varying systems obtained by the piecewise constant method,and the inverse system feedback control strategy is introduced,the trajectory tracking problem is solved by using the analysis method of finite-time stability.Then,the trajectory tracking problem of iterative learning control for repeated linear time-varying systems is investigated by using the analysis method of finite-time stability.According to the performance requirements of the actual engineering and stop conditions of iterative learning control,the finite repetition periods stability(i.e.,the stability within the term of finite times of repeated motions)problem of iterative learning control is studied.Based on the 2D system analysis method,the finite repetition periods stability problem of iterative learning control is transformed into the problem of finite-region stability for 2D systems.The sufficient conditions of finite repetition periods stability for iterative learning control are given on the basis of the conditions of finite-region stability for 2D systems.Further,the sufficient conditions of robust finite-region stability for uncertain 2D systems and the sufficient conditions of finite repetition periods stability for repeated uncertain linear time-varying systems are analyzed.In the analysis method of finite-time stability,the actual performance requirements and iterative learning control algorithms are integrated and designed.The learning gain can be directly obtained,which satisfies the actual performance requirements,without adjusting the controller parameters to choose a learning gain.(4)An iterative learning trajectory tracking algorithm for repeated linear timevarying systems with iterative-varying factors is presented by using the analysis method of finite-time stability,which improves the performance of iterative learning control.The characteristics of iteration-varying initial conditions and iteration-varying desired trajectories are considered,the finite repetition periods stability problem is transformed into the problem of finite-region boundedness for 2D systems.Based on the conditions of finite-region boundedness for 2D systems,a new iterative learning controller of finite repetition periods stability is designed to handle iteration-varying factors.The simulations verify that the controller gain designed by the proposed method can satisfy the performance requirements.