Research Of Ponit-to-Point Robust Iterative Learning Control And Performance Optimization Algorithm

Iterative learning control is a high-performance control method which is widely used to perform repetitive tasks.It continuously modifies and updates the control input signal of the current trial according to the input and output information of the previous trial,and finally achieves the complete tracking of the reference trajectory in a finite time.Combining optimization theory with iterative learning control technology,an optimal learning controller can be obtained to realize fast tracking.However,in the actual industrial process,it is often not necessary to fully track the system output reference trajectory,only needs to track the given reference value at some specific time points.For example,the robot's "take" and "put" operations only need to focus on the output of pick-up points and placement points,regardless of other time points.It is worth noting that there are many uncertain factors in the design of controller,such as input constraints,controlled system model uncertainty and the deviation of initial conditions of system operation.Therefore,in order to further improve the control accuracy and convergence speed of the iterative learning controller,the research on the point-to-point iterative learning control and its performance optimization algorithm was carried out by comprehensively considering a variety of complex control problems that may exist in practical applications.The research work of this thesis is summarized as follows:(1)Aiming at the point-to-point tracking problem of a class of linear discrete-time systems,a norm optimal point-to-point iterative learning control algorithm is proposed by combining optimization theory with iterative learning control technology.By transforming the matrix model of the input and output time series,a comprehensive multi-objective point performance index function is constructed.Then,the optimal iterative learning control law can be obtained through the quadratic optimal solution.At the same time,the sufficient conditions for convergence of the robust control algorithm in the form of largest singular value are given in the case of nominal and uncertain model.Furthermore,the control algorithm with input constraints is obtained based on convex optimization theory.Finally,the rationality and effectiveness of the algorithm are verified by a numerical simulation case.(2)For a class of linear discrete-time systems with additive uncertainties,the structural singular value analysis method is proposed under the assumption of bounded uncertainties,and the robust monotone convergence condition of the norm optimal point to point iterative learning control algorithm is obtained.However,due to the limitation of structural singular value analysis,it is impossible to maximize the flexibility of the point-to-point tracking task.A robust point-to-point iterative learning control algorithm with wider applicability is proposed.In the worst case,the design problem is transformed into a convex optimization problem and the optimal control input signal is derived.Finally,the rationality and effectiveness of the method are verified by a numerical simulation case.(3)For a class of linear discrete-time iterative learning control systems with initial conditions varying with trials,the performance of traditional iterative learning control algorithms is usually reduced when the initial conditions vary with trials.Therefore,a robust norm optimal point-to-point iterative learning control method in the worst case is proposed.The proposed algorithm considers the change of initial conditions and transforms the design problem into an optimization problem,which is further transformed into a convex optimization problem by using Lagrange dual function and then solved to get the optimal control input signal.Furthermore,it is proved that the proposed robust algorithm is equivalent to the traditional norm optimal point-to-point iterative learning algorithm with variable gain.Finally,the rationality and effectiveness of the method are verified by a numerical simulation case.