Optimal Gains of Iterative Learning Control with Forgetting Factor

带遗忘因子迭代学习控制最优增益研究

School of Mechanical&Electronical Engineering, Lanzhou University of Technology, Lanzhou 730050, China

Received: 12 October 2018

Abstract

In order to solve the optimization problems of convergence characteristics of a class of single-input single-output (SISO) discrete linear time-varying systems (LTI) with time-iteration-varying disturbances, an optimal control gain design method of PID type iterative learning control (ILC) algorithm with forgetting factor was presented. The necessary and sufficient condition for the ILC system convergence was obtained based on iterative matrix theory. The convergence of the learning algorithm was proved based on operator theory. According to optimization theory and Toeplitz matrix characteristics, the monotonic convergence condition of the system was established. The accurate solution of the optimal control gain and the relationship equation between the forgetting factor and the optimal control gains were obtained according to the optimal theory which ensures the fastest system convergence speed, thereby reaching the end of the system convergence improvement. The convergence condition is weaker than the known results. The proposed method overcomes the shortcomings of traditional optimal control gain in ILC algorithm with forgetting factor, effectively accelerates the system convergence speed, suppresses the system output track error fluctuation, and provides a better solution for LTI system with time-iteration-varying disturbances. Simulation verifies the effectiveness of the control algorithm.

摘要

针对一类含非严格重复扰动的单输入单输出（SISO）离散线性时不变系统（LTI）的收敛特性最优化问题，提出带遗忘因子迭代学习控制（ILC）算法的最优控制增益设计方法。根据迭代矩阵理论和Toeplitz矩阵特性得到含非严格重复扰动的系统收敛充要条件，并运用算子理论证明收敛。根据最优化理论给出系统的单调收敛条件，求解出算法最优控制增益的精确解，得到遗忘因子与最优控制增益之间的关系式，实现系统快速收敛，从而达到改善系统收敛特性的目的。该方法改进了传统最优控制增益在带遗忘因子ILC算法中应用的不足，放宽了系统收敛条件，有效加快系统收敛速度，抑制系统输出跟踪误差波动，同时也为含非严格重复扰动的LTI系统提供了一个更优的解决方案。仿真结果验证了控制策略的有效性。