基于广义正交多项式级数的迭代学习算法

Iterative learning control algorithm based on general orthogonal polynomials

针对一类受扰动的线性时变系统的轨迹跟踪控制问题,提出了基于广义正交多项式的迭代学习算法.该算法首先利用广义正交多项式展开技术将系统参数化,运用其乘积和积分运算矩阵,将微分方程化为代数方程.在此基础上,用迭代学习的方式来修正控制量的广义正交多项式展开系数.这种算法的优点是当系统不满足正则性或无源性时,仍可以用输出误差信号来构造学习律.最后将该方法运用到电液位置伺服系统的控制中,仿真结果表明了此算法能明显地提高电液位置伺服系统的控制精度.

An iterative learning control (ILC) algorithm via general orthogonal polynomials is developed to address the trajectory tracking of a class of linear time-varying systems with uncertain exogenous disturbance. The method parameterizes a linear time-varying system with disturbance by general orthogonal polynomials. Employing the product operation matrix and integration operation matrix of general orthogonal polynomials, the differential equations are converted into a set of linear algebraic equations, and the control problem is reduced to finding the general orthogonal polynomials coefficients of control variable. The proposed algorithm can use the error signals to update the control variable even when the systems do not satisfy regularity nor passivity. Simulation results show a high-performance motion control system for electrohydraulic position servo system can be obtained with the proposed approach.