基于正交多项式的迭代学习控制算法及其应用

针对存在不确定扰动的线性系统的轨迹跟踪控制问题，提出了基于正交多项式的迭代学习算法．该算法利用正交多项式级数将系统参数化，运用其积分运算矩阵，导出了一种基于多项式级数的线性系统的近似模型．在此模型基础上，用迭代学习的方式来修正输入量的多项式展开系数，并运用LMI方法求解学习增益矩阵．所得算法在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．将该方法运用到直线电机的控制中，仿真结果表明，新算法能明显地提高直线电机的控制精度。

Iterative Learning Control Algorithm Based on Orthogonal Polynomials and Its Applications

An iterative learning control ( ILC) algorithm viaorthogonal polynom ials is developed to ad- dress the trajectory tracking of a class of linear systems with uncertain exogenous d isturbance. First, the method parameterizes a linear system with d isturbance by using orthogonal polynom ials. Then, an approxima- ted model for the system is deduced by employing the operationalmatrix of integration of orthogonal polynom i- als. Based on the model, the orthogonal polynom ials coefficients of control function are ad justed by an itera- tive learning law, and the learning gain matrix is designed via LM I optim ization. The proposed algorithm can use the error signals to update the control variable even when the systems do not satisfy regularity nor passivi- ty. Simulation results demonstrate a high-performance motion control system for linear motor can be obtained with the new approach.