基于遗传算法的PID型迭代学习控制增益的选取方法

针对PID型迭代学习控制算法，首先讨论了其收敛的充要条件和单调收敛的充分条件，然后给出目前利用单调收敛的充分条件确定PID增益的方法，并指出其不足。在此基础上，提出了基于遗传算法的PID型迭代学习增益选择方法（PID型GA-ILC算法）。利用该算法可以得到不满足PID迭代学习控制系统单调收敛条件但依然能使该系统单调收敛的PID增益，给出了数值仿真实例，证明了PID型GA-ILC算法的有效性。

PID Type Iterative Learning Control with Optimal Gains Based on Genetic Algorithm

In this paper, the necessary and sufficient condition for PtD type iterative learning control （PID-type ILC） convergence and the sufficient condition for PID-type ILC monotonic convergence are discussed. Based on the sufficient condition for monotonic convergence, the method which is used to determine the gains of PID type ILC update law is given and the shortages of such approach are discussed. After this, an approach determining the PID gains is proposed based on genetic algorithm. The achieved PID gains do not meet sufficient condition for monotonic convergence, but they can make the PID-type ILC system converge monotonically. A numerical example is given to demonstrate the effectiveness of the presented technique.