Piecewise Iterative learning control for linear motors under random initial position

Abstract

A piecewise iterative learning control algorithm for suppressing random initial position deviation is proposed for a permanent magnet linear synchronous motor that performs repetitive tasks in a finite time interval. This algorithm is divided into two time intervals. In the first time interval, the control algorithm with initial error correction law is used to suppress the effect of random initial deviation on tracking performance. In the second time interval, only the second derivative of the tracking error is used to correct the control input, so that the system output can accurately track the desired output. At the same time, the right boundary of the first time interval, that is, the left boundary of the second time interval, gradually shifts to the left with the increase of the number of iterations. So that the first time interval that can not track the desired output is gradually shortened, and the second time interval of accurately tracking the desired output is gradually widened, eventually achieving the complete tracking of the desired output in the whole time interval when the number of iterations tends to infinity. Furthermore, the convergence of the proposed algorithm is proved by the compression mapping method, and the convergence condition of the algorithm is presented. Both theoretical and simulation results are given to demonstrate the effectiveness of the proposed algorithm.