A stochastic iterative learning control algorithm with application to an induction motor

Abstract

A recursive optimal algorithm, based on minimizing the input error covariance matrix, is derived to generate the learning gain matrix of a P-type ILC for linear discrete-time varying systems with arbitrary relative degree. It is shown that, in the case where the number of inputs is not greater than the number of outputs, the input error covariance matrix converges to zero at a rate inversely proportional to the number of iterations in the presence of uncorrelated random state disturbance, reinitialization errors and measurement noise. The state error covariance matrix converges to zero at a rate inversely proportional to the number of iterations in the presence of measurement noise. In the case where the number of inputs is greater than the number of outputs, then the system output error converges to zero at a rate inversely proportional to the number of iterations in presence of measurement noise. Another suboptimal recursive algorithm is also proposed based on unknown system dynamics and unknown disturbance statistics. The convergence characteristics are shown to be similar to the ones of the optimal recursive algorithm. The proposed ILC algorithms are applied to two different models of an induction motor for angular speed tracking control. One model describes its dynamics in stator fixed (a, b) reference frame without current loops and the other model is also in stator fixed reference(a, b) reference frame but with high-gain current loops. The simulation results show good tracking performance in the presence of noise with erroneous model parameters and noise statistics. An open-loop control is also proposed to improve the tracking rate of the proposed ILC algorithms.