State Space Discrete Time Learning and Repetitive Control

This paper presents a state space approach to discrete time learning and repetitive control. Specifically addressed is the problem of finding control histories to ensure that the states of a linear time-invariant system match a repetitive reference trajectory. In the learning control problem it is assumed that system is reinitialized to the same state before the control input is applied. This assumption is relaxed for the repetitive control problem. The paper develops sufficient conditions under which proportional, and proportional plus derivative type learning control can be successfully applied to the repetitive control problem. Experimental results illustrate the effectiveness of these learning control schemes in repetitive position and velocity tracking control of an electromechanical system.