Repetitive control of linear time varying systems with application to electronic cam motion control

This paper addresses repetitive control for linear time varying systems. A broad range of applications motivates this problem where periodic disturbances or reference signals are existent and synchronized with a rate varying process variable. In the area of motion control, this is a master-slave type electronic cam follower problem, where the slave axis motion must follow the master axis coordinate (process variable) according to a given cam profile while the master axis motion has a time varying speed. In the real-time domain, the disturbance/reference profile changes as master´s speed changes. However, in view of the master axis coordinate, which is called in the angle domain, the disturbance/reference profile is periodic with a fixed period even when the master axis changes speed. To exploit the internal model of repetitive control to achieve asymptotic tracking performance, it is advantageous to design the control system from the angle domain perspective. In the angle domain the slave´s time invariant dynamics become time varying and dependent on the master axis speed. Therefore, the problem of repetitive control for time varying systems arises. In this paper, model reference control is applied to compensate for the linear time varying system, rendering a linear time invariant input/output system. Asymptotic output tracking/regulation performance is achieved by employing repetitive control loop to compensate for the linear time invariant model.