Repetitive control of time-delay systems

To overcome time delay, three types of modified repetitive control systems are proposed: the state predictor approach, the finite spectrum assignment approach, and the spectral decomposition approach. It is shown that the combination of delay-free reduction by the state predictor and the frequency-domain approach can stabilize the system and yield small steady-state error with respect to both the reference command and the disturbance. The stability depends on the low-pass filter q(s). To release the restriction, q( s)-independent stabilization is proposed which uses the finite spectrum assignment. Furthermore, q(s)-free stabilization is proposed which uses an attenuator and spectral decomposition. Numerical examples are given