Analysis and Design of Repetitive Control Systems using the Regeneration Spectrum

The absolute and relative stability of continuous-time SISO repetitive control systems is examined here using a function of frequency termed the regeneration spectrum. The regeneration spectrum is easily computed and is related to important of the characteristic root distribution of such systems, for large values of the time delay. The regeneration spectrum is combined with other frequency domain measures of control system performance such as the sensitivity and complementary sensitivity functions to obtain improved insight into the trade-offs in repetitive control system design. The result is a more rational approach to repetitive control system design and is illustrated by an example.