Integral Action Controllers for Systems with Time Delays

Consider a stabilizing controller C-1 for a given plant P. If C-1 and P do not have any zeros at the origin, then one can use a cascade connected PI (proportional plus integral) controller C-pi with C-1 and keep the feedback system stable. In this work we examine the allowable range of the integral action gain in C-pi, and discuss how C-1 should be chosen to maximize this range for systems with time delays.