Generalized robustness regions for PID controllers

The problem of design a fixed PID controller for several LTI models is recognized as one of the fundamental problem in control theory. Recently, interesting results concerning the parameterization of all PID controllers stabilizing a given system were published. In this paper, the systematic procedure for construction of robustness regions in the parameter plane of the PID controller is presented when we require that the open loop Nyquist plot does not have an intersection with a given general conic. Further, it is shown how use this procedure for design of the fixed PID controller for several process models simultaneously.