Stability Regions Analysis of PID Controllers for Time-delay Systems

A novel approach to find the stabilizing regions in the PID parameter space for PID control systems with time-delay is proposed. The method is based on the observation that for a fixed value of Kd, the resulting set of stabilizing PID compensators form a set of polyhedral sets in the three-dimensional parameter space (Kp,Ki,Kd), and it is considerably simpler and faster to determine such regions compared with previous results. The proposed method is combined with dual-locus diagram to verify stability regions. The approach presented works well without sweeping over parameters, and do not need complex numerical calculations. It is useful and effective to determine search band of variables when designing advanced PID controllers using optimization methods.