An approach to optimal design of stabilizing PID controllers for time-delay systems

A novel approach to find the optimal stabilizing regions for PID control systems with time-delay is proposed. The method is based on the observation that the stabilizing PID compensators form a set of polyhedral sets in the three-dimensional parameter space. To avoid the lack of constraints problem, which prohibits the optimization of three PID controller parameters, the robustness constraint is integrated into the stable region determination algorithm. The constraint defines a set of controller parameters such that the maximum sensitivities are less than prescribed values. Compared with previous results it is considerably simpler and faster to determine such parameter regions by combining a so-called dual-locus diagram with the maximum sensitivity constrains with the integral gain K_i as the system performance measure. The approach presented works well without sweeping over parameters, and do not need complex numerical calculations to achieve the required performance. The simulations have shown the effectiveness of the method.