Synthesis of PID controllers with regional pole constraints

A new approach for calculating all PID controllers with regional pole constraints is developed in this paper. The method transforms the regional pole constraints problem into the stability problem, based on the coordinate parallel and rotation transformation. For a fixed value of k_d, the region of PID controller that guarantees the given pole requirement can be fast computed via plotting stability boundary locus in the k_p - k_i plane. By sweeping over different a priori k_d values, the intersection of PID controller parameters can be determined in the three-dimensions. How such sets can then be used to design a PID controller satisfying a series of performance specifications is also discussed. An example is used to demonstrate the effectiveness of the presented method.