Optimal tuning of PID controllers for integrating processes via the symmetrical optimum criterion

An analytical PI, PID type control law for type II closed loop control systems is proposed. Type-II closed loop control systems are capable of tracking step and ramp reference signals achieving zero steady state position and velocity error respectively. The development of the proposed control law is based on the well known Symmetrical Optimum criterion and focuses on optimizing output disturbance rejection in comparison with the conventional design. For the derivation of the optimal control law, a generalized transfer function of the process model is employed. Therefore, the proposed theory can be applied in any linear SISO stable or integrating process. For verifying the proposed control law, a comparison between the conventional Symmetrical Optimum criterion and the revised theory is per formed for several benchmark processes. The proposed control law shows significant improvement regarding output disturbance rejection, of up to 38%, in comparison with the conventional Symmetrical Optimum design.