Automatic tuning of PID type-III control loops via the symmetrical optimum criterion

The Symmetrical Optimum criterion is extended for the design of PID-type-III control loops. Main advantage of type-III control loops (compared to type-I,~II) is their ability to track fast reference signals since they eliminate higher order errors at steady state (zero steady state position, velocity and acceleration error.) Type-III control loops are characterized by the presence of three pure integrators in the open loop transfer function. The proposed PID control law consists of analytical expressions that can be applied to process models consisting of n poles plus time delay d. The application of the the proposed control law to a large class of processes (model with known transfer function) shows that regardless of the process complexity, the overshoot of the step response of the final closed-loop control system exhibits a certain level. This feature results effortlessly to the automatic tuning of the PID controller´s parameters since by exploiting the analytical expressions of the proposed PID control law, controller parameters are tuned such, so that the step response of the control loop exhibits the specific overshoot. For applying the proposed method, an open loop experiment of the process is necessary for starting up the algorithm. The proposed tuning technique assumes that access to the states is impossible as it frequently happens in many industry applications. Simulation results are presented, verifying the current approach.