Optimal automatic tuning of active damping PID regulators

Abstract An automatic tuning method for the PID controller in single-input-single-output control loops involving processes with conjugate complex poles is presented. The development of the method lies in the principle of the well known Magnitude Optimum criterion and considers two fundamental constraints met frequently in many industry applications; (1) the existence of a poor process model and (2) access to the output of the process and not to its states. The presentation of the method is carried out in two steps. Over the first step, the straightforward PID tuning via the Magnitude Optimum criterion in the ideal case of a known single input-single output linear process model reveals a feature of the method called ‘the preservation of the shape of the step and frequency response’ of the final closed-loop control system. This shape is characterized by specific performance in terms of overshoot (4.4%), settling and rise time of the closed-loop control system. Over the second step, the PID controller parameters are tuned automatically so that the aforementioned performance is achieved. In this case, the existence of a poor process model is adopted assuming access to its output and not to its states. For applying the method an open-loop experiment of the process is carried out which serves for (1) initializing the algorithm and (2) determining the two zeros of the proposed PID controller. The method starts with I-Lag control action to the process by tuning the integral gain. After this tuning is over, the parasitic time constant of the closed-loop system is estimated. I-Lag control is then turned into PID control and the integrator's time constant of the PID controller is tuned accordingly, so that the shape of the control loop's output exhibits the aforementioned performance. Since the tuning of the PID controller is based on the Magnitude Optimum criterion, optimal disturbance rejection is expected to be achieved at the output of the controlled process. The potential of the proposed method is justified via simulation examples for two benchmark process models met frequently in various industry applications.