On the automatic tuning of PID type controllers via the Magnitude Optimum criterion

The problem of on line tuning the PID controller used in type-I single input-single output control systems is investigated. This problem is met over many industry applications and involves two basic constraints 1) the existence of a poor process model and 2) inability to measure the states of the process. With respect to these constraints, a systematic method for automatic tuning of the PID controller is proposed. The method is inspired from the well known Magnitude Optimum design criterion. Throughout the investigation, it is shown that the straightforward application of the Magnitude Optimum principle for tuning the PID controller 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 a specific performance in terms of overshoot (4.47%), settling and rise time of the closed-loop control system. For that reason, the proposed method tunes the PID controller's parameters automatically, so that the step response of the control loop achieves the aforementioned specific performance. For applying the method, an open-loop experiment of the process is carried out which serves for initializing the algorithm. The method proceeds by identifying on line the dominant time constants of the plant and the ‘parasitic’ one of the closed-loop system. The potential of the proposed method is justified via simulation examples for two process models met in various industry applications.