Analytical Tuning Rules for Digital PID Type Controllers via the Magnitude Optimum Criterion

Analytical tuning rules for digital PID type-I control loops are presented. Controller parameters are determined explicitly as a function of the process parameters and the sampling time of the controller. For developing the proposed theory a generalized single-input single-output stable process model is employed consisting of n-poles, no zeros plus unknown time delay-d. The derivation of the proposed PID control law lies in the principle of the well known Magnitude Optimum criterion. The conventional PID tuning via the Magnitude Optimum criterion is compared with the revised PID control law for several process models met in various industry applications via simulation examples. The revised PID tuning achieves significant improvement of up to 47% reduction of settling time regarding output disturbance rejection and reference tracking even for benchmark processes with long time delay or dominant time constants.