Explicit analytical tuning rules for digital PID controllers via the magnitude optimum criterion

摘要

Abstract Analytical tuning rules for digital PID type–I controllers are presented regardless of the process complexity. This explicit solution allows control engineers 1) to make an accurate examination of the effect of the controller's sampling time to the control loop's performance both in the time and frequency domain 2) to decide when the control has to be I, PI and when the derivative, D, term has to be added or omitted 3) apply this control action to a series of stable benchmark processes regardless of their complexity. The former advantages are considered critical in industry applications, since 1) most of the times the choice of the digital controller's sampling time is based on heuristics and past criteria, 2) there is little a–priori knowledge of the controlled process making the choice of the type of the controller a trial and error exercise 3) model parameters change often depending on the control loop's operating point making in this way, the problem of retuning the controller's parameter a much challenging issue. Basis of the proposed control law is the principle of the PID tuning via the Magnitude Optimum criterion. The final control law involves the controller's sampling time T s within the explicit solution of the controller's parameters. Finally, the potential of the proposed method is justified by comparing its performance with the conventional PID tuning when controlling the same process. Further investigation regarding the choice of the controller's sampling time T s is also presented and useful conclusions for control engineers are derived. Highlights ? Closed form tuning formulas for PID digital controllers in SISO processes are presented. ? Optimal controller's sampling time selection is analytically derived and practical suggestions/remark concerning the same are made depending on the process / nature of application. ? Robust performance in terms of reference tracking and output disturbance rejection are achieved. ? The method can be applied to any SISO stable process regardless of its complexity. ? Evaluation results for several benchmark process models are presented.