Digital PID controller design using ARX estimation

• Published in: Computers & chemical engineering Vol. 20; no. 11; pp. 1317 - 1334
• Main Authors: Rivera, D.E., Gaikwad, S.V.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 1996; Elsevier
• Subjects: Applications of mathematics to chemical engineering. Modeling. Simulation. Optimization; Applied sciences; Chemical engineering; Exact sciences and technology; Digital control; Design; Distributed control; Control robustness; Process control; Differential integral proportional regulator
• ISSN: 0098-1354; 1873-4375
• DOI: 10.1016/0098-1354(95)00246-4

This paper describes a comprehensive methodology to obtain reduced-order models that satisfy the Prett-Garcia digital PID tuning rules, using prefiltered AutoRegressive with eXternal input (ARX) estimation as a basis. The Prett-Garcia tuning rules possess the advantage that they systematically relate all the controller parameters to the plant model and a low-pass filter with a single adjustable parameter, which directly influences the closed-loop speed-of-response. Furthermore, these rules avoid the problems of intersample rippling, excessive overshoot and undershoot that are a consequence of sampling. The essential aspect of the estimation method is the selection of the prefilter, which allows the reduced model to retain those plant characteristics that have the most effect on closed-loop system behavior. The design of the prefilter is performed systematically using the engineer's desired control requirements and the setpoint/disturbance characteristics of the problem. The benefits of this method are shown for a variety of simulated plants, which include a fourth-order system, plants with time delay and integrators, and a plant with zeros outside the unit circle.