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Robust Proportional−Integral−Derivative (PID) Design for Parameter Uncertain Second-Order Plus Time Delay (SOPTD) Processes Based on Reference Model Approximation

Lookup NU author(s): Dr Jie ZhangORCiD



This is the authors' accepted manuscript of an article that has been published in its final definitive form by American Chemical Society, 2017.

For re-use rights please refer to the publisher's terms and conditions.


To design robust proportional−integral−derivative (PID) controllers for second-order plus time delay (SOPTD) processes with parameter uncertainty, a reference model approximation method is proposed in this article. The central idea is to allow the frequency response of the PID controller to approximate that of a user-specified reference model. A convex hull is used to approximate the frequency template of the process with parameter uncertainty, and the maximum approximation error of the reference model among all candidate processes is bounded. To guarantee that the set-point response trajectory of each possible candidate model can well approach that of the reference model, a convex optimization problem is formulated to calculate the PID parameters by minimizing the upper bound for the approximation error. Constraints on the closed-loop maximum sensitivity peak are imposed on the reference-model approximation problem for loop robustness. The proposed method is able to ensure balanced tracking performance and disturbance rejection performance through a proper specification of the reference model; therefore, the alarms triggered according to performance indices can be more informative. Illustrative examples are presented to demonstrate the applicability.

Publication metadata

Author(s): Gao X, Zhang J, Yang F, Shang C, Huang D

Publication type: Article

Publication status: Published

Journal: Industrial & Chemical Engineering Research

Year: 2017

Volume: 56

Issue: 41

Pages: 11903-11918

Print publication date: 18/10/2017

Online publication date: 24/09/2017

Acceptance date: 23/09/2017

Date deposited: 25/10/2017

ISSN (print): 0888-5885

ISSN (electronic): 1520-5045

Publisher: American Chemical Society


DOI: 10.1021/acs.iecr.7b03155


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