Controller Design for Unstable Time-Delay Systems with Unknown Transfer Functions

Hsun-Heng Tsai, Chyun-Chau Fuh, Jeng-Rong Ho, Chih-Kuang Lin and Pi-Cheng Tung
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Hsun-Heng Tsai: Department of Biomechatronics Engineering, National Pingtung University of Science and Technology, Pingtung 912301, Taiwan
Chyun-Chau Fuh: Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan
Jeng-Rong Ho: Department of Mechanical Engineering, National Central University, Taoyuan 320317, Taiwan
Chih-Kuang Lin: Department of Mechanical Engineering, National Central University, Taoyuan 320317, Taiwan
Pi-Cheng Tung: Department of Mechanical Engineering, National Central University, Taoyuan 320317, Taiwan

Mathematics, 2022, vol. 10, issue 3, 1-23

Abstract: This study developed a method for designing parallel two-degree-of-freedom proportional-integral-derivative controllers for unstable time-delay processes with unknown dynamic equations. First, a performance index accounting for both transient response performance and disturbance rejection was developed. To obtain useful data even if the output of the system exceeds the allowable range, an effective penalty function was included in the performance index. The N–M simplex method was used to iteratively determine the optimal controller parameters. The proposed approach has the following advantages: (1) it can be used regardless of the stability of the open-loop system; (2) the mathematical model and parameters of the process need not be known in advance; (3) it can be used for processes that include measurement noise; (4) it has good transient response performance and is also robust against external disturbances; and (5) it enables more efficient controller design and reduces costs.

Keywords: control; optimization; penalty function; PID; simplex method; time-delay; unstable (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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