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

Hsun Heng Tsai, Chyun Chau Fuh, Jeng Rong Ho, Chih Kuang Lin, Pi Cheng Tung

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish
Article number431
Issue number3
StatePublished - 1 Feb 2022


  • Control
  • Optimization
  • PID
  • Penalty function
  • Simplex method
  • Time-delay
  • Unstable


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