PI tuning in terms of gain and phase margins

Ho Wang Fung, Qing Guo Wang, Tong Heng Lee

Research output: Contribution to journalArticlepeer-review

88 Citations (Scopus)


In this paper, a simple PI controller design method is proposed which can achieve user-specified gain and phase margins if they are suitable, or otherwise the automatically adjusted alternatives for performance enhancement. Unlike reduced-order model-based tuning methods, exact margins, once specified or adjusted, can be accomplished regardless of the process order and damping nature. The response of the closed-loop system using the proposed design is hence more predictable than those using model-based methods when performance specifications are given in gain and phase margins. The proposed method is based on finding the intersections between two graphs that are plotted using the frequency response of the process. The given gain and phase specifications can be achieved if intersections can be found, and each intersection corresponds to one solution. Suggestions are provided on how to modify the specifications for achieving satisfactory responses for cases where there are no solution or when the specifications can be met but poor responses result. Simulation examples are given to show the usefulness of the method.

Original languageEnglish
Pages (from-to)1145-1149
Number of pages5
Issue number9
Publication statusPublished - Sept 1998
Externally publishedYes


  • Frequency response
  • Gain margin
  • Graphical method
  • PID controller
  • Phase margin

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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