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Low-order digital controller design based on l2 parametric stability margin.

Dong-Xu Liu1, Jing-Wen Zhang2, Cui Wei3

  • 1College of Science, Yanbian University, No. 977, Gongyuan Road, Yanji, PR China; State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, No. 11, Wenhua Road, Shenyang, PR China..

ISA Transactions
|August 30, 2025
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Summary
This summary is machine-generated.

This study introduces a new digital PID controller tuning method. It maximizes stability margins for uncertain systems, ensuring robust performance and preventing fragility in controller parameters.

Keywords:
Chebyshev centerDigital control systemsLinear programmingPID controlParameter stabilizing set

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Area of Science:

  • Control Systems Engineering
  • Systems Theory
  • Applied Mathematics

Background:

  • Engineering control systems face complex uncertainties, often leading to significant plant parameter fluctuations.
  • Proportional-Integral-Derivative (PID) controllers are widely used but can be tuned near stability boundaries, risking system integrity.
  • Existing tuning methods may not adequately address parametric uncertainties, compromising controller robustness.

Purpose of the Study:

  • To propose a novel design strategy for digital PID controllers for second-order uncertain discrete-time systems.
  • To develop a tuning method that maximizes the parametric stability margin, ensuring system robustness.
  • To create a non-fragile PID controller design resilient to parameter variations.

Main Methods:

  • Derived the stabilizing set of PID parameters as convex polygons in 3D space based on closed-loop stability conditions.
  • Employed coordinate-axes rotation to simplify the geometric analysis of the stabilizing set.
  • Developed a linear programming algorithm to find the Chebyshev center of the stabilizing set for optimal parameter selection.

Main Results:

  • Identified the stabilizing set as a family of parallel convex polygons.
  • Successfully determined the Chebyshev center coordinates, representing optimal PID controller parameters.
  • Achieved the maximum l2 parametric stability margin for the digital PID controller.

Conclusions:

  • The proposed method provides a robust tuning strategy for digital PID controllers in uncertain systems.
  • The developed technique ensures controller non-fragility by maximizing the parametric stability margin.
  • This work offers a systematic approach to determining PID parameter stabilizing sets for second-order discrete-time systems.