Journal of Northeastern University(Natural Science) ›› 2023, Vol. 44 ›› Issue (12): 1679-1685.DOI: 10.12068/j.issn.1005-3026.2023.12.002

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Design of a Low-Order Digital Controller Based on Parametric Stability Margin

LIU Dong-xu1,2, LI Chun-hua1   

  1. 1. College of Science, Yanbian University, Yanji 133002, China; 2. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China.
  • Published:2024-01-30
  • Contact: LIU Dong-xu
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Abstract: Most control systems in the industry contain complex uncertainty and their model parameters sometimes may fluctuate. For inaccurate identification or fluctuation of system model parameters, the set of controller parameters with the largest stability margin in the parameters stabilizing sets should be selected in order to ensure the stability of the cloosed loop system. According to the characteristic of plants in industry when they run near the operating points, the proportional-integral-derivative(PID)controller is designed based on the second-order uncertain digital control system. First of all, the PID parameters stabilizing sets composed of a family of parallel convex polygons are obtained according to the stability condition of the closed loop system. Then coordinate axes are rotated to make the convex polygons perpendicular to one of the coordinate axes. Next, the Chebyshev center and its depth of each convex polygon are obtained by making use of the linear programming method. Finally, the coordinate of the Chebyshev center with the maximum depth is selected, and its coordinate in the original coordinate system is obtained by using the inverse axis rotation transformation, which is selected as the corresponding controller parameters.

Key words: PID control; parameter stabilizing sets; Chebyshev center; digital control systems; linear programming

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