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Novel Proportional–Integral–Derivative Control Framework on Continuous-Time Positive Systems Using Linear Programming

Author

Listed:
  • Qingbo Li

    (School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China)

  • Xiaoyue Zhou

    (School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Fengyu Lin

    (School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Yahao Yang

    (School of Information and Communication Engineering, Hainan University, Haikou 570228, China)

  • Junfeng Zhang

    (School of Information and Communication Engineering, Hainan University, Haikou 570228, China)

Abstract

This paper considers the proportional–integral–derivative (PID) control for continuous-time positive systems. A three-stage strategy is introduced to design the PID controller. In the first stage, the proportional and integral components of the PID control are designed. A matrix decomposition approach is used to describe the gain matrices of the proportional and integral components. The positivity and stability of the closed-loop systems without the derivative component of PID control are achieved by the properties of a Metzler and Hurwitz matrix. In the second stage, a non-negative inverse matrix is constructed to maintain the Metzler and Hurwitz properties of the closed-loop system matrix in the first stage. To deal with the inverse of the derivative component of PID control, a matrix decomposition approach is further utilized to design a non-negative inverse matrix. Then, the derivative component is obtained by virtue of the designed inverse matrix. All the presented conditions can be solved by virtue of a linear programming approach. Furthermore, the three-stage PID design is developed for a state observer-based PID controller. Finally, a simulation example is provided to verify the effectiveness and validity of the proposed design.

Suggested Citation

  • Qingbo Li & Xiaoyue Zhou & Fengyu Lin & Yahao Yang & Junfeng Zhang, 2024. "Novel Proportional–Integral–Derivative Control Framework on Continuous-Time Positive Systems Using Linear Programming," Mathematics, MDPI, vol. 12(4), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:617-:d:1341630
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    References listed on IDEAS

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    1. Tharanidharan, V. & Sakthivel, R. & Ren, Yong & Marshal Anthoni, S., 2022. "Robust finite-time PID control for discrete-time large-scale interconnected uncertain system with discrete-delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 370-383.
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