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Observer-Based PID Control Strategy for the Stabilization of Delayed High Order Systems with up to Three Unstable Poles

Author

Listed:
  • César Cruz-Díaz

    (Instituto Politécnico Nacional, ESIME Culhuacán, Av. Santa Ana 1000, Col. San Francisco Culhuacán, Mexico City 04440, Mexico)

  • Basilio del Muro-Cuéllar

    (Instituto Politécnico Nacional, ESIME Culhuacán, Av. Santa Ana 1000, Col. San Francisco Culhuacán, Mexico City 04440, Mexico)

  • Gonzalo Duchén-Sánchez

    (Instituto Politécnico Nacional, ESIME Culhuacán, Av. Santa Ana 1000, Col. San Francisco Culhuacán, Mexico City 04440, Mexico)

  • Juan Francisco Márquez-Rubio

    (Instituto Politécnico Nacional, ESIME Culhuacán, Av. Santa Ana 1000, Col. San Francisco Culhuacán, Mexico City 04440, Mexico)

  • Martín Velasco-Villa

    (Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Electrical Engineering Department, Mechatronics Section, Av. IPN 2508, Col. San Pedro Zacatenco, Mexico City 07360, Mexico)

Abstract

In this paper, a new method to manage the stabilization and control problems of n -dimensional linear systems plus dead time, which includes one, two, or three unstable poles, is proposed. The control methodology proposed in this work is an Observer-based Proportional-Integral-Derivative (PID) strategy, where an observer and a PID controller are used to relocate the original unstable open-loop poles to stabilize the resultant closed-loop system. The observer provides an adequate estimation of the delayed-free variables and the PID uses the delay-free variables estimated by the proposed observer. Also, step-tracking is achieved in the overall control scheme. Necessary and sufficient conditions are presented to ensure closed-loop stability based on the open loop parameters of the system. The observer-based PID strategy considers five to seven constant parameters to obtain a stable closed-loop system. A general procedure to implement the proposed control strategy is presented and its performance is evaluated by means of numerical simulations.

Suggested Citation

  • César Cruz-Díaz & Basilio del Muro-Cuéllar & Gonzalo Duchén-Sánchez & Juan Francisco Márquez-Rubio & Martín Velasco-Villa, 2022. "Observer-Based PID Control Strategy for the Stabilization of Delayed High Order Systems with up to Three Unstable Poles," Mathematics, MDPI, vol. 10(9), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1399-:d:799576
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    References listed on IDEAS

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    1. Chen, Wei-Ching, 2008. "Dynamics and control of a financial system with time-delayed feedbacks," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1198-1207.
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