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

César Cruz-Díaz, Basilio del Muro-Cuéllar, Gonzalo Duchén-Sánchez, Juan Francisco Márquez-Rubio and Martín Velasco-Villa
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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

Mathematics, 2022, vol. 10, issue 9, 1-17

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.

Keywords: observers; PID controller; linear delay systems; stabilization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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