Observer-Based PID Control Strategy for the Stabilization of Delayed High Order Systems with up to Three Unstable Poles
In this paper, a new method to manage the stabilization and control problems of <i>n</i>-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-Deri...
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MDPI AG
2022-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/9/1399 |
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| author | César Cruz-Díaz Basilio del Muro-Cuéllar Gonzalo Duchén-Sánchez Juan Francisco Márquez-Rubio Martín Velasco-Villa |
| author_facet | César Cruz-Díaz Basilio del Muro-Cuéllar Gonzalo Duchén-Sánchez Juan Francisco Márquez-Rubio Martín Velasco-Villa |
| author_sort | César Cruz-Díaz |
| collection | DOAJ |
| description | In this paper, a new method to manage the stabilization and control problems of <i>n</i>-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. |
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| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:56:40Z |
| publishDate | 2022-04-01 |
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| series | Mathematics |
| spelling | doaj.art-8309d5e2209b4fbf99bf72acaf1f040a2023-11-23T08:43:43ZengMDPI AGMathematics2227-73902022-04-01109139910.3390/math10091399Observer-Based PID Control Strategy for the Stabilization of Delayed High Order Systems with up to Three Unstable PolesCésar Cruz-Díaz0Basilio del Muro-Cuéllar1Gonzalo Duchén-Sánchez2Juan Francisco Márquez-Rubio3Martín Velasco-Villa4Instituto Politécnico Nacional, ESIME Culhuacán, Av. Santa Ana 1000, Col. San Francisco Culhuacán, Mexico City 04440, MexicoInstituto Politécnico Nacional, ESIME Culhuacán, Av. Santa Ana 1000, Col. San Francisco Culhuacán, Mexico City 04440, MexicoInstituto Politécnico Nacional, ESIME Culhuacán, Av. Santa Ana 1000, Col. San Francisco Culhuacán, Mexico City 04440, MexicoInstituto Politécnico Nacional, ESIME Culhuacán, Av. Santa Ana 1000, Col. San Francisco Culhuacán, Mexico City 04440, MexicoCentro 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, MexicoIn this paper, a new method to manage the stabilization and control problems of <i>n</i>-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.https://www.mdpi.com/2227-7390/10/9/1399observersPID controllerlinear delay systemsstabilization |
| spellingShingle | César Cruz-Díaz Basilio del Muro-Cuéllar Gonzalo Duchén-Sánchez Juan Francisco Márquez-Rubio Martín Velasco-Villa Observer-Based PID Control Strategy for the Stabilization of Delayed High Order Systems with up to Three Unstable Poles Mathematics observers PID controller linear delay systems stabilization |
| title | Observer-Based PID Control Strategy for the Stabilization of Delayed High Order Systems with up to Three Unstable Poles |
| title_full | Observer-Based PID Control Strategy for the Stabilization of Delayed High Order Systems with up to Three Unstable Poles |
| title_fullStr | Observer-Based PID Control Strategy for the Stabilization of Delayed High Order Systems with up to Three Unstable Poles |
| title_full_unstemmed | Observer-Based PID Control Strategy for the Stabilization of Delayed High Order Systems with up to Three Unstable Poles |
| title_short | Observer-Based PID Control Strategy for the Stabilization of Delayed High Order Systems with up to Three Unstable Poles |
| title_sort | observer based pid control strategy for the stabilization of delayed high order systems with up to three unstable poles |
| topic | observers PID controller linear delay systems stabilization |
| url | https://www.mdpi.com/2227-7390/10/9/1399 |
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