Design, Tuning, and Experimental Validation of Switched Fractional-Order PID Controllers for an Inverted Pendulum System
Stabilizing inverted pendulum systems remains a challenging and open control problem due to their inherent instability and relevance in a wide range of real-world applications, including robotics and aerospace systems. While PID and fractional-order PID (FOPID) controllers offer distinct advantages,...
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MDPI AG
2025-04-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/4/234 |
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| author | Matias Fernández-Jorquera Marco Zepeda-Rabanal Norelys Aguila-Camacho Lisbel Bárzaga-Martell |
| author_facet | Matias Fernández-Jorquera Marco Zepeda-Rabanal Norelys Aguila-Camacho Lisbel Bárzaga-Martell |
| author_sort | Matias Fernández-Jorquera |
| collection | DOAJ |
| description | Stabilizing inverted pendulum systems remains a challenging and open control problem due to their inherent instability and relevance in a wide range of real-world applications, including robotics and aerospace systems. While PID and fractional-order PID (FOPID) controllers offer distinct advantages, they individually suffer from trade-offs between performance and control energy. This paper presents the design, implementation, and experimental validation of a switched SW FOPID-PID controller for the stabilization of an inverted pendulum (InvP) system, aiming to achieve an improved balance between system performance and control energy used. The controller was tuned offline using particle swarm optimization (PSO) and a mathematical model of the system for simulation. Additional PID and FOPID controllers were also designed, tuned and validated for comparison purposes. Their performance was assessed through key indicators, including ITAE, ISI, settling time, peak values, and variance and compared against a manufacturer-provided PID controller. The experimental results demonstrated that all three designed controllers outperformed the manufacturer’s PID under nominal conditions. The SW FOPID-PID controller achieved the best overall performance, balancing control energy efficiency and response quality. Under external disturbances, the FOPID and SW FOPID-PID controllers exhibited superior robustness, with the switched controller being the most effective, responding quickly to disturbances while minimizing positional and angular errors. Still, this research is limited to a specific plant and switching strategy; thus, further validation on other systems and switching criteria is necessary to generalize these findings. |
| format | Article |
| id | doaj-art-19133bcd3a31420b930f8166deb8e59e |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
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| series | Fractal and Fractional |
| spelling | doaj-art-19133bcd3a31420b930f8166deb8e59e2025-08-20T02:28:14ZengMDPI AGFractal and Fractional2504-31102025-04-019423410.3390/fractalfract9040234Design, Tuning, and Experimental Validation of Switched Fractional-Order PID Controllers for an Inverted Pendulum SystemMatias Fernández-Jorquera0Marco Zepeda-Rabanal1Norelys Aguila-Camacho2Lisbel Bárzaga-Martell3Department of Electricity, Universidad Tecnológica Metropolitana, Av. José Pedro Alessandri 1242, Santiago 7800002, ChileDepartment of Electricity, Universidad Tecnológica Metropolitana, Av. José Pedro Alessandri 1242, Santiago 7800002, ChileDepartment of Electricity, Universidad Tecnológica Metropolitana, Av. José Pedro Alessandri 1242, Santiago 7800002, ChileDepartment of Electricity, Universidad Tecnológica Metropolitana, Av. José Pedro Alessandri 1242, Santiago 7800002, ChileStabilizing inverted pendulum systems remains a challenging and open control problem due to their inherent instability and relevance in a wide range of real-world applications, including robotics and aerospace systems. While PID and fractional-order PID (FOPID) controllers offer distinct advantages, they individually suffer from trade-offs between performance and control energy. This paper presents the design, implementation, and experimental validation of a switched SW FOPID-PID controller for the stabilization of an inverted pendulum (InvP) system, aiming to achieve an improved balance between system performance and control energy used. The controller was tuned offline using particle swarm optimization (PSO) and a mathematical model of the system for simulation. Additional PID and FOPID controllers were also designed, tuned and validated for comparison purposes. Their performance was assessed through key indicators, including ITAE, ISI, settling time, peak values, and variance and compared against a manufacturer-provided PID controller. The experimental results demonstrated that all three designed controllers outperformed the manufacturer’s PID under nominal conditions. The SW FOPID-PID controller achieved the best overall performance, balancing control energy efficiency and response quality. Under external disturbances, the FOPID and SW FOPID-PID controllers exhibited superior robustness, with the switched controller being the most effective, responding quickly to disturbances while minimizing positional and angular errors. Still, this research is limited to a specific plant and switching strategy; thus, further validation on other systems and switching criteria is necessary to generalize these findings.https://www.mdpi.com/2504-3110/9/4/234switched fractional-order PIDparticle swarm optimizationcontrol energy |
| spellingShingle | Matias Fernández-Jorquera Marco Zepeda-Rabanal Norelys Aguila-Camacho Lisbel Bárzaga-Martell Design, Tuning, and Experimental Validation of Switched Fractional-Order PID Controllers for an Inverted Pendulum System Fractal and Fractional switched fractional-order PID particle swarm optimization control energy |
| title | Design, Tuning, and Experimental Validation of Switched Fractional-Order PID Controllers for an Inverted Pendulum System |
| title_full | Design, Tuning, and Experimental Validation of Switched Fractional-Order PID Controllers for an Inverted Pendulum System |
| title_fullStr | Design, Tuning, and Experimental Validation of Switched Fractional-Order PID Controllers for an Inverted Pendulum System |
| title_full_unstemmed | Design, Tuning, and Experimental Validation of Switched Fractional-Order PID Controllers for an Inverted Pendulum System |
| title_short | Design, Tuning, and Experimental Validation of Switched Fractional-Order PID Controllers for an Inverted Pendulum System |
| title_sort | design tuning and experimental validation of switched fractional order pid controllers for an inverted pendulum system |
| topic | switched fractional-order PID particle swarm optimization control energy |
| url | https://www.mdpi.com/2504-3110/9/4/234 |
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