High-Performance Identification and Control of MIMO (Multiple Input—Multiple Output) Experimental Module with Fractional-Order Approach Application
This paper focuses on the application of fractional calculus techniques in the identification and control of multivariable (multiple input—multiple output) systems (MIMO). By considering a previously reported experimental set-up similar to a greenhouse, this study proposes the open-loop identificati...
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2025-04-01
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| author | Alexandre Marques de Almeida Alisson Luan Daga Rafael Palma Setti Penteado Lanzarini Ervin Kaminski Lenzi Marcelo Kaminski Lenzi |
| author_facet | Alexandre Marques de Almeida Alisson Luan Daga Rafael Palma Setti Penteado Lanzarini Ervin Kaminski Lenzi Marcelo Kaminski Lenzi |
| author_sort | Alexandre Marques de Almeida |
| collection | DOAJ |
| description | This paper focuses on the application of fractional calculus techniques in the identification and control of multivariable (multiple input—multiple output) systems (MIMO). By considering a previously reported experimental set-up similar to a greenhouse, this study proposes the open-loop identification of fractional order transfer functions relating to the controlled and manipulated variables, which were validated by experimental data. Afterward, the theoretical analysis of Fractional-order Proportional and Integral (FOPI) closed-loop control for this MIMO system was carried out. An important aspect concerns the use of Particle Swarm Optimization (PSO) metaheuristic algorithm for optimization tasks, both in parameter estimation and controller tuning. Moreover, comparisons with integer order models and controllers (IOPID-IMC) were performed. The results demonstrate the superior performance and robustness of the FOPI-PSO fractional control, which achieves up to 79.6% reduction in ITAE and 72.1% reduction in ITSE criteria. Without the need for explicit decouplers, the decentralized FOPI-PSO control structure demonstrated effective handling of interactions between the temperature and humidity control loops, simplifying the control design while maintaining performance. The fractional-order controllers exhibited robustness to measurement noise, as evidenced by stable and precise control responses in the presence of experimental uncertainties. Additionally, the optimized tuning of FOPI controllers implicitly compensated for disturbances and setpoint changes without requiring additional feedforward mechanisms. This study contributes to a better understanding of fractional calculus applications in designing FO–MIMO systems and provides a practical framework for addressing the identified gaps in the field. |
| format | Article |
| id | doaj-art-e8b0550a7b6e4169b6f1c575042cdb7d |
| 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-e8b0550a7b6e4169b6f1c575042cdb7d2025-08-20T02:28:14ZengMDPI AGFractal and Fractional2504-31102025-04-019422610.3390/fractalfract9040226High-Performance Identification and Control of MIMO (Multiple Input—Multiple Output) Experimental Module with Fractional-Order Approach ApplicationAlexandre Marques de Almeida0Alisson Luan Daga1Rafael Palma Setti Penteado Lanzarini2Ervin Kaminski Lenzi3Marcelo Kaminski Lenzi4Fractional Systems Engineering Lab, Department of Chemical Engineering, Federal University of Paraná, Curitiba 81531-980, BrazilFractional Systems Engineering Lab, Department of Chemical Engineering, Federal University of Paraná, Curitiba 81531-980, BrazilFractional Systems Engineering Lab, Department of Chemical Engineering, Federal University of Paraná, Curitiba 81531-980, BrazilDepartment of Physics, State University of Maringá, Maringá 87020-900, BrazilFractional Systems Engineering Lab, Department of Chemical Engineering, Federal University of Paraná, Curitiba 81531-980, BrazilThis paper focuses on the application of fractional calculus techniques in the identification and control of multivariable (multiple input—multiple output) systems (MIMO). By considering a previously reported experimental set-up similar to a greenhouse, this study proposes the open-loop identification of fractional order transfer functions relating to the controlled and manipulated variables, which were validated by experimental data. Afterward, the theoretical analysis of Fractional-order Proportional and Integral (FOPI) closed-loop control for this MIMO system was carried out. An important aspect concerns the use of Particle Swarm Optimization (PSO) metaheuristic algorithm for optimization tasks, both in parameter estimation and controller tuning. Moreover, comparisons with integer order models and controllers (IOPID-IMC) were performed. The results demonstrate the superior performance and robustness of the FOPI-PSO fractional control, which achieves up to 79.6% reduction in ITAE and 72.1% reduction in ITSE criteria. Without the need for explicit decouplers, the decentralized FOPI-PSO control structure demonstrated effective handling of interactions between the temperature and humidity control loops, simplifying the control design while maintaining performance. The fractional-order controllers exhibited robustness to measurement noise, as evidenced by stable and precise control responses in the presence of experimental uncertainties. Additionally, the optimized tuning of FOPI controllers implicitly compensated for disturbances and setpoint changes without requiring additional feedforward mechanisms. This study contributes to a better understanding of fractional calculus applications in designing FO–MIMO systems and provides a practical framework for addressing the identified gaps in the field.https://www.mdpi.com/2504-3110/9/4/226fractional open-loop identificationfractional-order controlmultivariable experimental modulemetaheuristic optimization |
| spellingShingle | Alexandre Marques de Almeida Alisson Luan Daga Rafael Palma Setti Penteado Lanzarini Ervin Kaminski Lenzi Marcelo Kaminski Lenzi High-Performance Identification and Control of MIMO (Multiple Input—Multiple Output) Experimental Module with Fractional-Order Approach Application Fractal and Fractional fractional open-loop identification fractional-order control multivariable experimental module metaheuristic optimization |
| title | High-Performance Identification and Control of MIMO (Multiple Input—Multiple Output) Experimental Module with Fractional-Order Approach Application |
| title_full | High-Performance Identification and Control of MIMO (Multiple Input—Multiple Output) Experimental Module with Fractional-Order Approach Application |
| title_fullStr | High-Performance Identification and Control of MIMO (Multiple Input—Multiple Output) Experimental Module with Fractional-Order Approach Application |
| title_full_unstemmed | High-Performance Identification and Control of MIMO (Multiple Input—Multiple Output) Experimental Module with Fractional-Order Approach Application |
| title_short | High-Performance Identification and Control of MIMO (Multiple Input—Multiple Output) Experimental Module with Fractional-Order Approach Application |
| title_sort | high performance identification and control of mimo multiple input multiple output experimental module with fractional order approach application |
| topic | fractional open-loop identification fractional-order control multivariable experimental module metaheuristic optimization |
| url | https://www.mdpi.com/2504-3110/9/4/226 |
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