Optimal <i>V</i>-Plane Robust Stabilization Method for Interval Uncertain Fractional Order PID Control Systems
Robust stability is a major concern for real-world control applications. Realization of optimal robust stability requires a stabilization scheme, which ensures that the control system is stable and presents robust performance for a predefined range of system perturbations. This study presented an op...
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MDPI AG
2021-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/1/3 |
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| author | Sevilay Tufenkci Bilal Senol Radek Matušů Baris Baykant Alagoz |
| author_facet | Sevilay Tufenkci Bilal Senol Radek Matušů Baris Baykant Alagoz |
| author_sort | Sevilay Tufenkci |
| collection | DOAJ |
| description | Robust stability is a major concern for real-world control applications. Realization of optimal robust stability requires a stabilization scheme, which ensures that the control system is stable and presents robust performance for a predefined range of system perturbations. This study presented an optimal robust stabilization approach for closed-loop fractional order proportional integral derivative (FOPID) control systems with interval parametric uncertainty and uncertain time delay. This stabilization approach, which is carried out in a <i>v</i>-plane, relies on the placement of the minimum angle system pole to a predefined target angle within the stability region of the first Riemann sheet. For this purpose, tuning of FOPID controller coefficients was performed to minimize a root angle error that is defined as the squared difference of minimum angle root of interval characteristic polynomials and the desired target angle within the stability region of the <i>v</i>-plane. To solve this optimization problem, a particle swarm optimization (PSO) algorithm was implemented. Findings of the study reveal that tuning of the target angle can also be used to improve the robust control performance of interval uncertain FOPID control systems. Illustrative examples demonstrated the effectiveness of the proposed v-domain, optimal, robust stabilization of FOPID control systems. |
| first_indexed | 2024-03-10T13:32:02Z |
| format | Article |
| id | doaj.art-8cf26377311f45f799517516d0ab6ecb |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T13:32:02Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-8cf26377311f45f799517516d0ab6ecb2023-11-21T07:56:51ZengMDPI AGFractal and Fractional2504-31102021-01-0151310.3390/fractalfract5010003Optimal <i>V</i>-Plane Robust Stabilization Method for Interval Uncertain Fractional Order PID Control SystemsSevilay Tufenkci0Bilal Senol1Radek Matušů2Baris Baykant Alagoz3Department of Computer Engineering, Inonu University, 44000 Malatya, TurkeyDepartment of Computer Engineering, Inonu University, 44000 Malatya, TurkeyCentre for Security, Information and Advanced Technologies (CEBIA–Tech), Faculty of Applied Informatics, Tomas Bata University in Zlín, 760 01 Zlín, Czech RepublicDepartment of Computer Engineering, Inonu University, 44000 Malatya, TurkeyRobust stability is a major concern for real-world control applications. Realization of optimal robust stability requires a stabilization scheme, which ensures that the control system is stable and presents robust performance for a predefined range of system perturbations. This study presented an optimal robust stabilization approach for closed-loop fractional order proportional integral derivative (FOPID) control systems with interval parametric uncertainty and uncertain time delay. This stabilization approach, which is carried out in a <i>v</i>-plane, relies on the placement of the minimum angle system pole to a predefined target angle within the stability region of the first Riemann sheet. For this purpose, tuning of FOPID controller coefficients was performed to minimize a root angle error that is defined as the squared difference of minimum angle root of interval characteristic polynomials and the desired target angle within the stability region of the <i>v</i>-plane. To solve this optimization problem, a particle swarm optimization (PSO) algorithm was implemented. Findings of the study reveal that tuning of the target angle can also be used to improve the robust control performance of interval uncertain FOPID control systems. Illustrative examples demonstrated the effectiveness of the proposed v-domain, optimal, robust stabilization of FOPID control systems.https://www.mdpi.com/2504-3110/5/1/3stability of linear systemsuncertain systemsrobust controloptimizationcomputer-aided control design |
| spellingShingle | Sevilay Tufenkci Bilal Senol Radek Matušů Baris Baykant Alagoz Optimal <i>V</i>-Plane Robust Stabilization Method for Interval Uncertain Fractional Order PID Control Systems Fractal and Fractional stability of linear systems uncertain systems robust control optimization computer-aided control design |
| title | Optimal <i>V</i>-Plane Robust Stabilization Method for Interval Uncertain Fractional Order PID Control Systems |
| title_full | Optimal <i>V</i>-Plane Robust Stabilization Method for Interval Uncertain Fractional Order PID Control Systems |
| title_fullStr | Optimal <i>V</i>-Plane Robust Stabilization Method for Interval Uncertain Fractional Order PID Control Systems |
| title_full_unstemmed | Optimal <i>V</i>-Plane Robust Stabilization Method for Interval Uncertain Fractional Order PID Control Systems |
| title_short | Optimal <i>V</i>-Plane Robust Stabilization Method for Interval Uncertain Fractional Order PID Control Systems |
| title_sort | optimal i v i plane robust stabilization method for interval uncertain fractional order pid control systems |
| topic | stability of linear systems uncertain systems robust control optimization computer-aided control design |
| url | https://www.mdpi.com/2504-3110/5/1/3 |
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