Discrete-Time Design of Fractional Delay-Based Repetitive Controller with Sliding Mode Approach for Uncertain Linear Systems with Multiple Periodic Signals
In this paper, a discrete-time design of a fractional internal model-based repetitive controller with a sliding mode approach is presented for uncertain linear systems subject to repetitive trajectory and periodic disturbance. The proposed algorithm, named a fractional delay-based repetitive sliding...
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MDPI AG
2025-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/1/41 |
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| author | Edi Kurniawan Azka M. Burrohman Purwowibowo Purwowibowo Sensus Wijonarko Tatik Maftukhah Jalu A. Prakosa Dadang Rustandi Enggar B. Pratiwi Amaliyah Az-Zukhruf |
| author_facet | Edi Kurniawan Azka M. Burrohman Purwowibowo Purwowibowo Sensus Wijonarko Tatik Maftukhah Jalu A. Prakosa Dadang Rustandi Enggar B. Pratiwi Amaliyah Az-Zukhruf |
| author_sort | Edi Kurniawan |
| collection | DOAJ |
| description | In this paper, a discrete-time design of a fractional internal model-based repetitive controller with a sliding mode approach is presented for uncertain linear systems subject to repetitive trajectory and periodic disturbance. The proposed algorithm, named a fractional delay-based repetitive sliding mode controller (FD-RSMC), aims to enhance tracking accuracy, transient response, and robustness against parametric variations beyond what is offered by conventional repetitive controllers. First, a fractional delay-based repetitive controller (FD-RC) that allows the periodic delay steps to be noninteger is presented to improve the trajectory tracking accuracy and good disturbance compensation of multiple periodic signals. Second, a sliding mode control (SMC) with a discrete-time reaching law is systematically incorporated into FD-RC to improve transient response, especially during the learning period of FD-RC, and also to provide system robustness against model uncertainties. Finally, the stability proof of the closed-loop system with the proposed controller is assessed based on a delayed-sliding mode-reaching condition. Finally, comparative simulation studies are presented to demonstrate the superior performance of the proposed controller. |
| format | Article |
| id | doaj-art-2c8e19ce13a04851a8cb83d2ea156433 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-2c8e19ce13a04851a8cb83d2ea1564332025-01-24T13:33:28ZengMDPI AGFractal and Fractional2504-31102025-01-01914110.3390/fractalfract9010041Discrete-Time Design of Fractional Delay-Based Repetitive Controller with Sliding Mode Approach for Uncertain Linear Systems with Multiple Periodic SignalsEdi Kurniawan0Azka M. Burrohman1Purwowibowo Purwowibowo2Sensus Wijonarko3Tatik Maftukhah4Jalu A. Prakosa5Dadang Rustandi6Enggar B. Pratiwi7Amaliyah Az-Zukhruf8Research Center for Photonics, National Research and Innovation Agency, Tangerang Selatan 15314, IndonesiaResearch Center for Photonics, National Research and Innovation Agency, Tangerang Selatan 15314, IndonesiaResearch Center for Photonics, National Research and Innovation Agency, Tangerang Selatan 15314, IndonesiaResearch Center for Photonics, National Research and Innovation Agency, Tangerang Selatan 15314, IndonesiaResearch Center for Photonics, National Research and Innovation Agency, Tangerang Selatan 15314, IndonesiaResearch Center for Photonics, National Research and Innovation Agency, Tangerang Selatan 15314, IndonesiaResearch Center for Photonics, National Research and Innovation Agency, Tangerang Selatan 15314, IndonesiaResearch Center for Photonics, National Research and Innovation Agency, Tangerang Selatan 15314, IndonesiaResearch Center for Photonics, National Research and Innovation Agency, Tangerang Selatan 15314, IndonesiaIn this paper, a discrete-time design of a fractional internal model-based repetitive controller with a sliding mode approach is presented for uncertain linear systems subject to repetitive trajectory and periodic disturbance. The proposed algorithm, named a fractional delay-based repetitive sliding mode controller (FD-RSMC), aims to enhance tracking accuracy, transient response, and robustness against parametric variations beyond what is offered by conventional repetitive controllers. First, a fractional delay-based repetitive controller (FD-RC) that allows the periodic delay steps to be noninteger is presented to improve the trajectory tracking accuracy and good disturbance compensation of multiple periodic signals. Second, a sliding mode control (SMC) with a discrete-time reaching law is systematically incorporated into FD-RC to improve transient response, especially during the learning period of FD-RC, and also to provide system robustness against model uncertainties. Finally, the stability proof of the closed-loop system with the proposed controller is assessed based on a delayed-sliding mode-reaching condition. Finally, comparative simulation studies are presented to demonstrate the superior performance of the proposed controller.https://www.mdpi.com/2504-3110/9/1/41repetitive controlinternal modelfractional delaysliding mode controluncertain linear systemsrepetitive trajectory |
| spellingShingle | Edi Kurniawan Azka M. Burrohman Purwowibowo Purwowibowo Sensus Wijonarko Tatik Maftukhah Jalu A. Prakosa Dadang Rustandi Enggar B. Pratiwi Amaliyah Az-Zukhruf Discrete-Time Design of Fractional Delay-Based Repetitive Controller with Sliding Mode Approach for Uncertain Linear Systems with Multiple Periodic Signals Fractal and Fractional repetitive control internal model fractional delay sliding mode control uncertain linear systems repetitive trajectory |
| title | Discrete-Time Design of Fractional Delay-Based Repetitive Controller with Sliding Mode Approach for Uncertain Linear Systems with Multiple Periodic Signals |
| title_full | Discrete-Time Design of Fractional Delay-Based Repetitive Controller with Sliding Mode Approach for Uncertain Linear Systems with Multiple Periodic Signals |
| title_fullStr | Discrete-Time Design of Fractional Delay-Based Repetitive Controller with Sliding Mode Approach for Uncertain Linear Systems with Multiple Periodic Signals |
| title_full_unstemmed | Discrete-Time Design of Fractional Delay-Based Repetitive Controller with Sliding Mode Approach for Uncertain Linear Systems with Multiple Periodic Signals |
| title_short | Discrete-Time Design of Fractional Delay-Based Repetitive Controller with Sliding Mode Approach for Uncertain Linear Systems with Multiple Periodic Signals |
| title_sort | discrete time design of fractional delay based repetitive controller with sliding mode approach for uncertain linear systems with multiple periodic signals |
| topic | repetitive control internal model fractional delay sliding mode control uncertain linear systems repetitive trajectory |
| url | https://www.mdpi.com/2504-3110/9/1/41 |
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