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Stabilization of Nonlinear Vibration of a Fractional-Order Arch MEMS Resonator Using a New Disturbance-Observer-Based Finite-Time Sliding Mode Control

Author

Listed:
  • Hajid Alsubaie

    (Department of Mechanical Engineering, College of Engineering, Taif University, Taif 21944, Saudi Arabia)

  • Amin Yousefpour

    (Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA)

  • Ahmed Alotaibi

    (Department of Mechanical Engineering, College of Engineering, Taif University, Taif 21944, Saudi Arabia)

  • Naif D. Alotaibi

    (Communication Systems and Networks Research Group, Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Hadi Jahanshahi

    (Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB R3T 5V6, Canada)

Abstract

This paper deals with chaos control in an arch microelectromechanical system (MEMS) from the fractional calculus perspective. There is a growing need for effective controllers in various technological fields, and it is important to consider disruptions, uncertainties, and control input limitations when designing a practical controller. To address this problem, we propose a novel disturbance-observer-based terminal sliding mode control technique for stabilizing and controlling chaos in a fractional-order arch MEMS resonator. The design of this technique takes into account uncertainty, disturbances, and control input saturation in the fractional-order system. The proposed control technique is practical for real-world applications because it includes control input saturation. The equation for a fractional-order arch MEMS resonator is presented, and its nonlinear vibration and chaotic behavior are studied. The design process for the proposed control technique is then described. The Lyapunov stability theorem is used to prove the finite-time convergence of the proposed controller and disturbance observer. The proposed controller is applied to the arch MEMS resonator, and numerical simulations are used to demonstrate its effectiveness and robustness for uncertain nonlinear systems. The results of these simulations clearly show the effectiveness of the proposed control technique.

Suggested Citation

  • Hajid Alsubaie & Amin Yousefpour & Ahmed Alotaibi & Naif D. Alotaibi & Hadi Jahanshahi, 2023. "Stabilization of Nonlinear Vibration of a Fractional-Order Arch MEMS Resonator Using a New Disturbance-Observer-Based Finite-Time Sliding Mode Control," Mathematics, MDPI, vol. 11(4), pages 1-14, February.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:978-:d:1068277
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    References listed on IDEAS

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    1. Li, Jun-Feng & Jahanshahi, Hadi & Kacar, Sezgin & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alotaibi, Naif D. & Alharbi, Khalid H., 2021. "On the variable-order fractional memristor oscillator: Data security applications and synchronization using a type-2 fuzzy disturbance observer-based robust control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Jahanshahi, Hadi & Yousefpour, Amin & Wei, Zhouchao & Alcaraz, Raúl & Bekiros, Stelios, 2019. "A financial hyperchaotic system with coexisting attractors: Dynamic investigation, entropy analysis, control and synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 66-77.
    3. Jahanshahi, Hadi & Sajjadi, Samaneh Sadat & Bekiros, Stelios & Aly, Ayman A., 2021. "On the development of variable-order fractional hyperchaotic economic system with a nonlinear model predictive controller," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Qijia Yao & Hadi Jahanshahi & Irene Moroz & Naif D. Alotaibi & Stelios Bekiros, 2022. "Neural Adaptive Fixed-Time Attitude Stabilization and Vibration Suppression of Flexible Spacecraft," Mathematics, MDPI, vol. 10(10), pages 1-17, May.
    5. Qijia Yao & Hadi Jahanshahi & Stelios Bekiros & Sanda Florentina Mihalache & Naif D. Alotaibi, 2022. "Indirect Neural-Enhanced Integral Sliding Mode Control for Finite-Time Fault-Tolerant Attitude Tracking of Spacecraft," Mathematics, MDPI, vol. 10(14), pages 1-18, July.
    6. Wang, Yong-Long & Jahanshahi, Hadi & Bekiros, Stelios & Bezzina, Frank & Chu, Yu-Ming & Aly, Ayman A., 2021. "Deep recurrent neural networks with finite-time terminal sliding mode control for a chaotic fractional-order financial system with market confidence," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    7. Xiong, Pei-Ying & Jahanshahi, Hadi & Alcaraz, Raúl & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alsaadi, Fawaz E., 2021. "Spectral Entropy Analysis and Synchronization of a Multi-Stable Fractional-Order Chaotic System using a Novel Neural Network-Based Chattering-Free Sliding Mode Technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
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    Cited by:

    1. Miguel Angel Hernández-Pérez & Gustavo Delgado-Reyes & Vicente Borja-Jaimes & Jorge Salvador Valdez-Martínez & Marisol Cervantes-Bobadilla, 2023. "An Adaptation of a Sliding Mode Classical Observer to a Fractional-Order Observer for Disturbance Reconstruction of a UAV Model: A Riemann–Liouville Fractional Calculus Approach," Mathematics, MDPI, vol. 11(24), pages 1-23, December.
    2. Majid Roohi & Saeed Mirzajani & Andreas Basse-O’Connor, 2023. "A No-Chatter Single-Input Finite-Time PID Sliding Mode Control Technique for Stabilization of a Class of 4D Chaotic Fractional-Order Laser Systems," Mathematics, MDPI, vol. 11(21), pages 1-22, October.
    3. Mingyuan Hu & Hyeongki Ahn & Yoonuh Chung & Kwanho You, 2023. "Speed Regulation for PMSM with Super-Twisting Sliding-Mode Controller via Disturbance Observer," Mathematics, MDPI, vol. 11(7), pages 1-15, March.

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