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Fault-Tolerant Terminal Sliding Mode Control with Disturbance Observer for Vibration Suppression in Non-Local Strain Gradient Nano-Beams

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 research investigates the stabilization and control of an uncertain Euler–Bernoulli nano-beam with fixed ends. The governing partial differential equations of motion for the nano-beam are derived using Hamilton’s principle and the non-local strain gradient theory. The Galerkin method is then applied to transform the resulting dimensionless partial differential equation into a nonlinear ordinary differential equation. A novel fault-tolerant terminal sliding mode control technique is proposed to address the uncertainties inherent in micro/nano-systems and the potential for faults and failures in control actuators. The proposed controller includes a finite time estimator, the stability of which and the convergence of the error dynamics are established using the Lyapunov theorem. The significance of this study lies in its application to the field of micro/nano-mechanics, where the precise control and stabilization of small-scale systems is crucial for the development of advanced technologies such as nano-robotics and micro-electromechanical systems (MEMS). The proposed control technique addresses the inherent uncertainties and potential for faults in these systems, making it a valuable choice for practical applications. The simulation results are presented to demonstrate the effectiveness of the proposed control scheme and the high accuracy of the estimation algorithm.

Suggested Citation

  • Hajid Alsubaie & Amin Yousefpour & Ahmed Alotaibi & Naif D. Alotaibi & Hadi Jahanshahi, 2023. "Fault-Tolerant Terminal Sliding Mode Control with Disturbance Observer for Vibration Suppression in Non-Local Strain Gradient Nano-Beams," Mathematics, MDPI, vol. 11(3), pages 1-17, February.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:789-:d:1057496
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    References listed on IDEAS

    as
    1. 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.
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