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

Hajid Alsubaie, Amin Yousefpour (), Ahmed Alotaibi, Naif D. Alotaibi and Hadi Jahanshahi
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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

Mathematics, 2023, vol. 11, issue 3, 1-17

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.

Keywords: robust adaptive control; non-local strain gradient theory; fault-tolerant terminal sliding mode control; finite time disturbance observer; nonlinear vibrations; Hamiltonian principle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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