Robust adaptive vibration control of nonlocal strain gradient

Document Type : Invited by Davoud Younesian


1 Professor, Department of Mechanical Engineering, University of Tehran, Tehran, Iran

2 Ph.D. Student, Department of Mechanical Engineering, Michigan State University, East Lansing, USA

3 MSc Student, Department of Mechanical Engineering, University of Tehran, Tehran, Iran


An Euler–Bernoulli nanobeam is stabilized using a robust adaptive sliding mode control. Using nonlocal strain gradient theory and Hamilton’s principle, a nonlinear partial differential equation is derived to demonstrate the vibration behavior of the considered nanobeam. Moreover, the obtained partial differential equation is converted to an ordinary differential equation using the Galerkin technique. To suppress the nonlinear vibration of the nanobeam and overcome the uncertainties, robust adaptive vibration control is designed using an extended Kalman filter and sliding mode control. Finally, simulation results show the performance of the designed robust adaptive controller. Furthermore, the traditional control schemes are used to illustrate the superiority of the proposed controller over them.


  • The nonlinear PDE of motion is obtained for a nonlocal strain gradient nanobeam.
  • A robust sliding mode controller is designed for controlling nanobeam vibrations.
  • Stability of the closed-loop system with uncertain parameters is proved.
  • The proposed controller is equipped with an extended Kalman filter.


Main Subjects

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