Robust adaptive vibration control of nonlocal strain gradient

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.

Keywords:

Nonlocal strain gradient theory , Hamiltonian principle , Nonlinear forced vibrations , Extended Kalman Filter , Robust adaptive sliding mode control