On suppression of chaotic motion of a nonlinear MEMS oscillator

Abstract

This work investigates the behavior of the linear and nonlinear stiffness terms and damping coefficient related to the dynamics of a microelectromechanical resonator. The system is controlled by forcing it into an orbit obtained from the analytical solution of the harmonic balance method. The control techniques considered are the polynomial expansion of Chebyshev, the Picard interactive method, Lyapunov–Floquet, OLFC control, and SDRE controls. Additionally, in order to study the thermal effects, the effect of damping with fractional-order was implemented. To analyze the behavior of the system in fractional-order, the wavelet-based scale index test was carried out. In addition, the control robustness is investigated analyzing the parametric errors, and the sensitivity of the fractional derivative variation.