Active and Time Delay Controls on Vibrations of the Micro-Electro-Mechanical System (MEMS) Resonator

Abstract

In this paper, the active control and time delay control are applied on a nonlinear mechanical system subjected to external force to reduce the resulted vibration. The system is modeled by a unique nonlinear differential equation. The multiple scale perturbation technique (MSPT) was applied to obtain an approximate solution and showing the response equation. The stability of the system at primary resonance case is investigated using both of phase plane and frequency response equation. Numerical solution is obtained using Runge – Kutta forth order method.Also, MATLAB 14.0 and Maple 18.0 programs were used to study the numerical solution and the effect of the different parameters for the response of the nonlinear dynamic mechanical system.

On the Existence of Time Delay for Rotating Beam with Proportional–Derivative Controller

“…where the values of [20,21], the necessary and sufficient condition for all characteristic roots of the characteristic equation (19) to have negative real parts if and only if the determinate D and all its principle minors are positive, where…”