Negative Derivative Feedback Controller for Repressing Vibrations of the Hybrid Rayleigh-Van der Pol-Duffing Oscillator

Abstract

Negative derivative feedback (NDF) controller is presented for suppressing the vibrations of a nonlinear dynamical system at the worst resonance case (Ω = ω1, ω2 = ω1). To obtain the approximate solution, we used the multiple scales technique. The behavior of uncontrolled and controlled system is presented using time histories. We used the frequency-response equations to investigate the stability of controlled system. The e ectiveness of closed loop parameters on the behavior of the main system and NDF controller has been studied. We found that all obtained solutions using multiple scales method are in a good agreement with the numerical solutions.