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

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.