Behavior of a Hybrid Rayleigh-Van der Pol- Duffing Oscillator with a PD Controller.

In our consideration, we studied the vibration analysis and dynamic responses of aHybrid Rayleigh-Van der Pol- Duffing oscillator. This system presented by one –degree-of - freedom containing the fifth order of nonlinear terms and an external force. To control the vibration of the main system, we applied the proportional derivative controller (PD). The average method used to obtain the approximate solution of the vibrating system. The stability of the system is investigated at the primary resonance case (   ). Numerically, we used Runge–Kutta of the fourth order to scrutinize the time histories of the system before and after using PD. For response curves, we investigated the performance of some chosen parameters of studied system. Finally, there is a good agreement between the approximate solution which obtained from the average method and the numerical one.