Outcomes of the NIPPF Controller Linked to a Hybrid Rayleigh – Van der Pol- Duffing Oscillator.

Abstract

In this study, we adjusted the equation of a hybrid Rayleigh – Van der Pol- Duffing oscillator by adding the Nonlinear Integral Positive Position Feedback (NIPPF) to control the vibrating system. The system is presented by a three-degree-of-freedom (3-DOF) containing the cubic nonlinear term and an external force. For getting the solution from the first approximation, we applied the multiple scales method (MSM). Graphically and numerically, we studied the system before and after adding the NIPPF controllers at the worst resonance case 1:1 internal and primary (,). We used the MATLAB program to simulate the efficacy of different parameters on both the main system and NIPPF controllers.