The effectiveness of nonlinear integral positive position feedback control on a duffing oscillator system based on primary and super harmonic resonances

Abstract

In this paper, we applied three different control methods; Positive Position Feedback (PPF), Integral Resonance Control (IRC) and Nonlinear Integrated Positive Position Feedback (NIPPF) added to a Duffing oscillator system subjected to harmonic force. An analytic solution is introduced using the multiple scales perturbation technique (MSPT) to solve the nonlinear differential equations, which simulate the system with NIPPF controller. Before and after control at the primary and superharmonic resonances, the nonlinear systems’ steady-state amplitude and stability are studied and examined. The influences of various parameters of the system after being connected to NIPPF are illustrated. Optimum working conditions for the NIPPF controller are obtained at internal resonance ratio 1:1. A Comparison is also made to validate the closeness between the numerical solution and the analytical perturbative one at time-history and frequency response curves (FRC). Finally, a comparison with the available results in the literature is presented. From this comparison, we find that the best control to the system is via the NIPPF controller.