Vibrations Control of the Harmonically Excited Nonlinear System via Positive Position Feedback Controller

Abstract

In this paper, the vibration reducing of the harmonically excited nonlinear system is presented via applying positive position feedback controller (PPF). The analytical results are obtained by applying the multiple-scale perturbation techniques (MSPT) up to second-order approximations. The frequency response equation (FRE) is studied to test the behavior of the steady state solutions near the simultaneous resonances. The effects of the several parameters and the behavior of the system at resonance case are investigated to illustrate the optimum working conditions for the PPF controller. The stability analysis for the uncontrolled system is investigated by applying the phase portrait technique. Moreover, numerical simulation is used to compare between time-history and the analytical solution. The analytical and numerical solutions are compared to show the validity of the results. Finally, a comparison with the available results in the literature is presented.

Hybrid rayleigh–van der pol–duffing oscillator: Stability analysis and controller

“…There are similar results for the effects of different controller and system parameters on the controlled FRC made by Amer et al, 38 El-Sayed and Bauomy, 42 Amer et al 44 and Saeed et al 45 A comparison of time history between the numerical solution of equations ( 28)-( 30) and the analytical solution of equation ( 71)-(74), when using the steady-state condition (i.e., _ a…”