On slow-flow dynamics, stability charts, and vibration elimination of a self-excited structure utilizing a novel control technique

Abstract

Abstract This work focuses on vibration elimination, bifurcation control, and stability achievement in a harmonically forced self-excited nonlinear oscillator. A novel control technique called the Integral Resonant Positive Position Feedback Controller ( IRPPFC ) has been introduced in this study. The proposed controller is composed of second-order and first-order filters, integrated into the targeted oscillator in nonlinear form. Then, the averaging equations governing the slow-flow dynamics of the coupled systems are deduced. Subsequently, the relevant nonlinear algebraic system, which characterizes the static bifurcation, is obtained. The effectiveness of the controller in eliminating system vibrations, controlling nonlinear bifurcations, and stabilizing the unstable motion is investigated through bifurcation diagrams, two-dimensional stability charts, and numerical simulations of the instantaneous vibrations. The conducted analyses approved that the IRPPFC not only can stabilize the unstable motion of the considered system, but also it can completely eliminate the self-excited vibration regardless of the forcing magnitude and excitation frequencies. Furthermore, a comparative analysis is conducted to evaluate the control performance of the IRPPFC in comparison to previously utilized control techniques for vibration control in self-excited systems. The comparative results demonstrate that the IRPPFC exhibits superior performance in terms of vibration elimination efficiency, bifurcation control, and stability achievement. Finally, numerical validation corroborated our analytical findings, showing alignment with the analytical solution. Moreover, the simulation results demonstrated that the IRPPFC effectively mitigates undesired vibrations, reducing them to zero in a short transient period.