Controlling self-excited vibration of a nonlinear beam by nonlinear resonant velocity feedback with time-delay

Abstract

In this paper, the efficacy of velocity feedback based nonlinear resonant controller is proposed to control the free and forced self-excited vibration of a nonlinear beam. The velocity signal obtained from the sensor is fed through a second-order filter and the nonlinear function of the derivative of the filter variable is used to obtain the control force. The resulting control system being a band-pass one, is believed to be superior to other resonant control schemes like Positive Position Feedback (PPF) control and Acceleration Feedback Control (AFC). To the best of the authors’ knowledge, it is the first attempt to explore the efficacy of resonant nonlinear velocity feedback controller for mitigating self-excited vibration. Analytical results are obtained using multiple time-scale method, are validated with the data obtained from direct numerical simulation carried out in Matlab Simulink model. Analytical results of the uncontrolled system show the periodic, quasi-periodic as well as chaotic behavior. It is observed that the proposed controller can reduce the amplitude of vibration by a significant level near primary resonance. Moreover, the Hopf bifurcations are eliminated by the control action. It is also observed that the proposed controller can reduce the amplitude of the chaotic oscillation significantly. The effect of the actuation delay in the feedback loop is also explored. It is observed that the effect of time delay is detrimental to system performance.