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.

在本文中，提出了基于速度反馈的非线性谐振控制器控制非线性梁自由和强迫自激振动的功效。从传感器获得的速度信号通过一个二阶滤波器馈入，并且使用滤波器变量的导数的非线性函数来获得控制力。所形成的控制系统是带通系统，被认为优于其他谐振控制方案，例如正位置反馈（PPF）控制和加速反馈控制（AFC）。据作者所知，这是首次尝试探索共振非线性速度反馈控制器减轻自激振动的功效。使用多重时标方法获得分析结果，通过在Matlab Simulink模型中进行直接数值模拟获得的数据对数据进行验证。不受控制系统的分析结果显示出周期性，准周期性以及混沌行为。可以看出，所提出的控制器可以将振动幅度降低至接近初级共振的水平。此外，通过控制动作消除了霍普夫分叉。还观察到，所提出的控制器可以显着减小混沌振荡的幅度。还探讨了驱动回路在反馈回路中的影响。观察到时间延迟的影响对系统性能有害。可以看出，所提出的控制器可以将振动幅度降低至接近初级共振的水平。而且，通过控制动作消除了霍普夫分叉。还观察到，所提出的控制器可以显着减小混沌振荡的幅度。还探讨了驱动回路在反馈回路中的影响。观察到时间延迟的影响对系统性能有害。可以看出，所提出的控制器可以将振动幅度降低至接近初级共振的水平。此外，通过控制动作消除了霍普夫分叉。还观察到，所提出的控制器可以显着减小混沌振荡的幅度。还探讨了驱动回路在反馈回路中的影响。观察到时间延迟的影响对系统性能有害。