Suppress the vibration of a nonlinear dynamical system subjected to external force using a positive position feedback control.

F. Osama, Y. Amer, K. Raslan
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Abstract

Vibration suppression using a positive position feedback (PPF) control for a nonlinear dynamical system which subjected to an external force is studied. The proposed model is the vertical dynamic excitation of structures induced by a single pedestrian walking along a straight path on flat and relatively stiff surfaces. The multiple scale perturbation technique was applied to derive the first order approximate solution of the system. The response equation and the stability criteria for the system were derived near the simultaneous primary and internal resonance cases. MATLAB 14.0 have been used for the numerical studying to show the time history of the main system with and without PPF controller. Also, the effect of the system parameters on the response system have been studied. A comparison between the approximate and numerical solutions is illustrated and it show a good agreement between them. It is found that (PPF) controller is very suitable for small natural frequency dynamical systems subjected to primary resonance excitations.
利用正位置反馈控制抑制非线性动力系统在外力作用下的振动。
研究了受外力作用的非线性动力系统的正位置反馈控制的振动抑制问题。所提出的模型是一个人在平坦和相对坚硬的表面上沿直线行走所引起的结构的垂直动力激励。采用多尺度摄动技术推导了系统的一阶近似解。推导了系统在主共振和内共振情况下的响应方程和稳定性判据。利用MATLAB 14.0进行数值研究,显示了主系统在有和没有PPF控制器时的时间历程。研究了系统参数对响应系统的影响。并对近似解和数值解进行了比较,结果表明两者吻合较好。结果表明,PPF控制器非常适用于受一次共振激励的小固有频率动力系统。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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