非线性积分正位置反馈 (NIPPF) 控制器对强制和自激非线性梁扑现象的影响

Symmetry Pub Date : 2024-09-03 DOI:10.3390/sym16091143
Khalid Alluhydan, Yasser A. Amer, Ashraf Taha EL-Sayed, Marwa Abdelaziz EL-Sayed
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引用次数: 0

摘要

本文介绍了一种新方法,用于对受到谐波激励的梁扑动系统中的非线性振动响应进行冲击调节。研究介绍了非线性积分正位置反馈 (NIPPF) 控制器的使用方法。该技术将系统建模为代表梁扑动的三自由度非线性系统,再加上代表 NIPPF 控制器的一阶和二阶滤波器。通过对线性化系统模型进行扰动分析,作者获得了带有控制器的自主系统的解析解。本研究旨在减小非线性动态系统的振动幅度,特别是在发生 1:1 内部共振时。利用 Routh-Hurwitz 准则来评估系统的稳定性。此外,频率响应曲线(FRC)在一定参数值范围内表现出对称性。研究结果表明,在与不同控制器进行比较后,振动抑制效果与 NIPPF 控制信号的乘积直接相关。使用四阶 Runge-Kutta 方法进行的数值模拟验证了分析解,并证明了系统的振幅响应。分析和数值结果之间的紧密相关性凸显了所建议方法的准确性和可靠性。
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The Impact of the Nonlinear Integral Positive Position Feedback (NIPPF) Controller on the Forced and Self-Excited Nonlinear Beam Flutter Phenomenon
This article presents a novel approach to impact regulation of nonlinear vibrational responses in a beam flutter system subjected to harmonic excitation. This study introduces the use of a Nonlinear Integral Positive Position Feedback (NIPPF) controller for this purpose. This technique models the system as a three-degree-of-freedom nonlinear system representing the beam flutter, coupled with a first-order and a second-order filter representing the NIPPF controller. By applying perturbation analysis to the linearized system model, the authors obtain analytical solutions for the autonomous system with the controller. This study aims to reduce vibration amplitudes in a nonlinear dynamic system, specifically when 1:1 internal resonance occurs. The Routh–Hurwitz criterion is utilized to evaluate the system’s stability. Furthermore, the frequency–response curves (FRCs) exhibit symmetry across a range of parameter values. The findings highlight that the effectiveness of vibration suppression is directly related to the product of the NIPPF control signal after comparing with different controllers. Numerical simulations, conducted using the fourth-order Runge–Kutta method, validate the analytical solutions and demonstrate the system’s amplitude response. The strong correlation between the analytical and numerical results highlights the accuracy and dependability of the proposed method.
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