Isola in a linear one-degree-of-freedom feedback system with actuator rate saturation

IF 3.4 Q1 ENGINEERING, MECHANICAL
Duc H. Nguyen, Thomas L. Hill, Mark H. Lowenberg
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引用次数: 0

Abstract

This short communication uses numerical continuation to highlight the existence of an isola in a simple one-degree-of-freedom harmonically forced feedback system with actuator rate limiting as its only nonlinear element. It was found that the isola (1) contains only rate-limited responses, (2) merges with the main branch when the forcing amplitude is sufficiently large, and (3) includes stable solutions that create a second attractor in regions where rate limiting is not expected. Furthermore, the isola is composed of two solutions for a given forcing frequency. These solutions have the same amplitudes in the state (pitch rate) projection; however, they have distinct phases, and their amplitudes are also distinct when projected onto the integrator state in the controller. The rich dynamics observed in such a simple example underlines the impact of rate limiting on feedback systems. Specifically, the combination of feedback and rate limiting can create detrimental dynamics that is hard to predict and requires careful analysis.

Abstract Image

具有执行器速率饱和的线性一自由度反馈系统中的Isola
这种简短的通信使用数值延拓来强调在一个简单的单自由度谐波强迫反馈系统中存在等值线,该系统的唯一非线性元件是执行器速率限制。研究发现,等值线(1)仅包含速率限制响应,(2)当强迫幅度足够大时与主分支合并,以及(3)包括在不期望速率限制的区域中产生第二吸引子的稳定解。此外,等值线由给定强迫频率的两个解组成。这些解在状态(俯仰率)投影中具有相同的振幅;然而,它们具有不同的相位,并且当投影到控制器中的积分器状态上时,它们的振幅也不同。在这样一个简单的例子中观察到的丰富的动力学强调了速率限制对反馈系统的影响。具体而言,反馈和速率限制的结合可能会产生难以预测且需要仔细分析的有害动态。
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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CiteScore
3.50
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