Feedback control of limit cycle amplitudes from a frequency domain approach
Feedback control of limit cycle amplitudes from a frequency domain approach
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DOI：
10.1016/s0005-1098(98)80010-1
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发表时间：
1998-12-01
期刊：
影响因子：
6.4
通讯作者：
Chen, GR
中科院分区：
文献类型：
--
作者：
Berns, DW;Moiola, JL;Chen, GR
本文研究了极限环幅值反馈控制问题。通过对系统振荡输出的幅度和频率进行高阶谐波平衡近似，开发了解决该分岔控制问题的图形方法。该方法从熟悉的 Hopf 分岔机制开始，并采用二阶、四阶和六阶谐波平衡近似来生成一系列图形测试，用于系统振荡输出的收敛分析。这种连续的图形测试可以精确地近似系统输出中小幅度的极限循环。简并Hopf分岔理论用于制定捕获小幅度极限环的适当控制目标，这可以避免达到不稳定平衡或其他不期望的极限集。提出了丰富的立方平面模型来说明所提出的控制方法。 (C) 1998 Elsevier Science Ltd. 保留所有权利。
In this paper, a problem in feedback control of limit cycle amplitudes is studied. A graphical approach for this bifurcation control problem is developed by means of higher-order harmonic balance approximations for both amplitude and frequency of the system oscillatory outputs. The approach starts with the familiar Hopf bifurcation mechanism, and employs the second, fourth, and sixth-order harmonic balance approximations to generate a sequence of graphical tests for convergence analysis of the system oscillatory outputs. This sequential graphical testing leads to accurate approximations of limit cycles of small amplitudes in the system outputs. Degenerate Hopf bifurcation theory is used to formulate an appropriate control objective of capturing small-amplitude limit cycles, which can avoid reaching unstable equilibria or other undesirable limit sets. A rich cubic planar model is presented for illustration of the proposed control method. (C) 1998 Elsevier Science Ltd. All rights reserved.