非线性系统稳定性分析中描述函数定性图示的一种方法
An Approach for the Qualitative Graphical Representation of the Describing Function in Nonlinear Systems Stability Analysis
AI总结：
本文提出了一种用于非线性系统稳定性分析中描述函数定性图示的新方法，通过简化绘图过程提升其在教育中的应用价值。
摘要：
描述函数法是用于非线性系统稳定性分析中极限环定性分析的一个有用工具。该方法本质上是近似的，因此应用于快速的定性分析。然而，绘制精确的描述函数需要大量的数学计算，这降低了其在控制教育中的吸引力。本文的目标是通过提供一种新的方法来改进描述函数法，该方法可用于对包含不连续性的分段非线性系统进行描述函数的定性绘图。与标准方法不同，所提出的方法允许通过本文中引入的规则，仅通过分析非线性形状即可直接手工绘制描述函数。所提出的案例研究显示，使用标准精确绘制描述函数的极限环估计结果与使用所提出的方法绘制描述函数的结果在定性上是相同的。
英文摘要：
The describing function method is a useful tool for the qualitative analysis of limit cycles in the stability analysis of nonlinear systems. This method is inherently approximate; therefore, it should be used for a fast qualitative analysis of the considered systems. However, plotting the exact describing function requires heavy mathematical calculations, reducing interest in this method especially from the point of view of control education. The objective of this paper is to enhance the describing function method by providing a new approach for the qualitative plotting of the describing function for piecewise nonlinearities involving discontinuities. Unlike the standard method, the proposed approach allows for a straightforward, hand-drawn plotting of the describing function using the rules introduced in this paper, simply by analyzing the shape of the nonlinearity. The proposed case studies show that the limit cycles estimation performed using the standard exact plotting of the describing function yields the same qualitative results as those obtained using the proposed qualitative method for plotting the describing function.
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