Analysis of self-exciting oscillation in nonlinear system with hysteresis characteristics
Analysis of self-exciting oscillation in nonlinear system with hysteresis characteristics
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具有磁滞特性的非线性系统自激振荡分析
DOI：
10.1002/ecja.4410711204
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
A. Kishima
中科院分区：
文献类型：
--
作者：
K. Okumura;T. Matsuo;A. Kishima
本文提出了一种用多输入描述函数数值分析具有滞环的非线性系统自激振荡的方法。在通过描述函数的传统分析中，以解析形式确定滞后的描述函数，并且需要非常复杂的计算来执行包括自激振荡的谐波分量的高精度分析。因此，在实践中，不可能解析地确定多输入的描述函数。此外，计算是不可能的描述功能，其中的滞后特性包含一个小回线。本文从这一观点出发，提出了一种分析自激振荡的方法和算法。在所提出的方法中，描述函数的数值确定的数字模拟的滞后，和离散傅立叶变换及其逆应用的结果。用这种方法，即使在多输入和有小回路的情况下，也可以用数值方法确定描述函数。因此，自激振荡可以分析考虑谐波分量和多模式。作为一个例子，分析了非线性系统的自激振荡的情况下，线性部分是由一个二阶传递函数或由这些功能的总和。
This paper presents a method of numerical analysis by the multiple input describing function for the self-excited oscillation in a nonlinear system with hysteresis. In the traditional analysis by the describing function, the describing function for the hysteresis is determined in an analytic form, and a very complex calculation is required to perform a highly accurate analysis including the harmonic components of the self-excited oscillation. Consequently, in practice, it has been impossible to determine analytically the describing function for the multiple input. Furthermore, the calculation is impossible for the describing function, where the hysteresis characteristics contain a minor loop. From such a viewpoint, this paper proposes a method and algorithm for the analysis of self-excited oscillation. In the proposed method, the describing function is determined numerically by the digital simulation of the hysteresis, and the discrete Fourier transform and its inverse are applied to the result. By this method, the describing function can be determined numerically even for the cases of multiple input and the case with a minor loop. Thus, the self-excited oscillation can be analyzed considering the harmonic components and the multiple mode. As an example, the self-excited oscillation of the nonlinear system is analyzed for the case where the linear part is represented by a second-order transfer function or by a sum of such functions.