频域分析法

在由开环频率特性确定闭环频率特性时，应用相同的比例尺，将尼柯尔斯图线绘制在透明片上，然后再把它覆盖在以相同比例尺绘制的系统开环传递函数对数幅相图上，则开环频率特性曲线G(jw)与M轨线和N 轨线的交点，就给出了每一频率上闭环频率特性的幅值M 和相角φ。

若 G(jw)轨迹与M轨线相切，切点处频率就是谐振频率，谐振峰值由M轨线对应的幅值确定。

频域（频率响应）法是研究控制系统的一种工程方法，属于经典控制理论最重要、最主要的分析方法。根据开环系统的稳态频率特性图，分析闭环系统的稳定性、稳定裕度及动态性能。

1932年，Nyquist 提出频域稳定判据；1940年，Bode 提出了在对数坐标系下简化作图的方法。

频域分析法的突出优点是可以通过实验直接求得频率特性来分析系统的品质；当然，通过传递函数一样也可以做到。应用频率特性分析系统可以得出定性和定量的结论，并具有明显的物理含义。频域法分析系统使用的工具可以是曲线、图表及经验公式。

时域分析法是分析控制系统的直接方法，比较直观、精确。频域分析法，是一种工程上广为采用的分析和综合系统的间接方法。

频域分析法是一种图解分析法。它依据系统的又一种数学模型——频率特性，对系统的性能，如稳定性、快速性和准确性进行分析。

频域分析法的特点是可以根据开环频率特性去分析闭环系统的性能（稳定性、稳定裕度及动态性能），并能较方便地分析系统参数对系统性能的影响，从而进一步提出改善系统性能的途径。

此外，除了一些超低频的热工系统，频率特性都可以方便地由实验确定。频率特性主要适用于线性定常系统。在线性定常系统中，频率特性与输入正弦信号的幅值和相位无关。但是，在一定条件下，这种方法也可以推广应用到非线性系统中。

翻译成英文：

Frequency domain analysis

When determining the closed-loop frequency characteristics from the open-loop frequency characteristics, apply the same scale to draw the Nichols plot on the transparent sheet, and then overlay it on the logarithmic phase diagram of the open-loop transfer function of the system drawn on the same scale Above.

The intersection of the open-loop frequency characteristic curve G(jw) and the M trajectory and the N trajectory gives the amplitude M and the phase angle φ of the closed-loop frequency characteristic at each frequency.

If the G(jw) trajectory is tangent to the M trajectory, the frequency at the tangent point is the resonance frequency, and the resonance peak is determined by the amplitude corresponding to the M trajectory.

The frequency domain (frequency response) method is an engineering method for studying control systems, and it is the most important and main analysis method of classical control theory.

According to the steady-state frequency characteristic diagram of the open-loop system, the stability, stability margin and dynamic performance of the closed-loop system are analyzed.

In 1932, Nyquist proposed a criterion for stability in the frequency domain; in 1940, Bode proposed a method of simplifying plots in a logarithmic coordinate system.

The outstanding advantage of the frequency domain analysis method is that the frequency characteristics can be directly obtained through experiments to analyze the quality of the system; of course, the same can be done through the transfer function.

The application of frequency characteristic analysis system can draw qualitative and quantitative conclusions, and has obvious physical meanings. The tools used by the frequency domain method analysis system can be curves, graphs and empirical formulas.

The time domain analysis method is a direct method to analyze the control system, which is relatively intuitive and accurate. Frequency domain analysis is an indirect method of analyzing and synthesizing systems widely used in engineering.

The frequency domain analysis method is a graphical analysis method. It analyzes the performance of the system, such as stability, rapidity and accuracy, based on another mathematical model of the system—frequency characteristics.

The characteristic of the frequency domain analysis method is that it can analyze the performance of the closed-loop system (stability, stability margin and dynamic performance) according to the open-loop frequency characteristics.

And can more conveniently analyze the influence of system parameters on the system performance, so as to further improve the system. The way to performance.

In addition, except for some ultra-low frequency thermal systems, the frequency characteristics can be easily determined by experiments. The frequency characteristic is mainly suitable for linear steady system. In a linear time-invariant system.

The frequency characteristic has nothing to do with the amplitude and phase of the input sinusoidal signal. However, under certain conditions, this method can also be applied to nonlinear systems.

参考资料：百度

英文翻译：Google翻译

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