一种研究死区非线性对系统频率特性影响的图解方法

A graphic method for studying the influence of dead zone nonlinearity on system frequency characteristics

基于描述函数法将控制系统中死区非线性环节等效为可变增益的线性环节。通过计算不同频率下控制系统在死区环节中的输入和输出值,得到其等效增益值。将控制系统等效变换为单位负反馈系统,先不考虑死区非线性,得到系统开环传递函数及其开环幅相特性曲线。在复平面上连接原点和不考虑死区的系统开环幅相特性曲线各频率下对应的点,每个频率都形成一条直线。死区非线性的效果是使各频率对应的点沿直线向原点移动。将等M圆、等N圆映射到开环幅相曲线上,可以得到系统闭环幅频特性和闭环相频特性。基于上述方法,研究了传动间隙对电动伺服系统闭环频率特性的影响。研究结果显示:可以通过等M圆、等N圆及线性部分的开环幅相曲线直观地观测到间隙对系统频率特性的影响;死区非线性对系统闭环频率特性的影响取决于不考虑死区环节时的线性部分;负载间隙比闭环内的间隙对系统闭环频率的影响更大。

Based on the description method, the dead zone nonlinear link in the control system is equivalent to the variable gain linear link.The equivalent gain is obtained by calculating the input and output values of the control system in the dead zone at different frequencies.The control system is equivalently transformed into a unit negative feedback system, and the open-loop transfer function and its open-loop amplitude phase characteristic curve are obtained without considering the dead time nonlinearity.In the complex plane, the corresponding points at each frequency of the open-loop amplitude and phase characteristic curve of the system without considering dead time are connected, and each frequency forms a straight line.The effect of dead zone nonlinearity is to make the points corresponding to each frequency move to the origin along a straight line.The closed-loop amplitude frequency characteristics and closed-loop phase frequency characteristics can be obtained by mapping equal M circle and equal N circle to the open-loop amplitude phase curve.Based on the above method, the influence of drive clearance on closed-loop frequency characteristics of electric servo system is studied.This method can reveal how the dead zone nonlinearity affects the closed-loop frequency characteristics of the control system.At the same time, the influence of dead time nonlinearity on the closed-loop frequency characteristics can be estimated by this method at the beginning of the control system design.