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当伺服机构(简称系统)主要负载是摩擦时,摩擦严重影响系统的品质。本文采用描述函数法(DF),求得带有摩擦负载的系统频率特性解析式,从而构筑系统的动态模型。它是由系统线性部份频率特性G(jw)和两个非线性环节组成。当输入角频率很小、幅度很大的谐波信号时,利用上述模型求得表征系统特性的主要参数表达式,如死区、回环宽度、相对静态误差等。利用动态模型自激振荡条件,求得系统稳定判据:摩擦所包围的线性部份之频率特性之虚部I_mG_2(jw)≤0;也可以用波波夫稳定判据验证之,从而求得系统参数稳定边界的表达式。本文以三阶液压伺服机构为例,用上述稳定判据与古尔维茨判据相比较,求得余项公式R。当R<0时,说明摩擦改善了系统的稳定性;反之,使系统稳定性变坏。系统中存在着良好的二阶低通滤波器,这是本文采用描述函数法的物理基础。
When the main load of the servo mechanism (referred to as the system) is friction, the friction seriously affects the quality of the system. In this paper, descriptive function method (DF) is used to obtain the analytic formula of the frequency characteristics of a system with a friction load so as to build a dynamic model of the system. It consists of the linear part of the frequency characteristics of the system G (jw) and two non-linear components. When the input harmonic signal is very small, the amplitude of the harmonic signal, the use of the above model to obtain the expression of the characteristics of the system parameters such as dead zone, loop width, the relative static error. Using the dynamic model self-excited oscillation conditions, the system stability criterion is obtained: the imaginary part of the frequency characteristic of the linear part surrounded by friction, I_mG_2 (jw) ≤0, can also be verified by the Popov’s stability criterion System parameters stable boundary expression. In this paper, the third-order hydraulic servo is taken as an example, and the remainder formula R is obtained by comparing with the Gurwitz criterion with the above stability criterion. When R <0, the friction improves the stability of the system; on the contrary, the stability of the system deteriorates. There is a good second-order low-pass filter in the system, which is the physical basis of the descriptive function method.