双闭环直流调速系统自持振荡的波波夫谐波线性化分析及仿真

E.П.Пoпов Harmonic Linearization and Simulation of DC Double Closed-Loop System

电机调速系统中的非线性元件将会导致系统的自持振荡。波波夫谐波线性化是一种经典的频域分析自持振荡的方法,同时还可根据已设定振荡参数值求出需要校正的元件参数值,从而优化振荡效果。但是该方法计算量比较大,特别在高阶矩阵的情况下很难用人工完成精确计算,从而限制了其在工程实践中的应用。本文提出使用Matlab与Mathematica平台针对双闭环直流调速系统进行建模与仿真,抽取其中的晶闸管装置与速度调节器作为自持振荡元件分别进行计算与分析。分别得出两种元件的傅里叶级数模型,并完成自持振荡在高阶系统中的稳定分析与修正。仿真结果说明波波夫谐波线性法与Matlab以及Mathematica相结合可以对自持振荡有着很好的控制作用。

Nonlinear elements of speed control systems always lead to self-oscillations.The method of E.П.Попов harmonic linearization has been well-known to provide frequency criterion for stability of such oscillations.It had the contribution of correcting the values of elements after parameters of certain oscillation had been set formerly for better performance.However,the un-sufficient attention was paid in use under practical conditions of this method in modern control systems because it was quite difficult to calculate the necessary and precise values of the method especially when high-dimensioned matrix was employed in discussion.In the present paper Matlab and Mathematica are introduced as new expressions to construct Е.П.Попов models and obtain simulation results in DC double closed-loop control system.Thyristors and speed controller are respectively researched as nonlinear elements leading to self-oscillation.The Fourier series-based models of two elements are constructed.The analysis of stability and correcting of self-oscillation are accomplished.The simulation shows that the proposed combination of advanced mathematical tools and Е.П.Попов methods can lead to a novice way of controlling self-oscillations.