基于Mathematica的控制系统根轨迹探究性实验  

Exploration-oriented experiments for root locus of control system based on Mathematica

作　　者：张晓东[1] 涂玲[1] 刘宝[1] ZHANG Xiaodong;TU Ling;LIU Bao(College of Control Science and Engineering,China University of Petroleum(East China),Qingdao 266580,China)

机构地区：[1]中国石油大学(华东)控制科学与工程学院,山东青岛266580

出　　处：《实验技术与管理》2022年第12期163-168,共6页Experimental Technology and Management

基　　金：山东省教学改革项目(M2020205);中国石油大学(华东)教学改革项目(ZY-202027,JY-B20183)。

摘　　要：为了使学生了解根轨迹法的思想并掌握其绘制与分析方法,设计了该实验教学方案。该方案从方程求根问题引入根轨迹概念,结合方程求根问题的发展历史,让学生领会求根问题对数系扩充和群论诞生等数学理论发展的推动作用。该方案设计了三种根轨迹绘制实验方法,利用Mathematica软件开发了根轨迹实验程序,能够通过交互式操作判断复平面上的点是否在根轨迹上。实验过程能够引导学生总结、发现根轨迹的绘制法则,并根据实验步骤掌握系统稳态和动态特性的分析方法。The experimental teaching scheme is designed to make students understand the idea of root locus and master the drawing and analysis methods. The scheme introduces the concept of root locus from root finding problem and provides its development history, so that the students can get an insight of the promotion of root locus in mathematical theories such as the extension of numeral system and the foundation of group theory. Three root locus drawing methods are designed, and a root locus experimental program is developed by using Mathematica software, which can interactively locate the point belonging to the root locus on the complex plane. The experimental process can guide students to summarize and find the drawing rules of root locus, and master the analysis methods of steady and dynamic characteristics of control systems by the given experimental steps.

关 键 词：根轨迹 MATHEMATICA 方程求根 代数方程 交互式实验 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]