自动控制原理 第四章(2015)
245页1、Automatic Control Theory,College of Information Science and Engineering,CSU 2015.4,2019/5/13,hanhua,2,根据前几章学过的知识,影响系统的运动即性能的主要因素是什么?,闭环极点,2019/5/13,hanhua,3,Chapter 4 Root Locus Method of Linear System (线性系统的根轨迹法),4.1 The Root Locus Concept 4.2 The Root Locus Procedure 4.3 generalized root Locus 4.4 the example of drawing root locus 4.5 the performance analysis of system 4.6 sensitivity and the root 4.7 Compensation by Using Root Locus Method Summary,2019/5/13,hanhua,4,4.1 The Root Locus Concept
2、 (根轨迹法的基本概念),The root locus is the path of the roots of the characteristic equation traced out in the s-plane as a parameter of open-loop system is changed from 0 to infinity. 根轨迹简称根迹,它是开环系统某一参数从零变到无穷时,闭环系统特征方程式的根在 s 平面上变化的轨迹。,1.the Root Locus Concept(根轨迹概念),指闭环极点,2019/5/13,hanhua,5,The root locus method was introduced by Evans in 1948 and has been developed and utilized extensively in control engineering practice. The root technique is a graphical method for sketching the locus of roots in the
3、s-plane as a parameter is varied. It is very useful to determine how the roots of the characteristic equation move around the s-plane as we change one parameter.,2. 根轨迹法的特点,2019/5/13,hanhua,6,The root locus method provides graphical information(根轨迹法提供了图形化信息) 1)stability 2)steay-state accuracy 3)dynamic performance The root locus method can be used to analyze and design a system.,2019/5/13,hanhua,7,Example,2019/5/13,hanhua,8,A second-order system,2019/5/13,hanhua,9,Location of roots for the chara
4、cteristic equation:,K S1 S2 0 0 -2 0.5 -0.3 -1.7 0.75 -0.5 -1.5 1.0 -1.0 -1.0 2.0 -1.0+j1.0 -1.0-j1.0 3.0 -1.0+j1.4 -1.0-j1.4 50.0 -1.0+j7.0 -1.0-j7.0,2019/5/13,hanhua,10,Analysis:,The root locus is a vertical line for K Ka =1.,Ka,return,根轨迹图怎样体现系统的性能?,稳态误差?,稳定性?,动态性能?,2019/5/13,hanhua,11,2.闭环零、极点与开环零、极点之间的关系,前向通道增益,前向通道根轨迹增益,前向通道根轨迹增益,2019/5/13,hanhua,12,The open-loop TF:,f +l=m , q+h=n,The closed-loop TF:,return,闭环零点,反馈通道传递函数极点,开环前向通道传递函数的零点,闭环极点,2019/5/13,hanhua,13,4.2 The Root Locus Procedur
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