自动控制原理-第四章(2015).ppt

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1、AutomaticControlTheoryCollegeofInformationScienceandEngineering,CSU2015.42021/8/23hanhua2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2021/8/23hanhua3Chapter4RootLocusMethodofLinearSystem(线性系统的根轨迹法)4.1TheRootLocusConcept4.2TheRootLocusProcedure4.3generalizedrootLocus4.4theexampleofdra

2、wingrootlocus4.5theperformanceanalysisofsystem4.6sensitivityandtheroot4.7CompensationbyUsingRootLocusMethodSummary2021/8/23hanhua44.1TheRootLocusConcept(根轨迹法的基本概念)Therootlocusisthepathoftherootsofthecharacteristicequationtracedoutinthes-planeasaparameterofopen-loopsystemis

3、changedfrom0toinfinity.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.theRootLocusConcept(根轨迹概念)指闭环极点2021/8/23hanhua5TherootlocusmethodwasintroducedbyEvansin1948andhasbeendevelopedandutilizedextensivelyincontrolengineeringpractice.Theroottechniqueisagraphicalmethodforske

4、tchingthelocusofrootsinthes-planeasaparameterisvaried.Itisveryusefultodeterminehowtherootsofthecharacteristicequationmovearoundthes-planeaswechangeoneparameter.2.根轨迹法的特点2021/8/23hanhua6Therootlocusmethodprovidesgraphicalinformation(根轨迹法提供了图形化信息)1)stability2)steay-stateaccur

5、acy3)dynamicperformanceTherootlocusmethodcanbeusedtoanalyzeanddesignasystem.2021/8/23hanhua7Example2021/8/23hanhua8Asecond-ordersystem2021/8/23hanhua9Locationofrootsforthecharacteristicequation:KS1S200-20.5-0.3-1.70.75-0.5-1.51.0-1.0-1.02.0-1.0+j1.0-1.0-j1.03.0-1.0+j1.4-1.0

6、-j1.450.0-1.0+j7.0-1.0-j7.02021/8/23hanhua10Analysis:TherootlocusisaverticallineforK>Ka=1.Kareturn根轨迹图怎样体现系统的性能？稳态误差？稳定性？动态性能？2021/8/23hanhua112.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2021/8/23hanhua12Theopen-loopTF:f+l=m,q+h=nTheclosed-loopTF:return闭环零点反馈通道传递函数极点开环前向通道传

7、递函数的零点闭环极点2021/8/23hanhua134.2TheRootLocusProcedure4.2.1MagnitudeandAngleRequirement4.2.2Rulesfordrawingrootlocus4.2.3利用MATLAB绘制根轨迹图4.2.4闭环极点和传递函数的确定2021/8/23hanhua14Rootlocusequation(negativefeedback)(根轨迹方程)开环零点开环极点4.2.1MagnitudeandAngleRequirement(模值条件和相角条件)(重点)2021/8/23h

8、anhua15magnituderequirement(模值条件)2021/8/23hanhua16anglerequirement(相角条件)2021/8/23h