chapter2-1.ppt

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1、Chapter2mathematicalmodelsofsystems2.1Introduction2.1.1Why？1)Easytodiscussthefullpossibletypesofthecontrolsystems—onlyintermsofthesystem’s“mathematicalcharacteristics”.2)Thebasisofanalyzingordesigningthecontrolsystems.2.1.3Howget？1)theoreticalapproaches2)experimentalapproaches3)discriminationlearn

2、ing2.1.2Whatis？Mathematicalmodelsofsystems—themathematicalrelation-shipsbetweenthesystem’svariables.Chapter2mathematicalmodelsofsystems2.2.1Examples2.1.4types1)Differentialequations2)Transferfunction3)Blockdiagram、signalflowgraph4)Statevariables2.2Theinput-outputdescriptionofthephysicalsystems—dif

3、ferentialequationsTheinput-outputdescription—descriptionofthemathematicalrelationshipbetweentheoutputvariableandtheinputvariableofphysicalsystems.Chapter2mathematicalmodelsofsystemsdefine:input→uroutput→uc。wehave：Example2.1:ApassivecircuitChapter2mathematicalmodelsofsystemsExample2.2:AmechanismDef

4、ine:input→F，output→y.Wehave:Comparewithexample2.1:uc→y,ur→F---analogoussystemsChapter2mathematicalmodelsofsystemsExample2.3:Anoperationalamplifier(Op-amp)circuitInput→uroutput→uc(2)→(3);(2)→(1);(3)→(1)：Chapter2mathematicalmodelsofsystemsExample2.4:ADCmotorInput→ua，output→ω1(4)→(2)→(1)and(3)→(1):Ch

5、apter2mathematicalmodelsofsystemsMake:Chapter2mathematicalmodelsofsystemsAssumethemotoridle:Mf=0,andneglectthefriction:f=0,wehave:thedifferentialequationdescriptionoftheDCmotoris:Comparewithexample2.1andexample2.2:----AnalogoussystemsChapter2mathematicalmodelsofsystemsExample2.5:ADC-Motorcontrolsy

6、stemInput→ur,Output→ω;neglectthefriction:Chapter2mathematicalmodelsofsystems（2）→（1）→（3）→（4），wehave：2.2.2stepstoobtaintheinput-outputdescription(differentialequation)ofcontrolsystems1)Identifytheoutputandinputvariablesofthecontrolsystems.2)Writethedifferentialequationsofeachsystem’scomponentinterms

7、ofthephysicallawsofthecomponents.*necessaryassumptionandneglect.*properapproximation.3)dispeltheintermediate(across)variablestogettheinput-outputdescriptionwhichonlycontainstheoutputandinputvariables.Chapter2math