西安理工大学自动控制理论双语chap 02-1ppt课件.ppt

Chapter2mathematicalmodelsofsystems 2 1Introduction2 1 1Why 1 Easytodiscussthefullpossibletypesofthecontrolsystems onlyintermsofthesystem s mathematicalcharacteristics 2 Thebasisofanalyzingordesigningthecontrolsystems 2 1 3Howget 1 theoreticalapproaches2 experimentalapproaches3 discriminationlearning 2 1 2Whatis Mathematicalmodelsofsystems themathematicalrelation shipsbetweenthesystem svariables Chapter2mathematicalmodelsofsystems 2 2 1Examples 2 1 4types1 Differentialequations2 Transferfunction3 Blockdiagram signalflowgraph4 Statevariables 2 2Theinput outputdescriptionofthephysicalsystems differentialequationsTheinput outputdescription descriptionofthemathematicalrelationshipbetweentheoutputvariableandtheinputvariableofphysicalsystems Chapter2mathematicalmodelsofsystems define input uroutput uc wehave Example2 1 Apassivecircuit Chapter2mathematicalmodelsofsystems Example2 2 Amechanism Define input F output y Wehave Comparewithexample2 1 uc y ur F analogoussystems Chapter2mathematicalmodelsofsystems Example2 3 Anoperationalamplifier Op amp circuit Input uroutput uc 2 3 2 1 3 1 Chapter2mathematicalmodelsofsystems Example2 4 ADCmotor Input ua output 1 4 2 1 and 3 1 Chapter2mathematicalmodelsofsystems Make Chapter2mathematicalmodelsofsystems Assumethemotoridle Mf 0 andneglectthefriction f 0 wehave thedifferentialequationdescriptionoftheDCmotoris Comparewithexample2 1andexample2 2 Analogoussystems Chapter2mathematicalmodelsofsystems Example2 5 ADC Motorcontrolsystem Input ur Output neglectthefriction Chapter2mathematicalmodelsofsystems 2 1 3 4 wehave 2 2 2stepstoobtaintheinput outputdescription differentialequation ofcontrolsystems 1 Identifytheoutputandinputvariablesofthecontrolsystems 2 Writethedifferentialequationsofeachsystem scomponentintermsofthephysicallawsofthecomponents necessaryassumptionandneglect properapproximation 3 dispeltheintermediate across variablestogettheinput outputdescriptionwhichonlycontainstheoutputandinputvariables Chapter2mathematicalmodelsofsystems 4 Formalizetheinput outputequationtobethe standard form Inputvariable ontherightoftheinput outputequation Outputvariable ontheleftoftheinput outputequation Writingthepolynomial accordingtothefalling powerorder 2 2 3Generalformoftheinput outputequationofthelinearcontrolsystems Anth orderdifferentialequation Suppose input r output y E2 14 P2 2 P2 3 P2 7 Chapter2mathematicalmodelsofsystems 2 3Linearizationofthenonlinearcomponents2 3 1whatisnonlinearity Theoutputofsystemisnotlinearlyvarywiththelinearvariationofthesystem s orcomponent s input nonlinearsystems orcomponents 2 3 2Howdothelinearization Suppose y f r TheTaylorseriesexpansionabouttheoperatingpointr0is Chapter2mathematicalmodelsofsystems Examples Example2 6 Elasticityequation Example2 7 Fluxographequation Q Flux p pressuredifference Chapter2mathematicalmodelsofsystems 2 4Transferfunction Anotherformoftheinput output external descriptionofcontrolsystems differentfromthedifferentialequations 2 4 1definition Transferfunction TheratiooftheLaplacetransformoftheoutputvariabletotheLaplacetransformoftheinputvariablewithallinitialconditionassumedtobezeroandforthelinearsystems thatis Chapter2mathematicalmodelsofsystems C s LaplacetransformoftheoutputvariableR s LaplacetransformoftheinputvariableG s transferfunction 2 4 2Howtoobtainthetransferfunctionofasystem 1 Iftheimpulseresponseg t isknown Notes Chapter2mathematicalmodelsofsystems Example2 8 2 Iftheoutputresponsec t andtheinputr t areknown Wehave Chapter2mathematicalmodelsofsystems Example2 9 Then 3 Iftheinput outputdifferentialequationisknown Assume zeroinitialconditions Make Laplacetransformofthedifferentialequation Deduce G s C s R s Chapter2mathematicalmodelsofsystems Example2 10 4 Foracircuit Transformacircuitintoaoperatorcircuit DeducetheC s R s intermsofthecircuitstheory Chapter2mathematicalmodelsofsystems Example2 11 Foraelectriccircuit Chapter2mathematicalmodelsofsystems Example2 12 Foraop ampcircuit Chapter2mathematicalmodelsofsystems 5 Foracontrolsystem Writethedifferentialequationsofthecontrolsystem MakeLaplacetransformation assumezeroinitialconditions transformthedifferentialequationsintotherelevantalgebraicequations Deduce G s C s R s Example2 13 theDC MotorcontrolsysteminExample2 5 Chapter2mathematicalmodelsofsystems InExample2 5 wehavewrittendownthedifferentialequationsas MakeLaplacetransformation wehave 2 1 3 4 wehave Chapter2mathematicalmodelsofsystems E2 2 E2 6 E2 15 E2 19 E2 20 E2 27 P2 7 P2 8 Chapter2mathematicalmodelsofsystems 2 5 1Proportioningelement Relationshipbetweentheinputandoutputvariables Transferfunction Blockdiagramrepresentationandunitstepresponse Examples amplifier geartrain tachometer 2 5TransferfunctionofthetypicalelementsoflinearsystemsAlinearsystemcanberegardedasthecomposingofseveraltypicalelements whichare Chapter2mathematicalmodelsofsystems 2 5 2Integratingelement Relationshipbetweentheinputandoutputvariables Transferfunction Blockdiagramrepresentationandunitstepresponse Examples Integratingcircuit integratingmotor integratingwheel Chapter2mathematicalmodelsofsystems 2 5 3Differentiatingelement Relationshipbetweentheinputandoutputvariables Transferfunction Blockdiagramrepresentationandunitstepresponse Examples differentiatingamplifier differentialvalve differentialcondenser 2 5 4Inertialelement Chapter2mathematicalmodelsofsystems Relationshipbetweentheinputandoutputvariables Transferfunction Blockdiagramrepresentationandunitstepresponse Examples inertiawheel inertialload suchastemperaturesystem Chapter2mathematicalmodelsofsystems 2 5 5Oscillatingelement Relationshipbetweentheinputandoutputvariables Transferfunction Blockdiagramrepresentationandunitstepresponse Examples oscillator oscillatingtable oscillatingcircuit 2 5 6Delayelement Chapter2mathematicalmodelsofsystems Relationshipbetweentheinputandoutputvariables Transferfunction Blockdiagramrepresentationandunitstepresponse Examples gapeffectofgearmechanism thresholdvoltageoftransistors 2 6 1Blockdiagramrepresentationofthecontrolsystems Chapter2mathematicalmodelsofsystems Examples 2 6blockdiagrammodels dynamic Portraythecontrolsystemsbytheblockdiagrammodelsmoreintuitivelythanthetransferfunctionordifferentialequationmodels Example2 14 Chapter2mathematicalmodelsofsystems FortheDCmotorinExam