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Analog computer



Developmentprofile

Inthe1930s,hebegantodevotehimselftotheresearchanddevelopmentoffullyelectronicanalogcomputers.

DuringWorldWarII,BellTelephoneLaboratoriesdevelopedtheM-9artillerycommander.

AfterWorldWarII,somepeopledevelopedanall-electronicDCanalogcomputerin1947basedontheoperationalamplifierintheM-9artillerycommander.Theappearanceofhigh-gainDCoperationalamplifiershasrevolutionizedthedevelopmentofanalogcomputers.Atthesametime,alldevelopedcountriesaredevelopinganalogcomputers.

In1948,thefirstcommercialsimulationcomputerwasdeveloped.

Commercializationwasrealizedinthe1950s;Chinaenteredthefieldofmodernanalogcomputerresearchanddevelopmentinthemiddleandlate1950s.

Inthemid-1960s,avarietyofmodelsofanalogcomputersweredeveloped.Large-scalehybridanalogcomputerssuchasM-2andM-6aretheresultsofthisperiod.

Classification

Accordingtotheclosedegreeoftheanalogyrelationshipbetweenthecomputerandthephysicalobject

TheanalogyorsimilarrelationshipofthesimulatedcomputerexistsinthesamephysicalphenomenonorprocessasSimulatethephysicalphenomenaorprocessesofthecomputeritself.Accordingtotheclosedegreeoftheanalogybetweencomputersandphysicalobjects,analogcomputersaredividedintodirect(dedicated)computersandindirect(general-purpose)computers.

Directcomputerisusedasaphysicalmodel.Inadditiontotheanalogymathematicalrelationshipbetweenthetwo,thereisalsoaone-to-onecorrespondencebetweenthephysicalparameters.Forexample,usinganetworkcomposedofinductors,capacitors,andresistorstosimulateamechanicalsystemcomposedofmass,elasticdamping,andviscousdamping,themathematicalequationsofthetwocanbewritteninthesameform:itcanbeseenthatthereisalsoadifferencebetweenthetwoparametersLCRandMKB.Thereisaone-to-onecorrespondence.

Theanalogyrelationshipbetweenthephysicalmodelformedbytheindirectcomputerandthephysicalobjectisonlytheanalogyofthemathematicalmodel.Therefore,themodelmustbecomposedaccordingtotherealequation.Becausethemodeliscomposedoffunctionalcomponents,inordertomeetawiderangeofrequirements,enoughvariousfunctionalcomponentsmustbeusedtoformahighlyversatileanalogcomputer,theso-calleduniversalanalogcomputer.Alargegeneral-purposeanalogcomputerhasabouttwotothreehundredoperationalamplifiers,acorrespondingnumberoflinearpotentiometers,dozensofmultipliersandfunctiongeneratorsandothercomponents.

Theabove-mentionedmechanicalsystemincludesaddition,multiplicationanddifferentiationoperations.Ontheuniversalsimulator,aslongasthecorrespondingpartsareconnected,itsmathematicalmodelcanbeestablished.

Accordingtothedifferentelementsandcomponentsused

Analogcomputerscanalsobedividedintoelectronicandmechanicalcategories.

Thecorecomponentofananalogcomputerisanoperationalamplifier,whichisahigh-gainnegativefeedbackamplifier.

AccordingtoKirchhoff’slaw,thefollowingequationcanbewritten:

Accordingtothedefinitionofmagnification,V0/E=-A,usuallycalledthegainoftheamplifier,itsorderofmagnitudeis105upanddown.TheIgofahigh-gainamplifierisgenerally104timessmallerthanIiandcanbeignored.ComparedwithitsV0andVi,thevoltageEcanalsobeignored.Sotheformula(3)issimplifiedto:

(4)Thisisthebasicrelationalexpressionoftheoperationalamplifier.Itcanbeseenfromthisthataslongasthegainoftheamplifierislargeenough,therelationshipbetweentheoutputvoltageandtheinputvoltagedependsonlyontheinputandfeedbackcomponents,andhasnothingtodowiththeinternalcharacteristicsoftheamplifier.Therefore,changingtheinputandfeedbackcomponentscanchangetheoperationalstateoftheoperationalamplifier.

①Integrator.ChangetheimpedanceZftothecapacitorC,andtheimpedanceZitotheresistanceR,whichisobtainedbyformula(4):

(5)wherePistheLaplaceoperator.Turning(5)intotheoriginalfunction,then

(6)thusrealizestheintegraloperation.Amongthem,V0(0)=V0|t=0,whichistheinitialvalue.

Inanalogcomputers,thedifferentialoperationisusuallydoneastheinverseoperationoftheintegral.

②Inverter.IfZi=Zf=R,thenV0=-Vi,forminganinverter.

③Adder.Ifthereareseveralinputterminals,andtheresistanceofeachinputterminalisequalandequaltothefeedbackresistanceatthesametime,therelationalexpressionthattheoutputvoltageisequaltothesumoftheinputvoltagescanbederived.

Inaddition,operationalamplifierscanalsobeusedtoformdifferentiators,multipliers,dividersandvariousfunctiongenerators.

Inordertosetupquestionsandoperate,inthesimulationcomputer,inadditiontotheabove-mentionedcomponents,therearealsocontrollers,setupboardsandoutputrecordingdevices.

AccuracyTheaccuracyoftheanalogcomputerismainlydeterminedbytheaccuracyofthecomponentsused.High-qualitylinearcomponents(suchasresistors)haveanerroroflessthan0.01%offullscale.Theerrorofnon-linearcomponentscanreach0.02%offullscale.Thecomponenterroroflow-qualitycomputersgenerallyexceeds10timestheabove-mentionedvalue.

Typicalsimulationproblemsrequiremanyelementsandcomponentstosolve,anditisdifficulttotellthespecificaccuracyvalue.Becausethetotalaccuracyisnotonlydeterminedbythequalityofthecomponents,butalsobythesizeofthequestionandthelayoutmethod.Forhigh-qualitycomputers,theerrorofsolvinglargeproblemsmaybecontrolledintheorderof0.5%.

Becausetheoutputofmostanalogsolutionsmustberecordedwithanx-yrecorderorataperecorder,thefinalaccuracyisusuallyinthesameorderofmagnitudeastheaccuracyoftherecordingequipmentused.

Theaccuracyofthesimulatedcomputerisgenerallyadaptedtothetasktobecompleted.Insolvingengineeringproblems,mostoftheinputdataisdeterminedbyexperience.Generallyspeaking,itislowerthantheaccuracyofthesimulatoritself.

ApplicationSimulationcomputercansolvevariousdifferentialequationsandpartialdifferentialequations.Anydynamicphysicalsystemthatcanbedescribedbytheseequationscanbesolvedandsimulatedonthesimulationcomputerinprinciple.Specifically,theapplicationrangeofanalogcomputerscanbesummarizedinthreeaspects:①Asacalculationtool.②Asaphysicalmathematicalmodelandsimulationequipment.③Asateachingandtrainingtool.

Withthedevelopmentofdigitalcomputers,theroleofanalogcomputersascomputingtoolsandgeneralsimulationequipmenthasbeenreplacedbydigitalcomputers.However,asspecialsimulationequipment,teachingandtrainingtools,analogcomputerswillcontinuetoplayarole.

Applicationofanalogcomputer

Theinputandoutputofeachofitsmaincomponentsarecontinuouslychangingphysicalquantitiessuchasvoltageandcurrent.Theanalogcomputeriscomposedofseveralintegrators,adders,multipliers,functiongeneratorsandothercomponentswithdifferentfunctionsandnumbers.Accordingtothemathematicalmodeloftheproblemtobestudied,theoutputofonecomponentisinterconnectedwiththeinputofanotherorseveralcomponents,sothatthemathematicalrelationshipbetweentheoutputandtheinputoftheentirecomputersimulatestheobjectiveprocessoftheproblembeingstudied.Thesolutionoftheequationy(t)isobtainedattheoutputend;theinterconnectionrelationshipbetweenanalogcomputercomponentsvarieswiththeproblem,andsomepeoplecallthedesignofthisconnectionrelationshipasaproblem-solvingprogram.

Accordingtoforeignmediareports,theMilkyWayweseetodayevolvedoverbillionsofyears.Inthebeginning,itwasjustamassofloosematerial,slowlyformingahugespiraldiskcomposedofstars.Facedwithsuchacomplexgalaxy,astronomershavebeentryingtounderstandmoredeeplyformanyyears.Now,withthemostdetailedcomputersimulationresults,wecanseetheformationoftheMilkyWayinafewseconds.

Previously,astronomershavealsotriedtousecomputersimulationstosolvetheproblemofdwarfgalaxies-knownasthe"disappearingsatellite"problem-buttherewasnofinalansweruntilnow.

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