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.