System Identificaton Open Loop

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IDENTIFICATIONfromDATA TOPREDICTtheOVIPVIhavingpostObservationsontheINPOT/Ovipvtrelationship BU PREDICTIONgnaspsonlytheOBSERVABUEandPREDICTABUEpartoftheVariable(yprd(t)): s nnlessyct)isa DETERMINISTICSIGNAL, theirispartofyct)thatisUNPREDICTABLE→ theRESIDUALERROR(ect)) 2APPROACHES OPENLOOP CLOSEDLOOP 9 INCONSISTENTIinPHYSIOLOGY, ult)andelt)areassumedtobeUNCORRELATED a ult)andect)becomescorrelataduetotheFEEDBACKallphysidogicalregulations ect)ma yct)- ult) are FEEDFORWARD+ FEEDBACK!! HEREtheCAUSALRELATIONSHIPhastobeCERTAIN ^ WecandeadwiththisproblembyanalyzingtheCANALRELATIONS PARAMETRICIDENTIFICATION AUOWSinmamyCasasa GOODCLOSED- COOPSYSTEMIDENTIFICATION, Butitisbasedon theANALYSISofCAUSALRELATIONS assumptionabouttheTEMPORALORDERoftheevents > PASTult)Causesyct)andthepostofyct)Causesult) ConverselyisalmostunfeasiblewithSINUSOIDS, sinceinthatCeasethisTEMPORAL/causaleRELATIONCan'tbeSdvedma FOURIERMETHODS thePROBLEMofCAUSALITY PROBLEM: IdentitytheCAUSALRELATIONSHIP→ whatistheINPUTandwhatistheOVIPVIbetweeu2correlatoVariables? USUALLYIt's notdifficultfromdata todetectCORRELATION, ButAlientheiristheproblemofdetermininowhatistheCAUSEandwhatistheEFFECT anditisImportanttoKelpinnindthatinsoneCasas(especiallyinclosedloop)theTIMEFactorisMEANINGUESS(Cynicevolution)or canbeeuenMISLEADING TOASSUMEan INVERSEDCAUSAUTYMearnstoMISTAKEtheFEEDFORWARDACTIONforFEEDBACKandviceversa, sotoconsideri imcorrectlyaPREVALENCEofFEEDBACKACTIONon theFEEDFORWARDACTION er GCW) APPROXIMATION(thatwasintroduceinPUPILDIMENSIONREGULATION)thatcanbemadetosimplifytheFlu)= 1+GCWIHCW) @CONTROLBWma Feedforwandactioniseffectiveso theLOOPFUNCTIONisnotrequiredGCWIHCS)« 1 㱺 FCW)= GCW) ButoutofCONTROLBWma FeedbackactionbecomesprevalenttotheOPENloopACTION GCW)Hcw)»1 㱺 FCW)= ^HCW) SOLUTION?OPENINGtheLOOPatsonepoint,…