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- Politecnico di Milano
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- Biomedical Engineering
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- Bioengineering of Physiological Control Systems
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- Notes · By topic
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NotesBy topic
System Identificaton Closed Loop
Study material for Bioengineering of Physiological Control Systems, shared by the Studwiz community and reviewed by moderators.
Bioengineering of Physiological Control SystemsBy topic
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CLOSEDLOOPIDENTIFICATIONwithDIRECTAPPROACH IDENTIFICATIONofCLOSEDCOOPSYSTEMS withSIGNALSfrom/Ns/DEtheloop "DEM'""GtheFEEDFORWARDBRANCHandtheFEEDBACKBRANCHseparate, (withOPENLOOPIDENTIFICATIONTECHNIQUESIGNORINGtheotherBRANCH) MEASURESofYaandYa TAKINGMOCONSIDERATIONBOTHCAUSARELATIONSHIPS e ' , Gaz= È Gas= howYaisaffectedbyYa howYaisaffectedbyY, pertnrbedbyif pertnrbedbyva STOCHASTICvs DETERMINISTICHEassumebothYaandYaas perturbatebyaSTOCHASTICSIGNALVa,Va >DETERMINISTICPART: theDETERMINI511CCausalerelationshipsbethlemYaeya(Gaz&Gas)theMIaimis toIdentitysSTOCHASTICPART: howthesystemmodulates CompletelyrandomINPVISEs,Ez~ VVN, renderingthestomaSticperturbations Va,V2(H1,Ha) •Es,EzhastobeWN(o,E) COLOUREDNOISES / \ UNCORRELATED: Vatua • va, J, arenotWN→ Va= HaEs and V2= HaEz ,butare ASSUMEDTOBE NON- MEASURABLE S iftheIDEIVIIFIEDMODELgivesRESIDUALSwitha Blas(㱺Es,E,✗WN)or cov(va,Va)=/O Mearnsthattheirisstilesomethi.mg(soneRELATIONSHIP) ⊥COLOUREDRESIDUALS thatShakalbeINCLUDEDIN/DESCRIBEDbytheMODEL • SPECTRUMofYai YaisPARTIALLYCORRELATEDtobothSTOCHASTICNOISES→ TheSPECTRUMofYaistheSunof butwithseparateComponents,sinceUsthe theSPECTRUMofyaGIVENUsand theSpectrumofYaGIVENI ¥OPENLOOPIDENTIFICATION DuetoFEEDBACK•CLid. hasadditionalconstnaintsandrequirementswrta-id. Stocleasticparts Y • CONSISTENCYontheSTOCHASTICPARTisrequiredtohaveCONSISTENCYontheDETERMINISTICPART(= UNBIASEDandCORRECTMODEL)ma (Ha,Ha) ^ è • CLOSEDLOOPid. ismoredifficultAlan0Lid. sincetheFEEDBACKACTION, whethereffective, REDUCESthe①y,/⊥(w)㱺Tcov(È,,(w)) > VEDIBIAS.isVEDIACCURACY INNOVATION BROADBANDSIGNALSINNOVATIONisFUNDAMENTALforthe systemIDENTIFICATIONprocessi ma • stabiles'°"" ""°" ""EPAR""(" we" """mal) aaaa allonstoshowthesystemREACTION INSIGHTSontheSYSTEMBEHAVIOUR toa WIDERANGEofINPUTW 㱺 Gyulz)= Gea(z)…
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