An iterative method for the identification of nonlinear systems using a Hammerstein model

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1、546IEEETR.INS.4CTIONSOSlUTOMATICCOXTROLJULYAnIterativeMethodfortheIdentScationofNonlinearSystemsUsingaHammersteinModelIi.s.S.iRESDR.i,SEKIORMEbIBER,IEEE,ASDP.G.G.LLkI.%S,STCDESTNEMBER,IEEEAbstract--Aniterativemethodisproposedfortheidentificationofnonlinearsystems

2、fromsamplesofinputsandoutputsinthepresenceofnoise.Themodelusedfortheidentificationconsistsofano-memorygain(ofanassumedpolynomialform)followedbyalineardiscretesystem.Theparametersofthepulsetransferfunc-tionofthelinearsystemandthecoefficientsofthepolynomialnon-linea

3、rityarealternatelyadjustedtominimizeameansquareerrorcriterion.Digitalcomputersimulationsareincludedtodemonstratethefeasibilityofthetechnique.INTRODUCTIOSSystemcharacterizationands>-stemidentificationarebasicprob-lemsinsystemstheoryandhavereceivedconsiderableattent

4、ioninthepast.\-bilesystemcharacterizationisconcernedprimarilywithsettingupmathematicalmodelstorepresentinput-outputrelation-ships,systemidentiticationdealswiththechoiceofaspecificmodelfromaclassofmodelswhichismathematicallyequivalenttoagivenph>-sicalsystem.Forasp

5、ecifiedinput,thisequivalenceisestablishedx.I'ssxss.I'sbycomparingtheoutputsofboththesystemandthemodeland.xxsxs.YxH.I'adjustingthemodeltominimizesomefunctionaloftheerror[I].Ifs.I'.I's.I's.xs.I'thisminimumofthefunctionalislessthanapredeterminedvalue,themodelandthesy

6、stemareconsideredequivalent.xsss.Y.I'Is.xVhilenumerousrealapplicationsexistwhichinvolvetheuseofasI'.Y.I'.I'ss.Yslinearmodel,veryfewwhichemployanonlinearmodelareavailablessx.I's.I'.I'.I'1'fortheidentificationofanunknownsystem.Thismaybeattributed.x.xI'x.I'.Yx.x2:pa

7、rtlytothefactthatmostoftheanalyticworkintheareaofnon-1000-10000linearidentificationassumestheinput(orprobesignal)tobearandom.signalwithprespecitiedproperties-usuallywhiteGaussiannoise-01000-1000(24)whileinpracticalsituations,theidentificationhastobeaccomplished001

8、000-100onthebaaisofexistinginput-outputdata.Further,sincethemathe-0001000-10maticalmodelmustbeidentifiable,nonlinearintegraloperatorssuch00001000-1'asth