一类离散时变系统的在线无限脉冲响应滤波逆控制

󰻓󱅣щ󰝼:1000−8152(2011)08−1056−07

󰥥󱇅󰧘󰪂󱃐󱂋󱂨

ControlTheory&Applications

Vol.28No.8Aug.2011

󱁂󰧋󰧖󰳛󰵈э󰼢󰹤󰖥󱄝󰽌󰻭󰽋󰪝Ԋ󰽙󱂋󰩲ѯ󰭉󰥥󱇅

󰨾󰡹ӄ1,2,󱂿

󰼩1,󰧙󰞟󰳀1,2

(1.󰗪Кն󰿐󰩀ӱ󰛽󱀼󱈸󰞆󱈱󰗮󰟄󰝓󰡅󱇗󰗄󰵌󱀒󰵩,󰨒󰭡󰴫󱀝110819;

2.󰗪Кն󰿐󰾐󰼏󰥓󰿐󱃐󰛽ӱ󰿐󱃽,󰨒󰭡󰴫󱀝110819)

󱅋󱀱:󱆌󰘓󱁂󰧋󰧖󰳛󰵈э󰼢󰹤,󰸴ԛ󰨔󱁂󱇕󰠎󱂿󱈱󰵡󱂋󰜸󰾟󰲃󱇗󰞆󱉔󰧬󱈰󰲕(AIW--CPSO)󰷘󰙅󰖥󱄝󰽌󰻭󰽋󰪝Ԋ󰽙󱂋(IIR)󰩲ѯ󱈱󰵡󱂋󰼢󰹤я󰵍󰙚󰙅,󰵌󰽃󰨬󰠞󰗄󰵌󰵈󰛵󱈶󰖥󰲆󰯄󰮥󰥥󱇅.IIR󰩲ѯ󰰖󰥖󰢳󰤥󱂵󰽋󰪝Ԋ󰽙󱂋(FIR)󰩲ѯ󰰖󱄝я󰵍󰵈э󰼢󰹤󰵈󱁹󰰃󰽍󰜱󰤇󱆔󰖥󰸫󱆘󱆴󰟶󰻭󰜿󰩰эն󰘷Ф󰯧󰧖󰽌󰿞󰨀󰖥󰻙󰸵.󰹝󰵈󱂻󰢆󰖮󰨔󱄝󰽌󰿞󰨀󰷮󰾳󰖥󰲃󱆴󰽟󰨈Ӊ󰘇,󰸴󰴶󰨔󱂪󰟄󱃐󰡹󰬆󰽲󰩱.Ч󰻓󰴡󰠹󰖥󱈱󰵡󱂋󰜸󰾟󰲃󱇗󰞆󱉔󰧬󱈰󰲕(AIW--CPSO)󰷘󰙅󰥖󱄝Ԯ󰹤󰧬󱈰󰲕󱂪󰟄(PSO)󰷘󰙅󰖥󰠎Ԥ󰴈󰛷󰝺󰖹󰢳󰤥󱁹󰿊󱂨IIR󰩲ѯ󰰖󰷮ջ󰦟󰖥󰲆󰤅󱂪󰟄󰻙󰸵.󰹙󰝖󰙟󱆇󰙳󰼅󰥖󱁛󰥁ԛ,󰘓󱂿Վ󰧋󰧖󰳛󰵈э󰼢󰹤,󰠎󱂿󱄝󰽌AIW--CPSO--IIR󰩲ѯ󰰖󰖥󱈱󰵡󱂋󰭉󰥥󱇅󰙚󰙅󰥖󱁛󰥹󰷎󱂵󰽲󰖥󰵌󰽃󰻃󱆩󰘓󰽠󰖥󱄝󰽌󰡹󰬆,󰹝󰵈󰵌󰵈󰛵󱈶󰵈э󰼢󰹤󰖥󰸫󱆘󱆴э󰟄.

󰜱󰡯Ս:󰧖󰳛󰵈э󰼢󰹤;󱈱󰵡󱂋󰭉󰥥󱇅;󰻭󰽋󰪝Ԋ󰽙󱂋󰩲ѯ󰰖;󰧬󱈰󰲕󱂪󰟄󰷘󰙅󱇏󰹭󰙳󰧋󰝼:TP273󰻓󰽄ѓ󰵍󰪒:A

Onlineinfinite-durationimpulseresponsefilteringinversecontrolfor

aclassofdiscretetime-varyingsystems

LIUJian-chang1,2,YUXia1,LIHong-ru1,2

(1.StateKeyLaboratoryofSyntheticalAutomationforProcessIndustries,NortheasternUniversity,

ShenyangLiaoning110819,China;

2.SchoolofInformationScienceandEngineering,NortheasternUniversity,ShenyangLiaoning110819,China)

Abstract:Foraclassofdiscretetime-varyingsystems,weproposedanonlineinfinite-durationimpulseresponse(IIR)filteringadaptivesystemidentificationmethodbasedontheadaptiveinertia-weightedcooperatedparticleswarmoptimization(AIW--CPSO)algorithm.Thisapproachachievestheperfectmatchingofzero-poleforthereal-timetrack-ingcontrol.TheIIRfilteravoidstheenforcedoff-linetrainingprobleminducedbytheirregularvariationintheeigenvaluesofthecorrelationmatrixinfinite-durationimpulseresponse(FIR)filterwhenidentifyingatime-varyingsystem.Italsore-ducestheweightingvectorlengthintheonlinetrainingprocess,andimprovestheefficiencyofoptimizationandmodeling.Onthebasisofthetraditionalstandardparticleswarmoptimization(PSO)algorithm,thedesignedAIW--CPSOalgorithmprovidesabettersolutiontotheglobaloptimizationprobleminselectingtheproperIIRthanthetraditionalstandardPSOalgorithm.Simulationanalysisshowsthat,fordiscretetime-varyingsystems,theadaptiveinversecontrolmethodbasedontheonlineAIW--CPSO--IIRfiltercanrealizethefastonlinemodelingofunknownplantseffectively,andtrackthereal-timevariationofeigenvaluesoftime-varyingsystems.

Keywords:discretetime-varyingsystem;adaptiveinversecontrol;infiniteimpulseresponsefilter;particleswarmoptimizationalgorithm

1󱂄󰿽(Introduction)

󰵌󰠽󰛽ӱ󱂋󱂨󱇏,Ф󰥥󰼢󰹤󰖥󰵈э󰽃󰽠󰯴ђթ󱄝.󰧨󰳂󱄝󰚯󱄖󰼢󰹤󰝖ӱ󰥥󱇅a󰝴󰥢󰝴󰸿󱁛󰠣󰠏󰰖󰲦󱄎󰗮󰥥󱇅󰖩󰨵󱃗,󰗻󰠇󰘟󰠇󰴒󰖥󰾳󱀱󰢳󰤥󰼢󰹤󰖥󰵈э󰻙󰸵.󱁛󰚯󱄖󰼢󰹤󰖥󰝖ӱ󰥥󱇅󰺹󰧨,󱄝󱅁󰛑󰝖ӱ󱇏,󱅁󰠏󰖥ҕ󰶔󰷛󱈢󱅁󱇅󰝖ӱ󰖥҂󰘎󰣉󰾛󰘷󰵌󰵈э󰟄,󰘷󰱏э󰟄󰙓󰺶󰺪󰺪󰢠ն(ӈ󱂨󱉋ն󱉋󰽬󱆴󱆭б󰦟󰞙󰨈).󱂻󰳂󰠏󰰖󰲦󰖥󰠏󰾀ф󱉓󰝅󰠖󰛵󱈶󰵈,󰰃󰜸󰾟

ҕ󰶔󱀹󰵞󰵈э󰖥,Ֆ󰘷󰵐󰼢󰹤󰖥󰗮󰧯󰿐ҕ󰶔󰴮󱇀󰢲󰜒󰘿󰴳э󰟄[1].ԢՎ󱆭󰺓,󱄝󰾸󰘟󰼢󰹤󱇏,󰛄󰲠󱄮󰴲󰖥󰵈э󱀹Ӯ󰺹󰼢󰹤҂󰲒󰗧󰾟󰵈э󱁹󰷍.󱁹Վ,󱆌󰘓󱆃󰽴󰵈э󰼢󰹤я󰵍󱃐󰥥󱇅󰖥󰿹󰣮󱄀󰦟󱄀Ф󰣍󰽴󰭍󰖥󰥥󱇅󰢸󰷮󰜱󱇿,Ӯ󰺹Ф󰜼󰙗󰸩󰪂󰖥󰲣󰗄󰻙󰸵󱆭󱁂[2∼4].󰛴󰤌󰼢󰹤󰖥󰵌󰠽󱄎󰾛󰱦󰦃,󰽃󰡼󰵈э󰼢󰹤󰙳󰺹ҕ󰶔󰵈эa󰢲󰜒󰵈э󱁛󰠣󰲠󰗮҂󰲒󰗧3󰧋.󰰃󱇏󰢲󰜒󰵈э󱄝󰬖󰽴󰱦󰦃󰼯󰥖󱂨󰱍󰟐󰥥󱇅󰖩󰙚󰙅󰢳󰤥;󰲠󰗮

󰵬󰛠󰲰󰯹:2010−05−28;󰵬󰾩󰚿󰛠󰲰󰯹:2010−10−20.

󰠎󰣁󰽛󰬢:󰝓󰡅󱈱󰲖󰥓󰿐󰠎󰣁󰞄Џ󰳶󰛑󰹍󰜢󰙺󱂵󰽋󰜄󰶳󰧳󰞆󱈧󱇹󰽛󰬢(50974145);󰨒󰭡󰴸󱈱󰲖󰥓󰿐󰠎󰣁󱈧󱇹󰽛󰬢(20092012).

󰖻8󰯹󰨾󰡹ӄ󰖩:󱁂󰧋󰧖󰳛󰵈э󰼢󰹤󰖥󱄝󰽌󰻭󰽋󰪝Ԋ󰽙󱂋󰩲ѯ󰭉󰥥󱇅1057

҂󰲒󰗧󱄵ӈӈФ󰝂󰺹󰩚Ͽ󰥥󱇅󰿹󰣮󰙓Ԑѩ󰱼󰖤󰨔󰞓󰝺󰖥󰽲󰝔;󰘷Ч󰻓󰡼󱇗󰗄󰸩󰪂󰜼󰙗թ󱄝󱂿󰥥󱇅󰼢󰹤󱇏aѩӈӈ󱂄󰰏󰼢󰹤󰖥󰗮󰷿󰠇󰣡󰷿󰾟󰬿󰞓նэ󰟄󰖥ҕ󰶔󰵈э󰼢󰹤󰥥󱇅󰻙󰸵.

󰣍󰭍󰦟,󰘓ҕ󰶔󰵈э󰼢󰹤󰖥󱈱󰵡󱂋󰥥󱇅󰿹󰣮󰙤ӈ󰠃󱄁,󱄪󰯹󰺪󰺪󰡼󰘓󰽠󰴡󰗧󰺹󰪤󰵈э󰼢󰹤,󰰃ҕ󰶔󰖥э󰟄󱄵󰖒󱉔󰻃󱆩󰲠󰗮.󰷙󰲖󱆃󱀢ԩ󰧘󰥖󱁛󰡥󰟄󰼢󰹤󰻗󰗧󰾟󰙳󰼅,󰖌󰘓󱂿Ф󰥥󰘓󰽠󰖥ҕ󰶔э󰟄󰷎󰘇󱁛󰠣э󰟄󰙓󰺶󰗻󱂵󰙤ӈ󰿸󰛬󰖥󰽋󱇅[5,6].󰹝󰵈,󱈱󰵡󱂋󰥥󱇅󰙚󰙅󰺪󰺪󰘓󱂿ҕ󰶔󰗧ӈ҂󰲒󰗧󰼢󰹤󰤎󱂵󰞓󰝺󰖥󰵬󰧻󰾟󱃐󰻗󰗧󰾟,󰖌󰖒ҕ󰶔󰵈э҂󰲒󰗧󰵈,󰺪󰺪ղ҂󰖞󰞓󰝺󰖥󰥥󱇅󰽲󰝔.󰺹Վ,󰞓󰘟󰿐󱆀󱀹󰸴ԛ󰨔󱁂󰽴󰤎С󰩚Ͽ󰾟󰬿󰖥󱈱󰵡󱂋󰥥󱇅󱁛󰠣󱈱󰵡󱂋󰗝ս󰿐󰼝󰖩󰥥󱇅󰙚󰙅[4,7],Վ󰧋󰥥󱇅󰙚󰙅󰷙󰲖󰘓󱂿󰤎󱂵󰲠󰗮󱄮󰴲󰖥󰵈э󰥥󱇅󰼢󰹤󱃐󰤎󱂵󱇛󰯹󰸫󰾟󰖥󰵈э󰥥󱇅󰼢󰹤󰤨󱂵󰞓󰝺󰖥󰥥󱇅󰽲󰝔,󰖌󰘓󱂿󰵈э󰸫󱆘󰺛󰲆҂󰲒󰗧󰖥󱁂󰧋󰵈э󰼢󰹤,󰥥󱇅󰼢󰹤󰖥󱆜󰸸і󰽃󰟎󱃹󱃹҂󰬿󰨷󰲦󰪡󱁩.

󰺹Վ,Ч󰻓󰭅Ґ󱂨󱈱󰵡󱂋󰭉󰥥󱇅󰙚󰙅󰦟󰢳󰤥Վ󰧋󰻙󰸵.󱈱󰵡󱂋󰭉󰥥󱇅[8]󰵞󱂮Widrow󰢝󰵱󰸴ԛ󰖥󱁂󱇕󰥥󱇅󰼢󰹤󰴡󰠹󰙚󰙅.󰚾󰙚󰙅󱂨󰘓󰽠󰬆󰾘󰖥󰭉󱉔󰺹󰼢󰹤󰖥󰤷󰟌󰗮󰷿󰥥󱇅󰰖,ѩ󱂮Վх󰫧󰨔о󰟌󰼢󰹤󱁛󰠣ҕ󰶔󰵈э󰷮󱂄󰰏󰖥҂󰻗󰗧󰽃󰽠[9].󱃐󱈱󰵡󱂋󰥥󱇅󰙚󰙅󰽍б,󱈱󰵡󱂋󰭉󰥥󱇅󰥖󱁛󱈱󰗮󰛵󱈶󰘓󰽠󰖥󰗮󰷿э󰟄ѩ󰡨󰴒󰼢󰹤󰖥󰗮󰷿󱄮󰴲,󰘷҂󰾳󱀱󰘓󰥥󱇅󰰖󰞄Ф󰥥󰘓󰽠󱉓󰝖󰘟󰖥󱀱󰱰󱃐󰽋󱇅.󰬢󰰭,󰧖󰳛󰼢󰹤󰖥󱈱󰵡󱂋󰭉󰥥󱇅󰘟󰵞󰠎󱂿󱂵󰽋󰪝Ԋ󰽙󱂋(finite-durationim-pulseresponse,FIR)󱈱󰵡󱂋󰩲ѯ󰰖[10,11]󰣉󰾛󰴡󰠹󰖥.󰖌Վ󰧋󰩲ѯ󰰖҂󰖤҂󱄝󰵬󰧻󰷎󰘇󱃐󰻗󰷿󰼂ҵ󰴈󰣉󰾛󱅼󱇏,󰹝󰵈󰘓󰽠󰖥󰗮󰷿󰸫󱆘󱀹󰥖󰬿󱂄󰰏󰥥󱇅󰰖󰖥󰵻󰳆󰽍󰜱󰤇󱆔󰸫󱆘󱆴эӉ,󱆃󱀢҂󰣇󰵐󰷘󰙅󰖥󰵬󰧻󰷎󰘇󰢆󰖮󰘷󰱏󰿞󰨀󰾽󰨙󱀹҂󰖤҂󰡆Ӊ.󱆃󱇕҂󰧦󱁹󰷍󰘓󱂿󰬪󰽴҂󰖤҂󰵐󱂨󱄝󰽌󰿞󰨀󰝖ӱ󰖥󰵈э󰼢󰹤󰦟󰶪(󰳂󰗈󰾐󰼢󰹤,󰶺󰚛󰼢󰹤󰖩),󰗻󰵞󱁂󰛱󰿸󱇗󰖥󰲌󰽊.󱆌󰘓FIR󰩲ѯ󰰖󰖥󱆃󱇕󰤅󰽋󰾟,󰽃Ґ󱂨󱈱󰵡󱂋󰻭󰽋󰪝Ԋ󰽙󱂋(infinite-durationimpulseresponse,IIR)󰩲ѯ󰰖󰣉󰾛󰘓󰽠󱄝󰽌я󰵍,󱁛х󰫧󰸫󱆘󱆴эӉ󰘓󰷘󰙅󰵬󰧻󰷎󰘇󰖥󱂕󰽙.󰖌IIR󰩲ѯ󰰖󰖥󰾟󰬿󰱷󰫫󱃐FIR҂󰹝(҂󰵞ѓ󱈙󰖥󰘽Ց󰾘󰱷󰫫),󱆃󰣼󱀱󰱰󰿞󰨀󰷘󰙅󰤎С󰞓󰝺󰖥󰲆󰤅󱂪󰟄󰬿󰧯.󰺹Վ,Ч󰻓󰡼󱉋󰣍󰸴ԛ󰖥󰞆󱉔󰧬󱈰󰲕(CPSO)󰷘󰙅[12]󰡆󱁛󰚿󰣉,󱄝Ќӻ󰰃󰲆󰤅󱂪󰟄󰾟󰬿󰖥󰠎Ԥ󰴈󰣉󱁂҄󰸴󰛚󰷘󰙅󱂪󰟄󰷎󰘇,󰴡󰠹ԛ󰤎󱂵󰜸󰾟󰲃󱇗󰖥󰞆󱉔󰧬󱈰󰲕(AIW--CPSO)󰷘󰙅,󱂨󱁛󱄝󰽌󰿞󰨀IIR󰩲ѯ󰰖󰖥󰲃󱆴󰽟󰨈.󰷛󰞪󰡼󱆃󱇕󰾍󰖥AIW--CPSO--IIR󰩲ѯ󰰖󱂨󱂿󱁂󰧋󰵈э󰼢󰹤󰖥󱄝󰽌󰭉󰥥󱇅,ѩ󰹙󰝖󰙟󱆇󰙳󰼅󱀒󱆣󰨔󰥥󱇅󰼢󰹤󰖥󱂵󰽲󰾟.

2AIW--CPSO--IIR󰩲ѯ󰰖󰢲󰜒󱃐󰷘󰙅(ThestructureandalgorithmofAIW--CPSO--IIRfilters)

2.1

󱂨󱂿󰵈э󰼢󰹤я󰵍󰖥IIR󰩲ѯ󰰖(TheIIRfil-tersfortime-varyingsystemsidentification)

󱄝󱈱󰵡󱂋󰩲ѯ󰧘󰪂󱇏,󱈱󰵡󱂋IIR󰩲ѯ󰰖󱄝󰼢󰹤я󰵍󰖥󱂋󱂨󱇏󰖥󱂪󰵝󱀱󰫼󰽁󰛚󰝖󰰃󰷰󰩲ѯ󰰖.󰵌󰠽󰴈,IIR󰩲ѯ󰰖󰖥󰠎Ч󰢲󰜒󱃐󱈱󰟭󰝂󰟁󰗮󰯜󰤨(ARMA)󰬆󰾘󰖥󰢲󰜒󰽍󰹝,󰰃󰵻󰳆󰵻ԛ󰜱󰼢󰗧󱁬󰺹[13]

y(n)=󰀁Pi=0

ai(n)u(n−i)+󰀁

Qi=1

bi(n)y(n−i),(1)

󰰃󱇏:ai(n)󰞄bi(n)󰵞ARMA󰬆󰾘󰖥󰥖󰗘ҕ󰶔,y(n)󰺹󰵻ԛ󰽟󰨈,u(n)󰺹󱈱󰵡󱂋󰩲ѯ󰰖󰖥󰵻󰳆󰽟󰨈,P󱃐Q󰙳љ󰺹󰩲ѯ󰰖󰨬󰠞󰗄󰛱󰶔(P󰀁Q).󰖒IIR󰩲ѯ󰰖󰖥󰼢󰶔󰜥󰗧҂э󰵈,󰥖󱂨󰳂󰼯󱈇󱁍󰝦󰶔󰖩󰽲󰖹і󱆘ARMA󰬆󰾘:

Pˆ(z)=A(z)1−B(z),(2)

󰰃󱇏A(z)󱃐B(z)󰙳љ󰺹

A(z)=󰀁Paiz−i

,B(z)=

󰀁Qi=0

i=1

biz−i.

(3)

󰚾IIR󰩲ѯ󰰖󱂨󱂿󱄝󰽌󰵈э󰼢󰹤я󰵍󰖥󱃰󰧘󰳂

󰹭1󰷮󰵕.

󰹭1IIR󰩲ѯ󰰖󰵈э󰼢󰹤я󰵍󱃰󰧘󰹭

Fig.1ThestructureofIIRfilterfortime-varying

systemidentification

󰹭1󱇏󰼂ҵ󰾐󰝼󰺹e(n)=yd(n)−yˆ(n),yd(n)󰺹󰯹󰺬󰽙󱂋󰾐󰝼.󱄝󱆃󰛱󰼢󰹤я󰵍󱂋󱂨󱇏,󰵻󰳆󰾐󰝼u(n)󰹝󰵈󰡆󰖞󰻃󱆩󰼢󰹤󰞄󱈱󰵡󱂋󰩲ѯ󰰖󰴈,󱂮Վ

󰙳љӁ󰴳󰯹󰺬󰽙󱂋yd(n)󰞄󰵌󰠽󰩲ѯ󰰖󰖥󰵻ԛy

ˆ(n).󱈱󰵡󱂋󰩲ѯ󰰖󰖥󰞆Ӯ󰲃󰽟󰨈w

ˆ(n)󰗧󱁬󰺹󰨆󱉆󰼢󰶔{ai(n)}Pi=0󰞄{bi(n)}Q

i=1󱁂󰰏󱉆Ӯ󰖥󰽟󰨈,󰠧

wˆ(n)=[a0(n)a1(n)···aP(n)

b1(n)b2(n)···bQ(n)]T.

(4)

󱁂Ϯ󰱦󰦃󰼯,ս󰡎󰝦󰶔ӈ󱂨󰤨󰙚󰼂ҵ(MSE)і󰵕,Ч󰻓󱀹󰡼󰿊󰱼󰚾󱆷ѓ󰦟і󱆘󱄝󰽌PSO󰷘󰙅󰖥󰧬󱈰󰵡

1058󰥥󱇅󰧘󰪂󱃐󱂋󱂨󰖻28󰤜

󱂋󰘇󰝦󰶔.󰘓󱂿󰹭1󰷮󰵕󰖥󱈱󰵡󱂋󰼢󰹤я󰵍󰦟󰶪,󰼢󰹤󰠎󱂿MSE󰖥ս󰡎󰝦󰶔󰳂󰼯:

Ji(n)=E[󰀆ei(n)󰀆2

].

(5)

󰖒Ji(n)ղ󰖞󰠞󰽬󱆴󰵈,󰩲ѯ󰰖ҕ󰶔󰠧і󱆘󰨔󰻃󱆩󰗮󰷿󰼢󰹤󰖥󱉋󱂪󰲃󱆴ҕ󰶔.

Ч󰻓󰭅Ґ󱂨󰧬󱈰󰲕(PSO)󰷘󰙅󱂪󰟄IIR󰩲ѯ󰰖󰲃󰽟󰨈,󱁹󰰃󰤎󱂵󰞓󰝺󰖥󰲆󰤅󱂪󰟄󰬿󰧯.󰘷󰘓󱂿PSO󰷘󰙅󰦟󰶪,󰧬󱈰󰖒󰰭󰻊󱇂󰖥󰝺󰟊󱂮󰵡󱂋󰘇󰝦󰶔󰦟󰲒󰗧,󱁹Վ󰧬󱈰󱈑󰦃󰖥󰝺󰟊󱂋󰛴󰤌ս󰡎󰝦󰶔Ji(n)󰦟󰞙󰨈.󱂮Վ󰥖󰡮,󰘓󱂿IIR󰩲ѯ󰰖󰖥󰴡󰠹󰘷󰿽,󰥖󰿊󱄴󰵔(5)󱉔󰺹󰵡󱂋󰘇󰝦󰶔.󱂮󰚾󰜄󰵔󰥖󱁛󰥁ԛ,󰖒󰰭󰧬󱈰󰖥MSEэ󰽬󰵈,і󰵕Ji(n)󱆞Я󰣍󱉋󱂪󱆴,󱀹󰣼󰵞󰶪,󰚾󰧬󱈰󰷮і󱆘󰖥󰩲ѯ󰰖ҕ󰶔󱂪󱂿󰰃󰷰󰧬󱈰.󰹙󰝖󰷘󰙅󰗝ս,󰥖󱁛󰖤ԛ󰖒󰷘󰙅󰷆󰷬󰖞󱉋󱂪󰢳󰵈,󰵡󱂋󰘇󰝦󰶔󱉋󰽬󰖥󰧬󱈰󰷮󰖤󰖥ҕ󰶔󰽟󰨈󰠧󰺹IIR󰩲ѯ󰰖󰖥󱉋󱂪󰲃󰽟󰨈.

󰼯󰫫󰢺󰴕󱂨󱂿󱄝󰽌󰿞󰨀IIR󰩲ѯ󰰖󰲃󰼢󰶔󰖥AIW--CPSO󰷘󰙅.

2.2

󱈱󰵡󱂋󰜸󰾟󰲃󱇗󰞆󱉔󰧬󱈰󰲕󰷘󰙅(Theadap-tiveinertiaweightcooperatedparticleswarmoptimizationalgorithm)

ѓ󱈙PSO󰷘󰙅[14]󱄝Ԛ󰵓󰵈󰥙թ󱄝N󰛱󰷛󰠏󰧬󱈰,󰫄󰛱󰧬󱈰󱂵M󰛱ր󱂪󰟄󰖥󰻃󱆩ҕ󰶔.󰫄󰛱󰧬󱈰սі󰢳󰥢󰡗󱇏󰖥󱁂󰛱󰗄,󰫄󰛱󰧬󱈰󰖥󰜱󰼢󰵡󱂋󰘇󰱼󰤥󱂿󱁂󰛱󱃧󰼵󰴡󰗧󰝺󰖥󰵡󱂋󰘇󰝦󰶔󰖥󰗝ս󰝖ӱ.󰵡󱂋󰘇󰝦󰶔󰥖󱁛і󰵕ԛ󱆃󰽴󰧬󱈰󱃐󰺷󱁂󱁂󰛱󰯹󰺬󱉋󱂪󰢳󰖥󰤏󰧖.󰫄󰛱󰗝ս󰵈󰥙n,󰖻i󰛱󰧬󱈰󰥖󱁛󱂮󰘟󰺻󰥢󰡗󱇏󰖥󱁂󰛱󰻊󱇂󰽟󰨈Xi(n)󰞄󱁂󰛱󰷎󰘇󰽟󰨈Vi(n)і󰵕.󱁹Վ,PSO󰷘󰙅󰥖󱁛󱂮󱁛󰼯󱁂󱉆󰻊󱇂󰞄󰷎󰘇󰽟󰨈󰗧󱁬:

Xi(n)=[x1(n)x2(n)···xM(n)],(6)Vi(n)=[v1(n)v2(n)···vM(n)].

(7)

󰷛󰞪PSO󰷘󰙅󰛳ԛ󰫄󰛱󰧬󱈰󱄝󰢳󰥢󰡗󱇏󰖥󱈑󰷿󰽟󰨈󰞄󰷎󰘇󰽟󰨈󰖥󰗝ս󰛷󰾍󰜄󰵔⎧:⎪⎨Vi(n+1)=ωVi(n)+c1r1[Pbest−Xi(n)]+

⎪⎩

c2r2[Gbest−Xi(n)],

(8)Xi(n+1)=Xi(n)+Vi(n+1),󰰃󱇏:Pbestսіֆ󰛱󰧬󱈰󱄝󰝖󰲀󰵈󰥙󰖥󱉋󱂪󰻊󱇂󰽟󰨈,ӫ󰺹󰛱󰸸󱉋󱂪󰻊󱇂;Gbestսі󰷮󱂵󰧬󱈰󱇏󰖥󱉋󱂪󰻊󱇂,ӫ󱆭󰺹󰲕󰸸󱉋󱂪󰻊󱇂.󰰃󱇏󰴡󱇕󰲕󰶔󰨈X=[X1X2···XM];r1,r2󰺹[0,1]󰡗󰖥󰷛󰠏э󰨈;c1,c2󰺹󰡆󰷎󰼢󰶔;ω󱁹󱈰󰺹󰜸󰾟󰲃󱇗.󱁂Ϯ󰱦󰦃󰼯,󰷎󰘇vi󰖥󰱼󱆴󰙓󰺶󰺹[−vmax,vmax],󰬢󰖥󰵞х󰫧󰧬󱈰󰺂󰧖󰢳󰥢󰡗.󰷛󰞪󰛴󰤌󰜄󰵔(8),󰧬󱈰󰽟󱉋󱂪󰻊󱇂󱁍󰗮,󰱏󱆃󰛱󰝖ӱ󰡼Ф󰿖󰟌󱆰󰖞󰪡󱉀󰹔󱆸󰹈󰡱.

󱄝󰞆󱉔󰷆󰿙󰬆󰵔󰼯,󰻓󰽄[15]󰸴ԛ󰨔PSO󰖥󰚿󰣉󰷘󰙅—--󰷛󰠏󰞆󱉔󰧬󱈰󰲕(CRPSO)󰷘󰙅,󰚾󰷘󰙅󰖥󰬢ѓ󰵞󰵐󱂨󰘟󰛱󱇕󰲕󰦟󰷆󰿙󰢳󰥢󰡗󰖥҂󰹝҆󰙳,󰹙󰝖Ґ󱂨󰷛󰠏󰞆󱉔󰠏󱇅󰦟󰯜󰞙󰲆󰤅󰷆󰷬󱃐󰤅҆󰷆󰷬󰬿󰧯.󰰃󱇏,󰫄󱁂󱈰󰲕󱇏󰖥󰧬󱈰󰹙󰝖󰷛󰠏󰙚󰵔󰿊󱄴󰰃󰷰󱈰󰲕󰘿󰽃󰖥󱉋󱂪󰻊󱇂󱂨󱂿󰛷󰾍󰧬󱈰󰖥󰷎󰘇󱃐󰻊󱇂.CRPSO⎧󰷘󰙅󰖥󰛷󰾍󰜄󰵔󰺹⎪⎨Vi(n+1)=ωVi(n)+c1r1[Pbest−Xi(n)]+

⎪⎩

c2r2[Gbest(r)−Xi(n)],

(9)Xi(n+1)=Xi(n)+Vi(n+1),󰰃󱇏:i=1,···,N󰺹CRPSO󰷘󰙅󱇏󱈰󰲕󰖥󰶔󰬢,r󰺹󰢺󱂿1󰖞N󱆭󰡗󰖥󰷛󰠏󱆜󰶔,󱂨󱂿󰿊󱄴҂󰹝󱈰󰲕󰡗󰖥󱉋󱂪󰻊󱇂Gbest(r),󱁛󰯹ղ󰖞󰾐󰼏󰜋󰽚󰖥󰬢󰖥.󰻓󰽄[12]󱂻󰡼󱆃󱁂󰷘󰙅󰣉󱁂҄󰚿󰣉,󰸴ԛ󰨔󰤎󱂵󰛷󰝺󰲆󰤅󱃐󰤅҆󰷆󰷬󰬿󰧯󰖥󰞆󱉔󰧬󱈰󰲕(CPSO)󰷘󰙅.󰚾󰷘󰙅󰹙󰝖󰷛󰠏󰙚󰵔󰵐󱂨󰰃󰷰󱈰󰲕󱉋󱂪󰻊󱇂Gbest(r),󰹝󰵈󰡼󰨆󱇕󱉋󱂪󰻊󱇂󱂨󱂿󱈰󰲕󱇏󰧬󱈰󰷎󰘇󱃐󱉋󱂪󰻊󱇂󰛷󰾍⎧

.󰚾󰷘󰙅󰖥󰛷󰾍󰜄󰵔󰺹⎪⎪⎪⎪V⎨i(n+1)=ωVi(n)+0.5c1r1[Pbest−Xi(n)]+0.5c2r2[Gbest−Xi(n)]+

⎪⎪(10)

⎪⎪⎩

0.5c2r2[Gbest(r)−Xi(n)],Xi(n+1)=Xi(n)+Vi(n+1).󰰃󱇏0.5󱂨󱂿󰯜󰞙󰧬󱈰󱉋󱂪󰻊󱇂Pbest,Gbest󱈰󰲕󱈱󰴦󱉋󱂪󰻊󱇂Gbest󱃐󰰃󰷰󱈰󰲕󱉋󱂪󰻊󱇂Gbest(r)󱄝󰛷󰾍󰜄󰵔󱇏󰖥󱉔󱂨.

󱃐Վ󰹝󰵈,󱆌󰘓Ԯ󰹤󰧬󱈰󰲕󰷘󰙅󰵬󰧻󰽲󰩱󰖥󰚿󰣉󰙚󰙅󱄝󰣍󰭍󰖥󰻓󰽄󱇏Ф҂󰘎󰸴ԛ[16,17].󱆃󰽴󰚿󰣉󰙚󰙅󱄝҂󰹝󰧋󰾘󰖥󰻙󰸵󱇏󰷮󰘿󰟨󰖥󱂪󰵝󰵞󱂵󰷮󰱵љ󰖥.󰖒󰻙󰸵󰖥󰞂󰾏󰠢󱇏󰖞󱄝Ќ󱆣󰷘󰙅󰲆󰤅󰵬󰧻󰖥󰠎Ԥ󰴈󰸴󰴶󱂪󰟄󰷎󰘇󰵈,󰜸󰾟󰲃󱇗󱄵эӮ󰨔󱆜󰛱PSO󰷘󰙅󱇏󰖥󱁂󰛱󰜱󰡯ҕ󰶔.Ч󰻓󱂄󰳆󰾍󰖥󱈱󰵡󱂋󰜸󰾟󰲃󱇗󰜄󰵔󰳂󰵔(11)󰷮󰵕[18]:

ω⎧

(n)=⎪⎪⎨1−1A0·ΔJ2(n)+2,ΔJ(n)󰀂0,⎪⎪(11)

⎩1A0·ΔJ2(n)+2,ΔJ(n)<0.

󰰃󱇏A0󰺹󰥖󰗘󰱷󰽌󰼢󰶔,󰹝󰵈󰽋󰗧󰨔󰜸󰾟󰲃󱇗󰖥󰱼󱆴󱄝[0,1]󱆭󰡗,ѩ󱂨ս󰡎󰝦󰶔󰖥э󰟄󱆴ΔJ(n)󰦟󰾩󱆞󰜸󰾟󰲃󱇗ω(n)󰖥󱆴,󰵐󰾍󰷘󰙅󰖥󰜸󰾟󰲃󱇗󰬿󰜔󰛴󰤌󰼢󰹤󰖥ս󰡎󰝦󰶔󱉓󱈱󰵡󱂋󰗘󱆜,󰠧ս󰡎󰝦󰶔󱆴󰖥󱄹󰡆󰡼󰟶󰖝󱇁󰜸󰾟󰲃󱇗󰖥󱆴󰷛󱆭󱄹󰡆,󰙑󱆭󱁧󰲖.󱂮󱂿󱄝󰹝󰧋󱈱󰵡󱂋󰜸󰾟󰲃󱇗󰚿󰣉󰷘󰙅󱇏[19],ӈҐ󱂨Sigmod󰝦󰶔󱈱󰵡󱂋󰜸󰾟󰲃󱇗.󱆃󱇕󰙚󰙅󱁹թ󱄝󱆷󰶔󱄎󰷘󰘷󱄝󰵌󰠽󱂋󱂨󱇏󰵳󰖞󰽋󱇅.Ֆ󰠹󰷘󰚯󱄖󰘇󰙚󰫫󰙳󰼅:Sigmoid󰝦󰶔󰣉󰾛󱆷󰶔󱄎󰷘󰖥󰵈󰡗󰚯󱄖󰘇

󰖻8󰯹󰨾󰡹ӄ󰖩:󱁂󰧋󰧖󰳛󰵈э󰼢󰹤󰖥󱄝󰽌󰻭󰽋󰪝Ԋ󰽙󱂋󰩲ѯ󰭉󰥥󱇅1059

󰺹󱆷󰶔󰢨O(2N),󰰃󱇏N󰺹󰷘󰙅󰜿󰬆;󰘷󰾍󰖥󰜸󰾟󰲃󱇗󰜄󰵔󱂮󱂿󱂨󰾩󱆞󰠓󰴙󰽌󰝦󰶔ս󰸹󰨔󱆷󰶔󰝦󰶔,󰡼󰰃󰠹󰷘󰚯󱄖󰘇󰢆󰖮󰖞󰨔󰽌󰾟󰢨O(N).󱁹Վ,󱄝󰷘󰙅󰜿󰬆󰽍󰹝󰵈,󰾍󰷘󰙅󰤎󱂵󰢠󰛚󰖥󱄎󰷘󰽲󰩱.

󱂄󰳆󰾍󰖥󰜸󰾟󰲃󱇗󰝦󰶔󰞪,󰥖󰖤󰾍󰖥󱈱󰵡󱂋󰲃󱇗󰞆󱉔󰧬󱈰󰲕⎧

(AIW--CPSO)󰷘󰙅󰖥󰛷󰾍󰜄󰵔󰺹

⎪⎪⎪⎪⎪Vi(n+1)=⎪⎪⎨ω(n)Vi(n)+0.5c1r1[Pbest−Xi(n)]+

⎪⎪0.5(12)

⎪c2r2[Gbest−Xi(n)]+⎪⎪⎪⎪⎩

0.5c2r2[Gbest(r)−Xi(n)],Xi(n+1)=Xi(n)+Vi(n+1).

󱈸󰴈󰷮󰶍,󰾍󰷘󰙅󱄝󰤎С󰨔CPSO󰷘󰙅󰖥󰲆󰤅󱃐

󰤅҆󰷆󰷬󰬿󰧯󰖥󰠎Ԥ󰴈󰣉󱁂҄󰸴󰴶󰨔󰷘󰙅󰖥󱂪󰟄󰷎󰘇,󰵐󰰃󰛷󰬿󰜔󰚘󰞆󱄝󰽌я󰵍󱃐󰥥󱇅󰖥󰾳󱀱.

3

󰠎󱂿󱄝󰽌AIW--CPSO--IIR󰩲ѯ󰰖󰖥󱈱󰵡󱂋󰭉󰥥󱇅󰼢󰹤(TheadaptiveinversecontrolsystemswithonlineAIW--CPSO--IIRfilters)

󰹭2󰺹󱈱󰵡󱂋󰭉󰥥󱇅󰼢󰹤󰥿󰹭[20].Ф󰥥҂󰲒󰗧󰼢󰹤󱂮󰘓󰽠󰥿і󰵕.󰺹҂󰴾󱁂Ϯ󰾟,󰘓󰽠󰲠󰗮󱂮󰡆󰾟󱄮󰴲v(n)і󰵕.󰺹󰵌󰽃󰘓󰼢󰹤󰖥󰭉󰥥󱇅󱂋󰼢󰹤я󰵍󰠯󰶌я󰵍ԛ󰘓󰽠󰬆󰾘P

ˆ,󰵮󰼵󱀱󱂨󱈱󰵡

(z)󰹤󰖥󰗮󰷿󰽙󱂋󱄝󰽌󱈱󰵡󱂋󰗘󱆜󰥥󱇅󰰖ˆ,󰲖󰞪󰛴󰤌󰼢(z).󰹭2󱇏,󰘓󰽠󰬆󰾘ˆC

󰽃󰢺󰴕󰭉󰥥󱇅󰰖C

ˆP

(z)󰖥я󰵍󰝖ӱ󰳂󰰭󰫫󰷮󰶍,(z)󰳂󰞅󰹙󰝖󱈱󰵡󱂋󰷘󰙅󰦟󰴡󰠹.󰥥󱇅󰰖󰖥󱇶󱀱󰬢ѓ󰵞󰵐Ф󰥥󰼢󰹤󰖥Ԯ󰖾󰝦󰶔󱉋ն

ӱ󰘇󰖹󰣍󰶻󱂿󱂨󰞼󰛴󰤌󰸫󰵹󰾳󱀱󰴡󰠹󰖥ҕ󰥉󰬆󰾘M(z).ҕ󰥉󰵻󰳆󰾐󰝼r(n)󰣜ҕ󰥉󰬆󰾘󰩲ѯ󰞪󰖤󰖞󱆜󰛱󰼢󰹤󰖥󰯹󰺬󰽙󱂋ds(n).󰘷Ф󰥥󰘓󰽠󰖥󰵌󰠽󰵻ԛys(n)󱃐󰯹󰺬󰽙󱂋ds(n)󰖥ҵ󰠧󰺹󰼢󰹤󰼂ҵ󰾐󰝼,󰗧󱁬󰺹ε(n).

󰹭2󱄝󰽌󱈱󰵡󱂋󰭉󰥥󱇅󰼢󰹤󱃰󰧘󰹭

Fig.2Thestructureofonlineadaptiveinversecontrolsystem

ҕ󰥉󰬆󰾘M(z)󰥖󰹙󰝖󰞓󰘟󰹯󰣥󰴡󰠹.󰛴󰤌Ԯ󰹤󰥥󱇅󰧘󰪂,ҕ󰥉󰬆󰾘󰖥󰴡󰠹󰞄󰘓󰼢󰹤󰖥󰸫󰾟󱀱󰱰󰵞󰽍󰜱󰖥.󱁹Վ,󰺪󰺪󰡼ҕ󰥉󰬆󰾘M(z)󰴡󰠹Ӯ󱂵󰘽󰢨󰢨󱄁󰽙󱂋󰖥󰽌󰾟󰼢󰹤󱁛󰪡󱉀󰴡󰠹󰜿󰙓,󱀹󰥖󰡼ҕ󰥉

󰬆󰾘󱆰󰢤󰴡󰺹1󱁛󰵌󰽃󰼢󰹤󰖥󰵻ԛ󰘓󰵻󰳆󱆷󰨷󰾐󰝼

󰖥󰛵󱈶.

C

ˆ󱄝󰽌󰭉󰥥󱇅󰰖󰖥󰴡󰠹󰙚󰙅󰳂󰼯[21]:󰿞󰨀󰥥󱇅󰰖(z)󱁛󰖤󰖞󱉋󰽬󰖥󰼢󰹤󰤨󰙚󰼂ҵ,󰷮󱁛,󰵮󰼵󰗧󱁬󰼢󰹤󰖥ս󰡎󰝦󰶔󰺹

Js(n)=E[󰀆ε(n)󰀆2

].

(13)

󰛴󰤌󰼢󰹤󱃰󰧘󰹭,󰖒ս󰡎󰝦󰶔󱉋󰽬󰵈,󰧘󰽘󰭉󰥥󱇅󰰖󰖥Wiener󰢳󱂋󰺹

Cˆ(z)=M(z)Pˆ(z)=M(z)·Pˆ1(z).(14)

󱂮󰜄󰵔(14)󰥖󱆩,󰧘󰽘󰖥󰥥󱇅󰰖󰬆󰾘󰥖󰥁󱉔ҕ󰥉󰬆

󰾘󱃐󰘓󰽠󰭉󰬆󰾘󰖥󰠒.󰖌󰵞󰵌󰠽󰴈󰵌󰽃.󱃰󱁹󱆭󱁂󱄝󱂿󰥥󱇅󰰖C

ˆ,󱆃󰛱󰢳󰺪󰺪󰬴󱁛

(z)҂󰵞󰻭󱃿󰶏󰖥,󰘷󰵞󱀱󰱰󰻗󰗧󰵬󰧻󰖥.󱁂Ϯ󰱦󰦃󰼯,ҕ󰥉󰬆󰾘󰪡󱉀󱆃

󰛱󰹈󰡱,󰖌󰘓󱂿󰘓󰽠󰬆󰾘P

ˆ(z)󰘷󰿽,я󰵍󰝖ӱ󱆺󰬿Ќ󱆣󰰃󰻗󰗧,󰖌ѩ҂󰬿Ќ󱆣󰰃󰭉󰬆󰾘󰻗󰗧󰱏󰵬󰧻.󱁹Վ,󰺪󰺪󰾳󱀱󰵐󱂨󰨶󱁂󰛱󱈱󰵡󱂋󰝖ӱ󰱰󰖤󰼢󰹤󰖥󰭉

󰥥󱇅󰰖ˆ(z).󰼯󰫫󰵞󰹙󰝖AIW--CPSO󰱰󰱼C

ˆC

--IIR󰩲ѯ󰷘󰙅(z)󰖥󰝖ӱ.󰴡󰭉󰥥󱇅󰰖󰬆󰾘󰺹C(z)=

Ac(z)

1−Bc(z),

(15)

󰰃󱇏:Az)󰞄B󰀁Pc(c(z)󰙳љі󰵕󰺹Ac(z)=i=0

aicz−i

󰞄Bc(z)=

󰀁

Qi=1

bicz−i.󰥥󱇅󰰖󰖥󰞆Ӯ󰲃󰽟󰨈wˆC(n)󰥖

󱂮{aic(n)}Pi=0󰞄{bic(n)}Q

i=0󰧳󰞆і󰵕󰳂󰼯:

wˆC(n)=[a0c(n)a1c(n)···aPc(n)

b1c(n)b2c(n)···bQc(n)]T.(16)

󰖒󰼢󰹤󰖥ս󰡎󰝦󰶔󱉋󰽬󰟄󰞪,󱈱󰵡󱂋IIR󰩲ѯ󰰖ҕ󰶔󰠧󰥖󱉔󰺹󱆜󰛱󰻃󱆩󰼢󰹤󰖥󱉋󱂪󰭉󰥥󱇅󰰖ҕ󰶔,ѩ󰛴󰤌󰘓󰽠ҕ󰶔󰖥󰵌󰵈э󰟄󰣉󰾛󱄝󰽌󱈱󰵡󱂋я󰵍.󰺹󰣉󱁂҄󰫭󰶍󱈱󰵡󱂋󰭉󰥥󱇅󰼢󰹤󱇏AIW--CPSO--IIR󰩲ѯ󰰖󰖥󰿐󰼝󰝖ӱ,󰽃󰛳ԛ󰼢󰹤󰖥󰛽󱉔҄󱇧󰳂󰼯:

҄󱇧1Ԛ󰵓󰟄󰧬󱈰󰲕,󰛳ԛ󱇕󰲕󰜿󰬆N,󰴡󰗧󰧬󱈰󰺻󰶔,Ԛ󰵓󰜸󰾟󰲃󱇗,󰷛󰠏󰴳Ӯ󰧬󱈰󰖥Ԛ󰵓󰻊󱇂Xi󱃐󰷎󰘇Vi.

҄󱇧2󰠹󰷘󰫄󰛱󰧬󱈰󰖒󰰭󰖥󰵡󱂋󱆴,󰠧󰧬󱈰xi󰖥󰵡󱂋󱆴f(xi),ѩ󰲒󰗧Ԛ󰵓󰖥Pbest󰞄Gbest.

҄󱇧3󰛷󰾍󰧬󱈰Ч󰖹󱉋󱂪󰢳Pbest,󰠧󰳂󰝔f(xi)҄󱇧4󰛷󰾍󰧬󱈰󰲕󱉋󱂪󰢳Gbest,󰠧󰳂󰝔f(xi)҄󱇧5󰷛󰠏Ӂ󰴳1󰖞N󱇏󰖥󰷛󰠏󱆜󰶔r.҄󱇧6

󰛴󰤌󰜄󰵔(11)󰛷󰾍󰜸󰾟󰲃󱇗ω(n).

1060󰥥󱇅󰧘󰪂󱃐󱂋󱂨󰖻28󰤜

҄󱇧7󰛴󰤌󰜄󰵔(12)󰠹󰷘󰧬󱈰󰷎󰘇Vi󱃐󰻊󱇂

Xi.

҄󱇧8󰿖󰟌󱇀҄󱇧2󱆰󰖞󰗝սՑ󰶔ղ󰖞󰗝ս󰴈󰽋󰠇󱆀󰼢󰹤󰪡󱉀󱉋󰽬󰼂ҵѓ󱈙,Վ󰵈󱂵󱉋󱂪󰵡󱂋󰘇󰖥󰧬󱈰󰷮󱄝󰻊󱇂Xi󰠧󰺹󰣍󰶻󱉋󱂪󰢳.

󱆴󰖤󱇿󱁩󰖥󰵞IIR󰩲ѯ󰰖󰖥󱄝󰽌󰻃󱆩󰘓󰽠я󰵍󱃐󰥥󱇅󰰖я󰵍󰖥󰱵љ󱄝󱂿󰵡󱂋󰘇󰝦󰶔f(xi)󰖥󰿊󱄴:󰘓󱂿󱄝󰽌󰘓󰽠я󰵍󰘷󰿽,󰵡󱂋󰘇󰖥󰿊󰱼󱂋󰺹󰘓󰽠󰬆󰾘󰼂ҵe(n);󰘷󰘓󱂿󰥥󱇅󰰖я󰵍,󰰃󰵡󱂋󰘇󰝦󰶔󱄵󱂋󰱼󰺹󰼢󰹤󰼂ҵε(n).

4󰙟󱆇󰙳󰼅(Simulationanalysis)

󰺹󰡟󱀒AIW--CPSO--IIR󰩲ѯ󰰖󱄝󰽌󰾟󰧖󰳛󱈱󰵡󱂋󰭉󰥥󱇅󰼢󰹤󱇏󰖥󰾟󰬿,󰽃󰱼󰻃󱆩󰵈э󰼢󰹤󰖥󰺱󰙳󰙚ӱ󰳂󰼯:

y(n+1)=0.7y(n)−p(n)·y(n−1)+

q(n)·u(n)+0.5u(n−1).

(17)

󰚾󰬆󰾘󱇏,p(n),q(n)󰙳љ󰺹րя󰵍󰖥󱂵󰢸󰵈эҕ󰶔,󰱏󰙳љ󰱼󰵈э󰝦󰶔󰺹:

p(n)=sin(0.05n),

(18)q(n)=(1−n)/(100+n)+0.5.

(19)

ҕ󰥉󰬆󰾘󰺹󰗧ӈ󰼢󰹤,󰰃ҵ󰙳󰙚ӱ󰺹

y(n+1)=0.7y(n)−0.1y(n−1)+

u(n)+0.5u(n−1).

(20)

󰙟󱆇󰵌󱀒󰖥󰳈󰡱󰟌󰣢󰺹MATLAB7.8.0(R2009a)ϱЧ󰼯󰖥Simulink󰙟󱆇󰯜󰷻,Ҡ󱉔󰼢󰹤󰺹Windows7Professional,PC󰠏󰮥󱇂󰺹Intel(R)Core(TM)2.53GHz,2G󰬽թ.󱂮󰹭2󰷮󰵕󰖥󱃰󰧘󰥿󰹭󰣉󰾛󰙟󱆇󰵌󱀒,󰘓󰽠я󰵍󱃐󰭉󰥥󱇅󰰖󱄝󰽌󰗘󱆜󰤨Ґ󱂨Ч󰻓󰷮󰸴ԛ󰖥AIW--CPSO--IIR󰩲ѯ󰷘󰙅,󰵻󰳆󰾐󰝼󰱼󰷛󰠏󰾐󰝼,Ґ󱀢󱇛󰯹0.1s,ѩ󰙳љҐ󱀢500Ց󱁛Ќ󱆣󰵬󰧻󰽲󰝔.

󰺹󰘓бAIW--CPSO󰷘󰙅󱃐󰰃󰷰󰹝󰧋󰷘󰙅󰖥󰾟󰬿,󱄝󰵈э󰼢󰹤󰖥󰡹󰬆󰢨󰘍,󰹝󰵈Ґ󱂨AIW--CPSO󰞄CPSO󰨆󱇕󰷘󰙅󰴡󰠹IIR󰩲ѯ󰰖ѩ󰣉󰾛󰻃󱆩󰵈э󰼢󰹤󰖥󰡹󰬆.󰺹Ќ󱆣󰙟󱆇󰢲󰝔󰖥󰥖б󰾟,CPSO--IIR󰩲ѯ󰰖󰖥󰲆҆ҕ󰶔󰤨󱃐AIW--CPSO--IIR󰩲ѯ󰰖󰖥󰴡󰗧󰽍󰹝:󱇕󰲕󰶔󰨈PopSize=25;󰱷󰽌󰼢󰶔A0=2;󰡆󰷎󰼢󰶔c1=c2=2;IIR󰩲ѯ󰰖󰨬󰗄󰛱󰶔P=5;󰠞󰗄󰛱󰶔Q=5.󰷮҂󰹝󰖥󰵞CPSO--IIR󰩲ѯ󰰖󰖥󰜸󰾟󰲃󱇗󰴡󰺹ω=0.35;AIW--CPSO--IIR󰩲ѯ󰰖󰖥Ԛ󰵓󰜸󰾟󰲃󱇗󰴡󰺹ω(0)=0.35.

󰹙󰝖󰙟󱆇󰵌󱀒󰡟ҩAIW--CPSO󰷘󰙅󰘓󱂿󰵈эҕ󰶔󰖥я󰵍󰽲󰝔,󰖤ԛAIW--CPSO--IIR󰩲ѯ󰰖󰘓󱂿󰵈эҕ󰶔p(n)󰞄q(n)󰖥󱄝󰽌я󰵍󰛵󱈶󰱷󰽌󰳂󰹭3(a)(b)󰷮󰵕.

(a)󰵈эҕ󰶔p(n)

(b)󰵈эҕ󰶔q(n)

󰹭3󰵈эҕ󰶔󱄝󰽌я󰵍󰛵󱈶󰱷󰽌

Fig.3Thereal-timetrackingcurvesforonlinetime-varying

parameteridentification

󰨆󱇕҂󰹝󰖥󰩲ѯ󰰖󰘓󱂿󱆜󰸸󰵈э󰼢󰹤󰖥󱄝󰽌я󰵍󰛵󱈶󰝅󰠖󰳂󰹭4(a)(b)󰷮󰵕.󰡹󰬆󰝖ӱ󰖥󰤨󰙚󰼂ҵ󰱷󰽌󰳂󰹭5(a)(b)󰷮󰵕.

(a)CPSO-IIR󰩲ѯ󰰖

(b)AIW--CPSO--IIR󰩲ѯ󰰖

󰹭4󰻃󱆩󰵈э󰼢󰹤󱄝󰽌я󰵍󰵻ԛ󰱷󰽌

Fig.4Theoutputcurvesofonlineidentificationfor

unknowntime-varyingsystem

(a)CPSO-IIR󰩲ѯ󰰖

󰖻8󰯹󰨾󰡹ӄ󰖩:󱁂󰧋󰧖󰳛󰵈э󰼢󰹤󰖥󱄝󰽌󰻭󰽋󰪝Ԋ󰽙󱂋󰩲ѯ󰭉󰥥󱇅1061

(b)AIW--CPSO--IIR󰩲ѯ󰰖󰹭5󰗝ս󰝖ӱ󰖥󰤨󰙚󰼂ҵ󰱷󰽌

Fig.5Themean-squareerrorcurveofiterationprocessing

Ֆ󰙟󱆇󰢲󰝔󰥖󱁛󰥁ԛ,AIW--CPSO--IIR󰩲ѯ󰰖󰘓󱂿󰵈эҕ󰶔p(n)󰞄q(n)󰤎󱂵󰢠󰥹󰷎󰖥󰛵󱈶я󰵍󰬿󰧯.󰹝󰵈󰽍бCPSO--IIR󰩲ѯ󰰖󰘷󰿽,AIW--CPSO--IIR󰩲ѯ󰰖󰘓󱂿󱆜󰸸󰵈э󰼢󰹤󰖥я󰵍󰽲󰝔󱁛󰠣󰤨󰙚󰼂ҵ󱀹󰨷󰲦󰪡󱁩.

󱄝Վ󰠎Ԥ󰴈,󰛴󰤌󰹭2ձ󰡹󱄝󰽌󱈱󰵡󱂋󰭉󰥥󱇅󰼢󰹤ѩ󰡟󱀒󰚾󰧖󰳛󰵈э󰼢󰹤󰘓󰷛󰠏󰾐󰝼󰖥󰛵󱈶󰬿󰧯.󰲯󰱼󰵻󰳆󱆷󰨷󰾐󰝼󰺹󱂵󱁂󰗧󰽋󰚖󰖥󰷛󰠏󰹋э󰾐󰝼,Ґ󱀢󱇛󰯹󰺹0.1s.ҕ󰥉󰬆󰾘󰖥ҵ󰙳󰙚ӱ󰳂󰜄󰵔(20)󰷮󰵕.󰥥󱇅󰼢󰹤󰖥󰙟󱆇󰝖ӱ󰡼AIW--CPSO--IIR󰩲ѯ󰰖󱃐󰴪󰣜󰺩󰪎󰣉󰾛󰘓б.󰰃󱇏AIW--CPSO--IIR󰩲ѯ󰰖󰖥ҕ󰶔󰴡󰗧҂э,󰴪󰣜󰺩󰪎󰿊󰱼󰥥󱇅󰼢󰹤󱇏ӈ󱂨󰖥3ҪBP󰺩󰪎󰢲󰜒,󰛴󰤌󰣜󱀒󰿊󰱼6󰛱󱂅Ҫ󰢫󰗄,󰾟󰬿󱆷ѓ󰴡󰗧󰺹1.0×10−5,󱉋ն󰗝սՑ󰶔󰴡󰗧󰺹2000Ց,󱂅Ҫ󰖥Ԯ󰖾󰝦󰶔Ґ󱂨Sigmoid󰝦󰶔,󰵻ԛҪ󰖥Ԯ󰖾󰝦󰶔Ґ󱂨󰽌󰾟󰝦󰶔.󰺩󰪎󰿞󰨀Ґ󱂨󰵬󰧻󰷎󰘇󰢠󰥹󰖥Levenberg-Marquardt󰷘󰙅,󰴪󰣜󰺩󰪎󰹝󰵈󱉔󰺹󰵈э󰼢󰹤󰖥я󰵍󰰖󰠣󰭉󰥥󱇅󰰖.󰙟󱆇󰖤ԛ󰨆󱇕󰵈э󰼢󰹤󰖥󰽙󱂋󰱷󰽌󱃐󰛵󱈶󰼂ҵ󰱷󰽌󰙳љ󰳂󰹭6(a)(b)󰞄󰹭7(a)(b)󰷮󰵕.

(a)BP󰴪󰣜󰺩󰪎

(b)AIW--CPSO--IIR󰩲ѯ󰰖

󰹭6󰵈э󰼢󰹤󰖥󱄝󰽌󰭉󰥥󱇅󰵻ԛ󰱷󰽌

Fig.6Theoutputcurvesofonlineinversecontrolfor

time-varyingsystem

(a)BP󰴪󰣜󰺩󰪎

(b)AIW--CPSO--IIR󰩲ѯ󰰖

󰹭7󰵈э󰼢󰹤󱄝󰽌󰭉󰥥󱇅󰖥󰛵󱈶󰼂ҵ󰱷󰽌

Fig.7Thetrackingerrorcurveofonlineinversecontrolfor

time-varyingsystem

Ֆ󰵌󰠽󰖥󰙟󱆇󰢲󰝔󰥖󱁛󰥁ԛ,󰠧󰵐󰘓󱂿󰷛󰠏󰵈э󰖥󱆷󰨷󰵻󰳆󰾐󰝼,󱃐BP󰴪󰣜󰺩󰪎󰽍бAIW--CPSO--IIR󰩲ѯ󰰖󱀹󰥖󱁛󰢠󰝺󰖹󰵌󰽃󰘓ҕ󰥉󰬆󰾘󰵻ԛ󰖥󰵌󰵈󰛵󱈶.󱆴󰖤󱇿󱁩󰖥󰵞,󰖒ҕ󰥉󰬆󰾘󰵻ԛds(n)ԛ󰽃󰢠ն󰚖󰘇󰖥󰹋э󰵈,󰼢󰹤󰖥󰵻ԛ󰽙󱂋󰟶󰶧󰵈󱃐ds(n)󰾙Ӯ󱁂󰗧󰖥󰼂ҵ,󱆃󰵞󰠫󰞬󰷮󱂵󰖥󰗮󰷿󰼢󰹤󱄝󰛵󱈶󰝖ӱ󱇏󰗻󰟶󱃛󰖞󰖥󰽃󰽠,󰖌󰘓б󰹭6󰱷󰽌,BP󰴪󰣜󰺩󰪎󰽁󰲖󰘓󱆃󱇕󰶧󰵈󰼂ҵ󰖥󰙑󱂋󰫀󱂵AIW--CPSO--IIR󰩲ѯ󰰖і󰽃󰖥󰫹󰛋.󰷛󱈢󰥥󱇅󰰖󰖥󰵌󰵈󱄝󰽌󰗘󰢫,AIW--CPSO--IIR󰩲ѯ󰰖󰖥󰛵󱈶󰼂ҵ󰟶󱄝󰘋󰵈󰡗󰬽󰢆󰖮󰖞󰞓󰽬󰖥󰙓󰺶󰬽,󰵐󱆜󰛱󱈱󰵡󱂋󰭉󰥥󱇅󰼢󰹤󰖥󰵻ԛ󰥹󰷎󰵌󰽃󰘓ҕ󰥉󰬆󰾘󰵻ԛ󰾐󰝼ds(n)󰖥󰛵󱈶.

󱂮Վ󰥖󰖤,Ч󰻓󰷮󰴡󰠹󰖥AIW--CPSO--IIR󰩲ѯ󰰖󱄝ԩ󰧘󰵈э󰼢󰹤󰖥󱄝󰽌󰭉󰥥󱇅󰻙󰸵󰴈󰖥і󰽃󱀱󱂪󱂿ӈ󱂨󰖥BP󰴪󰣜󰺩󰪎,󰬿󰜔󰚘󰞆󱈱󰵡󱂋󰭉󰥥󱇅󰼢󰹤󰖥󱄝󰽌󰿞󰨀󱀱󰱰,ѩ󰥖󱁛󰵌󰽃󰘓󱁂󰧋ҕ󰶔󰻃󱆩󰵈э󰖥󰧖󰳛󰼢󰹤󰖥󱄝󰽌󰛵󱈶󰥥󱇅.

5󰢲󰪂(Conclusion)

Ч󰻓󱆌󰘓󱁂󰧋ҕ󰶔󰻃󱆩󰵈э󰖥󰧖󰳛󰼢󰹤,󰸴ԛ󱁂󱇕󰾍󰖥󱄝󰽌AIW--CPSO--IIR󰩲ѯ󰭉󰥥󱇅󰙚󰙅.󱈱󰵡󱂋󰭉󰥥󱇅Ҧ󰩻󰥖󱁛󱈱󰗮󰛵󱈶󰘓󰽠󰖥󰗮󰷿э󰟄󰘷҂󰾳󱀱󰘓󰥥󱇅󰰖󰞄Ф󰥥󰘓󰽠󱉓󰿸󰛬󰖥󱀱󰱰󱃐󰽋󱇅,󱁹Վ󰪡󱉀󰨔ҕ󰶔󰵈э󰼢󰹤󰖥󰾳󱀱.󰘷IIR󰩲ѯ󰰖󱄵󰥖󱁛󰵌󰽃󰨬󰠞󰗄󰖥󰲆󰯄󰮥я󰵍,󰥘󰚛󰨔Ԯ󰹤FIR󰩲ѯ󰰖󱄝󰽌я󰵍󰵈󱂮󰽍󰜱󰤇󱆔󰸫󱆘󱆴э󰟄󱂄󰰏󰖥󰲃󰽟󰨈эӉ󰖥󰻙󰸵.󰹝󰵈,Ч󰻓󰴡󰠹ԛ󰾍󰖥AIW--CPSO󰷘󰙅󱂨󰦟󱂪󰟄IIR󰩲ѯ󰰖ҕ󰶔.󰚾󰙚󰙅󰠻󰥖󱁛х󰫧Ԯ󰹤PSO󰷘󰙅󰽊󰳆󰤅҆󰠞󰽬󱆴,󱂻󰬿󰜔󰥹󰷎я󰵍󰩲ѯ󰰖ҕ󰶔,󰵌󰽃󰵈э󰼢󰹤󰖥󱄝󰽌󰛵󱈶.󰙟󱆇󰙳󰼅󱄵і

1062󰥥󱇅󰧘󰪂󱃐󱂋󱂨󰖻28󰤜

󰫼,󰠎󱂿AIW--CPSO--IIR󰩲ѯ󰰖󰖥󱈱󰵡󱂋󰭉󰥥󱇅󰼢󰹤,󰘓󱂿󱁂󰧋ҕ󰶔󰵈э󰖥󰧖󰳛󰼢󰹤󰤎󱂵󰞓󰝺󰖥󰡹󰬆󰬿󰧯ѩ󰥖󱁛󰵐󱆜󰛱󰥥󱇅󰼢󰹤󰖥󰵻ԛ󰥹󰷎󱂵󰽲󰖹󰛵󱈶󱆷󰨷󰵻󰳆,󱂵󱈢󰨷󰲦󰪡󱁩󰖥󰥥󱇅󰽲󰝔.

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󱉔󱆀󰡥󰢺:

󰨾󰡹ӄ

(1960—),󰬳,󰢝󰵱,Ѱ󰵖󰴳󰖝󰴽,󰬢󰰭󰿹󰣮󰙚󰽟󰺹󱇆󰬿

󰥥󱇅a󰚯󱄖󰝖ӱ󰡹󰬆a󰥥󱇅󱃐󱂪󰟄,E-mail:liujianchang@ise.neu.edu.cn;

󱂿

󰼩

(1982—),󰭯,Ѱ󰵖󰿹󰣮󰴳,󰬢󰰭󰿹󰣮󰙚󰽟󰺹󱈱󰵡󱂋󰾐

󰝼ԩ󰧘a󱇆󰬿󰥥󱇅,E-mail:yuxia.neu@gmail.com;

󰧙󰞟󰳀

(1968—),󰬳,󰢝󰵱,󰬢󰰭󰿹󰣮󰙚󰽟󰺹󱇆󰬿󰥥󱇅a󰚯󱄖󰼢

󰹤󰡹󰬆󱃐󱂪󰟄,E-mail:lihongru@ise.neu.edu.cn.