一种基于模糊控制的两步法预测控制方法

14720107ELECTRICMACHINESANDCONTROLVol.14No.7July2010150080。。νu、Hammerstein。。HammersteinTP273A1007－449X201007－0075－06Researchmethodonatwo-stepgeneralpredictivecontrolbasedonfuzzycontrolWUJun-fengWANGShi-mingAutomaticInstituteHarbinUniversityofScienceandTechnologyHarbin150080ChinaAbstractApplicationsofpredictivecontrolforindustryareoftenlimitedtolinearsystemsandaremis-functionedonthevastmajorityofnon-linearsystemswhichcannotrealizetrackingdesiredsystemout-puts．Inordertorealizethatrealoutputvaluesofnonlinearsystemscanfollowthedesiredoutputvaluesthispaperconductedaresearchbyatwo-stepmethodofpredictivecontrolonnonlinearsystemsbasedonfuzzycontroldesignsedthecorrespondentfuzzyrulesconfirmedthefuzzyinputsandoutputsaswellasthemembershipfunctionandsetupthefuzzycontrolleraccordingtothecorrelationbetweentheinterme-diatevariablesvsolvedbypredictivecontrolmethodandtherealcontrolvariablesuimpactingonplantsformakingtheoutputvaluesfollowthedesiredoneswhichsolvedtheproblemthatitmaybehardtogetthesolutionsfortherealcontrolvariablesbecauseofitsuncertaintywhenapplyingtheHammersteinmodel．Meanwhileitillustratestherightnessandvalidityforapplyingthealgorithmofgeneralpredictivecontrolthroughsimulationexamples．Keywordstwo-steppredictivecontrolfuzzycontrolHammersteinmodelnon-linearsystemgeneralpredictivecontrol2009－10－1550975068200602140042009RFXXG0322009RFXXG0321959—、1984—。0。。two-stepmethodofpre-dictivecontrolTSMPCHammerstein。1。1－2。。Hammerstein。1generalpredictivecontrolGPC。、、。、3。GPCyk+i|k=M～iq－1Δuk+i－1|k+Hiq－1Δuk+Fiq－1ykM～iq－1=mi0+mi1q－1+…+mii－1q－i－1Hiq－1=hi1+hi2q－1+…+hinbq－nbFiq－1=fi0+fi1q－1+…+finaq－na。1q－1l=1－q－1M～iHiFi。kJk=E珓yk|k－ω→kT珓yk|k－ω→k+Δ珘uk|kλΔ珘uk|k2ω→k。2JkΔ珘uk|kΔ珘uk|k=dTω→k－Fz－1yk－Hz－1Δuk。34－5uk=uk－1+Δ珘uk|k4uk=uk－1+dTω→k－Fz－1yk－Hz－1Δuk。5dT=GTG+λI－1GT6G=g10…0g2g10gNugNu－1…g1gNgN－1…gN－Nu+17gij。2Hammerstein2.1HammersteinVolterrayt=∫t0g1τut－τdτ+∫t0∫t0g2τ1τ2ut－τ1ut－τ2dτ1dτ2+g3…+…8giτ1τ2…τiVolterray=fu1u2…un。Volterra。。5Hammerstein。Hammerstein1。6714淄（t）NLu（t）Ly（t）1HammersteinFig．1StructureofHammersteinmodal1NLνt=b1ut+b2u2t+…+bnunt。91Lyt=∫Ts0gτνt－τdτ10Tsgτ。Hammersteinyt=∫Ts0gτb1ut－τ+b2u2t－τ+…+bnunt－τdτ。1111Hammerstein4yk=k0+B1z－1Az－1uk－d+…+BPz－1Az－1uPk－d+Cz－1Az－1εk12Az－1=1+a1z－1+…+anz－nB1z－1=b10+b11z－1+…+b1nz－nBPz－1=bP0+bP1z－1+…+bPnz－nCz－1=1+c1z－1+…+cnz－n。132.2HammersteinHammerstein。νk=fukf0=014uν1。az－1yk=bz－1νk－115yaz－1=1+a1z－1+…+anz－nbz－1=b0+b1z－1+…+bnz－nab。Hammerstein。。Jk=∑N2i=N1yk+i|k－ysk+i2+∑Nuj=1λΔν2k+j－1|k16ysk+i。35Δνk=dTω－f←17ωf←。νk=νk－1+Δνk18。νkykω。ukfuk－νk=0。19uk=gνk。20206－10。33.1νuu。2。棕dTM1l淄-dTH-dTFF-1uB（z-1）A（z-1）y模糊控制器被控对象2HammersteinFig．2SchematicdiagramofgeneralizedpredictivecontrolofHammersteincombinedwithfuzzycontroller。1112777ννyu。ΔνΔu。3νuΔνΔu。ΔνΔuΔνΔu。3210-1-2-3驻u/驻淄0%%%%%%%%%%%%%%%%50%%%%%%%%%%%%%%100%%%%%%%%%%%%%150%%%%%%%%%%%%%200%%%%%%%%%%%%%250%%%%%%%%%%%%%300中间控制增量驻淄实际作用控制增量驻ut/%s（a）中间控制增量与实际作用控制增量对比图3210-1-2-3u/驻淄0%%%%%%%%%%%%%%%%50%%%%%%%%%%%%%%100%%%%%%%%%%%%%150%%%%%%%%%%%%%200%%%%%%%%%%%%%250%%%%%%%%%%%%%300t/%s（b）中间控制增量与实际作用控制增量对比图实际作用控制量u中间控制增量驻淄3ΔvΔuFig．3Comparativeanalysisdiagramanalyzingtherela-tionshipbetweenthecontrolincrementsΔvandΔuaswellastherelationshipbetweenthecontrolvar-iablesvkanduk2ΔνΔuGAUSS。3ΔνΔu。ΔνX=－4－3－2－101234NSBNBNMNSZPSPMPBPSB“－3”－2－24。ΔuY=－2－1012NBNSZEPSPB“－1”－10.25。NSBNBNMNSZPSPMPBPSB隶属度输入变量驻ν4ΔνFig．4FuzzycontrollerinputmembershipfunctiondiagramNBNSZEPSPB隶属度输入变量驻u5ΔuFig．5Fuzzycontrolleroutputmembershipfunctiondiagram33ΔνΔuaifVisNSBthenUisNB1bifVisNBthenUisNS1cifVisNMthenUisNS1difVisNSthenUisNS1eifVisZthenUisZE0.65fifVisPSthenUisPS1gifVisPMthenUisPB0.65hifVisPBthenUisPB1iifVisPSBthenUisPB1ΔνΔuΔu。e“”0.65。ΔνΔu。Δν2.2ΔuuνyyΔu8714Δu。Δuu。3.21HammersteinHammerstein。4。2。3ΔνΔuHammerstein。4u。。44.1ⅠⅠyk=yk－11+yk－12+uk－2。ykyk=ayk－1+buk－2。Hammersteinukyk。a=0.5003b=0.5101。4。。P=5M=2h=0.612。3.1453.1Δuu。ΔuΔν6。0.80.60.40.20-0.2-0.4-0.6-0.8驻u-2%%-1.5%%%%-1%%-0.5%%%%%0%%%%%0.5%%%%%1%%%%%1.5%%%%%2驻淄6ΔuΔvFig．6FuzzyrelationshipdiagrambetweenΔuandΔvuy。7。t/%s2.521.510.50y0%%%%%%%%%%%50%%%%%%%%%100%%%%%%%%%150%%%%%%%%200%%%%%%%%250%%%%%%%%300期望输出值F-TSGPC控制输出值7Fig．7Thecharacteristiccurveoffollowingthedesiredoutputsvalues1805。977。。4.2ⅡⅡyk=yk－1+yk－21+y2k－1+y2k－2+u2k－2。3.2。yk=ayk－1－byk－2+cuk－2。a=0.1955b=0.1896c=0.3589。8。2.521.510.50y0%%%%%%%%%%%50%%%%%%%%%100%%%%%%%%%150%%%%%%%%200%%%%%%%%250%%%%%%%%300t/%s期望输出值F-TSGPC控制输出值8Fig．8Thecharacteristiccurveoffollowingthedesiredoutputvalues。。。5Hammerstein。。1．M．2008．2．J．2006214457－461．NIUYongxiaoDINGBaocangSUNHexu．Robuststabilityoftwo-steppredictivecontrolforsystemswithinputnonlinearitiesJ．ControlandDecision2006214457－461．3．M．1993．4．M．1984．5．HammersteinJ．200318124－28．DINGBaocangLIShaoyuan．DesignandanalysisofHammersteinnonlinearcontrolsystemswithconstraintsJ．ControlandDeci-sion200318124－28．6．HammersteinJ．200824486－88．QIANJieQUANLiHUZijian．StudyonnonlinearpredictivecontrolofHammersteinmodelsJ．Control＆Automation200824486－88．7．M．1998．8．J．2004306954－960．DINGBaocangXIYugeng．Designandanalysisofthedomainofattractionforgenera