外文翻译-iterative sliding mode control（pag4—6）

本科毕业设计（论文）外文翻译专业电子信息工程所在学院电子信息工程学院二零一二年六月ITERATIVESLIDINGMODECONTROL（PAG46）BYTHESEASSUMPTIONS,WOULDREMAINLIPSCHITZFFNOWTOEVALUATETHEROBUSTNESSOFTHEPERTURBEDSYSTEM,2,THEROBUSTNESSALGORITHMISSUGGESTEDASFOLLOWSSTEP1OBTAINTHECONTROLLERGAIN,K,FROMTHEFOLLOWINGRELATIONDQKTXGIM,WHEREMISTHELIPSCHITZCONDITIONNUMBERFORTHEFUNCTION,ANDISADESIREDFDQNEGATIVEDEFINITEMATRIXCHOSENBYTHEDESIGNERSTEP2IMPLEMENTTHEGAINOFTHECONTROLLEROBTAINEDFROMTHEPREVIOUSSTAGETOTHESAMERELATIONASMENTIONEDINSTEP1BUTINAPERTURBEDMANNERTHEREFORETHEFOLLOWINGRELATIONISACHIEVEDDQKTXGIM,WHEREISTHELIPSCHITZCONDITIONNUMBERFOR,ISDERIVEDFROM“G”WHENITFGISPERTURBEDANDISADESIREDNEGATIVEDEFINITEMATRIXBYEXPANDINGTHEABOVEDRELATION,THEFOLLOWINGRELATIONSAREACHIEVED；DNNQKGTXIM,；NIDKG；IQND；KTX,；QACCORDINGTOTHEABOVEACHIEVEDRELATIONS,THEMATRIX,ISCONSTRUCTEDFROMTHEQDESIREDMATRIX,ANDOTHERTERMSASGIVENINTHEABOVERELATIONSNOTICETHATISDDQCHOSENBYADESIGNERBYDESIGNINGTHECONTROLLERIN3,THESYSTEM2WILLHAVEROBUSTNESSWITHRESPECTTOPERTURBATIONOFANDG,WHENTHEGAINOFTHECONTROLLERISOBTAINEDFROMFTHERELATIONINSTEP1INWHICHISSELECTEDLESSTHAN,WHERETHEDQDQMATRIXHASADESIREDFREENEGATIVEDEFINITEMATRIXKGIQNDDWHICHCANBECHOSENTOSATISFYTHEFOLLOWINGRELATION,TESTA5THECONVERGENCECONDITIONOFTHEMENTIONEDILCMETHODINTHENEWCASECANBEACHIEVEDASGIGINN1INMAXGNREMARKA2ROBUSTNESSWITHRESPECTTOLIPSCHITZCONDITIONNUMBERALTHOUGHOURPROPOSEDCONTROLLERISDERIVEDACCORDINGTORELATIONS3AND4,ANDTHELIPSCHITZCONDITIONNUMBERISIMPORTANTINTHISPROCESS,IFTHEDESIGNERSELECTSTHISNUMBERINCORRECTLY,SUCHASWHEREM,THISMETHODISSTILLRELIABLEIFLIESINTHEFOLLOWINGRANGETESTA4,SUPXTFMREMARKA3SELECTINGTHEDESIREDMATRIXSELECTINGTHEMATRIXDIRECTLYDQDQAFFECTSTHEPERFORMANCEOFTHECLOSEDLOOPRESPONSEINOTHERWORDS,APPEARSINTHEDERIVATIVEOFTHELYAPUNOVFUNCTIONANDIFITISSELECTEDSMALLER,THISMEANSTHATTHEDERIVATIVEOFTHELYAPUNOVFUNCTIONWILLBEMORENEGATIVEANDTHISFORCESTHEABOVEMENTIONEDFUNCTIONTOREACHTHEORIGINFASTERANDVICEVERSATESTA2REMARKA4FORGETTINGFACTORTHEFORGETTINGFACTORENABLESTHEDESIGNERTOCONTROLTHESPEEDOFTHERESPONSEDURINGVARIATIONOFTHESYSTEMACCORDINGTOPREVIOUSREMARK,BYASUITABLESELECTIONOFATTHEBEGINNINGDQOFTHEPROCESS,THEDESIGNERCANPERFORMTHEMENTIONEDTASKONLYONCE,BUTBYUSINGAFORGETTINGFACTORASADECREASINGTERMOFTHEFORM1EXPT/TWHERETREPRESENTSTHETIMEANDTISTHETOTALTIMEOFTHEPROCESS,THERATEOFDESCENTOFTHELYAPUNOVFUNCTIONCANBEADJUSTED,SOTHATTHESPEEDOFSTATESREACHINGTHEORIGINISCONTROLLABLEDURINGTHEPROCESSRUNTIMETESTA3REMARKA5SLIDINGSURFACEFROMTHEVIEWPOINTOFSLIDINGMODECONTROL,THESLIDINGSURFACEISKNOWNASASPECIALCASEOFTHELYAPUNOVSURFACEBYUSINGOURPROPOSEDALGORITHM,ONECANCLAIMTHATASUITABLESLIDINGSURFACECANBEOBTAINEDCONSIDERTHEFOLLOWINGRELATIONS,CXYNC,10ITNXX,1WHERETHESARESELECTEDINSUCHAWAYTHATCXISAHURWITZPOLYNOMIALICBYDEFINING“V”ASALYAPUNOVFUNCTIONANDFOLLOWINGTHEPROCEDUREBELOW,WEWILLHAVEXCCXYVTTTT21GUFGUFXXCGKMIXCGKMXVTTTTICQDIF,BYADJUSTINGTHEKMATRIX,WEMAKENEGATIVE,THENBASEDONTHELYAPUNOVVTHEOREMYMOVESTOTHEORIGINANDCX0SO,OR01NXC01121NXCXCBECAUSEYISHURWITZ,ALLOFTHESTATESMOVETOTHEORIGININTHISCASE,SCXISCALLEDSLIDINGSURFACEWHICHHASBEENCLAIMEDBYOURMETHODREMARKA6DESIGNEDCONTROLLERASANEWDEGREEOFFREEDOMBYIMPLEMENTINGOURDESIGNEDCONTROLLERTOTHESYSTEM,NOTONLYTHESTABILITYOFTHESYSTEMCANBESATISFIEDBUTITSQUALITYOFRESPONSECANALSOBESETUPBYSELECTINGADESIREDNEGATIVEDEFINITEMATRIX,SELECTINGAMORENEGATIVE,RESULTSINAFASTERRESPONSEOFTHEDQDQSYSTEMANDTHISMEANSTHATTHESTATESOFTHESYSTEMWITHASTEEPERSLIDINGSURFACEMOVETOTHEORIGINREMARKA7EXTENDINGOURDESIGNEDMETHODTODISCRETESYSTEMSSIMILARTOTHEPROOFFORCONTINUOUSSYSTEMS,OURDESIGNEDMETHODCANBEIMPLEMENTEDFORADISCRETESYSTEMASFOLLOWSKXVT1KTXVKXTCONSIDERTHESLIDINGSURFACEASBELOW1QWHEREQKISADESIREDNEGATIVEDEFINITEMATRIXTHEREFORETHISPROOFCANBECONTINUEDASBELOWKXKXQKVTTXTKXIKPIQKTKXVWHEREPKISADESIGNEDASANEGATIVEDEFINITEMATRIXANDQKISALSOANEGATIVEDEFINITEMATRIXWHICHISDERIVEDTHROUGHTHEFOLLOWINGIKPQKTCOLA4EXPERIMENTALRESULTSNOWTHERESULTSOFOURDESIGNEDMETHODAREILLUSTRATEDINNONLINEARSYSTEMSWITHOURPROBLEMFORMULATIONFOREACHSECTIONSEPARATELYTESTA1GISRECTANGULARILCMETHODCONSIDERTHESYSTEMWITHTHEFOLLOWINGSTATEEQUATIONSUXFTX321SINCOI312XF10320SIN3CO2XXG，5042DQ34IM01013ITSHOULDBENOTICEDTHATGISRECTANGULARTHISMEANSTHATTHENUMBEROFINPUTSANDOUTPUTSAREDIFFERENTNOWTHERESULTSFORCONTROLLINGTHISSYSTEMBYOURDESIGNEDMETHODAREPLOTTEDINFIGA1TESTA2SELECTINGTHEDESIREDMATRIXINTHEABOVEMENTIONEDSYSTEMTHEQDQMATRIXISCHANGEDANDTHERESULTSARESHOWNASFOLLOWS504215DQNOWCOMPARETHEAMPLITUDEOFTHECONTROLLERANDTHESPEEDOFCONVERGENCEFORSTATESANDTHECONTROLLERINTESTA1ANDTESTA2FIGA2TESTA3FORGETTINGFACTORTHEFORGETTINGFACTORANDITSEFFECTAREILLUSTRATEDINFIGA3ITISOBVIOUSTHATTHERATEOFCONVERGENCEISDIFFERENTINBOTHCASESASSHOWNINFIGA3TESTA4ROBUSTNESSWITHRESPECTTOLIPSCHITZCONDITONINTHISCASETHELIPSCHITZCONDITIONNUMBERHASBEENREDUCEDTOHALFOFITSVALUECOMPAREDTOTESTA1THEPLOTSENTIRELYSHOWTHEDIFFERENCEINTHETWOCONSIDEREDCASESFIGA4迭代滑模控制（46页）通过这些假设，需要保留李普希茨条件。FF现在来评估摄动系统的稳定性，2,稳定性的算法需按如下步骤第一步，从下面的关系式中，取一个控制性的增量KDQKTXGIM,M的位置是为了功能函数的李普希茨条件数值，是设计者期望的负值的明FDQ确的矩阵。第二步，把先前阶段取得的控制性增量以受干扰量的方式运用到第一步提到的那个关系式中。因此得到下列关系式DQKTXGI,的位置是为了函数的的李普希茨条件数值，来源于“”当它被干扰MFG的时候，是设计者期望的一个负值的明确的矩阵。通过放大上面的关系式，D得到下面的关系式；DNNQKGTXI,；NIDKGM；IQND；KTX,；通过上面得到的关系式，矩阵是从上述关系式中和其他形式期望矩阵构QDQ建来的。注意是设计者选择的。D通过在3中设计控制量，系统2中的和G将会有受干扰的稳定性，当F控制性增量是从第一步关系式中获得的，从中选择的小于，矩阵DQD有一个期望的负数矩阵可以满足以下关系式，TESTKGIQNDA5在新的例子中提到的方法的收敛条件可以如下表示GIGINN1INMAXGN备注A2（关于李普希茨条件数值的稳定性）。虽然我们提出的控制量是依据3和4关系式衍生的，李普希茨条件数值在这过程中很重要，如果设计者错误地选择了这个数字，比如M,M如果在以下范围内，这个方法仍然是可信赖的TESTA4,SUPXTF备注A3（选择期望矩阵。选择矩阵直接影响闭合回路反映的表现。换DQD种说法，出现在李雅普诺夫函数的衍生当中，如果它选的更小一点，这意味D李雅普诺夫函数的衍生将会是更加否定的，并且这强迫以上提到的函数更快达到起点，反之亦然。TESTA2备注A4遗忘因素。遗忘因素可以让设计者在系统的变化中控制反应的速度。跟住先前的备注，通过选择一个适当的（在过程开始的时候），设计者DQ只能进行一次上述提到的任务，但是通过把遗忘因素当做形式1中的减少量例如T/T（T代表时间，T是过程的总时间），李雅普诺夫函数的下降比率可以调节，因此达到起点的速度在整个的运营时间内是可以控制的TESTA3备注A5（滑动面积）。从滑动模型控制的角度看，滑动面积是李雅普诺夫函数面积的特殊值。通过运用我们提出的算法，可以得到一个合适的滑动面积。考虑下面的关系式,CXYNC,10ITNXX,1的选取要使CX是一个赫维茨多项式。IC通过将“V”定义为一个李雅普诺夫函数并且跟随下面的步骤，我们可以得到XCCXYVTTTT21GUFGUFXKMIKMTTTTCXIQD如果通过调节K矩阵，我们使成为负的，根据李雅普诺夫定理将Y推至起点V因此，0CXOR1NXC01121NXCXC因为Y是赫维茨多项式，所有的量都推至起点。在这种情况下，SCX被称为就是用我们的方法得到的滑动面积。备注A6（将设计的控制量当