质量未知的模型参考自适应控制

《应用非线性控制》，Jean-Jacques E.Slotine程代展译，P213Example 8.1: MRAC control of an unknown massConsider the co

Jean-JacquesE.SlotineP213 《应用非线性控制》，程代展译， Example8.1:MRACcontrolofanunknownmass Considerthecontrolofamassonahiciionlesssurfacebyamotorforce”with(heplantdynamics ， being mjr=w(8.1) [虱 Assumethatahumanoperatorprovidesthepositioningcommarh)iotheconUolsystem(possibly throughajoystick).A(easonablewayofspecifyingtl>eidealicsponseof(hecontrolledmas*tothe externalcommandr(/)isrousethefollowingreferencemodel 所*=入住. Kw4A242) ；) 电 withdiepositivecooManisXandchosenioreilecitheperioniiaiKespecificauons,andthe ) x referencemodeloutputbeingtheidealoutputof(hecontrolsystem(fe,ideafly,therrmsshouldgo m tothespecifiedpositiondr)likeawell-dampedmassspringdampersystem). m 。 Ifthmassisknowexactly,wecanu$ethefollowingcontrollawtoachieveperfeatracking u 工入入葭) m("-27- x with-Jf(r)-x(/)represencihgihetrackingerrorandXastrictlypositivenumber.Thisconirollaw w leadsio(heexpcxieniiallyconvergent(rackingencrdynamics : x +2Xi♦-0 notknownemcUy. 笛 Nowletu$sunxthatthemassisWemayusethefollowingcontrollaw “二众(着-入了一入工) 22(8.3> m. whichconrainstheadjustableparameterSubsiitucionof(hisconin>]lawinio<heplantdynamics leadsiotheclosed-looperrordynamics mi+ (84) 儿 whaeacombinedcrackingerrormeasure,isdefinedby 入 s=M+7 (8.5)