ࡱ> !# Y(bjbjWW/== ]dddd$ LH%%%  $  d E%"%%% ddYL%d8 dddd% j f  8j7l~ Modern teorie Yzen loha . 5  LQ Regultor Zadn: PYevete pYenos  EMBED Equation.3  na stavov popis a provete diskretizaci (Ts=0.1s) tohoto systmu. Pro rozn vhov funkce matice Q a R navrhnte asov invariantn LQ regultor a porovnejte frekven n vlastnosti otevYen regula n smy ky, probhy jednotlivch regula nch veli in a vlastn sla matice (M-NK) vzvislosti na tchto vhovch maticch. Vaechny vsledky simulujte. vod LQ regultor je kvadraticky optimln regultor pro linern systmy. Vtto loze se pokusme navrhnout nkolik LQ regultoro, kter Yea problm optimlnho pYechodu zdanho stavu x0 do po tku. Princip otimality Jestli~e optimlnm Yzenm u na intervalu T1=0, 1, & , t-1 pYivedeme systm do stavu x(k) a dle Ydme optimln na intervalu T2 = t, & , N  1 je Yzen na celm intervalu Tc=0, 1, .. N  1 optimln. Ztrtov funkce a tvar regultoru Ztrtovou funkci volme ve tvaru  EMBED Equation.3  Potom lze princip optimality zapsat ve tvaru  EMBED Equation.3  kde optimln hodnotu funkce V  ozna me V*. PYi hledn optimlnho Yzen pak mo~eme samostatn minimalizovat ka~d len ztrtov funkce po naje poslednm, kter je roven  EMBED Equation.3  Tuto rovnici lze vyjdYit jako kvadratickou formu stavu  EMBED Equation.3  a optimln Ydc posloupnost pak je  EMBED Equation.3  co~ lze interpretovat jako Yzen pomoc stavov zptn vazby  EMBED Equation.3 , kde Kje Kalmanovo zeslen, kter je vtomto pYpad asov promnn. Riccatiho rovnice a asov invariantn regultor Riccatiho diferen n rovnici zskme pYepisem rovnice zkonu optimality pomoc minimln hodnoty ztrtov funkce kvadratickou formou. Pro stabilizovan systmu a  EMBED Equation.3 konverguje Yeaen Riccatiho rovnice ke kvadratick form  EMBED Equation.3 , kter je pozitivn semidefinitn a symetrick. Ztoho zskme Kalmanovo zeslen pro sice suboptimln, ale asov invariantn regultor:  EMBED Equation.3  Amplitudov a fzov bezpe nost Vjednorozmrnm (SISO) pYpad se frekven n charakteristika otevYen regula n smy ky  EMBED Equation.3  vyhb kru~nici  EMBED Equation.3 . Odtud plyne Amplitudov bezpe nost -  EMBED Equation.3  fzov bezpe nost -  EMBED Equation.3  Xeaen Spojit systm spYenosem  EMBED Equation.3  jsme diskretizovali speriodou vzorkovn Ts=0.1s a transformovali na stavov model. 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