Modello interno e esterno

Pagina 1

IRt ∈ Modello Interno INt ∈ )()()( )()()( tudtxcty tubtxAtx += += )()()( )()()1( tudtxcty tubtxAtx += +=+ dbAc +−= −1 µ uy µ= dbAIc +−= −1)( µ xstx )( zps →← xztx )1( + udxcy ubxAxs += =− udxcy ubAIpx += −= −1)( udxcy ubxAxz += =− ( ) upGudbAIpcy def )()( 1 =+−= − Funzione di Trasferimento )0()()( 1 GdbAIscsG =→+−= − µ dbAIzczGG +−=←= −1)()()1( µ matrice nn × di polinomi di grado 1−≤ n in p polinomio caratteristico (di grado n in p ) di A polinomio di grado 1−≤ n in p polinomio di grado n≤ in p = )( pA∆ se )( pN e )( pD non sono coprimi polinomio di grado < n in p polinomio di grado < n in p )( )(,)()( 1)( 1 p pPpPpAIp AA ∆∆=− − )( )(,)( )()( )(~,)( )(~ )( pD pN pD pNpG pNdp pNpG A =       +∆= )( )(,)( )()( pd pn pd pnpG = upD pNupGy )( )()( == n nnn n nn ppppD pppN α α α β β β ++++= +++= −− −   2 2 1 1 1 10 )( )( upNypD )()( = Modello ARMA ussysss n nn n nnn )()( 1 10 2 2 1 1 β β β α α α +++=++++ −−−  uzzyzzz n nn n nnn )()( 1 10 2 2 1 1 β β β α α α +++=++++ −−−  )( )( tuus tyys   ↔ ↔ () njujtu yjty utu ytynj dt tudtu dt tydty uyuy Gu yG j j j j j j n j n jnn n j n j n n  1,)( )( )( )(1, 0)()( 0)()( 1 )1( 1 )0( )( )( 01 1 0 ==+ =+⇒= =⇐= == == ↑↑ =+= ↑↑ = + =→=←== ∑∑ ∑ ∑ β α β α αβ µ µ αβ µ )1( )1( +↔ +↔ tuuz tyyz )()()()()()()( )1( 1 )( 0 )2( 2 )1( 1 )( tutututytytyty n nn n nnn β β β α α α +++=++++ −−−  )()1()()()1()1()( 1011 tuntuntutytyntynty nnn β β β α α α ++−+++=++++−+++ −  tnt + )()1()()()2()1()( 1021 ntututuntytytyty nn −++−++−−−−−−−= β β β α α α  IRt ∈ Modello Esterno INt ∈ M.Miari – Politecnico di Milano – 1-3.10.04 2