Abstract
This paper analyzes a discrete variable structure system for control n-th order plants with nonminimum phase zeros in the input-output transfer function. The problem is solved by using the technique of stable system center. The first is a discrete mathematical model of the system in the normal canonical form for a given system. Then the synthesis of state generator and discrete 'time controller using the center of a stable system. The theoretical results are demonstrated in a numerical example.
Highlights
Teorema 3 - Ako je dat sistem (16), onda postoji stabilan klizni režim na kliznoj hiperpovršini sa ograničenim upravljanjem (13) kao u(k) = ueq (k) + U0 sign(g(k)), U0 > 0, gde su: ueq (k) = G(A11e z (k) + A22 e y (k)), U 0 = α T −1, α > ∆f m (k), . ∆f m (k) = ∆r(k) + Tφm (k)
The theoretical results are demonstrated in a numerical example
Summary
Razmatra se linearan vremenski invarijantan objekat upravljanja u uslovima poremećaja opisan sa: x(t) = (A + ∆A) x(t) + (b + ∆b) u(t) + f (t) , (1) y(t) = dx(t) , gde su: x ∈ Rn vektor stanja, u ∈ R upravljanje, f ∈ R poremećaj, y ∈ R izlaz objekta, A ∈ Rn×n matrica stanja, b ∈ Rn×1 , d ∈ R1×n matrice objekta, ∆A ∈ Rn×n , ∆b ∈ Rn×1 matrice promena. Matrica promena predstavljaju maksimalne moguće promene parametara objekta upravljanja, jer je reč o sistemu promenljive strukture. Cilj je sinteza digitalnog regulatora promenljive strukture (DRPS), koji ima dinamičku grešku u kliznom režimu za sistem (2), tako da je upravljanje (u sledecim izrazima k je zamena za kT ): u(k) = ueq (k) + usw (k) gde su: ueq(k) ekvivalentno upravljanje i Usw(K) komutaciono upravljanje. U ovom radu je analiziran sistem tipa regulatora (r(k)=const)
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