ABSTRACT
Note, the starred functions represent impulse transfer functions; e.g., Y*(s) represents the ideal impulse transform of Y(s). These equations are manipulated and transformed to yield the input/output z-domain relationships:
1 + L(z) L(z)
where = GzoP(z)Gl(z) (4.39)
(4.40)
P(s)
PD(z)=Z[P(s)D(S)}
TR(z)= F(z)L(z) \ + L(z)
(4.42)
(4.43)
_ PD(?) 1 + L(z)
Substituting Eq. (4.40) into Eq. (4.39) yields
L(z) = G!(z)(l - z -i )pe (z) = Gj (z)Pz (z)
Note, for a unit step disturbance input function, D(s) = 1/s, that
and thus
(4.46)
(4.48)
The QFT design is based upon the uncertain plant being defined by Eq. (4.41). Once L(z) has been synthesized then the controller G/(z). which is to be implemented, is readily determined.
