Fall 2001 16.3117-5 For consistency in the implementation with the classical approaches define the compensator transfer function so that Gc(sy From the state-space model of the compensator U(s) Cc(sI-AcB K(sI-(A-BK-LCDL Gc(s)=Cc(SI-Ac-B Note that it is often very easy to provide classical interpretations (such as lead lag)for the compensator Gc(s) e One way to implement this compensator with a reference command (t)is to change the feedback to be on e(t)=r(t-y(t)rather than just -y(t e ul Ge(s Gc(se=gas(r-y So we still have u=-Gc(sy if r=0 Intuitively appealing because it is the same approach used for the classical control, but it turns out not to be the best approach More on this laterFall 2001 16.31 17—5 • For consistency in the implementation with the classical approaches, define the compensator transfer function so that u = −Gc(s)y — From the state-space model of the compensator: U(s) Y (s) , −Gc(s) = −Cc(sI − Ac) −1 Bc = −K(sI − (A − BK − LC))−1 L ⇒ Gc(s) = Cc(sI − Ac) −1Bc • Note that it is often very easy to provide classical interpretations (such as lead/lag) for the compensator Gc(s). • One way to implement this compensator with a reference command r(t) is to change the feedback to be on e(t) = r(t) − y(t) rather than just −y(t) Gc(s) G(s) - - 6 — re y u ⇒ u = Gc(s)e = Gc(s)(r − y) — So we still have u = −Gc(s)y if r = 0. — Intuitively appealing because it is the same approach used for the classical control, but it turns out not to be the best approach. More on this later