Fall 2001 6.3117-4 The Compensator e Dynamic Output Feedback Compensator is the combina- tion of the regulator and estimator using u=-K3 i(t)=Ai(t)+ Bu(t)+L(y-y) A i(t)-BK2+L(y-Ca =a(t)=(A-BK-LCi(t)+Ly F Rewrite with new state c= S c= Acrc+ Bcy C where the compensator dynamics are given by A≌A-BK-LC,B全L,C≌K Note that the compensator maps sensor measurements to ac tutor commands, as expected Closed-loop system stable if regulator/estimator poles placed in the LHP, but compensator dynamics do not need to be stable Ai(A- BK-LC)=??Fall 2001 16.31 17—4 The Compensator • Dynamic Output Feedback Compensator is the combina￾tion of the regulator and estimator using u = −Kxˆ ˙ xˆ(t) = Axˆ(t) + Bu(t) + L(y − yˆ) = Axˆ(t) − BKxˆ + L(y − Cxˆ) ⇒ ˙ xˆ(t)=(A − BK − LC)ˆx(t) + Ly u = −Kxˆ • Rewrite with new state xc ≡ xˆ x˙ c = Acxc + Bcy u = −Ccxc where the compensator dynamics are given by: Ac , A − BK − LC , Bc , L, Cc , K — Note that the compensator maps sensor measurements to ac￾tuator commands, as expected. • Closed-loop system stable if regulator/estimator poles placed in the LHP, but compensator dynamics do not need to be stable. λi(A − BK − LC) =??