Fall 2001 16.3116-4 Does this guarantee that a=0v t? Or even that→0ast→∞?( which is a more realistic goal - Response is fine if (0)=0. But what if (0)+0? ● If a stable,then→0ast→oo, but the dynamics of the estima- tion error are completely determined by the open-loop dynamics of the system(eigenvalues of A) Could be very slow no obvious way to modify the estimation error dynamics Open-loop estimation does not seem to be a very good idea Closed-loop Estimator An obvious way to fix this problem is to use the additional informa- tion available How well does the estimated output match the measured output? Compare:y= C with y=Ci Then form y=y-y≡CxFall 2001 16.31 16—4 • Does this guarantee that ˜x = 0 ∀ t? Or even that ˜x → 0 as t → ∞? (which is a more realistic goal). — Response is fine if x˜(0) = 0. But what if x˜(0) 6= 0? • If A stable, then ˜x → 0 as t → ∞, but the dynamics of the estima￾tion error are completely determined by the open-loop dynamics of the system (eigenvalues of A). — Could be very slow. — No obvious way to modify the estimation error dynamics. • Open-loop estimation does not seem to be a very good idea. Closed-loop Estimator • An obvious way to fix this problem is to use the additional informa￾tion available: — How well does the estimated output match the measured output? Compare: y = Cx with ˆy = Cxˆ — Then form ˜y = y − yˆ ≡ Cx˜