Fall 2001 16.3116-18 Filter Interpretation: Recall that A=(A-LC)i+ Ly e Consider a scalar system. and take the Laplace transform of both sides to get L Y) sI-(A- LC ● This is the transfer function from the“ measurement” to the“esti- mated state It looks like a low-pass filter Clearly, by lowering r, and thus increasing L, we are pushing out the pole DC gain asymptotes to1/CasL→∞ Scalar TF from Y to hat x for larger LFall 2001 16.31 16–18 • Filter Interpretation: Recall that ˙ xˆ = (A − LC)ˆx + Ly • Consider a scalar system, and take the Laplace transform of both sides to get: Xˆ (s) Y (s) = L sI − (A − LC) • This is the transfer function from the “measurement” to the “esti￾mated state” – It looks like a low-pass filter. • Clearly, by lowering r, and thus increasing L, we are pushing out the pole. – DC gain asymptotes to 1/C as L → ∞ 10−1 100 101 102 103 104 105 106 10−2 10−1 100 Scalar TF from Y to \hat X for larger L Freq (rad/sec) |\hat X / Y| Increasing L