Fall 2001 16.3117-7 Simple example Let G(s)=1/s2 with state-space model given by A B 00 D=0 Design the regulator to place the poles at s=-4+ 43 A(A-BK)=-4±4→K=[328] Time constant of regulator poles Tc =1/Swn A 1/4=0.25 sec Put estimator poles so that the time constant is faster Te N 1/10 Use real poles, so e(s)=(s+10) L=重2(A CA 01 01 10 00/+20 1000 00 01 10020 100Fall 2001 16.31 17—7 Simple Example • Let G(s)=1/s2 with state-space model given by: A = ∙ 0 1 0 0 ¸ , B = ∙ 0 1 ¸ , C = £ 1 0 ¤ , D = 0 • Design the regulator to place the poles at s = −4 ± 4j λi(A − BK) = −4 ± 4j ⇒ K = £ 32 8 ¤ — Time constant of regulator poles τc = 1/ζωn ≈ 1/4=0.25 sec • Put estimator poles so that the time constant is faster τe ≈ 1/10 — Use real poles, so Φe(s)=(s + 10)2 L = Φe(A) ∙ C CA ¸−1 ∙ 0 1 ¸ = Ã∙ 0 1 0 0 ¸2 + 20 ∙ 0 1 0 0 ¸ + ∙ 100 0 0 100 ¸! ∙ 1 0 0 1 ¸−1 ∙ 0 1 ¸ = ∙ 100 20 0 100 ¸ ∙ 0 1 ¸ = ∙ 20 100 ¸