>> s=tf('s') Transfer function: s >> p=1 p = 1 >> G1=(1/16)/(s/p+.95) Transfer function: 0.0625 -------- s + 0.95 >> G1 Transfer function: 0.0625 -------- s + 0.95 >> G1_can=(0.0625/0.95)/(s/0.95+1) Transfer function: 0.06579 ----------- 1.053 s + 1 >> K1=dcgain(G1_can) K1 = 0.0658 >> tau1=1/p/.95 tau1 = 1.0526 >> G2=1/(s/1.95+1.05) G2 = 1.95 --------- s + 2.047 Continuous-time transfer function. >> K2=dcgain(G2) K2 = 0.9524 >> [wn,zeta,p] = damp(G2) wn = 2.0475 zeta = 1 p = -2.0475 >> tau2=1/wn tau2 = 0.4884 >> Kratio=K1/K2 Kratio = 0.0691 >> tauratio=tau1/tau2 tauratio = 2.1553 >> Gpar=G1-G2 Gpar = -1.887 s - 1.725 --------------------- s^2 + 2.997 s + 1.945 Continuous-time transfer function. >> zpar=zero(Gpar) zpar = -0.9137 >> p_min=K2/K1*tau1/tau2 p_min = 31.2000 >> p=35 p = 35 >> tau1=1/0.95/p tau1 = 0.0301 >> G1_can=K1/(tau1*s+1) Transfer function: 0.06579 ------------- 0.03008 s + 1 >> GP=G1_can-G2_can Transfer function: 0.003487 s - 0.8866 -------------------------- 0.01469 s^2 + 0.5185 s + 1 >> z=zero(GP) z = 254.2351 >> p=pole(GP) p = -33.2500 -2.0476 >> KP=dcgain(GP) KP = -0.8866 >> GM=1/ARco=1.13 at the stability boundary: GM=1 AR_lim=1 AR_lim=ARco(Kc=1)*GM=1 GM=Kc_lim/1 ((Kc=1)) zero_D=-1/tauD