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+. +. R(s). K. G 1 (s). C(s). G 2 (s). -. -. K t. Forward paths. Loops. Link: 2.1 Step resp. 2. Transfer function of closed loop system. Example 2.1. MEE 3017- Lecture 08D. Forward paths: KG 1 G 2. L oops: KG 1 G 2 (-1) , G 1 K t (-1). Mason formu la. Example 2. 2. R. (.
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+ + R(s) K G1(s) C(s) G2(s) - - Kt Forward paths Loops Link: 2.1 Step resp. 2. Transfer function of closed loop system Example 2.1 MEE 3017-Lecture 08D Forward paths: KG1G2 Loops: KG1G2(-1), G1Kt (-1) Mason formula
R ( s ) Example2.3 clc,clear,nc=6*[0.24,2.1,1];dc=[2.1,0]; np=[6];dp=conv(conv([1,1],[1,2]),[1,3]); nh=conv(nc,np);dh=polyadd(conv(dc,dp),conv(nc,np)); Eigenvalues of open loop system: Dp=0 p1=-1, p2=-2, p3=-3 Eigenvalues of closed loop system: D(s)=DcDp+NcNp=0, roots(dh) p1=-4.526, p2,3=-0.4993±2.7883i, p4=-0.4753
for p4 , for p1 , for p2,3 , p1=-4.526, p2,3=-0.4993±2.7883i, p4=-0.4753 for closed loop system: Δt=0.0703, tss=13.2181 dt=0.0703;tson=13.2181;t=0:dt:tson; tfh=tf(nh,dh);[c,t]=step(tfh,t);plot(t,c), max(c) Overshoot: % 43.19 Link: 2.1 Step resp.