2. Transfer Function of Closed Loop Control Systems

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2. Transfer Function of Closed Loop Control Systems Example 2.1 System Mod. 08D G1(s) Kt + - K G2(s) C(s) R(s) KG1G2R=(1+KG1G2+KtG1)C Mason’s formula Forward paths: KG1G2 Closed loops: KG1G2(-1) , G1Kt (-1)

Example 2.2

Example 2.3 ) s ( R 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 closed loop system: Δt=0.0703, tss=13.2181 p1=-4.526, p2,3=-0.4993±2.7883i, p4=-0.4753 p1 için p3,4 için p4 için For closed loop system: Δt=0.0703, tss=13.2181 dt=0.0703;ts=13.2181;t=0:dt:ts; tfh=tf(nh,dh);[c,t]=step(tfh,t);plot(t,c), max(c) Overshoot: % 43.19 Overshoot Identical