1. 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)

2. Example 2.2

3. 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= p1=-1, p2=-2, p3=-3
Eigenvalues of closed loop system: D(s)=DcDp+NcNp=0, roots(dh)
p1=-4.526, p2,3= ±2.7883i, p4=

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