Question 11.15.2: Compute the transfer function of the system that is shown in...
Compute the transfer function of the system that is shown in the figure below. The transfer functions of the subsystems are H_1(s) = s/(s\ +\ 4), H_2(s) = s/(s^2\ +\ 4), and H_3(s) = s^2/(s^2 \ +\ 4).
num1=[1 0];
den1=[1 4];
H1=tf(num1,den1);
num2=[1 0];
den2=[1 0 4];
H2=tf(num2,den2);
H12=parallel(H1,H2)
% H12=H1+H2.
The transfer function of the two parallel-connected subsystems is
Transfer function: \frac{s^\wedge 3\ +\ s^\wedge 2\ +\ 8s}{s^\wedge 3\ +\ 4s^\wedge 2\ +\ 4s\ +\ 16}
num3=[1 0 0];
den3=[1 0 4];
H3=tf(num3,den3);
H=series(H12,H3)
% H=H12 - H3
The overall system transfer function is Transfer function:
\frac{s^\wedge 5\ +\ s^\wedge 4\ +\ 8s^\wedge 3}{s^\wedge 5\ +\ 4s^\wedge 4\ +\ 8s^\wedge 3\ +\ 32s^\wedge 2\ +\ 16s\ +\ 64}
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