Frequency Response Analysis

The provided assignment content is about analyzing the frequency response and transient response of three transfer functions H1, H2, and H3. The first part of the code calculates the magnitude and phase responses of these transfer functions over a frequency range from 0 to 100 Hz. Then, it plots the magnitude and phase responses for each transfer function separately. The second part of the code simulates the transient response of the third transfer function H3 to three different input signals with frequencies 1 Hz, 3 Hz, and 5 Hz respectively. Finally, it plots the step responses of all three transfer functions using the pzmap and step functions.

%Task2
M1=0.001;B1=0.1;K1=1
M2=0.001;B2=0.01;K2=1
M3=0.001;B3=0.001;K3=1
H1=tf([1],[M1 B1 K1])
H2=tf([1],[M2 B2 K2])
H3=tf([1],[M3 B3 K3])
f=0:0.1:100; %Frequancy in Hz
w=2*pi*f; %Frequancy in rad/s
G1=freqresp(H1,w);
Test1=G1(1,1,:)
mag_H1=20*log10(abs(Test1(:)));
ph_H1=unwrap(angle(Test1(:)));
G2=freqresp(H2,w);
Test2=G2(1,1,:)
mag_H2=20*log10(abs(Test2(:)));
ph_H2=unwrap(angle(Test2(:)));
G3=freqresp(H3,w);
Test3=G3(1,1,:)
mag_H3=20*log10(abs(Test3(:)));
ph_H3=unwrap(angle(Test3(:)));
figure()
subplot(2,1,1)
plot(mag_H1,'red')
hold on
plot(mag_H2,'blue')
hold on
plot(mag_H3,'black')
title('Magnitude for H1,H2,H3')
subplot(2,1,2)
plot(ph_H1,'red')
hold on
plot(ph_H2,'blue')
hold on
plot(ph_H3,'black')
title('Phase Response for H1,H2,H3')
%task3
t=[0:1/20000:10]
A=1;
f1=1;
x1=A*sin(2*pi*f1*t);
f2=3;
x2=A*sin(2*pi*f2*t);
f3=5;
x3=A*sin(2*pi*f3*t);
figure()

subplot(3,1,1)
lsim(H3,x1,t)
hold on
subplot(3,1,2)
lsim(H3,x2,t)
hold on
subplot(3,1,3)
lsim(H3,x3,t)
figure()
pzmap(H1,'red')
hold on
pzmap(H2,'blue')
hold on
pzmap(H3,'black')
figure()
step(H1,'red')
hold on
step(H2,'blue')
hold on
step(H3,'black')