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Lab 7: Studying Second Order Transfer Function FA06_BET_
Lab Task
Write down 2nd^ order transfer function with following inputs:
G(s) = wn^2 / (s^2 + 2ζwns + wn^2 )
Where; wn: Frequency ζ: Damping Ratio
wn = 0.5 rad/sec, 1 rad/sec, 2 rad/sec
ζ = 0, 0.1, 0.2, 0.5, 0.7, 0.9, 1,2,10, 100
For Pole Zero Plot:
zeta = [0 0.1 0.2 0.5 0.7 0.9 1 2 10 100];
wn = [0.5 1 2];
for i=1:
figure(i)
for j = 1:
num = (wn(i))^2;
den = [1 2zeta(j)wn(i) (wn(i))^2];
tr = tf(num, den);
pzmap(tr)
hold on
end
end
Matlab Code:
Lab 7: Studying Second Order Transfer Function FA06_BET_
Results:
For Pole Zero Plot:
zeta = [0 0.1 0.2 0.5 0.7 0.9 1 2 10 100];
wn = [0.5 1 2];
for i=1:
for j = 1:
Lab 7: Studying Second Order Transfer Function FA06_BET_
For the case ζ = 0, the system is marginally stable or undamped. i.e. the conjugate pair of poles lies on the imaginary axis. As ζ decreases, poles move down in the left half plane. Both the rise time and peak time increases. For ζ = 1, both the poles are at the same point. In this case the over shoot is zero. As ζ increases, the poles disperse. ζ is not equal to zero, because in that case, the poles will be in the right half plane, making the system unstable.
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