Automatic Control (AC)
Question 1: Feedback Control Systems
August 2017 (Published in Jul 2019)
Problem 1
a) $ \frac{C(s)}{R(s)} = \frac{4}{s(s+1)} $
b) $ \frac{B(s)}{E(s)} = \frac{2}{s+1}+\frac{4}{s(s+1)} = \frac{2s+4}{s(s+1)} $
c) $ \frac{C(s)}{R(s)} = \frac{\frac{4}{s(s+1)}}{1+\frac{2s+4}{s(s+1)}} $
d) $ 1+\frac{2s+4}{s(s+1)} = 0 $
e) $ s(s+1)+2s+4 = 0 \Rightarrow s^2+3s+4=0 $
$ \therefore \omega_n^2 =4, \; 2\zeta \omega_n = 3 \Rightarrow \tau = \frac{1}{\zeta \omega_n} = \frac{3}{2} $
