Question 3. (i) The closed loop transfer function for a second order system is given as
T(s)=(36)/(s^(2)+4.2s+36)
, find the damping ratio, natural frequency, peak time, rise time and percentage overshoot of its time response. (ii) In state space, a system is represented by
x^(˙)=([0,1,0],[0,0,1],[-3,-2,-5])x+([0],[0],[10])U(t)
;
y=([1,0,0])x;,
. Obtain its transfer function and deduce the system's initial and steady states.