Question 4 (25 marks)
a) For a first order system with the transfer function shown below, find the relevant
response specifications.
$$
\frac{Y(s)}{R(s)} = \frac{80}{s+80}
$$
i.
Time constant, t
[3 Marks]
ii.
Settling time, ts
[2 Marks]
iii.
Rise time, tr
[2 Marks]
b) Consider the second order system as below, analyze the system by finding
relevant response specifications.
$$
\frac{Y(s)}{R(s)} = \frac{100}{s^2 + 15s + 100}
$$
i. Provide the general second order system equation
[2 Marks]
ii.
Natural frequency, Wn
[2 Marks]
iii.
Damping ratio, ξ
[3 Marks]
iv.
Peak time, tp
[3 Marks]
V.
Settling time, ts
[3 Marks]
vi.
Overshoot, %OS
[3 Marks]
vii.
State nature of this system
[2 Marks]
