Test: Time Domain Analysis of Control Systems - 1 - Electrical Engineering (EE)

Taking Laplace transform on both sides of the given differential equation, we get (s² + 2s + 2) Y(s) = 3

Since, ξ < 1, therefore given system is underdamped.

If ξ < 1, system is underdamped.
If ξ > 1, system is overdamped.
If ξ= 1, system is critically damped.

Delay time (t_d) is the time required for the response curve to reach 50% of the final value.

Undamped natural frequency = ω_n and maximum overshoot,

Since M_p is independent of ω_n, therefore with increase in ω_n, M_p remains constant

The general relation between ξ and gain K is 

Since ξ > 1, therefore the system is overdamped. Hence, there will be no peak overshoot in the output response of the system.

It’s characteristic equation is (s + 2) (s + 5) = 0 
or, s² + 7s +10 = 0

Thus, damping ratio ξ > 1.
Hence, option (c) is false.

Time constant of the system, 

When  is increased means damping is reduced, thus steady state error reduces.
Also, when gain of the system increases, then damping reduces and therefore, steady state error reduces.