Test: Time Domain Analysis of Control Systems - 1 - Electronics and Communication Engineering (ECE) MCQ

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.

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.

The correct answer is option 3): Settling time

Concept:

• The time that is required for the response to reach and stay within the specified range (2% to 5%) of its final value is called the settling time.

• Peak Time. It is the time required for the response to reach the peak value for the first time. It is denoted by t_p.
• The time is defined as "the time required for the response to rise from x% to y% of its final value", with 0% to 100% rise time common for underdamped second order systems, 5% to 95% for critically damped and 10% to 90% for overdamped ones.
• Peak time (t_p) is simply the time required by response to reach its first peak i.e. the peak of first cycle of oscillation, or first overshoot. On differentiating the expression of c(t)