Correct Answer - Option 3 : 0.2
Concept:
Final value theorem:
- A final value theorem allows the time domain behavior to be directly calculated by taking a limit of a frequency domain expression
- Final value theorem states that the final value of a system can be calculated by
\(f\left( \infty \right) = \mathop {\lim }\limits_{s \to 0} sF\left( s \right)\)
Where F(s) is the Laplace transform of the function.
- For the final value theorem to be applicable system should be stable in steady-state and for that real part of poles should lie in the left side of s plane.
Initial value theorem:
\(C\left( 0 \right) = \mathop {\lim }\limits_{t \to 0} c\left( t \right) = \mathop {\lim }\limits_{s \to \infty } sC\left( s \right)\)
It is applicable only when the number of poles of C(s) is more than the number of zeros of C(s).
Calculation:
Transfer function will be
\(\begin{array}{l} \frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{{G\left( s \right)}}{{1 + G\left( s \right)H\left( s \right)}}\\ = \frac{{20}}{{{s^2} + 20s + 100}} \end{array}\)
Apply final value theorem,
\(\mathop {\lim }\limits_{s \to 0} sC\left( s \right) = \mathop {\lim }\limits_{s \to 0} s\frac{{20}}{{{s^2} + 20s + 100}} \times \frac{1}{s} = 0.2\)
