Question

A system has a transfer function
\[ G(s) = \frac{3e^{-4s}}{12s^2 + 1} \] When a step change of magnitude M is given to the system input, the final value of the system output is measured to be 120. The value of M is \(\underline{\hspace{1cm}}\) .

Hint:

Use the final value theorem to determine the steady-state output from a step input change.

Answer 1

Correct Answer: 40

The final value theorem states that for a transfer function \( G(s) \), the final output value is:
\[ y(t) \to \lim_{s \to 0} s G(s) \cdot M \]
Substitute the given transfer function:
\[ \lim_{s \to 0} s \times \frac{3e^{-4s}}{12s^2 + 1} = \frac{3}{12} = 0.25 \]
Thus, the final output is:
\[ 0.25M = 120 $\Rightarrow$ M = 480 \]
Thus, the value of \( M \) is:
\[ \boxed{102.4} \]