Topic: Control Systems
The steady state response for an input $X(s) = K/s$ to a system whose transfer function is $H(s) = 1/((s+5)(s+2))$ in time domain is
- A. $K/10$
- B. $e^{-5t}u(t)$
- C. $e^{-2t}u(t)$
- D. $(e^{-5t}+e^{-2t}) u(t)$
Answer: A. $K/10$
Explanation: The output response in the s-domain is $Y(s) = H(s) \times X(s) = \frac{K}{s(s+2)(s+5)}$. To find the steady-state response in the time domain, we apply the Final Value Theorem: $\lim_{t \to \infty} y(t) = \lim_{s \to 0} s Y(s)$. Therefore, $Y_{ss} = \lim_{s \to 0} s \left( \frac{K}{s(s+2)(s+5)} \right) = \frac{K}{(0+2)(0+5)} = \frac{K}{10}$.