Topic: Control Systems
$s^{2}-0.75s+0.25$ is the characteristic equation of a second order system. Its response to unit step function will be,
- A. Over damped
- B. Under damped
- C. Critically damped
- D. Exponential growth
Answer: D. Exponential growth
Explanation: The characteristic equation $= s² - 0.75s + 0.25 = 0$. Since the characteristic equation contains a negative coefficient, the roots (poles) will lie on the right half of the s-plane. Thus, the system is unstable and its response will be an exponential growth.