Example 1: Determine the position, velocity, and acceleration error constants for each of the unity-feedback systems represented by the following open-loop transfer functions; also calculate the steady-state error.
1. G(s) = 5/(s^2 + 15s + 25)
2. G(s) = s/(s^3 + 3s^2 + 5s + 6)
3. G(s) = s/(s^2 + s + 1)
Example 2: The open-loop transfer function of a unity-feedback system is given by:
G(s) = 108
Determine the static error constants and steady-state error for the input given by:
r(t) = 2t + 5t^2 + 2