2nd Order System Response
This page summarizes step and frequency responses of second order system of
- Stable = (a0 > 0 and a1 > 0).
Settling time rule from 1st order system (i.e. response is within 2% of
steady state value at 4τ) does not hold (see example 4).
Input: step A
Output (steady state amplitude):
Output (steady state amplitude trend):
Change Response Speed
σ times faster:
- Gain (K): unchanged
- New natural frequency (undamped frequency): σωn
- Damping ratio (ζ): unchanged
- Example 1: Speed up response 5 times.
- Example 2: Design critically damped amplifier for servo.
- Example 3: Design to a specific zeta.
- Example 4: Critically damped and undamped system (and settling time).