# Is it possible to calculate Over Shoot percentage and settling time of an Underdamped 2nd order system with Ramp input?

Most of the books derive Over Shoot percentage, settling time for 2nd order underdamped it for unit step response. Do these parameters exist for 2nd order underdamped system for Ramp response too? If yes where to find the formulas?

• Are you familiar with the derivations of the overshoot and settling time for the step response? It may be possible to derive the same for ramp response in a similar fashion.
– AJN
Sep 17 at 17:06
• Yeah, I've tried that approach. The math becomes a bit too complicated. Then I asked myself if finding such parameter had meaning or physical interpretation behind it. Like step response has a final constant value where natural response part dies out. But the Ramp's response has no such constant value. Sep 17 at 17:39
• Yes, it's an interesting and relevant question. Ramp inputs occur any time there is a system that enforces rate limits. For analysis: The infinite ramp is the integral of the unit step. A finite ramp is the difference of two of these, with the second one delayed. That should be enough to calculate the laplace transform. Then apply your system in laplace domain, then invert it back to time domain. Exercise for the reader =) Sep 18 at 1:45