# Overshoot percentage of a critically damped system

My textbook explains how we recognize an underdamped , overdamped or a critically damped system and all their characteristics.

Later on, in another chapter, without going into much detail I'm given the following two transfer functions and the systems' responses. $$G_1(s)=\frac{1}{(s+1)^2}\\ G_2(s)=\frac{s+0,5}{(s+1)^2}$$

It is known and written that these are two critically damped systems. It is then just stated that the overshoot happens because of the s=-0,5 zero of the second system. Should that be a good enough explanation for me ? Because I don't get why it happens.

Also , if I'm asked to adjust the systems so that I have a certain overshoot percentage how would I achieve that ? I'm only aware of a formula for underdamped systems which doesn't stand here.

• I would recommend to expand the denominator $D(s)$ and put it under a 2nd-order canonical form $D(s)=1+\frac{s}{Q\omega_0}+(\frac{s}{\omega_0})^2$ then identify the terms. Check my comments here to understand how $Q$ affects the response (electronics.stackexchange.com/questions/316825/…). You must find the formula linking the overshoot to $Q$ (or the damping ratio) in your textbook. Watch-out, it is usually valid without zero(s). – Verbal Kint Jul 17 '17 at 15:48