Undershoot and Overshoot: Testing the Limits of Rules of Thumb [Focus on Education]

One way of characterizing a system is to consider its response to a unit step function (a function whose value is zero until l
t
= 0 and is one thereafter). When considering the system's
step response
, a typical goal is to determine whether it is ever negative (even though the steady-state response is positive), in which case the system suffers from
undershoot
. An additional goal is to determine whether or not the system?s step response ever exceeds its steady-state output, in which case the system suffers from overshoot. For more on the significance of under- and overshoot, see "Why Undershoot and Overshoot Are Significant." This article presents precise conditions under which systems will suffer from undershoot and overshoot. Some easier-to-use rules of thumb are also provided. Although these are useful, it will be shown that the given conditions are not actually necessary and, in the case of overshoot, are not sufficient either.