Overshoot contours for second-order transfer function with a pair of complex poles and a negative real zero†

Abstract

For a second-order all-pole transfer function, the maximum overshoot of the step response is the same for all poles lying on the same radial line. Therefore the radial lines themselves are contours of equal maximum overshoots. With a negative real zero introduced into this transfer function, the overshoot contours are different from the radial lines of the all-pole case. These modified contours are presented in this article.