A general theory quantifying the root sensitivity function

In this report, we present a geometric method for representing the classical root sensitivity function of linear time-invariant systems. The method employs gain plots that expand the information presented in the root locus plot in a manner that permits determination of both the real and imaginary components of the root sensitivity function by inspection. • ' f | ' i ;^ H-1 ;• "K I. The Root Sensitivity Function In classical control theory the root sensitivity, Spj is defined as the relative change in the system roots or eigenvalues, X{ (i = 1,.-, n), with respect to a system parameter, p. Most often, the parameter analyzed is the forward proportional controller gain, k. The root sensitivity with respect to gain is given by