On the synthesis of feedback systems with open-loop constraints

A method is presented for synthesizing a feedback system under the constraints that the open-loop transfer function must have specified K
v
and contain real poles at prescribed locations. The method is based on examination of the inverse root-locus plot for the closed-loop poles and zeros. Algebraic equations are obtained for the open-loop pole and zero locations. Examples are given for systems through fourth order in which the resulting linear algebraic equations are readily solved for the required compensation poles and zeros.