-plane design of compensators for feedback systems

The poles and zeros of a compensator affect the -plane gain and phase of the open-loop system at every point in the -plane. These effects are studied for open-loop poles and zeros on the negative real axis, and a family of curves summarizes the results. A design technique is developed which permits compensation design to satisfy simultaneous specifications of root location and system gain. The method clearly defines the minimum number of compensator sections required and leads to a logical interpretation of relative needs for phase-lead and phase-lag compensators.