Circle Criteria and Complete Root Contours

摘要

The root locus technique is simple, powerful and especially useful for educational purposes. However by comparing such technique with the available tools in the frequency domain, it is apparent that Bode and Nyquist approaches are more powerful.Unfortunately the RL method apparently hides important information to the designer with respect to standard frequency domain techniques. In this paper it is shown that all circle criteria in the frequency domain can be reformulated as complete rootcontours. Applications to phase margins, sensitivity, bandwidth computations and absolute stability are reported. Besides the educational advantages, complete root contours may prove valuable for computer aided design.