Complete Root Contours for Circle Criteria and Relay Autotune Implementation

A general and simple framework for recovering information in the root locus (RL) plane supplied by circles in the Nyquist plane was provided. All circle criteria in the frequency domain was expected to be reformulated as complete root contours. Applications to phase margins, sensitivity, bandwidth computations, constant N-contours and absolute stability were reported. The sinusoidal autotune variation (SATV) technique was used for a practical evaluation of the critical frequencies of the plant intersecting circles.