Complete root contours for circle criteria and relay autotune implementation

A framework to explore how the information supplied by circles in the Nyquist plane can be recovered in the RL plane. In this article, all circle criteria (including off-axis circles) in the frequency domain can be reformulated as complete root contours. In this way, some difficulties of analysis in the frequency domain are overcome by means of the Evans technique (1948, 1950). Applications to phase margins, sensitivity, bandwidth computations, constant N-contours, and absolute stability were reported, along with a practical implementation in laboratory tests via a modified relay autotune method, called SATV. The SATV technique was successfully used for a practical evaluation of the critical frequencies of the plant intersecting circles. Its robustness was tested, even in the presence of measurement noise, based on an integration of the periodic input signal over several periods.