A reformulation of the Nyquist criterion for discrete systems

摘要

The Nyquist criterion is a useful method in checking the closed-loop stability of linear systems. However, in its existing formulation, it is cumbersome to apply when the open-loop system has poles on the unit cycle of the z plane. An alternative formulation of the Nyquist criterion that is easier to apply than the existing one is presented. Instead of having to determine the images of the detours around the unit circle poles and then determine the number of encirclements about the (-1,0) point in the open-loop transfer function G(z) plane as required by the usual Nyquist criterion, the angle swept by the vector pointing from the (-1,0) point to the polar plot of G(z) is checked in order to determine the closed-loop stability.