37 Introduction to the Nyquist Criterion The NyC relates the stability of a closed-loop system toopened-loop frequency response and open loop pole locationThus knowledge of the opened-loop system's frequency res-ponse yields information about the stability of the closed-loop system.
40 Nyquist Stability Criterion If a contour A that encircles the entire right half-plane ismapped through G(s)H(s), then the number of closed-looppoles, Z, in the right half-plane equals the number of open-loop poles, P, that are in the right half plane minus the numberof counterclockwise revolutions, N, around -1 of the mapping;that is, Z=P-N. The mapping is called the Nyquist diagram, orNyquist plot of G(s)H(s).
41 Mapping examples: a. contour does not enclose closed- loop poles; b. contour doespoles
42 Detouring around open-loop poles: a. poles on contour;b. detour right;c. detour left
43 Gain Margin and Phase Margin Nyquist diagramshowing gain andphase margins