Errata: In Example 9.6, the critical gain is k = 0.5 instead of k = 1
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Location: page 276, lines -6, -2; page 277, line 4
In Example 9.6, the value of the critical gain is listed incorrectly: it should be k = 0.5 instead of k = 1. The paragraph after the displayed equation has several changes (highlighted in blue):
We have L(0) = − 2k and. If k > 0.5, the Nyquist curve encircles the critical point s = − 1 in the counterclockwise direction when the Nyquist contour γ is encircled in the clockwise direction. The number of encirclements is thus N = − 1. Since the loop transfer function has one pole in the right half-plane (P = 1), we find that Z = N + P = 0 and the system is thus stable for k > 0.5. If k < 0.5, there is no encirclement and the closed loop will have one pole in the right half-plane.
In addition, in the caption of Figure 9.8, the Nyquist plot is given for gain k = 1.
(Contributed by F. Zabala, 23 Dec 09)
