Frequency response data for a process are tabulated below. These results were obtained by introducing a sinusoidal change in the controller output (under manual control) and recording the measured response of the controlled variable. This procedure was repeated for various frequencies.

(a) If the PT controller is adjusted so that ?1 = 0.4 mm, what value of K will result in a phase margin of 45??

(b) If the controller settings in part (a) are used, what is the gain margin?

(c) If the Ziegler-Nichols settings for a PT controller are used, estimate MT. the maximum amplitude ratio for the complementary sensitivity function T(s).

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+ (deg) a (rad/min) AR -3 0.1 0.10 0.20 2.40 1.25 -12 -22 -41 -60 0.90 0.50 0.5 0.29 1.0 --82 0.15 2,0 0.05 0.017 0.008 --122 5.0 -173 10.0 -230 15.0