For the satellite control system of Problem 7.5-6, the frequency response for G(z) was calculated by computer and is given in Table P7.7-3.

(a) Sketch the Nyquist diagram for the open-loop function G(z)H , with H = 0.02 ⇒ − 34.0 dB .

(b) Use the results in part (a) to determine the range of K for stability.

Problem 7.5-6

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TABLE P7.7-3 Frequency Response for Problem 7.7-3 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2.0 3.0 4.0 5.0 0.100 0.200 0.300 0.399 0.499 0.599 0.699 0.799 0.899 0.999 1.993 2.977 3.947 4.899 ()G| 1000.01200 250.01250 111.12360 62.51249 40.01249 27.79027 20.42065 15.63749 12.35817 10.01249 2.51247 1.12354 0.63738 0.41231 a )G| 60.00 47.95 40.91 35.91 32.04 28.87 26.20 23.88 21.83 20.01 8.00 1.01 -3.91 -7.69 GJ) -180.28 -180.57 -180.85 -181.14 -181.43 -181.71 -182.00 -182.29 -182.57 -182.86 -185.71 -188.53 -191.30 -194.03