Use the Nyquist stability criterion to determine the ranges of K > 0 (if any) for which the closed-loop system is stable.

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1. Use the Nyquist stability criterion to determine the ranges of K > 0 (if any) for which the
closed-loop system is stable. 

A negative unity-feedback LTI system has a forward element consisting of an amplifier with adjustable
real-valued gain K in cascade with a transfer function G(s), the loop gain KG(s) for some fixed K > 0
known to generate the asymptotic Bode plot description shown in Figure 4.
Magnitude (dB)
(deg)
Phase
60
40
20
80
-20
-40
-60
-80
90
45
0
-45
-90
-135
-180
-225
10
4
40 100 400 1000
Frequency (rad/sec)
Figure 4: Asymptotic Approximation of Bode Plot for KG(s) for some fixed K > 0
0.01
0.1 0.4 1
10000
Transcribed Image Text:A negative unity-feedback LTI system has a forward element consisting of an amplifier with adjustable real-valued gain K in cascade with a transfer function G(s), the loop gain KG(s) for some fixed K > 0 known to generate the asymptotic Bode plot description shown in Figure 4. Magnitude (dB) (deg) Phase 60 40 20 80 -20 -40 -60 -80 90 45 0 -45 -90 -135 -180 -225 10 4 40 100 400 1000 Frequency (rad/sec) Figure 4: Asymptotic Approximation of Bode Plot for KG(s) for some fixed K > 0 0.01 0.1 0.4 1 10000
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