control engineering-duein 4 hours
prof wesly
problem_four-work.docxProblem Four
An amplifier has the following open loop gain transfer function:
1. Draw Nyquist plots for loop gain for the following values of the feedback parameter β:
β = 0.1
β = 0.01
β = 0.001
1. Using the results in part a) determine which value of beta produces a stable amplifier.
1. Using the results from parts a) and b), determine the gain and phase margins of the stable amplifier.
Use the Bode plots below to measure the gain and phase margins.
Based on the values derived in part a), determine how much the gain can be increased so that the amplifier would still be stable.
log ω
log ω
0
Φ
GAIN
MARGIN
PHASE
MARGIN
-180º
-90º
40
30
20
10
βAO(jω) dB
(
)
÷
ø
ö
ç
è
æ
+
÷
ø
ö
ç
è
æ
+
÷
ø
ö
ç
è
æ
+
=
3
5
10
1
500
1
10
1
10
s
s
s
s
A
O
