Advanced control engineering (S.R. Burns, 2001)
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Open-Loop Gain (db)
30 |
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0.25 dB |
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25 |
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0.5 dB |
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20 |
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1dB |
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–1 dB |
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15 |
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10 |
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3 dB |
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ω = 2.2 |
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6 dB |
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–3 dB |
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5 |
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0 |
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ω = 1.58 |
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(a) |
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–6 dB |
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–5 |
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ωB = 2.1 |
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(b) |
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–10 |
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ωB = 2.02 |
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–12 dB |
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–15 |
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ω = 2.66 |
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–150° |
–120° |
–90° |
–60° |
–30° –20° –10° |
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–20 |
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–20 dB |
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–200 |
–180 –160 |
–140 –120 |
–100 –80 |
–60 |
–40 |
–20 |
0 |
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Open-Loop Phase (deg)
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$ $ |
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$ $ |
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Gain (dB)
10
(b)Response with Mp = 3 dB (Bandwidth = 2.1 rad/s)
0
(a)Best flatband response 
(Bandwidth = 2.02 rad/s)
–10
–20
–30
–40
–50
–60 |
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10–1 |
100 |
101 |
Frequency (rad/s)
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$ $ |
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$ $ $ |
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$ $
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R2 |
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R1 |
C2 |
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vi(t) |
– |
vo(t) |
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C1 |
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+ |
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Gain dB
K dB
20
15
+6 dB/octave
10
5
0
1 |
Frequency (rad/s) |
1 |
T1 |
(a) Log Modulus |
T2 |
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60
φm
50 |
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40 |
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Phase |
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(degrees) |
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20 |
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10 |
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0 |
ωm |
1 |
Frequency (rad/s) |
1 |
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T1 |
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T2 |
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(b)Phase Advance
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70 |
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60 |
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50 |
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φm |
40 |
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(degrees) |
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30 |
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20 |
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10 |
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0 |
0.5 |
1 |
1.5 |
2 |
2.5 |
3 |
3.5 |
4 |
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0 |
(spacing (octaves)
$
$ |
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# |
Open-Loop Phase Gain (dB)
30 |
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0.25 dB |
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25 |
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0.5 dB |
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20 |
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1 dB |
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15 |
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10 |
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3 dB |
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5 |
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6 dB |
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ω = 1.9 |
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0 |
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–5 |
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–10 |
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–15 |
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–20 |
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–240 |
–220 |
–200 |
–180 |
–160 |
–140 |
–120 |
–100 |
–80 |
–60 |
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Open-Loop Phase (deg) |
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$ $ $
$ $
Open-Loop Gain (dB)
30 |
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0.25 dB |
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25 |
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0.5 dB |
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20 |
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1 dB |
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15 |
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10 |
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3 dB |
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5 |
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6 dB |
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(a) |
(b) |
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0 |
ω = 3.0 |
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ω = 2.0 |
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–5 |
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–10
–15
–20
–240 |
–220 |
–200 |
–180 |
–160 |
–140 |
–120 |
–100 |
–80 |
–60 |
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Open-Loop Phase (deg) |
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$ |
# |
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$
$
$
$ |
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$ |
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20 |
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10 |
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11.6 dB |
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0 |
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–3 |
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C(jω) |
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R |
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dB –10 |
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–20 |
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–30 |
100 |
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10–1 |
3.4 |
Frequency (rad/s)
$
$
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