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NDSU
8: Frequency Domain Techniquess
ECE 461
Gain Compensation Using a Nyquist Plot
On a Nyquist plot
The X-axis plots real(G(jw))
The Y axis plots imag(G(jw)).
M-circles define a constant distance to -1. An example is shown below.
2
0dB
3dB
1
6dB
9dB
12dB
0
-1
-1
-2
-3
-2
-1
real
0
Nyquist diagram. M-circles mark points where
1
G
1+G
= constant.
Two ways to use a Nichols chart to find a feedback gain follow:
Method #1: (useful if using MATLAB)
i) Plot G(jw) as imag(G(jw)) vs. real(G(jw)).
ii) Scale G(jw) up or down until
The system is stable ( G(jω) < 1 when crossing 1800.)
G(jω) is tangent to the desired M-circle.
iii) K is equal to the scaling used to make G tangent to the M-circle. If G(jw) is 2x larger, K=2.
JSG
1
rev 02/27/02