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University of California, Davis
Department of Chemical Engineering and Materials Science
ECH 157
Process Dynamics and Control
Ahmet Palazoglu
EXAM 2
Fall 2010
(Open book and no notes)
1.
(5 pts) The loop transfer function (
) for a feedback system is given as:
OL
g
)
1
2
)(
1
(
2
)
(
+
+
=
s
s
s
g
OL
Sketch
the Bode and Nyquist diagrams for this system. Your sketch should show all
key
features of the diagram including the low frequency gain and the high frequency
asymptotic behavior. Calculate
the frequency at which the Nyquist diagram crosses the
imaginary axis.
The Bode diagram yields:
10
2
10
1
10
0
10
1
0
0.5
1
1.5
2
10
2
10
1
10
0
10
1
200
150
100
50
0
The Nyquist diagram looks like:
1
0.5
0
0.5
1
1.5
2
1.5
1
0.5
0
0.5
1
1.5
Nyquist Diagram
Real Axis
Imaginary Axis
1
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View Full Document It starts at low frequencies from the steadystate gain which is 2.
It is a secondorder
system so its phase shift is 180
0
, thus the sketch should remain in the lower half of the
Complex Plane, asymptotically approaching the origin.
Note that MATLAB also plots
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This note was uploaded on 04/01/2011 for the course ECH 157 taught by Professor Palagozu during the Spring '08 term at UC Davis.
 Spring '08
 PALAGOZU

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