0
0~
0
10-2
ElectronicFeedback Systems
Blackboard 10.1
Viewgraph 10.1
+
VO
V.
IGain-of-ten amplifier
Compensation Examples
105
I
I
I
i
I
Viewgraph 10.2
00
Magnitude
-90~
t
--,0
Angle
3
3
3
r
-180
0.11
0.1
-2700
1
10
100
103
to(rad/sec) -
104
101
106
Bode plot for uncompensated
gain-of-ten amplifier
af = 5 x 104/[(s + 1)(10~4s + 1)(10~s + 1)].
Viewgraph 10.3
+ a(s)V.
+
i
+
C
Circuit
A
Gain-of-ten amplifier with lead
network in feedback path.
-
10-3
10-4
Electronic Feedback Systems
Viewgraph 10.4
Vi
VO
Block diagram
Gain-of-ten amplifier with lead
network in feedback path.
Viewgraph 10.5
1
I
I
I
0
i
M agnitd
itude
-90o
ngle
- 0
.3
3
3
-1800
0.11L_
0.1
-2700
10
100
10
104
105
106
cw(rad/sec)
Bode plot for uncompensated
gain-of-ten amplifier
af = 5 x 104 /[(s + 1)(10- 4s + 1)(10~ 5s + 1)].
CompensationExamples
Viewgraph 10.6
v
0-1~
Vi (
Circuit
Gain-of-ten amplifier with lag
compensation.
Vi
--
R
10.7
'm+Viewgraph
VO
Block diagram
Gain-of-ten amplifier with lag
compensation.
10-5
10-6
Electronic Feedback Systems
Viewgraph 10.8
VO
Vi
Block diagram
Gain-of-ten amplifier with lag
compensation.
Viewgraph 10.9
V.
VO
Block diagram following
rearrangement.
Gain-of-ten amplifier with lag
compensation.
CompensationExamples
Viewgraph 10.10
00
900
-
t
-0
Angle
3
3
-1800
3
;
-2700
100
10
10,
104
106
101
w(rad/sec) Bode plot for uncompensated
gain-of-ten amplifier
af = 5 x 104 /[(s + 1)(10- 4 s + 1)(10
10,
I
I
I
I
1
5
s + 1)].
Viewgraph 10.11
00
Magnitude
-- 900
Angle
3
-180
0.11L
0.1
1
10
100
103
104
105
3
3
-2700
106
w(rad/sec)
Bode plot for lag compensated
gain-of-ten amplifier.
a"f " = 5 X 104 (1.5 X 10- 3 s + 1)/
[(s + 1)(10- 4 s + 1) (10- s + 1) (9.3 X 10- 3s + 1)] .
10-7
10-8
ElectronicFeedback Systems
Viewgraph 10.12
t
M
0.11
0.01
1
1
0.1
1
1
1
100
10
w(rad/sec)
103
1 \
\X
104
10
Effects of various types of
compensation on loop-transmission
magnitude.
Viewgraph 10.13
j
jw.
s plane
-- 105
-104
(a) Uncompensated
-1
a
106
Compensation Examples
Viewgraph 10.14
s plane
-*-x-x-
-2.5 X 10' -10s
-1
(b) Lead compensated
Viewgraph 10.15
*i
s plane
-105
-104
(c) Lag compensated
o-
10-9
10-10
ElectronicFeedback Systems
Demonstration Photograph
10.1 Gain-of-ten amplifier
demonstration
Demonstration Photograph
10.2 Close-up of gain-of-ten
amplifier
CompensationExamples
This lecture's analysis and the associated demonstrations show
how the compensation methods developed earlier can be applied
to a physical system. The demonstration system is, admittedly,
somewhat contrived so that the required manipulations can be easily performed with accuracy. In many actual systems, exact system
parameters are less certain. However, analysis parallel to that presented in the lecture generally provides an excellent first cut at the
appropriate compensator, which may then be refined based on test
results.
Comments
It is important that participants in this course have first-hand
experience with the kind of analysis and measurements required
for compensation. Toward this end, the problem (P5.15) suggested
below, which includes substantial laboratory effort, is a very necessary part of the course.
I suggest aiming for 470 of phase margin in the lag-compensated
system without much justification for the design objective. The
reason is effectively an educational one. We choose the lead compensation to provide the maximum possible phase margin given
the constraints of the topology. This approach is reasonable,
because the maximum achievable value of 47* is adequate, but certainly not overly conservative.
Clarification
In the case of lag compensation, larger values of phase margin
could be obtained by using larger values of a. The value of 47* was
chosen so that direct stability and speed of response comparisons
could be made with the lead-compensated amplifier.
Textbook: Sections 5.2.4 through 5.2.6.
Reading
10-11
10-12
Electronic Feedback Systems
Problems
Problem 10.1 (P5.8)
Problem 10.2 (P5.12)
Problem 10.3 (P5.13): In calculating the settling time for the lagcompensated gain-of-ten amplifier, make the simplifying assumption that the loop transmission is second order. That is, the poles
of Equation 5.15 at 104 and 10' rad/sec may be ignored, and a"(s)
approximated by
5 X 105(1.5 X 10- 3s + 1)
a"(s) ~(s + 1)(9.3 X 10~3s + 1)
Problem 10.4 (P5.15)
MIT OpenCourseWare
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RES.6-010 Electronic Feedback Systems
Spring 2013
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