EE3530-4-1 - Chapter 4 Basic Properties of Feedback...

Chapter 4: Basic Properties of Feedback
Sensitivity of Open Loop Control Systems
An open loop control system operates without feedback and gen-
erates the actuating signal in response of an input signal.
y
Controller
D
ol
Plant
G
Input shaping
H
r
U
W
R
If the plant G ( s ) involves variations Δ G , then it induces a relative
error of the overall system
T ( s ) = G ( s ) D
ol
( s ) H
r
( s )
Δ T ( s ) = Δ G ( s ) D
ol
( s ) H
r
( s )
Δ T
T
=
Δ G ( s ) D
ol
( s ) H
r
( s )
G ( s ) D
ol
( s ) H
r
( s )
=
Δ G ( s )
G ( s )
that is the same as the relative error of the original plant.
1

Why Use Feedback?
• Under modeling: The mathematical model can not describe com-
plete dynamics of the process, or it is too complex to be useful.
• Uncertain parameters: Some physical parameters may change
with respect to operating conditions, or difficult to measure ac-
curately.
• External disturbance: Physical process can’t be insolated com-
pletely from outside world, and disturbance may affect the output
performance.
• The use of feedback suppresses uncertainties due to modeling,
parameter variations, and external disturbances.
• The price: feedback devices.
2

Example: Operational amplifier.
R
R
1
2
V
V
i
o
V
e
A
+
-
I
I
1
2
Usually A >> 1 and is very uncertain:
V
o
= - AV
e
.
With connection of R
1
and R
2
we have a feedback system. Since
A >> 1,
V
i
- V
e
R
1
≈
V
e
- V
o
R
2
.
Solving V
e
gives
V
e
=


V
i
R
1
+
V
o
R
2




1
R
1
+
1
R
2


- 1
=


R
1
R
2
R
1
+ R
2




V
i
R
1
+
V
o
R
2


.