Fuzzy PI Control of an Industrial
Weigh Belt Feeder
Yanan Zhao and Emmanuel G. Collins, Jr.
Department of Mechanical Engineering
FAMU-FSU College of Engineering
August 2001
Department of Mechanical Engineering
Florida State University
Contents
ƒ
ƒ
ƒ
ƒ
Introduction
PI-like Fuzzy Logic Controller
PI Fuzzy Logic Controller
Conclusions
Department of Mechanical Engineering
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Introduction
ƒ IIndustrial
d t i l weigh
i h belt
b lt
feeder from Merrick
I d ti
Industries,
Inc.
I
ƒ
ƒ
ƒ
Transports solid materials
i t a manufacturing
into
f t i
process at a constant rate.
In current practice
practice, the PI
tuning is performed
manually.
An automated tuning
process is desired.
p
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Introduction (cont
(cont’d)
d)
ƒ The nonlinearities of the weigh belt feeder are:
ƒ
ƒ
ƒ
motor saturation (control signal with [0,10] volt
motor friction
friction,
significant sensor quantization.
ƒ M
Model-based
d l b d friction
f i ti compensation
ti methods
th d have
h
limitations:
ƒ
characteristics of friction are difficult to analyze
ƒ Fuzzy logic control (FLC) is a solution.
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Introduction (cont
(cont’d)
d)
Inference
mechanism
Rule-base
Defuuzzification
reference
fuzzzification
Fuzzy logic controller
control
signal
Plant
plant
performance
ƒ FLC is p
particularlyy useful when the plant
p
model
is unknown or difficult to develop.
fuzzification the rule
ruleƒ FLC has four main parts: fuzzification,
base, the inference engine, and defuzzification.
ƒ Fuzzy PID control has been widely studied
studied.
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Introduction (cont
(cont’d)
d)
ƒ PID-like
PID like ffuzzy logic cont
controller
olle (FLC)
(FLC):
Δu = F(e, Δe), u = F(e, Δe), Δu = F(e, Δe, Δ2e)
ƒ
The
h structure is analogous
l
to that
h off the
h
conventional PID controller.
ƒ PID FLC
FLC:
u (k ) = (K
ƒ
ƒ
p
+ K
i
z
+ K
z −1
d
)e(k )
The gains are tuned on-line with fuzzy reasoning.
This requires more experience with the system.
ƒ Both PI-like and PI FLCs are designed and
implemented.
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PI-like
PI
like Fuzzy Logic Control
r
e
+
-
e(k) \ Δe(k)
NB
NM
NS
ZE
PS
PM
NB
NB
NB
NB
NB
NM
NS
NM
NB
NM
NM
NM
NS
ZE
Δe
NS
NB
NM
NS
NS
ZE
PS
Ge
GΔe
NE
NM
NM
NS
ZE
PS
PM
Δu
PI like
PI-like
FLC
u
GΔu +
+
plant
y
1/z
PS
NS
NS
ZE
PS
PS
PM
PM PB
NS ZE
ZE PS
PS PM
PM PB
PM PB
PM PB
PB ZE PS PS PM PB PB PB
Fuzzy Rules for Computation of
Δu
MFs of e, Δe, and Δu
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PI-like
PI
like FLC(cont
FLC(cont’d)
d)
ƒ Scaling
g factors (SFs)
(
) appear
pp
as follows:
eN = Gee, ΔeN = GΔeΔe, Δu = Gu ΔuN
ƒ The SFs play a role similar to that of the
gains of a conventional controller.
ƒ Selection
S l ti off the
th SFs
SF are b
based
d on expertt
knowledge and adjustment rules
d
developed
l
d by
b evaluating
l ti the
th control
t l
results.
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PI-like
PI
like FLC(cont
FLC(cont’d)
d)
ƒ For the weigh
g belt feeder,, controllers were
designed for setpoints of 1, 2, …, 5 volts.
ƒ Constant scaling factors were used.
ƒ The output SF needs to be tuned due to its
strong influence on the performance and stability.
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Gain Scheduling of PI
PI-like
like FLC(cont
FLC(cont’d)
d)
Gain
scheduling
r
e
+
-
Δe
Ge
GΔe
PI-like
FLC
Δu
u
GΔu +
+
plant
y
1/z
ƒ Adjust
djust tthe
e output sca
scaling
g factor
acto us
using
g
G Δu ,sp = G Δu , 0 ⋅ γ, γ =
1
1 + 0.1 ⋅ sp
ƒ The control effort is decreased with the
increasing of the setpoint.
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Self-tuning
Self
tuning of PI
PI-like
like FLC(cont
FLC(cont’d)
d)
α
Fuzzy
reasoning
r
e
+
-
Δe
Ge
GΔe
PI-like
FLC
Δu
u
GΔu +
+
plant
y
1/z
ƒ Adjust
djust tthe
e output sca
scaling
g factor
acto as
Δu = (α ⋅ G u ) ⋅ Δu N
ƒ The updating factor α is tuned online
based on fuzzy reasoning using the error
and change of error at each sampling
time.
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Self-tuning of PI-like FLC(cont
FLC(cont’d)
d)
MFss for
o
MFs for
e(k) \ Δe(k)
N ZE P
ƒ Rule-bases for
N B M S
ZE M S M
computation of
P S M B
The domain of the updating factor is also
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tuned.
Florida State University
Comparison of the gain scheduled
and the self-tuning FLCs
Setpoint
Type of FLC
IAE
ISE
ITAE
ITSE
1
GS
523 8
523.8
372 2
372.2
3251 4
3251.4
811 6
811.6
ST
456.0
303.2
3114.4
585.3
GS
755.1
1032.0
4200.5
1625.4
ST
689.6
883.6
4161.0
1241.6
GS
1071.1
2192.9
5172.5
3132.6
ST
948.5
1952.1
4223.3
2440.7
2
3
C
Comparison
i
Using
U i Different
Diff
t Performance
P f
Indices
I di
The self-tuning PI-like FLC yields better performance.
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Comparison of the gain scheduled
and the self-tuning FLCs(cont’d)
Comparison of the Performance at Setpoints of 1, 2 and 3 Volts
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Comparison of the gain scheduled
and the self-tuning FLCs(cont’d)
Gain scheduled FLC
changes only the range
of the output
p surface.
Self tuning FLC changes
Self-tuning
both the range and the
shape of the output surface.
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PI Fuzzy Logic Control
Fuzzy
reasoning
r
e
+
-
Δe
Ge
GΔe
Fuzzy
reasoning
Ti
Kp
ƒ PI controller:
H(z) = K p + K i
PI
Controller
u
plant
y
z
1 z
)
= K p (1 +
z −1
Ti z − 1
ƒ The proportional gain K p and integral
time constant T i are adjusted on-line
by fuzzy reasoning.
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PI FLC (cont
(cont’d)
d)
MFs of e(k) and Δe(k)
MFs of Kp
MFs of Ti
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PI FLC (cont
(cont’d)
d)
ƒ Fuzzyy rules for
computation of Kp:
e(k) \ Δe(k)
N
N B
ZE S
P B
e(k) \ Δe(k)
ƒ Fuzzy rules for
computation of Ti:
ZE
B
B
B
N ZE
N S S
ZE B M
P S S
P
B
S
B
P
S
B
S
ƒ For different setpoints the range of Kp is
1
ρ=
adjusted. K = ρ ⋅ K
1 + 0.2 ⋅ sp
p , max
ma
p , max
ma 0 ,
ƒ MFs of Ti for different setpoints are also
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adjusted.
PI FLC (cont
(cont’d)
d)
ƒ Experimental results at Setpoints of 1
1, 2
2, 3:
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Comparison of the self
self-tuning
tuning PI
PIlike FLC and PI FLC
S e tp o in t T y p e o f
FLC
1
2
3
IA E
IS E
IT A E
IT S E
PI
3 1 7 .6
1 4 9 .8
2 6 1 9 .8
2 3 9 .4
ST
4 5 6 .0
3 0 3 .2
3 1 1 4 .4
5 8 5 .3
PI
5 0 1 .6
5 9 0 .6
2 9 4 3 .5
5 9 1 .0
ST
6 8 9 .6
8 8 3 .6
4 1 6 1 .0
1 2 4 1 .6
PI
7 5 9 .6
1 5 2 2 .1
3 7 9 8 .5
1 5 9 2 .1
ST
9 4 8 .5
1 9 5 2 .1
4 2 2 3 .3
2 4 4 0 .7
ƒ The PI FLC performed better.
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Co c us o s
Conclusions
ƒ T
Two categories
t
i off ffuzzy PI controllers
t ll
were
designed:
ƒ
gain-scheduled PI-like FLC, self-tuning PI-like FLC
ƒ
PI FLC with g
gains tuned byy fuzzyy reasoning
g
ƒ The self-tuning PI-like FLC performed better than
the gain scheduled PI-like FLC
FLC.
ƒ The PI FLC performed better than the two PI-like
FLCs.
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Conclusions(cont d)
Conclusions(cont’d)
ƒ As more user knowledge is incorporated into
the controller design, the performance of the
FLC improved.
i
d
proposed
p
are quite
q
simple,
p
ƒ All of the rules p
making the methods suitable for
implementation in an industrial environment.
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