Diaz, Control
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T
T
c
h
Twc
Twh
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x
y
200 mm
20mm
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.2
0.4
0.6
0.8
1
1.2
1.4
y
Temperatu
re
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.2
0.4
0.6
0.8
1
1.2
1.4
y
Velocity
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0 0.5 1 1.5 2 2.5 3 3.5 40.93
0.94
0.95
0.96
0.97
0.98
0.99
x
0 0.5 1 1.5 2 2.5 3 3.5 40.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x (a)
(b)
Q
(x)
Q
(x)
const
var
(
(
Q
Q
const
var
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a
Ti n
ma
mw
Ti n
w
a
Tou t
w
Tou t
(a)
(b)
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103
104
105
102
101
N
A
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103
104
105
102
101
N
4-5-5-1
4-4-1
4-5-1
4-5-5-5-1
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0 1 2 3 4 5 6 7 8 9 10
0
10
20
30
40
50
60
70
80
90
100
ANNNumerical
X
Y
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Q [W]
QANN
[W]
0 2 4 6 8 10 12 14 16 18 200
2
4
6
8
10
12
14
16
18
20
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QANN
Q [W]
[W]
0 50 100 150 200 250 3000
50
100
150
200
250
300
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0 50 100 150 200 250 3000
50
100
150
200
250
300
QANN
[W]
Q [W]
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0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
Q [W]
[W]
QANN
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0
1
2
3
4
5
6
7
8
9
10
x
104
01
02
030
N
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i
0
10
20
30
40
50
60
70
0.8
5
0.
9
0.9
5
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ma
.
Tina
Tinw
mw
.Q.
0 1000 2000 3000 4000 5000 6000 7000 8000 90000
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Q [W]
[W]
Qcor
QANN
,
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t
f(t)
x(t)
x(t-t)
f(t)
x(t)
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0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
1 2 3 4 5 6 7 8
t
x(t)
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0
0.
5
1
1.
5
2
2.5
3
2 4
t
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0
0.5
1
1.5
2
2.5
3
3.5
4
0.2
0.3
t
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0
0.5
1
1.5
2
2.5
3
3.5
4
4
.5
5
00.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0
0.2
0.4
0.6
0.8
1
(c)
(d)
t
t
z(t)
x(t)
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0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
2
1.5
t
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0
0.2
0.4
0.6
0.8
1
1.2
1.4
0.48
0.485
0.49
0.495
0.5
0.505
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0.1
0.15
0.2
0.25
0.3
0.35
(c)
(d)
t
x(t
t
x(
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0
50
100
150
200
250
300
350
400
15
0
50
100
150
200
250
300
350
400
22
24
26
28
30
32
34
tt
Touta
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x(t-t)
f(t-t)
x(t)x(t-2t)
x(t-nt)
0 100 200 300 4000.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 100 200 300 4000.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 100 200 300 4000.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
n = 1 n = 2 n = 3
ANN
Experiments Experiments
ANN ANN
Experiments
s s s
a
Tout
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0 100 200 300 400 500 60025
30
35
40
45
50
55
60
65
Water outlet temperature
Air outlet temperature
ExperimentsANNExperiments
ANN
t
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Water outlet temperature
Air outlet temperature
Experiments
ANN
ExperimentsANN
0 50 100 150 200 25030
35
40
45
50
55
t
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Water outlet temperature
Air outlet temperature
Experiments
ANN
ExperimentsANN
0 50 100 150 200 25030
35
40
45
50
55
t
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0 500 1000 1500 2000 2500 300020
22
24
26
28
30
32
34
36
38
40
time [s]
AirTemperatures[oC]
Disturbance Rejection with PI control (LabView)
Air inlet Temp.
Air outlet Temp.
Air heaterremoved.
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0 500 1000 1500 2000 2500 300010
15
20
25
30
35
time [s]
Inlet air Temp.
Air Speed x 30
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0 100 200 300 400 500 600 700 800 900 1000
t [s]
0 100 200 300 400 500 600 700 800 900 1000
0.05
0.1
0.15
0.2
0.25
31.2
31.4
31.6
31.8
32
32.2
t [s]
T
[
C]
out
a
m
[kg/s]
w
(a)
(b)
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0 0.2 0.4 0.6 0.8 1 1.2 1.426
28
30
32
34
36
38
40
42
m [kg/s]a
T
[C]
aout
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P
C
M
-
- +
+
+
+
+F
-
I
Reference
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0 50 100 150 200 250 300 35031.5
32
32.5
33
33.5
34
34.5
35
35.5
36
36.5
ANNPIDPI
100 120 140 160 180 200 220 240 260 280 300
35.4
35.6
35.8
36
36.2
36.4 ANN
PI
PID
t [s]
T
[C]
aout
T
[C]
aout
t [s]
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0 50 100 150 200 250 300 350 4000
100
200
300
t [s]
m
[kg/s]
w
0 50 100 150 200 250 300 350 40034.5
35
35.5
36
36.5
t [s]
T
[C]
out
a
0 50 100 150 200 250 300 350 4000.1
0.2
0.3
0.4
0.5
t [s]
am
[kg/s]
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Memory
y i
y i-1
x i
x i-1xi
ANNy i+1
Memory xi
ANNy i+1
y i
y i-1
x i-1
x i-2
y i
y i-1
x i-1
x i-2
y*
Controller
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0 5 10 15 20 25 30 35 40 45 50
yi+1
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
i
yi+1
0 5 10 15 20 25 30 35 40 45 50
0.6
0.62
0.64
0.66
0.6
0.62
0.64
0.66
0.114
0.116
0.118
0.12
0.122
r
i
yi
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yi+1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
yi+1
0 5 10 15 20 25 30 35 40 45 50
0
0.2
0.4
0.6
0.8
0
0.2
0.4
0.60.8
0
0.5
1
1.5
r
yi
i
i
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0 5 10 15 20 25 30 35 40 45 50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0 5 10 15 20 25 30 35 40 45 50
0
0.2
0.4
0.6
0.8
0
0.2
0.4
0.6
0.8
0
1
2
3
yi+1
yi+1
r
yi
i
i
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0 5 10 15 20 25 30 35 40 45 50
yi+1
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
i
yi+1
0 5 10 15 20 25 30 35 40 45 50
0.4896
0.4898
0.49
0.4902
0.4896
0.4898
0.49
0.4902
5.87
5.88
5.89
5.9
10
4
r
i
yi
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0 5 10 15 20 25 30 35 40 45 50
yi+1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
i
yi+1
0 5 10 15 20 25 30 35 40 45 50
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
1
0
1
2
3
r
i
yi
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0.3 0.4 0.5 0.6 0.7 0.8
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
y
y
D
E
y = yi+1 i
i
i+1
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0 20 40 60 80 100 120 140 160 180 200 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Unstable fixed point
Stable fixed point
t
yi+1
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0 5 10 1515
10
5
0
w1112
w213
1
0.030014
0.060025
0.0
90037
0.03
0014
0.06
0025
a
b
c
d
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0 5 10 1515
10
5
0
w11
12
w21
31
1.4838 1.
0386 0
.593
51
0.14838
a
b
c
d
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30 32 34 36 38 40 420.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
Tout
air [ C]
Spectralradius
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0 50 100 150 200 250 300 350 40030
30.5
31
31.5
32
32.5
33
33.5
34
34.5
35
t [s]
T
[C]
airo
ut
C
C
1
2
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PlantController
Parameter
Adaptation
Desired
performace
Reference
u y
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0 5 10 15 20 25 30 35 40 45 50
0 5 10 15 20 25 30 35 40 45 50
1
0.5
0
0.5
1
1
0.5
0
0.5
1
i
i(a)
(b)
ANN
y
;y
i
i
ANN
y;y
i
i
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0 20 40 60 80 100 120 140 160 180 2000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
i
yi+1
a
b
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0
2
4
6
8
100 1
2 3 4 5
6 7 8 9
10
10
8
6
4
2
0
yx
z
ii
i
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t [s]
Ta o
ut
[
C]
va[m/s]
0 20 40 60 80 100 120 140 160 180 200
0 20 40 60 80 100 120 140 160 180 200
32.5
33
33.5
34
34.5
1.5
2
2.5
3
3.5
t [s]
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Ta
out
[C]
t [s]
va
[m/s]
0 50 100 150 200 250 300 350 400 450 500
0 50 100 150 200 250 300 350 400 450 500
33
33.5
34
34.5
35
0.5
1
1.5
2
2.5
3
t [s]
Tw
out
[C]
0 50 100 150 200 250 300 350 400 450 50040
42
44
46
48
50
t [s]
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0 50 100 150 200 250 300 350 400 450
0 50 100 150 200 250 300 350 400 450
33.5
34
34.5
35
0
1
2
3
4
5
T
aout
[
C]
t [s]
t [s]
va
[m/s]
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0 50 100 150 200 250 300 350
0 50 100 150 200 250 300 350
33
33.5
3434.5
35
35.5
1
1.5
2
2.5
3
3.5
4
4.5
t [s]
t [s]
Ta o
ut
[
C]
va[m/s]
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0.5
1
1.5
2
2.5
3 0.05
0.1
0.15
0.2
0.25
0.3
0.1
0.15
0.2
0.25
0.3
0.35
mw[kg/s]
av [m/s]
E
[kW]
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t [s]
Ta o
ut
[
C]
va
[m/s]
0 50 100 150 200 250
0 50 100 150 200 250
33.6
33.8
34
34.2
34.4
1
1.5
2
2.5
3
t [s]
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0 50 100 150 200 250 300 350 400 450
0 50 100 150 200 250 300 350 400 450
38
39
40
41
42
43
44
0
0.5
1
1.5
2
2.5
3
Tout
a
[C]
Airspeed[m/s]
t [s]
t [s]
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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
=0.0
=0.5
=1.0
s
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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.4
0.2
0
0.2
0.4
0.6
0.8
1
1.2
K =10
K =5
K =1
p
p
p
s
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=1
=0
u
l
on off
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=1
=0
u
l
1
2
1
2
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0 1 2 3 4 5 6
0 1 2 3 4 5 6
0.3
0.40.5
0.6
0.7
0.8
0.9
1
0
2
4
6
8
10
12
14
-
1
2
p
(a)
(b)
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0 5 10 150.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
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0 100 200 300
0 100 200 300
0 100 200 300
0 100 200 300
39
39.540
40.5
41
41.5
42
42.5
0
0.5
1
1.5
2
2.5
39
39.540
40.5
41
41.5
42
42.5
0
0.5
1
1.5
2
2.5
Ta
o
ut
[C]
va
[m/s]
t [s]
t [s]
(a) (b) (c)
0 100 200 300
0 100 200 300
39
39.540
40.5
41
41.5
42
42.5
0
0.5
1
1.5
2
2.5
-
8/10/2019 Diaz, Control
155/179
-
8/10/2019 Diaz, Control
156/179
-
8/10/2019 Diaz, Control
157/179
100 200 300 400 500 6002
1.5
1
0.5
0
0.5
1
1.5
2
2.5
3
Ln(|T(t)-T
|)
t
-
8/10/2019 Diaz, Control
158/179
20 40 60 80 1004
6
8
10
12
14
16
18
200 300 400 500 6004
6
8
10
12
14
16
18
20 40 60 80 100200
300
400
500
600
0.4 0.6 0.8 1400
600
800
1000
1200
Delay [s]
Amplitude[C]
Period[s]
Delay [s]
Amplitude[C]
Period [s]
Q[
W]
va [m/s]
(a)
(b)
(c)
(d)
-
8/10/2019 Diaz, Control
159/179
-
8/10/2019 Diaz, Control
160/179
0.3 0.4 0.5 0.6 0.7 0.8 0.9 110
20
30
40
50
60
70
80
90
100
Air speed [m/s]
Delay[s]
-
8/10/2019 Diaz, Control
161/179
-
8/10/2019 Diaz, Control
162/179
0 100 200 300 400 500 600 700 800 900 100030
31
32
33
34
35
36
37
38
39
40
t [s]
Tout
a
[C]
-
8/10/2019 Diaz, Control
163/179
300 400 500 600 700 200 250 300 350 4000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
t [s]t [s](a) (b)
-
8/10/2019 Diaz, Control
164/179
-
8/10/2019 Diaz, Control
165/179
-
8/10/2019 Diaz, Control
166/179
-
8/10/2019 Diaz, Control
167/179
-
8/10/2019 Diaz, Control
168/179
-
8/10/2019 Diaz, Control
169/179
-
8/10/2019 Diaz, Control
170/179
-
8/10/2019 Diaz, Control
171/179
-
8/10/2019 Diaz, Control
172/179
-
8/10/2019 Diaz, Control
173/179
-
8/10/2019 Diaz, Control
174/179
-
8/10/2019 Diaz, Control
175/179
-
8/10/2019 Diaz, Control
176/179
-
8/10/2019 Diaz, Control
177/179
-
8/10/2019 Diaz, Control
178/179
-
8/10/2019 Diaz, Control
179/179
