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building a fuzzy system that imitates the natural functionality of β-cells in healthy persons to tightly and optimally regulate glucose concentration in Type 1 diabetic patients
Introduction Literature Review Physiological Model PID-FLC , PD-FLC, and PI-FLC MFB PID-FLC, MFB PD-FLC, and MFB PI-FLC Optimization Robustness Tests Conclusions
human body , energy, food, carbohydrates, and Glucose.
glucose & insulin interaction
Diabetic patients : Type 1 or Type 2 Type 2 : (90-95)% , Type 1 : (10-5)% In 2001 :120 million by the year 2025 :300 million In Jordan : in 2002:6.4%, in 2004: 7.5% United States : 21 million in 2005, sixth rank among
causes of death, 132 billion dollars , 10% of the health care budget
Complications : kidney failure, blindness, heart attack, immune system
Classical control : PID by E. Renard Model Predictive Control (MPC) : L. Magni comparative studies between FLCs and conventional
techniques: Ibbini and Masadeh :closed-loop fuzzy logic controller, classical PID-controller. Ibbini :PI-FLC, a classical PI, a classical PID, an optimal LQR and a classical fuzzy logic controller.
M. Khalil : P-FLC, PD-FLC, PI-FLC, and PID-FLC, glucose-insulin model by H.Wang .
))(())(())(())(()(253432
tIftIftGftGftGdt
dGin
))(()( tIdtIdt
dIiin
(min)2404505.0
(min)45151545
45505.0
(min)15015
505.0
)(
t
tt
tt
tGin
(min)24012012025.0
(min)12030)30120
301(25.0
(min)305)2530
301(25.0
)(min5025.0
)(
tt
tt
t
tIin
di>0=0.0076, 2= 15 min, 3= 5 min. An individual has a meal every 4 hours (i.e.
240 min) and the glucose intake duration is 45 min.
Lispro insulin
Glucose-insulin physiological model
Externally injected insulin,
Iin
Glucose intake rate, Gin
Plasma Glucose
level
Error
Change in ErrorFuzzy
controller
Glucose intake rate, Gin
Iin Plasma Glucose level
Glucose-insulin physiological
model/Patient model
Setpoint Fixed/
Time-varying
n
t
elfuzzyelGGG
nMAPE
0
modmod/)(
1
0 500 1000 150080
90
100
110
120
130
140
150
simulation time
gluc
ose
mg/
dl
-1 -0.5 0 0.5 1
0
0.2
0.4
0.6
0.8
1
ERROR
Deg
ree o
f m
em
bers
hip
E-NL E-NM E-NS E-Z E-PS E-PM E-PL
-1 -0.5 0 0.5 1
0
0.2
0.4
0.6
0.8
1
CH-ERROR
Deg
ree
of
mem
ber
ship
CE-NL CE-NM CE-NS CE-ZCE-PS CE-PM CE-PL
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
INSULIN
Deg
ree o
f m
em
bers
hip
NL NM NS Z PS PM PL paramet
er
GE GCE GIin
value 0.0646 0.4036 0.7705
λ (PI-FLC) 0.9875
β (PD-FLC) 0.0132
0
0.5
1
1.5
2
2.5
3
PD-FLC PI-FLC PID-FLC
2.5938
1.3787
1.4136
MA
PE
(%
)
695
700
705
710
715
720
725
reference model
PD-FLC PI-FLC PID-FLC
705.25
723.4995
708.8412708.1953
da
ily
infu
sed
insu
lin
(m
U/k
g/d
ay
)
0 500 1000 150080
90
100
110
120
130
140
150
simulation time
glu
ocse m
g/d
l
reference model
PI-FLC
PD-FLC
PID-FLC
λ (MFB PI-FLC) 0.0054
β (MFB PD-FLC) 1.0465
0
1
2
3
4
5
6
MFB PD-FLC
MFB PI-FLC MFB PID-FLC
1.7921
5.995
1.7704MA
PE
(%)
685
690
695
700
705
710
715
720
725
730
reference model
MFB PD-FLC
MFB PI-FLC MFB PID-FLC
705.25
700.4594
725.5572
703.2602
da
ily
infu
sed
insu
lin
(m
U/k
g/d
ay
)
controller Pervious work
(MAPE %)
My work (MPE %)
, (MAPE %)
controller MPE (%),
(MAPE %)
PD-FLC 12.2407 2.5938 MFB PD-FLC 1.7921
PI-FLC 5.73413 1.3787 MFB PI-FLC 5.995
PID-FLC 6.08743 1.4136 MFB PID-FLC 1.7704
controller Pervious work
(daily insulin
mU/kg/day)
My work (daily
insulin
mU/kg/day)
controller (daily insulin
mU/kg/day)
PD-FLC 1786.72 723.4995 (40.5
%)
MFB PD-FLC 700.4594
(39.2 %)
PI-FLC 1087.18 708.8412
(65.2 %)
MFB PI-FLC 725.5571
(66.7 %)
PID-FLC 940.379 708.1953
(75.31 %)
MFB PID-FLC 703.2602
(74.8 %)
Uncertainty in the Clearance Rate Factor
Error in Sensor Measurements Severe Initial Condition Changing the Glucose Intake Profile Unexpected Glucose Intake
iiiddUPd *
iiiddDownd *
0
2
4
6
8
10
12
14
16
PD-FLC PI-FLC PID-FLC
11.7188
14.995 15.0234
MA
PE
(%)
0
5
10
15
20
25
MFB PD-FLC MFB PI-FLC MFB PID-FLC
4.4458
21.4467
3.5441
MA
PE
(%)
815
820
825
830
835
840
845
850
855
860
865
PD-FLC PI-FLC PID-FLC
860.4559
832.345 833.381
da
ily
infu
sed
insu
lin
(m
U/k
g/d
ay
)
805
810
815
820
825
830
835
840
MFB PD-FLC MFB PI-FLC MFB PID-FLC
836.765
817.4924
839.388
da
ily
infu
sed
insu
lin
(m
U/k
g/d
ay
)
0 500 1000 150050
65
80
95
110
125
140
155
170
185
200
215
230
245250250
simulation time
glu
ocse m
g/d
l
uncertain reference model
PI-FLC
PD-FLC
PID-FLC
0 500 1000 150080
95
110
125
140
155
170
185
200
215
230
245250250
simulation time
glu
ocse m
g/d
l
MFB PI-FLC
MFB PD-FLC
MFB PID-FLC
uncertain reference model
0
2
4
6
8
10
12
14
16
18
PD-FLC PI-FLC PID-FLC
7.7514
17.3114 17.2457
MA
PE
(%)
0
2
4
6
8
10
12
MFB PD-FLC MFB PI-FLC MFB PID-FLC
7.1329
10.6656
7.1581
MA
PE
(%
)
598.5
599
599.5
600
600.5
601
601.5
602
PD-FLC PI-FLC PID-FLC
601.7913
601.2317
599.5973
da
ily
infu
sed
insu
lin
(m
U/k
g/d
ay
)
560
570
580
590
600
610
MFB PD-FLC MFB PI-FLC MFB PID-FLC
575.1973
602.2983
576.2602d
ail
y im
fuse
d in
suli
n
(mU
/kg
/da
y)
0 500 1000 15000
15
30
45
60
75
90
105
120
135
150
165
180
195200200
simulation time
glu
ocse m
g/d
l
uncertain reference model
PI-FLC
PD-FLC
PID-FLC
0 500 1000 15000
15
30
45
60
75
90
105
120
135
150
165
180
195200200
simulation time
glu
ocse m
g/d
l
MFB PI-FLC
MFB PD-FLC
MFB PID-FLC
uncertain reference moddel
)( xNGGfuzzymeasured
0 500 1000 1500-1.5
-1
-0.5
0
0.5
1
1.5
time
mg/
dl
Gaussian White noise with Variance=0.1 and Mean=0
0
2
4
6
8
10
PD-FLC PI-FLC PID-FLC
9.2793
4.4765
5.6695
MA
PE
(1
00
%)
0
5
10
15
20
25
MFB PD-FLC MFB PI-FLC MFB PID-FLC
11.4596
14.024
11.5753
MA
PE
(%
)
0 500 1000 150050
65
80
95
110
125
140
155
170
185
200200
simulation time
glu
ocse m
g/d
l
reference model
PI-FLC
PD-FLC
PID-FLC
0 500 1000 150050
65
80
95
110
125
140
155
170
185
200200
simulation time
glu
ocs
e m
g/d
l
reference model
MFB PI-FLC
MFB PD-FLC
MFB PID-FLC
0
20
40
60
80
100
120
140
PD-FLC PI-FLC PID-FLC
122.5
89.835 90.04
tim
e (m
inu
te)
116
118
120
122
124
126
128
130
132
MFB PD-FLC MFB PI-FLC MFB PID-FLC
124.6637
130.675
120.914
tim
e (m
inu
te)
0 120 240 360 480 600 720 840 960108012001320144015001500
65
80
95
110
125
140
155
170
185
200200
simulation time
glu
ocse m
g/d
l
reference model
PI-FLC
PD-FLC
PID-FLC
0 120 240 360 480 600 720 840 96010801200132014401500150080
100
120
140
160
180
200
simulation time
glu
ocse m
g/d
l
reference model
MFB PI-FLC
MFB PD-FLC
MFB PID-FLC
(min)240120))120(120(01.0
(min)120001.0)(
2
2
arg
tt
tttG
elin
0 500 1000 15000
5
10
15
t
Gin
distu
rban
ce
0
2
4
6
8
10
12
14
16
18
PD-FLC PI-FLC PID-FLC
16.7494
12.760211.9346
MA
PE
(%)
0
5
10
15
20
MFB PD-FLC MFB PI-FLC MFB PID-FLC
5.4796
19.1079
4.8881MA
PE
(%)
650
700
750
800
850
900
PD-FLC PI-FLC PID-FLC
893.1328
747.638 746.994
da
ily
infu
sed
insu
lin
(m
U/k
g/d
ay
)
694
696
698
700
702
704
706
708
710
712
714
MFB PD-FLC MFB PI-FLC MFB PID-FLC
710.0188
701.2719
713.703
da
ily
infu
sed
insu
lin
(m
U/k
g/d
ay
)
0 500 1000 150080
95
110
125
140
155
170
185
200200
simulation time
glu
ocse m
g/d
l
MFB PI-FLC
MFB PD-FLC
MFB PID-FLC
reference model
otherwise
ttG
ectedun0
(min)772768100)(
exp
))(())(())(())(()()(253432exp
tIftIftGftGftGtGdt
dGectedunin
700 720 740 760 780 800 82095
110
125
140
155
170170
simulation time
glu
ocse m
g/d
l
MFB PI-FLC
MFB PD-FLC
MFB PID-FLC
reference model
PID : high participant rate of the controller with the smallest MAPE.
PI-FLC ≈ PID-FLC . MFB PD-FLC ≈ MFB PID-FLC .
MFB PD-FLC and MFB PID-FLC better in 1)
uncertainty test 2) changing glucose intake profile
PI-FLC & PID-FLC better in 1 ) corruption in the sensor output and 2) patient experiences an elevated glucose concentration at the beginning of the simulation.
All the techniques retain glucose normal when a sudden glucose intake was assumed at a local peak glucose concentration.
The performance of the MFB PI-FLC was poor in about four of five robustness tests. This controller is unfit for model-flower applications since its response time is slow.
The MFB PID-FLC, the MFB PD-FLC, the PI-FLC, and the PID-FLC are good candidates to be used as control systems to drive a miniaturized insulin pump and regulate glucose elevation in Type 1 diabetic patient with an acceptable error.
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