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DESIGN OF H DESIGN OF H CONTROLLER FOR CONTROLLER FOR BLOOD GLUCOSE REGULATION BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran , Dr.S.Raghavan Dr.N.SIVAKUMARAN M.E. Ph.D., Assistant Professor Modeling and Simulation Laboratory Department of Instrumentation and Control Engineering National Institute of Technology Trichy-620015 [email protected]

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Page 1: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

DESIGN OF HDESIGN OF H∞∞ CONTROLLER FOR BLOOD CONTROLLER FOR BLOOD GLUCOSE REGULATIONGLUCOSE REGULATION

P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran, Dr.S.Raghavan

Dr.N.SIVAKUMARAN M.E. Ph.D.,

Assistant ProfessorModeling and Simulation Laboratory

Department of Instrumentation and Control EngineeringNational Institute of Technology

[email protected]

Page 2: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

OVERVIEW

• Objectives• Literature Survey• Introduction to Diabetes• Human Body Model• Identification of human body system• Robust H∞ and Predictive Controller

• Conclusion• References

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Page 3: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

OBJECTIVES OF THE PAPER

To design a Robust H inf and predictive controller for Diabetic model.

To Compare the performance of the controller for servo and regulatory problems.

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Page 4: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

LITERATURE SURVEY

1. Y.Ramprasad et. al.(2004), Robust PID controller was designed using Shen tuning method, Cohen-coon tuning method and IMC.

2. Y.Ramprasad et. al. (2006), IMC and enhanced IMC controllers were designed to reject the meal disturbances.

3. E. Ruiz-Vellazqueza et. al. (2008), H∞∞ control is applied to obtain a robust controller for the automatic insulin delivery rate. The control action permits to prevent the hyperglycemia levels in a type I diabetic patient.

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Page 5: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

Diabetes is a chronic condition that occurs when the pancreas does not produce enough insulin or when the body cannot effectively use the insulin it produces. Hyperglycaemia and other related disturbances in the body’s metabolism can lead to serious damage to many of the body’s systems, especially the nerves and blood vessels.

There are two basic forms of diabetes: Type 1: people with this type of diabetes produce very little or no insulin. Type 2: people with this type of diabetes cannot use insulin effectively. Most people with diabetes have type 2.

A third type of diabetes, gestational diabetes mellitus (GDM), develops during some cases of pregnancy but usually disappears after pregnancy.People with type 1 diabetes require daily injections of insulin to survive. People with type 2 diabetes can sometimes manage their condition with lifestyle measures alone, but oral drugs are often required, and less frequently insulin, in order to achieve good metabolic control.

Common symptoms of type 1 diabetes include: excessive thirst; constant hunger; excessive urination; weight loss for no reason; rapid, hard breathing; vision changes; drowsiness or exhaustion. These symptoms may occur suddenly.

People with type 2 diabetes may have similar, but less obvious, symptoms. Many have no symptoms and are only diagnosed after many years of onset. As a consequence, almost half of all people with type 2 diabetes are not aware that they have this life-threatening condition.

What is Diabetes?

Page 6: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

How do people get diabetes?Type 1 • Genetic element/mutation, susceptibility to triggers:

– Viral infections– Stress– Environmental exposure - exposure to certain chemicals or drugs

• White blood cells, T lymphocytes, produce immune factors called cytokines which attack and destroy cells of pancreas

• Can take 7yrs. or longer to develop to absolute, by the time know something is wrong 80% - 90% of cells are destroyed

• 10% chance of inheriting if first degree relative has diabetes• Most likely to inherit from father• Increase incidences would take at least 400 years if genetic factors were the only cause

Viruses• Infection introduces a viral protein that resembles a cell protein• T-cells and antibodies tricked by this resemblance into attacking protein and virus

• Cases rising in certain areas of U.S. – particularly Northeastern region• Cow’s milk – certain protein which may trigger attack on cells• Breast milk – hormones which protect body from attack on cellsType 2• Inheritance pattern, first degree relatives with type 2 have much higher risk for developing• Perhaps inheriting a tendency towards obesity since 85% obeseGestational• Genetically predisposed, have greater chance for developing type 2 later in life

Page 7: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

Being in ControlNon-diabeticGenerally between 80mg/dL-120mg/dL• Fasting glucose level: <110mg/dL• 2 hours after a 75g carb meal: <140mg/dL• 110mg/dL-125mg/dL: impaired fasting glucose• By definition 2 fasting glucose above 126 mg/dL – positive for diabetes

Diabetic Goals • 90mg/dL-130mg/dL before meals• 110mg/dL-150mg/dL bedtime

HbA1c (glycosylated hemoglobin) – measures the level of glucose irreversibly bound to hemoglobin, 90 day measure of average blood sugar – can be misleading

• <6.0% for non diabetics = 114mg/dL• <7.0% for diabetics = 147mg/dL

• Control best obtained with pre-meal testing, 2 hour post meal testing, and bed time = 7x per day

• Lows more frequent in controlled diabetics, can’t feel them as well

• Long term diabetics, may not feel lows as well• Lows can occur more in less educated diabetics• Exercise – increases insulin sensitivity

Feelings of High Blood Sugars

Feelings of Low Blood Sugars

Frequent Urination Shakes

Increased Thirst Dizzy

Lethargy Feeling of confusion, disorientation

Irritability Sweaty

Anxiety

Headache

Page 8: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

3D Structure of Insulin

Page 9: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

Insulin Secretion• Glucose transported into cell by a glucose

transporter• Results in membrane depolarization and an influx of

extracellular calcium• Fusion of insulin storage vesicle in plasma occurs• Hexamer released from cell as crystal and dissolves

to monomerReasons for monomer transformation:

– Change in pH– Loss of ligands due to dilution, dissociation of allosteric ligands– Endogenous chelator removes the His B10 Zn2+ ions

Page 10: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

The Good News…

• By managing the ABCs of diabetes, people with diabetes can reduce their risk for heart disease and stroke.

A stands for A1CB stands for Blood pressureC stands for Cholesterol

Page 11: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

Ask About Your A1C

• A1C measures average blood glucose over the last three months.

• Get your A1C checked at least twice a year.

A1C Goal = less than 7%

Page 12: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

Key Steps for Lowering A1C

• Eat the right foods.

• Get daily physical activity.

• Test blood glucose regularly.

• Take medications as prescribed.

Page 13: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

Need for Blood Glucose (BG) regulation

• A high glucose concentration exerts an osmotic pressure in the extracellular fluid, and causes cellular dehydration. This excessive BG level causes loss of glucose through urination (glycosuria), leading to osmotic diuresis that depletes the body further of fluids and electrolytes.

• Too low a BG level carries the risk of hypoglycaemic coma. The BG level should not drop below a certain level because glucose is the only nutrient that can be used for energy by the brain, retina, and germinal epithelium of the gonads.

• Too high a glucose concentration (>11.1 mmol/l) can affect wound healing and interfere with human neutrophil function.

• Therapy that maintains BG level at below 11.9 mmol/l improves the longterm outcome in diabetic patients with acute myocardial infarction.

Page 14: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

Block diagram of feedback control system

Glucose sensor

patientInsulin infusionpumpcontroller+

-

Desired glucose concentration81.1mg/dL

Glucose concentration of the patient

Page 15: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

MATHEMATICAL MODEL OF HUMAN BODY

• Parker Model.

• Bergman Model.

• Sorenson model.

• Puckett model.

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Page 16: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

SCHEMATIC REPRESENTATIONS OF COMPARTMENTS

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Page 17: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

GLUCOSE MODELBRAIN:

HEART AND LUNGS:

GUT:

LIVER:

KIDNEY:

CBB

TBT

BCBC

B

BCB

CH

CB vT

vGG

v

qGGG )()(

TB

BU

B

TB

CB

TB vT

GGG

1

)(

CH

RBCUHCHP

CPK

CKL

CLB

CB

CH

vqGqGqGqGqGG

1)(

CS

SUCS

mealCS

SCS

CH

CS

vvv

qGGG

)(

CL

HGUCL

HGPCL

LCLS

CSA

CH

CL

vvvqGqGqGG

1)(

CK

KECK

KCK

CH

CK

vv

qGGG

)(

(1)

(2)

(3)

(4)

(5)

(6)

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Page 18: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

PERIPHERY:

INSULIN MODEL:BRAIN:

CP

GP

TPC

PTPC

P

PCP

CH

CP

vT

vGG

v

qGGG )()(

TP

PGUGP

TP

CP

TP

vTGGG

1)(

HGP

CL

IHGP AI

A 8885.043.21

669.1tanh138.12088.125

1

NHGPNHGP A

NA

2

1)388.0tanh(7.2

65

1

IHGU

CL

IHGU AI

A43.21

549.0tanh225

1

CB

BCB

CH

CB

V

QIII

(7)

(8)

(9)

(10)

(11)

(12)

18

Page 19: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

HEART AND LUNGS:

GUT:

LIVER:

KIDNEY:

PERIPHERY:

GLUCAGON MODEL:

CH

IVIHCHP

CPK

CKL

CLB

CB

CH

VQIQIQIQIQII

1

C

S

SCS

CH

CS

V

QIII

CL

LCPIRCL

LCLS

CSA

CH

CL

VVQIQIQII

1

CK

KCCK

KCK

CH

CK

VV

QIII

CP

IP

TPT

PCPC

P

PCP

CH

CP

VT

VII

V

QIII

TP

PCSIAI

P

TP

CP

TP

VTIII

1

N

PNCPNR V

FNN

(13)

(14)

(15)

(16)

(17)

(18)

(19)

19

Page 20: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

0 200 400 600 800 1000 120040

50

60

70

80

90

100

110

120

130

time(min)

glu

cose c

oncentr

ation(m

g/d

L)

50% 22.5% 5%

Transient response of a perturbed patient model with step change in insulin from its nominal value of 22.3 mU/min.

Open Loop Response

Page 21: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

Stabilizing set of Controller parameters

3916.1PK

0IK

096.135126.141 ID KK

8796.193878.19 ID KK

For

Stabilizing region of (KI,KD)

Page 22: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

Steady state I/O Plot for the system

22

14 16 18 20 22 24 26 28 30 3250

60

70

80

90

100

110

Insulin Infusion rate(mU/min)

Blo

od G

luco

se

Leve

l(mg/

dL)

Non-Linearity I/O Checking

Page 23: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

IDENTIFICATION OF HUMAN BODY SYSTEM

Using the ident box in MATLAB a linear ARX model was identified and the transfer function is

23

032.17007842.0

905253.0077.223

2

sss

ss

Page 24: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

MODEL VALIDATION

0 500 1000 1500 2000 250080

90

100

110

120

130

140

150

160

170

Time(min)

Blo

od G

luco

seLe

vel(m

g/dl

)

Step responses of actual and predicted model

predicted

actual

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Page 25: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

ROBUST H∞ CONTROLLER

• A Controller is said to be robustly stable if it controls the process at all uncertainties.

• H∞ methods are used in control theory to synthesize controllers achieving robust performance or stabilization.

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Page 26: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

STEPS TO DESIGN A ROBUST HH∞∞ CONTROLLER

1. The system along with uncertainties is modeled.2. Designing of weighting functions is most important in

Robust HH∞∞ controller.

3. Open loop system is designed so that we can get TF of uncertainties to disturbance.

4. Sub-optimal controller is designed in MATLAB.5. Controller is tested for both nominal and worst case

uncertainties.

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Page 27: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

Uncertainties in three parameters are considered.

• Effect of Glucose on Hepatic Glucose Uptake (40%)• Effect of Glucose on Hepatic Insulin (40%)• Fraction of Hepatic Insulin clearance (20%)

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Page 28: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

For closed loop stability it is necessary to satisfy the below condition

where Wp, Wu are the weighting functions. K is the controller. G is the process along the uncertainties

G = FU(Gmds,Δ)

11

1

GKIKW

GKIW

u

p

110

1

ssWp

100

1sWu

28

Page 29: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

Controller designed is

15186388369654994350

68392492941498765)(

2345

234

sssss

sssssGc

The controller is tested for full order non-linear model for both nominal and worst case models.

29

Page 30: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

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Sensitivity and inverse weighting functions

Page 31: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

Modified form of classical optimal control problem Can systematically and optimally handle

Multivariable interactionsOperating input and output constraintsProcess nonlinearities

Basic Idea Given a model for plant dynamics, possible consequences of the

current input moves on the future plant behavior (such as possible constraint violations in future etc.) can be forecasted on-line and used while deciding the input moves.

• Explicit use of a model to predict the process output at future instants.• Constraints on input and outputs( Physical constraints and Safety constraints)

can be integrated in the calculation of control signal.• Calculation of a control sequence by minimizing an objective function

Model Predictive Control

Page 32: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,
Page 33: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

CONTROL LEVEL

T+1 TT+2 + PCONTROL HORIZON

PREDICTION HORIZON

T

PAST FUTURE

PREDICTED PLANT OUTPUT

PLANT OUTPUT

SET POINT

T + C

MPC Formulation

Camacho and Bordons,1999

-Utilize a model to predict the output in future and minimize the difference between the predicted output and the desired one by computing appropriate control actions.

Page 34: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

The optimization cost function is given by:

without violating constraints (low/high limits).wherexi : ith control variable (e.g. measured temperature)

ri : ith reference variable (e.g. required temperature)

ui : ith manipulated variable (e.g. control valve)

: weighting coefficient reflecting the relative importance of xi

: weighting coefficient penalizing relative big changes in ui etc.

34

N

i

N

iiuiix uxrJ

ii1 1

22)(

Model Predictive Control…..

Page 35: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

Parameters for the MPC

35

Parameters Variation

Settling Time(min)

Peak Overshoot (%)

xi=8,ui=2 9.8 4

xi=6,ui=1 13.8 2.3

From the table it is quite clear that top parameters will give good response for the system.

Page 36: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

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Page 37: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

For the nominal case non-linear model

20 30 40 50 60 70 80 90 10075

80

85

90

95

100

Time(min)

Bloo

d Glu

cose

Leve

l(mg/

dL)

H-inf

MPC

37

Page 38: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

For the worst case non-linear model

20 40 60 80 100 120 140 160 180 20070

80

90

100

110

120

Time(min)

Bloo

d Glu

cose

Leve

l(mg/

dL)

MPCH-inf

38

Page 39: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

CONCLUSION

• Thus, the human body model is constructed in MATLAB software using 19 differential equations.

• The MPC controller eliminates the undershoots and Robust optimal H∞ controller settles faster.

• When uncertainties are introduced into the system, the performance of MPC are not satisfactory.

• As the nominal parameters vary from patient to patient, Robust H∞ controller is best suitable.

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Page 40: DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION DESIGN OF H ∞ CONTROLLER FOR BLOOD GLUCOSE REGULATION P.Satheesh kumar, T.Vinopraba, Dr.N.Sivakumaran,

REFERENCES1. Y.Ramprasad, G.P.Rangaiah, S.Lakshminarayanan, “Robust

PID Controller for Blood Glucose Regulation in Type I Diabetics”, Industrial Engineering & Chemical Research, vol.43, pp.8257-8268, 2004.

2. R.S.Parker, F.J.Doyle, J.H.Ward, N.A.Peppas, “Robust H∞ Glucose Control in Diabetes using a Physiological Model” , AIChE J., vol.46, pp.2537-2549, 2000.

3. C.Fredrick, F.Tyrone, Closed-Loop Control of Blood Glucose, Springer, 2007.

4. Da-Wei Gu, Petko Hristov Petkov ,Mihail Mihaylov Konstantinov,Robust control Design in MATLAB, Springer,2005.

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5. T.Sorensen, “A Physiologic Model of Glucose Metabolism in Man and its use to Design and Assess improved Insulin Therapies for Diabetes”, Ph.D thesis, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, 1985.

6. Parker, R. S.; Doyle, F. J., III; Ward, J. H.; Peppas, N. A. “Robust H∞ Glucose Control in Diabetes Using a Physiological Model”, AIChE J. 2000, 46, 2537-2549.

7. T.Vinopraba, N. Sivakumaran, T.K.Radhakrishnan, S.Raghavan, Optimal Control of Blood Glucose Regulation for Type-I Diabetics, Proc. International Conference on TIMA, MIT, Anna University, 2009.

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THANK YOU

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