Dr.N.SIVAKUMARAN M.E. Ph.D., Assistant Professor Modeling and Simulation Laboratory

1. Design of H∞ Controller for Blood Glucose RegulationP.Satheeshkumar,T.Vinopraba, Dr.N.Sivakumaran, Dr.S.Raghavan Dr.N.SIVAKUMARANM.E. Ph.D., Assistant Professor Modeling and Simulation Laboratory Department of Instrumentation and Control Engineering National Institute of Technology Trichy-620015 nsk@nitt.edu

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

3. 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.

4. Literature Survey • Y.Ramprasad et. al.(2004), Robust PID controller was designed using Shen tuning method, Cohen-coon tuning method and IMC. • Y.Ramprasad et. al. (2006), IMC and enhanced IMC controllers were designed to reject the meal disturbances. • 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.

5. What is Diabetes? 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.

6. 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 b cells of pancreas • Can take 7yrs. or longer to develop to absolute, by the time know something is wrong 80% - 90% of b 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 b cell protein • T-cells and antibodies tricked by this resemblance into attacking b protein and virus • Cases rising in certain areas of U.S. – particularly Northeastern region • Cow’s milk – certain protein which may trigger attack on b cells • Breast milk – hormones which protect body from attack on b cells Type 2 • Inheritance pattern, first degree relatives with type 2 have much higher risk for developing • Perhaps inheriting a tendency towards obesity since 85% obese Gestational • Genetically predisposed, have greater chance for developing type 2 later in life

7. Being in Control Non-diabetic Generally 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

8. 3D Structure of Insulin

9. Insulin Secretion • Glucose transported into b 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 monomer Reasons for monomer transformation: • Change in pH • Loss of ligands due to dilution, dissociation of allosteric ligands • Endogenous chelator removes the His B10 Zn2+ ions

10. The Good News… • By managing the ABCs of diabetes, people with diabetes can reduce their risk for heart disease and stroke. A stands for A1C B stands for Blood pressure C stands for Cholesterol

11. 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%

12. Key Steps for Lowering A1C • Eat the right foods. • Get daily physical activity. • Test blood glucose regularly. • Take medications as prescribed.

13. 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.

14. Block diagram of feedback control system Desired glucose concentration 81.1mg/dL Glucose concentration of the patient Insulin infusion pump controller patient + - Glucose sensor

15. MATHEMATICAL Model OF Human body • Parker Model. • Bergman Model. • Sorenson model. • Puckett model.

16. Schematic representations of compartments

17. Glucose model Brain: Heart and lungs: Gut: Liver: Kidney: (1) (2) (3) (4) (5) (6)

18. Periphery: Insulin model: Brain: (7) (8) (9) (10) (11) (12)

19. Heart and lungs: Gut: Liver: Kidney: Periphery: Glucagon model: (13) (14) (15) (16) (17) (18) (19)

20. Open Loop Response 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.

21. For Stabilizing set of Controller parameters Stabilizing region of (KI,KD)

22. Steady state I/O Plot for the system

23. Identification of Human body system Using the ident box in MATLAB a linear ARX model was identified and the transfer function is

24. Model VALIDATION

25. 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.

26. STEPS TO DESIGN A ROBUST H∞ CONTROLLER • The system along with uncertainties is modeled. • Designing of weighting functions is most important in Robust H∞ controller. • Open loop system is designed so that we can get TF of uncertainties to disturbance. • Sub-optimal controller is designed in MATLAB. • Controller is tested for both nominal and worst case uncertainties.

27. 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%)

28. 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)

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

30. Sensitivity and inverse weighting functions

31. Model Predictive Control • Modified form of classical optimal control problem • Can systematically and optimally handle Multivariable interactions Operating input and output constraints Process 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

33. FUTURE PAST SET POINT PREDICTED PLANT OUTPUT PLANT OUTPUT CONTROL LEVEL T + C T+1 T + P T T+2 CONTROL HORIZON PREDICTION HORIZON MPC Formulation -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. Camacho and Bordons,1999

34. Model Predictive Control….. The optimization cost function is given by: without violating constraints (low/high limits). where xi : 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.

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

37. For the nominal case non-linear model

38. For the worst case non-linear model

39. 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.

40. References • 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. • 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. • C.Fredrick, F.Tyrone, Closed-Loop Control of Blood Glucose, Springer, 2007. • Da-Wei Gu, Petko Hristov Petkov ,Mihail Mihaylov Konstantinov,Robust control Design in MATLAB, Springer,2005.

41. 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. • 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. • 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.

42. THANK YOU