Pharmacologyonline 1: (2011) ewsletter Shamsara et al.

Transcription

1 Pharmacologyonline : () ewsletter Shamsara et al. New Approach for Stailizing of Glucose Concentration Level Using Non-Linear Control Strategies: Improvement of Sliding Mode Control and Fuzzy Logic Technique Elham Shamsara, Omid Shamsara and Nasser Mehrshad 3 Astract Diaetes is a serious disease during which the ody's production and use of insulin is impaired, causing glucose concentration level to increase in the loodstream. The lood glucose dynamics is descried using the Bergman minimal model. In this paper, higher-order sliding mode control techniques, in specific prescried convergence law, super-twisting control algorithm, is used to roustly stailize the glucose concentration level of a diaetic patient in presence of the parameter variations and meal disturance. Intelligent systems have appeared in many technical areas, such as consumer electronics, rootics and industrial control systems. Many of these intelligent systems are ased on fuzzy control strategies which descrie complex systems mathematical model in terms of linguistic rules. By advent of these methods, new techniques have appeared from which fuzzy logic een applied extensively in medical systems. This paper surveys the utilization of fuzzy logic control. Based on this method, fuzzy logic controller is designed to tackle a control prolem of the resulting highly nonlinear plant. It was shown also that the proposed schemes can perform well in simulation experiments. Finally the otained results from these two methods, are verified ased on comparison via digital computer simulation y MATLAB. Index Terms Diaetes, higher-order sliding mode control, super-twisting control algorithm, fuzzy logic control. C I. INTRODUCTION OMPLEXITY of a human iological system typically als its relations to e expressed only in a nonlinear way. Because of this complexity, it is not simple to achieve insulindependent diaetic therapies autonomously. Diaetes mellitus is a metaolic disorder of endogenous insulin aling excessive amount of glucose to stay in lood. In general, lood glucose is transformed into energy required y human activities, such as, walking, and this transformation requires insulin functionality. However, in diaetes mellitus, since a human ody fully or partially lacks the insulin functionality, unchanged glucose remains in lood. This work was supported in part y the Control Department of Islamic Azad University of Gonaad. Department of Pure Mathematics, Faculty of Mathematical sciences, Ferdowsi University, Mashhad, Iran. Control Engineering of Islamic Azad University of Iran, Gonaad ranch (Phone: ; Shamsara_Omid@yahoo.com). 3 Nasser Mehrshad is currently an Assistant Professor with Birjand University, Birjand, Iran. ( ..mehrshad@gmail.com). A condition of high lood glucose profiles results in several complications, such as, eye, kidney, and nerve damage, called hyperglycemia. Thus, in order to avoid the hyperglycemia, a continuous supply of exogenous insulin is required, and the insulin dependent diaetic therapy usually does this. On the contrary, too much insulin supply may lead to a condition of lood glucose profiles resulting in drowsiness, mental malfunctioning, irritaility, and loss of consciousness []. This condition is called hypoglycemia and also dangerous to the diaetic. Thus, the insulindependent diaetic therapy must concern oth hyperglycemia and hypoglycemia y providing an appropriate amount of exogenous insulin timely. Implementing tight glucose control in critically ill patients is the most important issue in diaetes management. The current medical treatments suggest three to four daily glucose measurements and an equivalent numer of sucutaneous insulin injections []. Finding less invasive and less frequent methods has een the suject of interest for many researchers who are working in this area. An alternative approach is to deliver insulin using a closed-loop device like a pump, which works like an artificial pancreas [3,4]. This closed-loop device would include a glucose sensor imedded under the skin and an insulin pump implanted in the adomen. The sensor can measure lood glucose concentration and pass the information to a feedack control system that would calculate the necessary insulin delivery rate using roust higher-order sliding mode control algorithms [5 7], to keep the patient under metaolic control. Imprecisely defined classes play an important role in human thinking. Fuzzy set theory derives from the fact that most natural classes and concepts are fuzzy rather than crisp nature. On the other hand, people can approximate well enough to perform many desired tasks. The fact is that they summarize from massive information inputs and still function effectively. For complex systems, fuzzy logic is quite suitale ecause of its tolerance to some imprecision. In the foling sections a rief description is given of the key contriution which fuzzy control, estimation, and measurements technology have made in each of the topics which have een identified in a medical literature search. In this paper, higher-order sliding mode control techniques, in specific prescried convergence law, super-twisting control algorithm, is used to roustly stailize the glucose concentration level of a diaetic patient in presence of the parameter variations and meal disturance. Intelligent systems 68

2 Pharmacologyonline : () ewsletter Shamsara et al. have appeared in many technical areas, such as consumer electronics, rootics and industrial control systems. Many of these intelligent systems are ased on fuzzy control strategies which descrie complex systems mathematical model in terms of linguistic rules. By advent of these methods, new techniques have appeared from which fuzzy logic een applied extensively in medical systems. This paper surveys the utilization of fuzzy logic control. Based on this method, fuzzy logic controller is designed to tackle a control prolem of the resulting highly nonlinear plant. It was shown also that the proposed schemes can perform well in simulation experiments. Finally the otained results from these two methods, are verified ased on comparison via digital computer simulation y MATLAB. system (glucose sensor) evaluates an input (glucose levels) and uses a control system (e.g. algorithm programmed into a computer) to predictaly control the output of that system (insulin infusion rate, see figure ). Input Glucose Levels Glucose Sensor Control System Algorithms Insulin Delivery via Pump II. THE HUMAN INSULIN-GLUCOSE MODEL To procure the mathematical models of the human insulin glucose system, several approaches are taken y researchers. In these approaches, empirical and fundamental methods are preferaly used y them. These approaches aim to descrie the insulin-glucose dynamics as a couple of mathematical equations that should e easy to manipulate for the insulin therapies and should fully descrie the characteristics of the internal insulin-glucose metaolism [8]. Basically, the empirical method uses a model structure (formula or equation) which is determined theoretically with several parameters. The ehavior of this model structure is determined y only the input-output data of the system from a numer of experiments. In this method, capturing the system ehavior or data is the most time-consuming process. In an example of the linear structure of the insulin-glucose system, to represent glucose effects, two parameters are used, and to represent insulin effects, other two parameters are also used in order to close the model to the actual system. In addition to the input-output data, semi empirical method utilizes other physiological factors, such as dynamic ehavior and kinetics to create a closer model of diaetic patients [8]. In the fundamental methods, a mathematical representation of the human internal system which is already known sufficiently y researchers constructs an insulin glucose model. This system ehavior includes kinetics and material transport. According to investigating the internal system, a lot of data from the literature can e used to determine the system parameters. Usually the model averages studied ehaviors. In particular, in constructing a fundamental diaetes model, the authors in [9] applied the insulin-release data of the β cells of the pancreas from a numer of examinations to a mathematical representation. III. HISTORY OF CLOSED-LOOP CONTROL METHODS Over the last half century, automated systems for delivery of insulin have een a topic of much interest, envisioned as an intelligent treatment paradigm for the insulin-deficient patient. The concept of an artificial pancreas and the evolving algorithms during this time parallel the rise of the electronic, digitized computer age. The control of lood glucose levels has een likened to industrial processes in which a monitoring Output Insulin Infusion Rate Feedack Through Sensor Fig.. Principles of control systems applied to glycemic control This system of artificially maintaining glycemic control requires three main components:. Glucose sensing device (continuous or very frequent).. Control device for analyzing lood glucose data and computing insulin dosing (computer or microprocessor). 3. Insulin delivery device (usually a sucutaneous mechanical pump, potentially an implantale pump). Only within the last decade have continuous glucose sensing devices (the afferent lim of a closed loop system) een approved y regulatory agencies after overcoming accuracy and staility issues. Three currently-availale models which are inserted into sucutaneous tissue have een approved in the USA due to success in clinical trials (Medtronic Guardian or Paradigm, Dexcom Seven, and Aott Navigator). A fourth, the Gluco-Day sensor, a microdialysis device (Menarini), is approved in parts of Europe. Even without closed loop control, a recent 6-month study found that usage of these devices led to a sustantial improvement in hemogloin AC without an increase in hypoglycemic episodes in persons with Type diaetes []. Intravenous (IV) glucose sensors have een investigated in smaller trials [] ut IV devices are not typically used. In contrast to sucutaneous sensors, intravenous sensors are accompanied y more severe risks such as thromosis, emolization, and intravascular infection. There have also een advances in insulin pump technology over the past decades. Commercially-availale insulin pumps deliver insulin y the sucutaneous route, though 68

3 Pharmacologyonline : () ewsletter Shamsara et al. intraperitoneal delivery (leading to faster asorption and action than sucutaneous) is eing studied in limited research settings []. Nonetheless, sucutaneous insulin delivery does not compare favoraly with the physiological secretion of eta-cells directly into the lood stream, and confers risks when used in the setting of closed-loop management. For example, delay of sucutaneous insulin asorption and action, even with fast-acting analog insulin, constitutes a fundamental prolem of most closed loop systems in persons with diaetes: the efferent delay. Specifically, elevated glucose levels after meals due to this delay lead to late and often excessive insulin delivery, leading in turn to hypoglycemia (overcorrection hypoglycemia). Stated in engineering terminology, there is an instaility characterized y large oscillations in the controlled variale (glucose) due to marked efferent delay. Recently, a semi-closed loop or hyrid system involving open-loop insulin delivery efore meals has een shown to lead to tighter glycemic control than fully closed loop treatment []. The attractiveness of a hyrid system rests on the well-known delay etween administration of sucutaneous fast-acting insulin and its action. Insulin given efore the meal in this fashion can e thought of as anticipatory rather than reactive. There have een multiple mathematical concepts with initial linear equations using first-order dynamics utilized in algorithms for closed loop glycemic control [3]. These early concepts could not e fully tested in animal or human studies and were rudimentary in terms of their aility to control lood glucose. Over the years, there came a clear need for models of glucose-insulin interaction that descried the dynamics of carohydrate homeostasis. A very early concept, Bolie s twocompartment model [3], gave way to Cerasi s threecompartment model [4,5]. Later, the Bergman/Coelli wellknown minimal model of carohydrate metaolism was pulished [6], and continues to provide an important contriution to some closed loop algorithms. This model generates indices of insulin action and insulin secretion and utilizes frequent glucose and insulin measurements during glucose clamp testing or intravenous glucose tolerance testing. It assumes a closed-loop relationship etween glucose, insulin secretion and insulin action etween a single glucose compartment and two insulin compartments [6]. It has een instrumental in defining the disposition index, a constant product of insulin sensitivity and insulin secretion [7]. Coelli et al have modified the original model in order to improve the accuracy of estimating insulin action and glucose secretory characteristics [8]. The ultimate role of any insulin delivery system is provision of insulin in a manner mirroring, as closely as possile, the human eta-cell. Beta-cell physiology and pathophysiology is an important topic of research and recent work emphasizes the acute effects of incretins and the chronic effects of amyloid [9]. Earlier eta cell reviews were silent on these issues and instead emphasized the many hormonal and non-hormonal input signals which regulate pancreatic insulin secretion []. These reviews of pancreatic eta cell secretion reveal something very important to this discussion. The strongest single regulatory factor affecting eta-cell insulin secretion is the concentration of glucose. IV. INSULIN-GLUCOSE REGULATION MODEL Until now, a wide range of models has een used to descrie the insulin glucose regulatory system dynamics in the human ody. One of the pioneers in this task was Dr Richard Bergman, who developed the so-called Minimal Model. Bergman minimal model, which is a commonly referenced model in the literature, approximates the dynamic response of a diaetic patient s lood glucose concentration to the insulin injection using the foling nonlinear differential equations []: G& ( t) = p [ G( t) G ] X ( t) G( t) D( t) X & ( t) = p X ( t) p3[ I ( t) I ] () I& t = n I t I γ G t h t u t ( ) [ ( ) ] [ ( ) ] ( ) where t = shows the time glucose enters lood, sign shows the positive reflection to glucose intake and G(t), the glucose concentration in the lood plasma (mg/dl); X(t), the insulin s effect on the net glucose disappearance, the insulin concentration in the remote compartments (/min); I(t), the insulin concentration in plasma at time t (µu/ml); G, the asal pre-injection level of glucose (mg/dl); I, the asal preinjection level of insulin (µu/ml); p, the insulin-independent rate constant of glucose uptake in muscles and liver (/min); p, the rate for decrease in tissue glucose uptake aility (/min); p 3, the insulin-dependent increase in glucose uptake aility in tissue per unit of insulin concentration aove the asal level [(µu/ml)/min ]; n, the first-order decay rate for insulin in lood (/min); h, the threshold value of glucose aove which the pancreatic β cells release insulin (mg/dl); γ, the rate of the pancreatic β cells release of insulin after the glucose injection with glucose concentration aove the threshold [(µu/ml)/min /(mg/dl)]. To show the complete dynamics of the glucose insulin regulatory system, two other terms are considered in Equation (). D(t) shows the rate at which glucose is asored to the lood from the intestine, foling food intake. Since in diaetic patients, the normal insulin regulatory system does not exist, this glucose asorption is considered as a disturance for the system dynamics presented in (). This disturance can e modeled y a decaying exponential function of the foling:.5t ( t).5e D = () where t is in (min) and D(t) is in (mg/dl/min). u(t), which is the controller, defines the insulin injection rate and replaces the normal insulin regulatory system of the ody, which does not exist in diaetic patients. Therefore, the goal is to employ higher-order sliding model technique to design the appropriate control function, u(t) to compensate the uncertainties and disturances and to stailize the lood plasma glucose concentration of a diaetic patient at the asal level. It should e mentioned that the dynamics of the pump is neglected in the model introduced in Equation (). It is worth noting that in reality D(t) is supposed to reduce 68

4 Pharmacologyonline : () ewsletter Shamsara et al. to zero or some constant value in finite time, and the asymptotic model () is an approximation of a real process. Since higher-order sliding model control (SMC) accounts for the worst case scenario, i.e. considering D(t) and its derivatives at their maximum values, the controller design will e the same for model () or any other more realistic models. The system introduced in Equation () can e rewritten in state-space form as fols: x& = p [ x G ] x x D( t) x& = p x p 3 [ x 3 I ] (3) x& 3 = n[ x 3 I ] γ [ x h] t u( t ) Stailizing the glucose concentration in the diaetic patient s lood at the asal level G is an output-tracking prolem thus, the tracking error is defined as the difference etween the glucose concentration level and its in the diaetic patient s lood as e = G G t = G x (4) ( ) Given the dynamical system introduced in Equation (3), the controller u(t) must e designed such that e in presence of the uncertainties, parameter variations, and disturances, oral food intake, D(t). First the relative degree of the system must e defined. Assuming y = x, the relative degree would e defined with the numer of successive differentiation until the control appears in the equation. Relative degree r means that the controller u(t) first appears explicitly in the r th total derivative of σ. Using (3), the control function appears in the equations after the third differentiation, i.e : ( 3 x ) ( x t ) p x u ( t ) = ϕ, (5) 3 Since p 3, x = and p 3 x є [. -4, 3 - ], system (3) has a well-defined relative degree, r = 3. This als us to design the controller for the system in Equation (3) that satisfies e. V. HIGH-ORDER SMC TECHNIQUE: SUPER TWIST CONTROL DESIGN The super-twist control algorithm continuously controls the system with relative degree, r =, in presence of ounded disturances. In order to achieve relative degree, the sliding variale is designed as : σ = && c e& c e (6) e where c and c are real-valued constants chosen such that Equation (6) has the desired ehaviour. To check the existence condition of the sliding mode control, the dynamics of the sliding variale must e derived using (6) as σ = &&& e c e&& c e& (7) & Using (4), (5) and (7) can e written as : &&& σ = &&& &&& x c e&& c e& = ϕ G &&& x c e&& c e& = ( x, t) p3xu( t) ce&& c Comining and simplifying the terms in (8) will give σ& p x u t (9) =ψ ( ) ( ) t 3 (8) Where ψ t = ϕ x, t c e& c & () ( ) ( ) e & For the sliding mode to exist Ψ (t) must e ounded y a positive real numer [()], i.e. ψ& ( t) () From Equations (3) (5) it is ovious that the aove condition is met and therefore sliding mode exists and the controller can e designed for the system of (3). Consider the foling first-order nonlinear differential equation: σ ( σ ) dτ f ( ) & α σ β sign = t () where f (t) L. It has een proven [] that the solution of this nonlinear differential equation and its first time derivative will converge to zero in a finite time if α.5 (L) (/) and β 4L, where L is a real positive constant. The super-twist control function can then e designed as u ( σ ) = α σ β sign dτ (3) The super-twist control algorithm (3) provides finite time convergence of the sliding variale (6) to zero ut asymptotic convergence of the tracking error e due to the equation = && c e& c e, i.e. the lood glucose will e σ e stailized at its asal level asymptotically. The asymptotic convergence would not create any prolem since in case of insulin glucose regulatory, the process itself is inherently asymptotic. VI. SIMULATION RESULTS (PART ) A. Comparison Between PID Algorithm and Sliding Mode Control PID algorithms are offshoots of proportional derivative (PD) systems. A PD system from the company Nikkiso, in Japan, is used in hospital settings with continuous glucose monitoring, in order to control glucose. Garry Steil and his colleagues have een instrumental in conceptualizing and testing PID algorithms for closed loop control. The results of the simulations with PID algorithm are included in this part of paper. MATLAB is used to simulate the closed-loop system in order to show the validity of the proposed design according to Fig.. Desired Glucose Level Error Signal - Control Strategy In Patient Out oisy Measurements Fig.. Simulation of closed-loop system y MATLAB using PID controller Glucose Level 683

5 Pharmacologyonline : () ewsletter Shamsara et al. Glucose level(mg/dl) By assumption K p =., K i =.985 and K D =5 (for PID controller) and c =3.4-4, c =.55, α=63.36 and β=.3493 (for SMC), Fig. 3 shows the response of a sick person to the presence of the meal disturance in t= using two methods. 7 7 asal Fig. 3. Comparison proposed methods (PID & SMC) in lood glucose regulatory pid smc It is ovious that the glucose is completely stailized at the asal level y using high-order SMC technique faster than PID algorithm. In the next part, MATLAB is used to simulate the closedloop system in order to show the response of a sick person to the presence of sudden variations in lood glucose concentration level. Fig. 4 illustrates the performance of closed-loop system in these conditions B. Roustness Analysis patient Fig. 5. Curve of the response of a sick person to the presence of the sudden disturances in lood glucose concentration level using SMC method To validate the proposed SMC method in Equation (3), the control function is applied to system (3) and the response of a sick person in presence of the meal disturance is examined. To check the roustness of the control algorithm to the parameter variations, a set of parameters for three different patients have een used. Figure 6 shows the results otained from the simulation. It is ovious that the transient responses of the different patients to the same controller are different, ut in all three cases, the glucose is completely stailized at the asal level in a reasonale time interval. patient patient patient patient Fig. 4. Curve of the response of a sick person to the presence of the sudden disturances in lood glucose concentration level using PID controller As similar way, these conditions are used to simulate the closed loop system in order to show the response of a sick person to the presence of sudden variations in lood glucose concentration level using high-order SMC technique. Fig. 5 illustrates the performance of closed-loop system using this method Fig. 6. Closed-loop glucose regulatory system using the proposed controller for roustness analysis using SMC method The values that have een used in implementing the model and its parameters are given in Tale I. To check the roustness of the PID algorithm to the parameter variations, a set of parameters for three different patients have een used too. Figure 7 illustrates the results otained from the simulation. 684

6 Pharmacologyonline : () ewsletter Shamsara et al. Parameter p p p 3 γ n h G I Tale I. Parameter Values Patient I Patient II Patient III patient patient patient3 of all these, high, and proper concentrations. ) Rules: After defining the fuzzy concept of input, we should make rules to decide what the output should e: more drug, a little drug, or no drug. For example, we define the foling rule: if the concentration of glucose is high and the rate of glucose is rising, then the drug should e more. 3) Defuzzification: After the rule, we get the output of fuzzy concept, for example, more of.8 and little of.. But the output which is the oject model s input must e an exact numer that needs to e defuzzified. By defuzzification, the output gets an exact numer. Fig. 8 shows configuration of a fuzzy system. In this paper, it is assumed that there are two different inputs of the concentration of glucose and the change rate of concentration, and one output of the change rate of insulin injection. Fuzzy logic controller is designed according to the structure of Mamdani. 7 7 Real Valued Inputs Fuzzifier Fuzzy Rule Base Fuzzy Inference Engine Fuzzy Output Sets Defuzzifier Fuzzy Input Sets Fig.7. Closed-loop glucose regulatory system using the proposed controller for roustness analysis using PID method VII. SIMULATION RESULTS (PART ) A. Comparison Between PID Algorithm and Fuzzy Logic Technique Various therapeutic situations are related to control prolems. Although the early medical systems appeared at the same time as the article y Zadeh (965), there has een little communication etween the research fields, ut recently this has changed due to the developments in computer systems, and rapid development of the literature searching methods motivated y the internet and the World Wide We. Many systems are eing developed which utilize fuzzy logic and fuzzy set theory. Fuzzy logic control is also an advanced process control, which imitates the logic of human thought, and much less rigid than the calculations computers generally perform [3]. There are three steps for the process of a fuzzy logic algorithm: fuzzification, rules, and defuzzification. ) Fuzzification: the input of a controller is an exact numer, for example, the concentration of glucose is mg/dl. What the fuzzification does is to fuzzify the concentration such as concentration, high concentration, and proper concentration. Every exact numer has the weight Real Valued Outputs Fig. 8. Configuration of a fuzzy system with fuzzifier and defuzzifier It can e seen all required data for fuzzy logic controller in Tale. II-IV. Fig. shows memer functions that they have een used for input variales. It is illustrated output memer function y Fig. 9. It is important that the doctor prescries suitale value of lood glucose concentration level and so proposed controller identifies the change rate of concentration according to the lood glucose concentration. It has een selected input and output memer functions as triangular. Degree of memership normal ok h igh high very high dosage Fig. 9. Output memership function 685

7 Pharmacologyonline : () ewsletter Shamsara et al. Tale II. Input Variales Characteristics Input Variales Blood Glucose Concentration The Change Rate of Blood Glucose Range [4 4] [- ] negative zero Memership Functions normal OK_high high positive very high Tale III. Output Variale Characteristics Output Variales The Change Rate of Insulin Injection Range [ ] Memership Function normal OK_high high very high Degree of memership Blood Glucose Concentration very high high OK_high normal normal ok igh h high very high Tale IV. Rules for Fuzzy Logic Controller The change Rate of Concentration negative positive zero very high very high high high high OK_high OK_high OK_high normal normal normal Two types of algorithms are used for a feedack controller design that stailizes the lood glucose concentration of a diaetic patient at the desired level in this paper. Now, we can compare performance of these methods in the same conditions. By assumption of this, we will otain to Fig. for accurate comparison etween PID method and fuzzy logic method..5.5 pid flc Degree of memership glucose negative zero positive Glucose level(mg/dl) asal Fig.. Comparison proposed methods (PID & FLC) in lood glucose regulatory glucose rate Fig.. Input memership functions In this part, The results of the simulations with the fuzzy logic control are included. MATLAB is used to simulate the nonlinear model of system. The values that have een used in implementing the model and its parameters are given in Tale 686

8 Pharmacologyonline : () ewsletter Shamsara et al. I. At first, we can indicate to the effect of noise in measurement. This can create y unexpected disturance. Unexpected disturance may happen, for example, a patient might eat an apple in nonmeal time, and this should e considered ut oviously is difficult to deal with y using the traditional discrete time methods. Taking this into account, simulation experiments, has een shown in Fig.. It is assumed a white noise y.5 amplitude for the error measurement in lood glucose evaluation. Fig. shows the response of a sick person to the presence of noise in the meal disturance in t= and t= Sec. 9 8 patient VIII. SIMULATION RESULTS (PART 3) SMC and FLC methods are used for a feedack controller design that stailizes the lood glucose concentration of a diaetic patient at the desired level in this paper. Now, we can compare performance of these methods in the same conditions. By assumption of this, we will otain to Fig. 4 for accurate comparison etween high-order SMC technique and fuzzy logic method. It is ovious that the glucose is completely stailized at the asal level y using fuzzy logic control faster than high-order SMC technique. 7 7 smc flc Fig.. Curve of the response of a sick person to the presence of noise in the meal disturance in lood glucose concentration level y fuzzy logic controller It is easy to see that the performance of proposed controller is suitale and it can e stailize glucose value at the asal level in the presence of noise in the meal disturance. B. Roustness Analysis To check the roustness of the fuzzy logic control to the parameter variations, a set of parameters for three different patients have een used. Figure 3 shows the results otained from the simulation. It is ovious that the transient responses of the different patients to the same controller are different, ut in all three cases, the glucose is completely stailized at the asal level in a reasonale time interval. 7 7 patient patient patient Fig. 3. Closed-loop glucose regulatory system using fuzzy logic controller for roustness analysis Fig. 4. Comparison proposed methods in lood glucose regulatory IX. CONCLUSION The diaetes management as one of the challenging control prolems in human regulatory systems has een discussed. The treatment of the disease via roust feedack control design has een considered. In this research, two types of algorithms are used for a feedack controller design that stailizes the lood glucose concentration of a diaetic patient at the desired level. Higher-order sliding mode control techniques, in specific prescried convergence law, super-twisting control algorithm, is used to roustly stailize the glucose concentration level of a diaetic patient in presence of the parameter variations and meal disturance. In fact, This stailization has een done in presence of the external disturances such as food intake and model parametric uncertainties, which affect high-accuracy and roustness of the entire system. The roust high-accuracy performance of the super-twist controller is checked and confirmed y computer simulations. Intelligent systems have appeared in many technical areas, such as consumer electronics, rootics and industrial control systems. Many of these intelligent systems are ased on fuzzy control strategies which descrie complex systems mathematical model in terms of linguistic rules. By advent of these methods, new techniques have appeared from which fuzzy logic een applied extensively in medical systems. This paper surveys the utilization of fuzzy logic control. Based on this method, fuzzy logic controller is designed to tackle a 687

9 Pharmacologyonline : () ewsletter Shamsara et al. control prolem of the resulting highly nonlinear plant. It was shown also that the proposed schemes can perform well in simulation experiments. Finally the otained results from these two methods, are verified ased on comparison via digital computer simulation y MATLAB. The main purpose of the current paper is to employ proposed methods and design a roust control in order to maintain lood glucose level at the. The theoretical results are checked via computer simulations. Also, for future studies, the effect of measurement noise is to e assessed and attenuated, as well as chattering analysis is to e performed. It is ovious that the glucose is completely stailized at the asal level y using fuzzy logic control faster than high-order SMC technique. G(t) X(t) I(t) G I p p p 3 n h γ APPENDIX The Glucose Concentration in the Blood Plasma for at Time t The Iinsulin s Effect on the Net Glucose Disappearance The Insulin Concentration in Plasma at Time t The Basal Pre-injection Level of Glucose The Basal Pre-injection Level of Insulin The Insulin-independent Rate Constant of Glucose Uptake in Muscles and Liver The Rate for Decrease in Tissue Glucose Uptake Aility The Insulin-dependent Increase in Glucose Uptake Aility in Tissue per unit of Insulin Concentration Aove the Basal Level The First-Order Decay Rate for Insulin in Blood The Threshold Value of Glucose Aove which the Pancreatic β Cells Release Insulin The Rate of the Pancreatic β Cells Release of Insulin After the Glucose Injection with Glucose Concentration Aove the Threshold ACKNOWLEDGMENT The authors would like to express their sincere gratitude and appreciations to Dr Asef Zare for his criticisms, valuale guidance and consistent encouragement throughout the course of this research work. REFERENCES [] Blood sugar, Wikipedia, the free encyclopedia, sugar. [] DCCT/The Diaetes Control and Complications Trial Research Group. The effect of intensive treatment of diaetes on the development and progression of long-term complications in insulindependent diaetes mellitus. New England Journal of Medicine 993; 39: [3] Jaremco J, Rorstad O. Advances toward the implantale artificial pancreas for treatment of diaetes. Diaetes Care 998; : [4] Alisser A, Leiel B, Ewartz T, Davidovac Z, Botz C, Zingg W. An artificial endocrine pancreas. Diaetes Care 9; 3: [5] Shtessel YB, Shkolnikov IA, Brown MDJ. An asymptotic second order smooth sliding mode control. Asian Journal of Control 3; 5(4): [6] Levant A. Higher-order sliding modes, differentiation and output feedack control. International Journal of Control 3; 76: [7] Levant A. Quasi-continuous high order sliding mode controllers. IEEE Transactions on Automatic Control 5; 5():8 86. [8] R. S. Parker, F. J. Doyle III, and N. A. Peppas, A modelased algorithm for lood glucose control in type diaetic patients, IEEE Transactions on Biomedical Engineering, vol. 46, no., pp , 999. [9] M. Nomura, M. Shichiri, R. Kawamori, Y. Yamasaki, N. Iwama, and H. Ae, A mathematical insulin-secretion model and its validation in isolated rat pancreatic islets perifusion, Computers and Biomedical Research, vol. 7, no. 6, pp , 984. [] Tamorlane, W.V.; Beck, R.W.; Bode, B.W.; Buckingham, B.; Chase, H.P.; Clemons, R.; Fiallo-Scharer, R.; Fox, L.A.; Gilliam, L.K.; Hirsch, I.B.; Huang, E.S.; Kollman, C.; Kowalski, A.J.; Laffel, L.; Lawrence, J.M.; Lee, J.; Mauras, N.; O'Grady, M.; Ruedy, K.J.; Tansey, M.; Tsalikian, E.; Weinzimer S.; Wilson, D.M.; Wolpert, H.; Wysocki, T.; Xing, D. Continuous glucose monitoring and intensive treatment of type diaetes. N Engl J Med 8, 359(4), [] Renard, E.; Costalat, G.; Chevassus, H.; Bringer, J. Artificial etacell: clinical experience toward an implantale closed-loop insulin delivery system. Diaetes Meta 6, 3(5 Pt ), [] Weinzimer, S.A.; Steil, G.M.; Swan, K.L.; Dziura, J.; Kurtz, N.; Tamorlane, W.V. Fully automated closed-loop insulin delivery versus semiautomated hyrid control in pediatric patients with type diaetes using an artificial pancreas. Diaetes Care 8, 3(5), [3] Bolie, V.W. Coefficients of normal lood glucose regulation. J Appl Physiol 96, 6, [4] Cerasi, E.; Fick, G.; Rudemo, M. A mathematical model for the glucose induced insulin release in man. Eur J Clin Invest 9, 4(4), [5] Cerasi, E. An analogue computer model for the insulin response to glucose infusion. Acta Endocrinol (Copenh) 967, 55(), [6] Bergman, R.N.; Phillips, L.S.; Coelli, C. Physiologic evaluation of factors controlling glucose tolerance in man: measurement of insulin sensitivity and eta-cell glucose sensitivity from the response to intravenous glucose. J Clin Invest 98, 68(6), [7] Elein, S.C.; Wegner, K.; Kahn, S.E. Reduced eta-cell compensation to the insulin resistance associated with oesity in memers of caucasian familial type diaetic kindreds. Diaetes Care, 3(), -7. [8] Vicini, P.; Caumo, A.; Coelli, C. The hot IVGTT two-compartment minimal model: indexes of glucose effectiveness and insulin sensitivity. Am J Physiol 997, (5 Pt ), E4-3. [9] Marchetti, P.; Dotta, F.; Lauro, D.; Purrello, F. An overview of pancreatic eta-cell defects in human type diaetes: implications for treatment. Regul Pept 8, 46(-3), 4-. [] Ward, W.K.; Beard, J.C.; Porte, D. Islet B-cell function in human sujects, in Methods of Diaetes Research; Clarke, W.L., Larner, J. and S. Pohl, Eds.; Vol II, Wiley and Sons: New York, 986; pp [] Parker RS, Doyle III FJ, Peppas NA. A model-ased algorithm for lood glucose control in type I diaetic patients. IEEE Transactions on Biomedical Engineering 999; 46(): [] Lynch SM, Bequette BW. Model predictive control of lood glucose in type I diaetes using sucutaneous glucose measurements. Proceedings of the American Control Conference, Anchorage, AK, U.S.A., 8 May ; [3] J. Chen, K. Cao, Y. Sun, Y. Xiao, and X. Su, Continuous drug infusion for diaetes therapy: a closed-loop control system design, Eurasip Journal on Wireless Communications and etworking, vol. 8, Article ID 49585, pages,