[ieee 2011 ieee jordan conference on applied electrical engineering and computing technologies...

Intelligent Control of Glucose Concentration Based on an Implantable Insulin Delivery System for Type I

Diabetes Mohamed Al-Fandi#1, Mohammad A. Jaradat#2, Yousef Sardahi #3, Lina Al-Ebbini , Maysa Khaleel

#Mechanical Engineering Department, Jordan University of Science and Technology Irbid, JORDAN

[email protected], [email protected], [email protected]

Abstract— In this paper, the performance of a closed-loop Proportional-Integral-Derivative (PID) fuzzy logic controller (FLC) is evaluated as an automation scheme for an implantable insulin delivery system in type I diabetes therapy. The incredible progression in micro and nanotechnology has brought the concept of an “artificial pancreas” closer to reality. Manufacturing miniaturized, implantable insulin sensing and delivery devices are in fact feasible. The key to a successful implantable delivery system is the development of a self-regulated arrangement that mimics the performance of the real pancreas. The PID-FLC can be an effective control strategy for implantable insulin delivery system. It combines all the necessary components that react to the possible changes of glucose concentration in the blood stream. This paper is concerned with the parallel structure design of the PID-FLC which is achieved by combining the Proportional-Integral (PI-FLC) and Proportional-Derivative (PD-FLC) controllers. The PID-FLC is implemented on the nonlinear delay differential model of the glucose-insulin regulatory system, which describes how glucose and insulin interact in healthy individuals. Compared with other controlling approaches, the PID-FLC gives more than satisfactory results in maintaining near-normal glycemia and saving the amount of the daily delivered insulin.

Keywords— Intelligent control; implantable insulin delivery; fuzzy logic controllers; diabetes; insulin;glucose

I. INTRODUCTION Type I Diabetes Mellitus (TIDM) is a chronic metabolic

illness characterized by the absence or complete destruction of the pancreatic β-cells, which results in the rising of the blood glucose concentration above its normal level. The consequences of this disease are mostly long-term, such as kidney failure, blindness, nerve damage, heart attack, and ineffectiveness of the immune system [1]. In addition to these serious complications, the financial burden of treating this disease is considerable. For instance, in 2002, the United States spent about $132 billion on diabetes. This accounts for 10% of the health care budget at that time [2], [3]. Consequently, diabetes mellitus is a serious metabolic disease that must be artificially regulated. From an engineering point of view, the development of an artificial pancreas requires the availability of three key elements: a safe and reliable insulin delivery device, an accurate glucose-sensing unit, and a control system that modulates insulin delivery according to

blood glucose levels and variation trends [5], [6]. This paper focuses on a new control system (PID-FLC) that would be incorporated in a miniaturized implantable artificial pancreas for the treatment of TIDM.

Regarding the control part of an artificial pancreas, several approaches have been developed during the last three decades to control the deficient blood glucose system of the human body. Classical PID control strategies as they have previously been formulated [7]-[8], were shown to be primarily very robust in a variety of conditions for a simulated, average diabetic patient. Since these classical strategies, the literature has been oriented into two directions: adaptive control and robust control techniques to strengthen several specific issues and requirements that the control system must meet, such as robustness and accuracy of decision-making in delivering the insulin. Non-linear predictive controllers [9] and intelligent soft computing techniques (e.g. fuzzy and neuro-fuzzy methods) have been reported in numerous studies [10]-[14]. The objective of these approaches was to cope with parameter uncertainty and the nonlinear dynamics of the metabolic process. Furthermore, a recent study [15] investigated the use of fuzzy controllers in improving the performance of an expert PID algorithm, which behaves differently than a conventional PID controller. In addition, due to the low complexity of the membership functions formulation for both the inputs and the outputs, the performance of the overall controller cannot be considered efficient for each patient individually. In fact, most of the applied control methods were focused on simple linearized models that are usually minimal ones, such as the Bergman mathematical model [16], resulting in low complexity of the proposed controllers and parameters and hence less efficient treatment. From a practical point of view, the designed controllers were true only for a few patients since they were applied on the simple Bergman model. To derive this model, blood samples were taken from only one fasting subject at regular intervals of time [16]. Moreover, mishandled situations often appear, such as a dangerous case of hypoglycemia, possibly leading to coma. Most of all, unpredictable glycemia oscillations remain the unacceptable fate of insulin-treated patients because the tuning of insulin doses relies more on rough estimations than on reliable and factual information about blood glucose status at all times. Collectively, the blood-glucose control is a difficult problem

2011 IEEE Jordan Conference on Applied Electrical Engineering and Computing Technologies (AEECT)

978-1-4577-1084-1/11/$26.00 ©2011 IEEE

to be solved. One of the main reasons is that individual patients are extremely diverse in their needs and their characteristics and demographic data are time-varying. Therefore, the advent of a newer approach to a more ideal artificial pancreas has grown rapidly in recent years.

In this spirit, a new control model for an implantable insulin delivery system has been developed which has not been examined before. The novelty of this control system resides in developing a parallel structure of PD-FLC and PI-FLC that demonstrates robustness against rapid high levels and meal disturbances. Ultimately, the developed PID-FLC model is more plausible than its predecessors; once it has been designed it will not only help to raise the patient’s quality of life, but will also increase the time spent in normoglycemia by delivering the optimal amount of insulin used to control the disease. Further, safety issues will be resolved by automated insulin infusion on the long term. In other words, the seriousness of hyperglycemia and hypoglycemia occurrence will be reduced by keeping the glucose level within an ideal range.

For simulation purpose, a more realistic mathematical model compared to that used in the previous control approaches was used. This model has been developed by Haiyan Wang et al. [17], in which the delay differential equation model is adopted. In fact, such a model describes the human blood glucose and insulin dynamics in healthy persons, as well as having the uniqueness of a stable periodic solution that corresponds to insulin secretion oscillations.

II. MATHEMATICAL MODEL In this paper, the simulation studies were based on a

mathematical model developed by Haiyan Wang et al. [17]. It closely simulates the dynamics of insulin-glucose interactions for human body. Thus, this model could be easily devoted to model insulin therapies for the patients whose pancreas does not produce enough insulin to properly control plasma glucose concentration levels. Briefly, the adopted model for type I diabetes with malfunctioned pancreas is as follows:

))-(())-(())((-))((-)( 253432 ττ tIftIftGftGftGdtdG

in += (1)

)()(d- i tItIdtdI

in= (2)

Where, dG/dt is the change of glucose level with respect to

time and dI/dt denotes the change of insulin level with respect to time (for more details about the model refer to [17]). The functions and parameters in this model were based on experimental data taken from normal subjects as reported in [17]. In particular, Haiyan Wang et al. [17] investigated how the delay differential equation (DDE) model behaves under periodic exogenous glucose and insulin infusions. Further, they studied the feasibility and possibility of an exogenous insulin infusion method that may restore the normal glucose–insulin metabolic system in type I diabetic patients.

III. THE PROPOSED PID-FLC

There are several structures of the decomposed PID as illustrated in [18],[19]. In this paper, the configuration in Figure 1 has been exploited for implementing a new insulin delivery system. This structure avoids the difficulties associated with the other PID-FLC configurations, which include rule dimensions, tuning and implementation. That is, it is very hard to join three inputs (error, change of error, integration of the error) and an output with a fuzzy rule and tune all of these variables. Therefore, the design procedure in this study is based on the parallel scheme of PI/PD- FLC controller through computation of two inputs instead of three-current system error (e) and error change rate (ce)- as shown in Figure 1 which also incorporates the insulin glucose model explained in Section II . These inputs inquire the fuzzy expert system by using fuzzy inference system (FIS) to provide online adjustment to the PI and PD control combined commands [19]. The fuzzy controller developed here is a two–input and one–output controller. The two inputs are e (mg/dl) and ce (mg/dl/min). The output is the delivered-insulin (MicroU).In particular; the optimal management of the PID-FLC operation depends on the right combination amount of the PD-FLC and PI-FLC. In other words, the required dose of insulin can be managed when PD and PI functions are multiplied by constants. These constants determine how much the PID controller depends on each term (i.e. PD and PI terms). The PD and PI parameters were manually tuned using eq. (3) and eq. (4) to get the desired values of the optimal PID-Fuzzy controller.

YPID = α1× YPD + α2× YPI (3)

( ))(),(2

1ii

ii DDIMPE ααα

== ∩

(4)

where, α1 is the participation rate of PD-FLC, α2 is the participation rate of PI-FLC, DDI is the daily delivered insulin and MPE is the mean percentage error as in eq. 5.

1

1Fuzzy Normal

Normal

n G GMPE

n Gt

−= ∑

= (5)

Where, GNormal is the normal glucose level and GFuzzy is the glucose level under the fuzzy controller.

The result of equation 3 when α1 =1 and α2 =0 is a full PD-FLC, and when α1 =0 and α2 =1, the result is a full PI-FLC. However, the intent of this study is to attain the best of these controllers. So, a process of selecting optimum values of α1 and α2 has been achieved as described in the results.

A. PD-FLC for Glucose-Insulin System The design of this controller was based on two input-

linguistic variables (e and ce) and one output variable representing the delivered-insulin. Each input variable was partitioned into a number of fuzzy subsets. The error e was divided into five triangular membership functions (Extremely


Figure 1.Th

Negative Error (X-NE), Negative Error

(ZE), Positive Error (PE) and Extremely PE)) with a range of (-15–11) mg/dl/min a2 .Similarly, the rate of error change (ce) watriangular membership functions within (-0as illustrated in Figure 3. Also, the oudivided into five triangular membership fuLarge Insulin (X-LI), Large Insulin (LI), Small Insulin (SI) and Extremely Small Insrange of (0.7–1.5) mU as shown in Figure 4the inputs and output were specified duringthe PD-FLC by noticing the maximum values of each fuzzy variable. Once the inpwere defined and the membership functionsfuzzy IF-THEN rule was derived from linoutput membership functions. The total nrules was 25 as depicted in Table 1

Figure 2. PD-FLC: Membership function

(b) Figure 3. PD-FLC: Membership function

PI-FLC

PD-FLC

�

d/dt

d/dt

Ref.

Error

Error

_

he structure of PID-FLC

r (NE), Zero Error Positive Error (X-

as shown in Figure as divided into five 0.5–0.4) mg/dl/min utput variable was unctions (Extremely

Zero Insulin (ZI), sulin (X-SI)) with a 4. These ranges of g the simulation of and the minimum put and output sets s were addressed, a

nking the input and number of possible

ns of input (1)

ns of input (2).

Figure 4. PD-FLC: Membership

TABLE 1. RULES

de/dt e X-NC NC

X-NE ELI ELI

NE ELI ELI

ZE ELI LI

PE LI ZI

X-PE ZI SI

B. PI-FLC for Glucose-InsulinThere are two different struc

Figure 13). The PI-FLC’s structintegrator at the output was usefed by two-input variables (e aneach input was fuzzified into depicted in Figures 5 and 6. Theof change is (-40–16) mgrespectively. As in the PD-FLCafter the simulation of the PI-FLsmallest values of the fuzzy vaoutput variable representing thwas also portioned into five mrange of (-0.02–0.02) mU/mAccordingly, 25-rules were dewhich describes the PI-FLC dyn

Insulin- glukinetics

Implantable insulin pump

α1

α2

�

+

+

functions of the output variable.

OF THE PD-FLC

ZC PC X-PC

ELI LI ZI

LI ZI SI

ZI SI ESI

SI ESI ESI

ESI ESI ESI

n System ctures of PI-FLC (refer to [21] ture which is a PD type with an ed. In this type, the rule base is nd ce). Similar to the PD-FLC, five membership functions as e range of the error and its rate

g/dl and (-2–2) mg/dl/min, , these ranges were determined

LC by recording the largest and riables. On the other hand, the

he change in delivered insulin membership functions over the min as shown in Figure 7. erived as depicted in Table 2 namics.

ucose s �

Disturbance

+

Glucose body level


Figure 5. PI-FLC: Membership functions of

Figure 6. PI-FLC: Membership functions o

Figure 7. PI-FLC: Membership functions of the

TABLE 2. RULES OF PI- FLC.

de/dt e NLC NSC PC PSC

NLE NL NL NL NS

NSE NL NL NS Z

ZE NL NS Z PS

PSE NS Z PS PL

PLE Z PS PL PL

For both the PD-FLC and the PI-FLC, M

inference engine was used to inquire the cobased on the fuzzy expert rules for a giveaddition, the center of area (CoA) of the resset of the combined membership functioprovide crisp output of the fuzzy controller.

f input (1)

of input (2)

e output variable.

C PLC

S Z

PS

S PL

L PL

L PL

Mamdani-Min-Max ontroller command n set on inputs. In sulted output fuzzy

on was utilized to

IV. RESULTS AN

For simulation purposes, the mfrom [17]. Basically, it was assuLispro, whose activity starts witthe patient under treatment follo

In this paper, simulations weFLC, PI-FLC as well as PID-Fwas considered acceptable if iproposed in [1].

The simulation results of thewell as the normal model are shthis figure, the range of the bloothe P-FLC, PD-FLC, and the P124 mg/dl, and 84-130 mg/dl, the normal range. Regarding theinsulin, the normal model injecof insulin. While, the PI-FLC, about 1055.56 mU/day/kg, 1mU/day/kg of the lispro insnoticed that the amount of insulthan that of the normal model.

For the PID-FLC, several coexamined (by trial and error mand 0.6 and α2= 0.6, 0.9 anreferring to eq.4, both of the ainsulin levels and the error wvalues of α which resulted in insulin as well as small error difficult to decide the optimumbecause there are four differentto satisfy the desired PID-FLC (i) variation of glucose level glucose level must not vary frovariation of insulin level (i.e.insulin must not vary from ppercentage error (MPE) (eq. 5daily delivered insulin shouhypoglycemia as much as pooptimal values, first the combinbe eliminated, because the maxvaried widely between two cascminimum values of glucose leeliminated because it lowered period to the critical value. Finaα1= 0.1 and α2=1. This impliesFLC and a small contribution PID-FLC lowers the daily con13%; keeping it within the norm

ND DISCUSSION

model parameters were adopted umed that the used insulin was thin 5-15 min of delivery , and

owed a diet as described in [17]. ere conducted for P-FLC, PD-FLC. The blood glucose level it was in the range 70-140 as

e four developed controllers as hown in Figure 8. As shown in od glucose concentration under PI-FLC is 112-125 mg/dl, 85-

respectively, which is within e amount of the daily delivered cted about 1262.52 mU/day/kg P-FLC , and PD-FLC infused

1288.64 mU/day/kg, 1786.18 sulin, respectively. It can be lin under the PI-FLC is smaller

ombinations of α1 and α2 were method) including: α1= 0.1, 0.2 nd 1. During these trails and amounts of the daily delivered were recorded. After that, the

small amount of the secreted were selected. In fact, it was m combination of α1 and α2 t qualifications that must exist output of the delivered insulin:

(i.e. the minimum value of om one period to another), (ii) . the maximum value of the period to another), (iii) mean 5) must be small, and (iv) the uld avoid both hyper- and ossible. Hence, to choose the nations in which α2 = 0.6 must ximum values of insulin level cading periods and affected the evel. Moreover, α1 = 0.6 was

the glucose level in the first ally, the most optimal choice is s a large contribution of the PI-

of the PD-FLC. The resulted nsumption of insulin by about mal range.


After applying the best selected values to the system, the glucose concentration was 85-132 mg/dl as shown in Figure 4. In addition, the daily infused amount of lispro insulin was 927.63 mU/day/kg, which is smaller than that of the PI-FLC.

Figure 8. Blood glucose level of the four fuzzy controllers

V. SYSTEM ROBUSTNESS In order to evaluate the proposed control method for

realistic conditions in patients with type I diabetes, a complete one-day simulation study was performed. This study was mainly intended to monitor the robustness of the automated insulin delivery system under a change in the clearance rate value, an unexpected glucose intake amount, and a sudden glucose increase at a local peak glucose level.

1) Changing Clearance Rate The clearance rate can be defined as the measurement of

insulin degradation relative to the amount of delivered insulin. Experiments have shown that insulin degradation is proportional to insulin concentration [17]. Thus, as in [17], we assume the clearance rate is a constant and denote it by di > 0. In this issue, system robustness was tested by changing the di value from 0.0076 to di 0.0077.

The closed loop robust performance to this perturbation is shown in Table 3. It can be seen that, an excellent compromise between the daily delivered insulin value and MPE was achieved with the conducted control scheme compared to individual controller commands, where the two values were minimized and the controller was able to handle such variations.

2) Unexpected Glucose Intake This test aims to test the performance of the introduced

controllers under a sudden change of glucose level. In this experiment, the glucose intake Gin proposed in [17] was changed to be glucose disturbance (GDis), as described in equation (6). Under this test, the performance of the four fuzzy controllers for 1440 minutes of simulation (one day) is shown in Figure 9. The P-FLC output exceeds 150 mg/dl.

TABLE 3. DAILY DELIVERED INSULIN AND THE MPE FOR DI = 0.0077

Type of Controller

Daily Delivered Insulin (mU/day) MPE

P-FLC 1311.9 7.69755%

PD- FLC 1787.63 10.7698%

PI- FLC 1107.85 5.91429%

PID- FLC 962.478 6.18286%

On the other hand, the PD-FLC, PI-FLC and PID-FLC operate in a more realistic behavior with the disturbance; since the blood glucose range does not exceed 150 mg/dl, but the PID-FLC controller records the least maximum peak at the minute of 120. The PD-FLC recovers the situation after 240 minutes. This is faster than the PI-FLC and PID-FLC. This observation demonstrates that the PID-FLC can be considered a key element of implantable insulin delivery system, since it has the capability to overcome a sudden bolus of glucose within a short time and by using the minimum amount of insulin consumption necessary compared to the other types of controllers. Further, this highly personalized and dynamic approach to insulin administration attempts to regulate the blood glucose level of the diabetic patient to maintain long-term normoglycemia.

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

<≤−−

<≤=

240120,))120(120(01.01200,01.0

2

2

tttt

G Dis

(6)

Figure 9. The systems output of glucose level under GDis for 1440 min.

3) Severe rise in the blood glucose level In healthy subjects, the blood glucose concentration may

reach as high as 300 mg/dl. As a result, the pancreas secretes the suitable amount of insulin to retrieve the glucose level back to its normal range (70-140 mg/dl). To simulate this reality, it was assumed that the diabetic patient experiences a severe increase in the glucose level at a time point (at t=800 minute). The performance of the four fuzzy controllers under this test is shown in Figure 10. In this test, the PI-FLC

0 200 400 600 800 1000 1200 1400

85

95

105

115

125

135

Simulation Time(min)

Glu

cose

Lev

el (

mg

/dl)

Normal glucose levelglucose level under the P-FLCglucose level under the PD-FLCglucose level under the PI-FLC glucose level under the PID-FLC

0 200 400 600 800 1000 1200 1400

758595

105115125135145155

Glu

cose

Lev

el(m

g/d

l)

Simulation time(min)

Normal glucose levelP-FLC glucose levelPD-FLC glucose level PI-FLC glucose levelPID-FLC glucose level


recorded the fastest time (about 15.24 minutes) to return the glucose level bake to its desired range. The PID-FLC had the second fastest time (15.81 minutes) followed by the PD-FLC (15.82 minutes), while the P-FLC was the slowest (about 20 minutes). However, in the study presented in [22], the PI-FLC applied on the Simple Bergman model was the fastest among the other introduced controllers and took about an hour to return the glucose level bake to a pre-specified set point (80 mg/dl). This demonstrates the superiority of the controllers proposed in this paper over those developed in the previous studies.

Figure 10. The performance of the fuzzy controllers under a severe rise in

the blood glucose concentration

VI. CONCLUSIONS In this study, a PID-FLC has been proposed; combining the

parallel structure of PD-FLC and PI-FLC to maintain the normoglycaemic average of type I diabetic patients in a way that imitates the natural pancreas. This study demonstrates that the PI-FLC and PID-FLC can control the insulin delivery system with the smallest MPE in comparison with the PD-FLC. Although the MPE from the PID-FLC was slightly larger than that recorded by the PI-FLC, the fact that the PID-FLC required the least amount of the daily-secreted insulin cannot be ignored. The use of such a parallel structure controller can save up to 13% of the daily consumption of the PI-FLC.

All the designs of the fuzzy logic controllers show robustness against diverse human variations such as model parameters, an unexpected glucose intake and a severe rise in the blood glucose level. However, the PID-FLC demonstrates an acceptable compromise between the amount of the daily delivered insulin and the MPE. As a result, the proposed PID-FLC achieved better performance and is an ideal candidate for automated implantable delivery systems.

VII. REFERENCES [1] C.V. Doran, J.G. Chase, G.M. Shaw, K.T. Moorhead, and N.H. Hudson,"

Derivative weighted active insulin control modeling and clinical trials for ICU patients", Medical Engineering & Physics 26(10) (2004) 855-866.

[2] G. Marchetti, M. Barolo, L . Jovanovic, H. Zisser, and D. Seborg, "A feedforward-Feedback Glucose control Strategy for type 1 Diabetes Mellitus" , Process Control 18(2) (2008) 149-162.

[3] D. Takahashi , Y. Xiao , F. Hu , and M. Lewis , "A survey of insulin-Dependent Diabetes---Part1: Therapies and devices", EURASIP Journal on Wireless Communications and Networking (2008) 639019.

[4] W. Liua and F. Tang, "Modeling a simplified regulatory system of blood glucose at molecular levels", Journal of Theoretical Biology 252 (2008),p. 608-620.

[5] F.J. Doyle, "Control and Modeling of Drug Delivery Devices for the Treatment of Diabetes", Proceedings of the American Control Conference (1996),p. 776-780.

[6] E. Renard, "Implantable closed-loop glucose-sensing and insulin delivery: the future for insulin pump therapy", Current Opinion in Pharmacology 2 (6) (2002) ,p.708-716.

[7] M.B.G. Marchetti, L. Jovanovic, H. Zisser, and D. E. Seborg, "An Improved PID Switching Control Strategy for Type 1 Diabetes", IEEE Trans. Biomed. Eng. 55 (3) (2008), p. 857-865.

[8] C.Li and R. Hu, "PID Control based on BP Neural Network for the Regulation of Blood Glucose Level in Diabetes", Paper presented at the Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering Boston (2007) ,p.1168 - 1172

[9] R. Hovorka , V. Canonico, L. J. Chassin, U. Haueter, M. Massi-Benedetti, M. Orsini Federici, T. R. Pieber, H. C. Schaller, L. Schaupp, T. Vering and M. E. Wilinska, "Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes", Physiological measurement 25(4) (2004), p. 905-920.

[10] D. U. Campos-Delgado,M. Hernández-Ordoñez, R. Femat, and A. Gordillo-Moscoso, "Fuzzy-Based Controller for Glucose Regulation in Type-1 Diabetic Patients by Subcutaneous Route", IEEE Trans. Biomed. Eng. 53 (11) ( 2006) ,p.2201-2210.

[11] S. Yasini, M.B. Naghibi-Sistani and A. Karimpour, "Active Insulin Infusion Using Fuzzy-Based Closed-loop Control", Paper presented at the 3rd International Conference on Intelligent System and Knowledge Engineering, Xiamen ( 2008) ,p.429 - 434.

[12] W.A. Sandham, D.J. Hamilton, A. Japp, K. Patterson, "Neural Network and Neuro-Fuzzy Systems For Improving Diabetes Therapy", Proceedings of the 20th Annual International Conference of the IEEE Engineering in Medicine and Biology Society 20 (3) ( 1998), p. 1438-1441.

[13] A.G. L. Kovács, B. Benyó, Z. Benyó and A. Kovács, "Soft computing control of Type 1 diabetes described at molecular levels", 5th International Symposium on Applied Computational Intelligence and Informatics ( 2009) ,p.99-104.

[14] M.G.Tsipouras, T.P. Exarchos , and D.I. Fotiadis, "Automated creation of transparent fuzzy models based on decision trees - application to diabetes diagnosis", 30th Annual International IEEE EMBS Conference Vancouver (2008),p. 3799-3802.

[15] R. Susanto-Lee, T. Fernando, and V. Sreeram, "Simulation of Fuzzy-Modified Expert PID Algorithms for Blood Glucose Control", Paper presented at the 10th Intl. Conf. on Control, Automation, Robotics and Vision (2008), p. 1583 - 1589.

[16] R.N. Bergman, L.S. Phillips and C. Cobelli, "Physiologic evaluation of factors controlling glucose tolerance in man: measurement of insulin sensitivity and beta-cell glucose sensitivity from the response to intravenous glucose", Journal of Clinical Investigation 68 (1981),p. 1456 - 1467.

[17] H. Wang, J. Li , and Y. kuang, "Mathematical modeling and qualitative analysis of insulin therapies", Mathematical Biosciences,(2007),p. 17-33.

[18] M. Golob, "Decomposed fuzzy proportional-integral-derivative controllers", Appl. Soft Comput. 1 (2001) , p.201-214.

[19] B.M. Mohan and A. Sinha, "Analytical structure and stability analysis of a fuzzy PID controller", Applied Soft Computing 8 (2008),p. 749-758.

[20] S. Bhattacharya, A. Chatterjee, and S. Munshi, "A new self-tuned PID-type fuzzy controller as a combination of two-term controllers", ISA Transactions 43 (2004) , p.413-426.

[21] J. Aracil and F. Gordillo," Describing function method for stabilty anaylsis of PD and PI fuzzy controllers", Fuzzy sets and systems 143(2004), p.233-249.

[22] M. Ibbini, "A PI-fuzzy logic controller for the regulation of blood glucose level in diabetic patients", Journal of Medical Engineering & Technology 30 (2) (2006) ,p.83 - 92.

0 500 1000 150050

100

150

200

250

300

350

Simulation time (min)

Glu

cose

leve

l (m

g/d

l)

Normal Glucose levelP-FLC glucose levelPD-FLC glucose levelPi-FLC glucose levelPID-FLC glucose level


[ieee 2011 ieee jordan conference on applied electrical engineering and computing technologies...

Documents