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Al-Khwarizmi 

  Engineering  
Journal 

Al-Khwarizmi Engineering Journal,Vol. 13, No. 3, P.P. 55- 63 (2017) 

 

 

Performance Comparison of Different Advanced Control Schemes 

for Glucose Level Control under Disturbing Meal 
 

Bashar Fateh Midhat*          Amjad Jaleel Humaidi** 
*,**Department of Control and Systems Engineering / University of Technology 

  *Email: basharfm88@yahoo.com 

       **Email: aaaacontrol2010@yahoo.com 

 
(Received 30 October 2016; accepted 7 March 2017) 

https://doi.org/10.22153/kej.2017.03.003 

 
 

Abstract 
       

In this work, diabetic glucose concentration level control under disturbing meal has been controlled 

using two set of advanced controllers. The first set is sliding mode controllers (classical and integral) and 

the second set is represented by optimal LQR controllers (classical and Min-, ax). Due to their 
characteristic features of disturbance rejection, both integral sliding mode controller and LQR Minmax 

controller are dedicated here for comparison. The Bergman minimal mathematical model was used to 

represent the dynamic behavior of a diabetic patient’s blood glucose concentration to the insulin injection. 

Simulations based on Matlab/Simulink, were performed to verify the performance of each controller. In 
spite that Min-max optimal controller gave better disturbance rejection capability than classical optimal 

controller, classical sliding mode controller could outperform Min-max controller. However, it has been 

shown that integral sliding mode controller is the best of all in terms of disturbance rejection capability. 
 
Key words: Optimal LQR control, Optimalminimax control, Sliding mode control, Integral sliding mode control. 

 

 

1. Introduction 
 

     Diabetes mellitus is the human disease which 
results from the presence of high level of blood 

sugar for prolonged period due to inadequate 

generation of insulin in blood [1]. 
In human body, the beta cells in pancreas are 

responsible for producing the insulin, which 

regulates the glucose consumption. In diabetes, 

beta cells fails to produce enough insulin 
concentration in blood and the human body will 

be unable to control the blood glucose level. 

    Type I diabetes mellitus patients cannot 
produce any insulin and insulin shots are given 

several times a day to help regulate their blood 

glucose level. A typical patient is then serving 
himself as a control system [2]. On the other hand, 

any patient that suffers from diabetes and not 

receives the insulin cure properly can lead to 

complications such as nerve damage, brain 

damage, amputation and eventually death.  
   In the human body, the normal blood glucose 

level varies in a narrow range (70-110) mg/dL. 

The diabetes is diagnosed if the human body is 
not able to control the normal glucose-insulin 

interaction [3]. For this reason, the blood glucose 

must be regulated by injecting the insulin [4]. 
In general, the closed loop glucose regulation 

system requires three components, which are: 

glucose sensor, insulin pump and control method 

for determining the necessary insulin dosage 
based on the glucose measurements [5]. Figure (1) 

shows the block diagram of closed loop glucose 

control system. 
 

 

 

 



Bashar Fateh Midhat                        Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 55- 63 (2017) 
 

56 

 

 
 

 

 

 

 

 

 

 

 

Fig. 1. Block diagram of closed loop insulin 

regulation system [10]. 

 
 

Several approaches have been previously 

addressed to design the feedback controller for 
insulin delivery, such as classical methods like 

Proportional Integral Derivative (PID) controllers 

[6, 7] and pole placement [8], which require a 
linearized mathematical model for the design of 

the controller, as well as model predictive control 

(MPC) [9, 10]. In [6] a PID controller based on 

BP neural networks is proposed in order to reduce 
the time of lowering blood glucose. In [11], the 

parameters of Hammerstein controller were 

optimized in order to minimize the time that takes 
for blood glucose to come back to its basal level. 

Also there are some efforts to use model 

independent based controller such as fuzzy 

controllers. In [12], a closed-loop control system 
applying fuzzy logic control introduced and the 

performance of this controller is tested on three 

different diabetic patients. Maryam [13] tried to 
tune the PD fuzzy controller with PSO algorithm. 

These fuzzy controllers were just able to control 

the glucose concentration, and suffer from lack of 
insulin and pump control. The works referred in 

[14, 15] suggested robust controllers such as 

disturbance rejection LQ controller, ��   and �� 
controller to regulate glucose-insulin system for 
Type I diabetic patients under meal disturbance.  

     In this paper, four different controllers (optimal 

LQR, minimax optimal, sliding mode, integral 
sliding mode) are addressed and designed for the 

glucose concentration level control problem in 

diabetic patients under meal disturbance.  

 
 

2. Mathematical Model  
 

Bergman minimal mathematical model, which 

is the most common referenced model in the 
literature, approximates the dynamic behavior of a 

diabetic patient’s blood glucose concentration to 

the insulin injection. The main advantage of using 

Bergman minimal model is that the number of 
parameters is minimum and it describes the 

relation between main two factors, insulin and 

glucose concentrations, without getting into 
biological complicated details. In the present 

work, nonlinear three-state minimal model of 

Bergman is considered [7]; �� ��� = −������ − 
�������� + �� � + ℎ��� 
� ��� = −��
��� + ������ �� ��� = −������� + �� � + ���� ��⁄                  …(1) 
Where G(t) is plasma glucose deviation, [mg/dL], 

X(t) is remote compartment insulin utilization, 

[1/min] and  Y (t) is plasma insulin deviation, 

[mU/dL]. The control variable ���� is the 
exogenous insulin infusion rate (mU/min), while 

the disturbance ℎ ��� represents the exogenous 
glucose infusion rate (mg/dL min). 

The physical parameters ��and�� are the basal 
glucose level (��/��), and basal insulin level 
(��/��), respectively, and �� is the insulin 
distribution volume (��). The model parameters 
are:  �� �1 �� ⁄ �, �� �1 �� ⁄ �, �� ��� ��� �� �⁄ �� 
and �� �1 �� ⁄ �. 
If the unmeasurable variable 
��� is assumed a 
slow variable, then 
� ��� = 0. From Eq.(1), the 
expression 
��� = ���/��� � ��� can be found. 
Substitution this expression into the first equation, 

the model of Eq.(1) is reduced to the following 

[13]: �� ��� = −������ − ���� ��������� + �� � + ℎ��� �� ��� = −������� + �� � + ���� ��⁄                  …(2) 
 

The linearization of Eq.(2) is performed by taking 

the variation of ���� = �" + ∆���� and ���� =�" + ∆����around equilibrium points (�", Y0, ℎ", �"). The perturbed version of Eq.(2) is given by;  ∆�� = $−�� − ����  �"% ∆����                                            − ��& + �� � ���� ∆���� ∆�� ��� = −�� ∆���� + ∆ ���� ��⁄                      …(3) 
 

If∆���� is defined as the first state variable'����, ∆���� is set as second state variable '���� 
and(��� is assigned to control input 
variation∆����, then the previous equation can be 
written in the following state space form, 

)� ��� = *−�� − �� �"�� − ��& + �� � ����0 −�� + )��� +  , 01 ��⁄ -  (��� +  .10/  ℎ���                              …(4) 0��� = .1 00 1/ )��� 



Bashar Fateh Midhat                        Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 55- 63 (2017) 
 

57 

 

 

For control objectives, the linearization in state 

space of the above model is taken at the 
equilibrium points of the following specified 

values; ℎ" = 0, �" = ���� �� , �" = 0 
Therefore, the obtained linearized model can be 
written as; 

'� ��� = *−�� − ��  ����0 −��
+ '��� + ,10 01 ��⁄ - (1 ��� 

2��� = .1 00 1/ '��� +                                        …(5)             
where (1 ��� = 3ℎ��� (���45. Equation(5) can be 
written in compact form as; '� ��� = 6 '��� + 7 (���                                   …(6) 2��� = 8 '���  
It is easily to show that the linearized model is 

completely controllable.  
 

 

3. Controller Design 
 

Four structures of advanced controllers will be 

presented and designed here for controlling the 
glucose level in human blood under meal 

disturbance. Later, the performance of such 

controllers will be verified and compared to each 
other using Matlab/Sumlink.  

 

 

3.1. Sliding Mode Controller 
 
   Sliding mode control is a discontinuous 

feedback control forces the system states to reach 

and remain on a specific surface within the state 

space (called sliding surface).  
The first stage of design is the selection of the 

discontinuity surface such that sliding motion 

would exhibit desired properties.  

Let us define a surface 9 in the state space as 
follows [16, 17]; 9 = '� + : '�                                                        …(7) 
If a controller ( was designed to make the system 
trajectories head to the surface  9 = 0, then Eq.(7) 
can be written as, '� + :'� = 0                                                         …(8) 
From Eq. (5), one can find that '� � = −��'� − ��� �� ��⁄ �'�                            …(9) 
Rearranging the above equation results in '� = −  �����'� + '� �� ��� ���⁄                     …(10) 
Substituting '� from the above equation into 
Eq.(8) results in − �����'� + '� �� ��� ���⁄ + :'� = 0            …(11) 
or, 

'� � + ��� − : �� �� ��⁄ �'� = 0                       …(12) 
The time solution for the equation above is written 

as '� = '��0�;<�=><? @A =B =C⁄ � 1                           …(13) 
such that ��� − : �� �� ��⁄ � D 0. 
Equation (13) shows that if the state trajectories 

are forced to move on surface 9 = 0, then '� will 
tend to zero exponentially after a finite time 
interval or one can say, '��� = ∞� = 0 → ���� = 0                             ...(14) 
To ensure that the state trajectories will head 

toward the surface 9 = 0, the following reaching 
condition should be fulfilled 99� G 0                                                                  …(15) 
Since 9� = '� � + :'� �, then  99� = 9 3'� � + :'� �4 = 9 3−��'� + (��� ��⁄ − ��'�                          −��� ���⁄ '� + ℎ���4              …(16)   
  If one assumes that the control defined as a 

discontinuous function for the surface 9 as below (��� = −H ∗ 9�� �9�                                       …(17) 
Substituting for the control(��� in Eq.(16), we 
have 99� = −�� 9 '� − H 9 9�� �9� ��⁄  −��9 '� − ��� ��⁄ � 9 '� + 9 ℎ���                 …(18) 
Using the fact that 9 ∗ 9�� �9� = |9| and from 
linear algebra, the inequality KL M |K||L| holds 
and results in the following; 99� M |9| N|��||'�| − H ��⁄ + |��||'�| +|�� ��⁄ |'� + |ℎ���|O G 0                              …(19) 
Solving for H, we have H D ��  N|��||'�| + |��||'�| + |�� ��⁄ |'� +|ℎ���|PQR O                                                        …(20) 
 

 

3.2. Integral Sliding Mode Control for 
Disturbance Rejection 

 
In what follows, integral sliding mode controller 

is designed for control and disturbance rejection 

of glucose systems. Starting with rewriting the 

control law as follows,  ( = (& + (�                                                         …(21)     
where(& is designed to make the system follows a 
specified trajectory '& in the state space which is 
based on optimal LQR controller, while the design 

of (� is dedicated to cancel the disturbance ℎ���. 
 Rewriting Eq.(4) by separating the control 

input ���� from disturbance ℎ��� and then 
substituting the control signal from Eq.(21) to 
have; )� = 6 '��� + 7S(& ��� + 7S(���� + T ℎ��� 
                                                                      …(21) 

WhereT = 31 045  and 7S = 30 1 ��⁄ 45. 



Bashar Fateh Midhat                        Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 55- 63 (2017) 
 

58 

 

The first stage of design is to select the 

discontinuity surface 9 such that sliding motion 
would exhibit desired properties. The surface 9 is 
defined in the state space as follows 9 = 9& + U                                                           …(22) 
WhereU represents the integral part which cancels 
the disturbance and 9& represent the desired path 
in the state space given by  9& = 8 '                                                               …(23) 
   In order to keep the system on the specified 

trajectory 9& the time derivative of the surface 9 
should equal zero. In other words, the system 

trajectory will not leave the surface 9&. 9� = 9�& + U� = 0 = 8'� + U� = 0                                                     …(24) 
or, 9� = 836 '��� + 7S(&��� + 7S (���� +                    T ℎ���4 + U� = 0                              …(25)             
In order to ensure that 9��� = 9&��� for all � D 0 
the following condition should be 

fulfilled7S(���� = −T ℎ���                            …(26) 
Substitute in 9� we get U� = −8 36 '��� + 7S(& ���4                           …(27) 
or, U = −8 V 36)��� + 7S(&���411W ��                  …(28) 
Thus, substitution for U is the surface equation 9 
will ensure that the system trajectories will remain 

on the surface 9 even under external disturbances. 
If (� considered to be a nonlinear function, then (� = −H�  9�� �9�                                             …(29) 
whereH� is the discontinuous controller gain. The 
final control law can be rewritten as follows; ( = (& + (�  ( = −X ' − H�  9�� �9�                                   …(30) 
To ensure that 9� = 0 for ∀� ≥ 0 in Eq.(25), the 
following condition has to be satisfied 87S(���� = −8 T ℎ���                                    …(31) 
Multiplying out the matrices in the above equation 

results in, − H�9�� �9� ��⁄ = ℎ���                                   …(32) 
Taking the worst case disturbance ℎ���PQR, the 
integral sliding mode gain H� can be evaluated as 
follows H� ≥ ��  ℎ���[\]                                                                   …(33) 
 

 

3.3. Optimal LQR Control 
 

The requirement of classical LQ control 

method is to minimize the following quadratic 
cost functional:  ^�(���� = �� V N25 _ 2�& + (5 ` ( O ��           …(34) 
The classical LQ attempts to find an optimal (∗ ���, � ∈ 30, ∞4 such that ^�(∗���� M ^�(��� for 

all (���, � ∈ 30, ∞4 under properly chosen c and _. The matrix _ (n×n) and  ` (m×m) are 
selected by the design engineer. 

The first element of input vector is the insulin 

rate ����, and the second element is the exogenous 
glucose ℎ��� which stands for disturbance. The 
objective is to minimize the effect of disturbance 
on the output. However, the elements of diagonal 

matrix c are responsible for overweighting and 
underweighting of the input elements. The first 

component of matrix c, namely c�� , is chosen to 
give high importance to disturbance input, ℎ���, 
while the element c��  has to giveless 
importanceto insulin rate. Less importance to 

insulin means that we relief the constraint on 
insulin or permit it to take higher level. Therefore, 

high value is assigned to c��  and low value is 
assigned to c�� . On the other hand, the elements 
of _give the weights on system outputs, plasma 
glucose deviation and plasma insulin deviation. 

Normally in this application, the same weight is 

given to both outputs. 
Based on optimal control theory, the following 

control Riccatiequation is established as [18], d6 + 65 d + 85 8 − d75 `<�7 d = 3e4     …(35)  
Since Matlab package is used here, a special built-

in function called care is used to solve above 

Ricatti equation for matrix d. Positive 
definiteness of matrix d is a necessary condition 
of solution. The optimal solution can be found in 

terms of d-matrix as follows; (∗ ��� = −`<�75 d)∗���                                  …(36) 
The closed-loop system based on optimal control 
input is given by [18]; )� ∗��� = 36 − 7 f4)∗���                                  …(37) 
where f = `<� 75 d. 
The closed-loop system will exhibit different 

performance depending on how design parameters 

are selected. Generally speaking, selecting _ with 
large terms means that, to keep gsmall, the state )��� must be smaller. On the other hand selecting ` with large terms means that the control input (��� must be smaller to keep ^ small. This means 
that larger values of _ generally result in the 
closed loop poles of the system matrix �6 − 7f� 
being further left in the s-plane so that the state 

decays faster to zero. On the other hand, larger c means that less control effort is used, so that the 
poles are generally slower, resulting in larger 

values of the state )���. 
 
 

 



Bashar Fateh Midhat                        Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 55- 63 (2017) 
 

59 

 

3.4. Optimal LQR Control with 
Disturbance Rejection (Minimax)  

 
The disturbance rejection LQ method is a 

generalization of classical LQ method and is 

based on the minimax criteria. This techniques is 
dedicated for optimal control and disturbance 

rejection puposes. Figure (2) shows the general 

structure of disturbance rejection LQ (minmax) 
control strategy.   

The system dynamic given by Eq.(4) is re-

formulated by separating the control input ���� 
from disturbance ℎ���. Therefore, the dynamic 
system can be written as; '� = 6 '��� + 7S ���� + T ℎ���                      …(38) 2��� = 8 '��� + h ( 
where7S = 31 1 ��⁄ 45 andT = 31 045 . 
 

 

 

 

 

 

 
 

 

 

 

Fig. 2.General structure of Minimax Control [15]. 

 

 
In this case, the quadratic cost functional will 

be modified with the disturbance explicitly 

^i����j = 12 l N25 ��� 2���
�

& + �5 ��� ���� −m� ℎ5 ��� ℎ��� O ��                                           …(39) 
wherem is a design parameter, which is concerned 
in system stability analysis. 

It is clear that the disturbance tries to maximize 

the cost, so it appears with negative sign. 

Meanwhile, the objective is to find a control ���� 
that could minimize the maximum cost achievable 

by the disturbance. The unique solution of cost 

function, �∗���andℎ∗���, exists and satisfies the 
saddle point condition, ^ i�∗���, ℎ���j M ^ i����, ℎ∗���j M  ^ i�∗���, ℎ∗���j                                             …(40)  
where�∗��� is the optimal control and ℎ∗��� is the 
worst-case disturbance. These functions can be 

computed as: �∗��� = −7S5 d)��� ℎ∗��� = �1 m�⁄ �T5  '���                                    …(41) 
whered is positive symmetric matrix. The 
numeric values of matrix entries are determined 

by the solution of the following Modified Control 
Riccati Equation (MCRE); d6 + 65 d + 85 8 − d�7S5 7S − TT5 �d = 304 
                                                                      …(42) 

To solve Riccatiequation using Matlab  built-in 
CARE function, the structure of above Riccati 

equation is modified to be rewritten as 

d6 + 65 − d3T7S4 ,−m� 00 1-
<� 3T5 7S5 4d +85 8 = 304                                                         …(43) 

where, ` =  ,−m� 00 1- and n = 3T7S4.  
The RE described by Eq.(43) finds a 

straightforward solution with the help of CARE 
function as indicated in Appendix (A).  

  

 

4. Simulation Results 
 
Both sliding mode and optimal LQR 

controllers have been applied to the diabetic 

model. The effectiveness and robustness of 

suggested controllers are assessed using 
simulation results based on Matlab-Simulink 

(Ra2012).  

 Figure (3) shows meal disturbance function 

behavior, which represents the exogenous glucose 
infusion. Figure (4) shows the Simulink modeling 

of sliding and optimal controllers for controlling 

the glucose level against disturbing meal. The 
meal disturbance is saved inside a look-up table 

(see Appendix B). 

 

 
 

Fig. 3. Disturbance meal function (exogenous 

glucose infusion). 

0 200 400 600
0

0.2

0.4

0.6

0.8

1

1.2

time(min)

h
(t
) 
(m

g
/d

l⋅m
in
)



Bashar Fateh Midhat                        Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 55- 63 (2017) 
 

60 

 

 
 

Fig .4. Matlab-Simulink Modeling of Sliding Mode 

Controller and Optimal Controllers. 

 

 
The model parameters are listed below [15]: �� = 0.028, �� = 0.025, �� = 0.00013, �� = 0.093, �t = 110, �t = 1.5, �& = 16.67.  

Based on the above values, the design parameter f is calculated using Eq.(13). Then, the value of f is equal −2.23. 
    For the optimal LQR controller, the matrices `and _ are set at the following values; 
` = ,1 00 1 1000⁄ -, w = ,1 1000⁄ 00 1 1000⁄ -, 
     Considering the above  d = . 0.0140 −0.0560−0.0560 0.3130 / 
Then, it is easily to find the optimal gain matrix f f = . 0.0000   −0.0001−0.4664     2.6086 / 
Based on critical value of m = 17.086, which lead 
to positive definite matrix solution and stable 

closed loop system, the matrix y resulting from 
Eq.(31) is given by d = . 3.5822 −3.2982−3.2982 7.02982 / 
This gives the following feedback gain matrix  

f = . 0.0123   −0.0113−27.4853   58.5570 / 
To determine the stability of the system one can 

easily substitute the values of gain matrix Kinto 

the closed loop equation represented by Eq.(5) 
and find the location of the closed loop as in the 

following manner: )� = �6 − 7f�) 
Then, the eigenvalues of the matrix (6 − 7f) are 
the roots of the characteristic equation which 

calculated as follows [18] |z{ − 6 + 7f|= |.z 00 z/ − .−0.0280 −0.5720 −0.093/+ ,1 00 1/120- . 0   0−0.4664     2.6086/| = }.z + 0.0280 −0.5720 z + 0.093/+ . 0 0−0.0039 0.2174/}= }.z + 0.0280 −0.572−0.0039 z + 0.3104/} Solving for λyields  λ� = −0.361,   λ� = −3.023 
     Repeating the same procedure for the optimal 

Minimax controller we get z� = −0.503,   z� = −5.587 
     Initially, both controllers have the roots in the 

left hand of the s-plane meaning that the system 

under the proposed controllers is stable. However, 
it can be noted that with the optimal Minimax 

controller the roots lie further from the origin 

resulting in more stable performance and a faster 
response. 

     Figure (5) shows the glucose level under meal 

disturbance of Figure (2) with different four 

controllers. The figure shows that the glucose 
level reaches 136 (mg/dL) when using classical 

optimal LQR controller. This stands for 12.36% 

above basal glucose level. However, Minimax 
optimal controller could reduce the maximum 

value of glucose level to reach to 125 (mg/dL), 

which is about 11.36% above the basal level. 
Sliding mode controller (SMC) gives better 

performance than both optimal controllers. With 

this controller, the maximum glucose level does 

not exceed 123 (mg/dL); i.e, the controller permits 
11.18% change over the basal glucose level. It is 

evident from the figure that integral sliding mode 

controller shows the best robustness 
characteristics than all the above controllers. The 

percentage change of ISMC is approximately 

10.63% above the basal level which is the 
minimum percentage than others. 

 

 

t

time

table

in

insulin 
input

h

h(t)

g

glucose 
level

-C-

basal insulin level

Switch

In1

In2
Out1

LQR

1/s

Integrator2

1/s

Integrator1

1/s

Integrator

g

y

z

uo

u1

dz

fcn

Integral
sliding mode

g

y

h

i

dg

dy

fcn

Glucose Model

110

Gb

Clock



Bashar Fateh Midhat                        Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 55- 63 (2017) 
 

61 

 

 
 

 

 
 

 

 

 
 

 

 
 

 

 

 
Fig. 5. Plasma glucose level 

 
 

Figure (6) shows the insulin rate resulting from 
each controller. It has been shown that the more 

robust controller, the higher level of insulin rate 

which is taken by human body. This physically 

indicates that more robust controller of requires 
more insulin rate to be injected; this is the price of 

robustness.  

 

 
 
Fig. 6. Plasma glucose level. 

 

 

5. Conclusion 
 
     In this paper, different controllers were 

addressed for the problem of blood glucose 

concentration level control. Simulation was 

performed using MATLAB/Simulink in order to 
investigate the performance of suggested 

proposed controllers under a meal disturbance. 

The four designed controllers could successfully 
control the glucose level successfully and retain 

the glucose level back to its basal level. However, 

the simulation has showed relative differences in 
the performance of addressed controllers. 

It can be noted that the integral sliding mode gives 

the best disturbance rejection capability over other 
controllers such that it prevents the glucose level 

to exceed 118 mg/dl. Moreover, sliding mode 

controller outperforms the characteristics of 

Minmax controllers. The latter could keep the 
glucose level within 125 mg/dl. However, it can 

be seen that the optimal LQR controller have the 

worst performance where the glucose level 
reaches the value of 135 mg/dl. 

From Fig. (6), it can be concluded the price of 

getting better control performance is the increased 

level of insulin infusion in order to counteract the 
glucose evolution. Therefore, it can be noted that 

the integral sliding mode has the highest insulin 

infusion compared to the other controllers, while 
the lowest level is shown in LQR controller. 

  

 

6. References 
 
[1] Bergman R.N., Philips L.S., Cobelli C., 

"Physiologic Evaluation of Factors Controlling 

Glucose Tolerance in Man, Journal of Clinical 

Investigation," Vol.68, pp. 1456–1467, 1981. 
[2] O. Vega-Hernandez, D. U. Campos-Delgado, 

and D. R. Espinoza Trejo, "Increasing Security 

in an Artificial Pancreas: Diagnosis of 
Actuator Faults," Proc. of Pan-American 

Health Care Exchanges Conference, Mexico 

City, Mexico, pp. 137-142, 2009. 
[3] V. R. Kondepati and H. M. Heise, "Recent 

Progress in Analytical Instrumentation for 

Glycemic Control in Diabetic and Critically Ill 

Patients, "Anal Bional.Chem., Vol. 38,pp. 545-
563, 2007. 

[4] Thomson, S., D. Beaven, M. Jamieson, S. 
Snively, A.Howl and A. Christophersen, "Type 
II diabetes: Managing for Better Health 

Outcomes," in PriceWater House Coopers 

Report, Diabetes New Zealand Inc., 2001. 

[5] Topp, B., K. Promislow and G. De Vries, "A 
Model of �-cell Mass, Insulin and Glucose 
kinetics, "Pathways to diabetes. J. Theor. Bio, 

pp.605-619, 2000. 
[6] C. Li and R. Hu, "PID Control Based on BP 

Neural Network for the Regulation of Blood 

Glucose Level in Diabetes", in Proceeding of 
the 7th IEEE International Conference on 

Bioinformatics and Bioengineering, Boston, 

pp. 1168-1172, 2007. 

[7] Chee F, Fernando TL, Savkin AV, Heeden 
VV. "Expert PID Control System for Blood 

0 200 400 600
15

20

25

30

35

time (min)

I(
t)
 (
m

U
/m

in
)

 

 

LQR

Minimax

SMC

ISMC

0 200 400 600
105

110

115

120

125

130

135

140

time(min)

G
(t
) 
(m

g
/d

l)

 

 

LQR

Minimax

SMC

ISMC



Bashar Fateh Midhat                        Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 55- 63 (2017) 
 

62 

 

Glucose Control in Critically Ill Patients," 
IEEE Transactions on Information Technology 

in Biomedicine, pp.419– 425, 2003. 

[8] Salzsieder E, Albrecht G, Fischer U, Freyse E-
J. "Kinetic Modeling of the Glucoregulatory 

System to Improve Insulin Therapy," IEEE 

Transactions on Biomedical Engineering, 

Vol.32, pp.846–855, 1985. 
[9] Parker R.S., Doyle F.J., Peppas NA., "A 

Model-based Algorithm for Blood Glucose 

Control in Type I Diabetic Patients," IEEE 
Transactions on Biomedical Engineering, 

Vol.46, No.2, pp.148–157, 1999. 

[10] S. M. Lynch and B. W. Bequette,"Model 
predictive Control of Blood Glucose in Type I 
diabetes Using Subcutaneous Glucose 

Measurements, "in Proceedings of the 

American Control Conference, U.S.A, pp. 

4039–4040, May 2002. 
[11] K. Beyki, M. Dashti Javan, K. Shojaee 

and M.M. Neshati, "An Intelligent Approach 

for Optimal Regulation of Blood Glucose 
Level," In 17th Iranian Conference of 

Biomedical Engineering, pp.1-5, 2010. 

[12] S. Yasini, M.B. Naghibi-Sistani and A. 
Karimpour, "Active Insulin Infusion Using 
Fuzzy-based Closed-loop Control", in 3rd 

International Conference on Intelligent System 

and Knowledge Engineering, Mashhad, Iran, 
pp. 429-434, 2008. 

[13] D. N. Maryam Abadi, A. Alfi, M. Siahi, 
"An Improved Fuzzy PI Controller for Type 1 
Diabetes," Research Journal of Applied 

Sciences, Engineering and Technology, Vol.4, 

No.21, pp. 4417-4422, 2012. 

[14] Levente Kovacs, Béla Palancz, Endre 
Borbely, "Robust Control Algorithm for Blood 

Glucose Control Using Mathematica," Acta 

Electrotechnicaet Informatica, Vol. 10, No. 2, 
pp. 10–15, 2010. 

[15] Levente Kovacs, Béla Palancz, "Glucose-
Insulin Control of Type1 Diabetic Patients in �� ��⁄ Space via Computer Algebra," 2nd 
International Conference, Australia, July, 

2007. 

[16] Vadim Utkin, Jürgen Guldner, Jingxin 
Shi, "Sliding Mode Control in Electro-

Mechanical Systems," CRC Press, 2009. 

[17] Jinkun Liu, Xinhua Wang, "Control for 
Mechanical Systems Design, Analysis and 

MATLAB Simulation," Tsinghua University 

Press, Beijing and Springer-Verlag Berlin 
Heidelberg, 2012. 

[18] Donald E. Kirk, "Optimal Control 
Theory: Introduction, "Dover Publications, 

Inc., 1998. 
 

 

Appendix (A) 

 
Matlab function of solution of Equation (12), 
using CARE function; 

gama=17.086; 

C=[1 0]; 

Q=C'C 
L=[1;0];  

Bu=[0; 1/120]; 

B=[L   Bu]; 
R=[-gama^2  0; 0   1]; 

Pm=care(A,B,Q,R) 

Km=inv(R)*B'*Pm 

 

Appendix (B) 

 
The Table below lists the data of disturbing meal 

behavior 
Table 1, 

 Disturbance meal function 

Time (t) 

 [min] 

Glucose (h(t)) 

[mg/(dL.min] 

0 0 

25 0.185 

50 0.495 

75 0.765 

100 0.975 

125 1.15 

150 1.07 

175 0.82 
200 0.575 

225 0.335 

250 0.225 

275 0.145 

300 0.098 

325 0.06 

350 0.035 

375 0.02 

400 0.01 

450 0.005 

1000 0 

  

  

  

  

  



 )2017( 55-63، صفحة 3د، العد13دجلة الخوارزمي الهندسية المجلم             بشار فاتح مدحت                                               

63 

 

 

 

تحت تاثير  جسم البشريالمقارنة االداء بين مسيطرات متقدمة للسيطرة على مستوى السكر في 
  االضطراب الغذائي

  

  **امجد جليل حميدي                  *مدحت بشار فاتح
  الجامعة التكنولوجية/ قسم هندسة السيطرة والنظم*,**

basharfm88@yahoo.com :البريد االلكتروني* 
       aaaacontrol2010@yahoo.com  :البريد االلكتروني** 

  
 

 
 

  

 الخالصة
 

السيطرة على تركيز الكلوكوز في الجسم البشري وذلك باقتراح نوعين من المسيطرات: المسيطرات المثالية والمسيطرات ذات النمط  تتم البحثفي هذا 
ن من المسيطرات المثالية التي تم ابخواص تقليل تاثير االضطراب المسلط على المنظومة. هناك نوعن من المسيطرات االنوع ذانهمتاز . اذ ياالنزالقي

العليا. اما النوع االخر فتم استخدام مسيطرين ذات النمط االنزالقي وهما -طريقة الدنياالوهي المسيطر المثالي التقليدي والمسيطر الذي يستند على احاها اقتر
  المسيطر التقليدي والتكاملي. 

فان المسيطر ذات النمط االنزالقي التكاملي قد اظهر خواص  ،قد اعطى نتائج جيدة العليا-بالرغم من ان المسيطرالمثالي الذي يستند على الطريقة الدنيا
  وجبة طعام. على شكل والتي تم تمثيلها المسلط افضل من المسيطرات المقترحة وذلك من ناحية تقليله تاثير االضراب