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1 

  
Al-Khwarizmi 

Engineering   
Journal Al-Khwarizmi Engineering Journal, Vol. 14, No. 1, March, (2018) 

P.P. 145- 155 

 
Design of Hybrid Neural Fuzzy Controller for Human Robotic Leg 

System  
  

            Ekhlas H. Karam*       Ayam M. Abbass**      Noor S. Abdul-Jaleel***      
*, **Department of Computer Engineering/ University of Al-Mustansyria 
***Department of Electrical Engineering/ University of Al-Mustansyria 

*Email: ekhlashameed@yahoo.co.uk 
**Email: ayammohsen@yahoo.com 

***Email: mail_ns1@yhoo.com 
 

(Received 10 January 2017; accepted 7 August 2017)  

https://doi.org/10.22153/kej.2018.08.007 

 
Abstract 

 
In this paper, the human robotic leg which can be represented mathematically by single input-single output (SISO) 

nonlinear differential model with one degree of freedom, is analyzed and then a simple hybrid neural fuzzy controller is 

designed to improve the performance of this human robotic leg model. This controller consists from SISO fuzzy 
proportional derivative (FPD) controller with nine rules summing with single node neural integral derivative (NID) 

controller with nonlinear function. The Matlab simulation results for nonlinear robotic leg model with the suggested 

controller showed that the efficiency of this controller when compared with the results of the leg model that is 

controlled by PI+2D, PD+NID, and FPD-ID controllers. 

 
Keywords: Fuzzy proportional derivative controller, Matlab simulation results, Nonlinear differential leg model, PID 

controller, single node neural controller.  

1. Introduction 
 

The classical robots are commonly used for 

industrial automation and use in applications that 

are remote from human life and activities. 
However, recently the usage of robots has been 

changed from industrial applications to helpful for 

human robot system. With increasing aging 
societies, robots that used to support human in his 

activities in daily environments such as in offices, 

homes, school and hospitals are expected. 

Particularly, because of anthropomorphism, 
helpful design for humanity, application of 

positioning and movement, and so on, powerfully 

expected to manufacture of humanoid robots [1]. 
     Present control techniques to locomotion of 

robotic legged depends on centralized planning 

and path follow or corresponding motion pattern. 

Central control is not available to the robotic help 

devices that make integration with humans, and 
correspond to predefined patterns strongly limits 

from user ability. By difference, biological 

systems show big legged ability even when  the 
system of the central nervous is separated from 

spinal cord that belong to these legged, pointing 

that   feedback  controls  of   neuromuscular is 

harnessed for encoding stability, compatibility, 
and maneuverability into robotic legged systems 

[2]. 

Currently, control systems design is done by a 
big number of requirements caused by 

augmentation of competition, requirements of 

environment, energy and the costs of components 
and the request for robustness, system of error 
tolerance. These considerations introduce extra 


Ekhlas H. Karam                          Al-Khwarizmi Engineering Journal, Vol. 14, No. 1, P.P. 145- 155 (2018) 
  

146 

 
needs for effective process modeling techniques. 
Several systems are not agreeable to traditional 

modeling approaches, caused when the precision 

is not found, about the system having formal 
knowledge, caused from strong behavior for 

nonlinearities, big degree of suspicion, or variance 

characteristic of the time [3]. 

     Neural networks and fuzzy logic systems are 
recently used for different control problems with 

acceptable results. Both the neural networks and 

fuzzy logic systems are general approximations 
caused several adaptive control strategies for 

nonlinear systems that used fuzzy logic systems, 

or neural networks have been introduced to get 

more control performance [4]. 
     As two important strategies of artificial 

intelligence, fuzzy logic systems and Artificial 

Neural Networks (ANNs) have several 
applications in different fields such as availability 

of product, control systems, diagnostic, 

observation, etc. They developed and became 
better throughout the years for adaptation of the 

rising requirements and the develop of 

technology. While these two controllers have been 

frequently used together, explain that the concept 
of a fusion began to take shape [5]. 

     The neuro-fuzzy system is more efficient and 

more effective than either neural network or fuzzy 
logic system which has been widely applied in 

control systems, pattern recognition, medicine, 

expert system, and etc. The advantage of this 
controller is the dealing with it more quickly than 

other traditional controllers [6]. 

     Different types of neuro-fuzzy have been 

shown in the literature. These types can be 
determined depend on the structure of the neuro-

fuzzy, the fuzzy model used, and the learning 

algorithm taken. On the first hand, corresponding 
to the neuro-fuzzy structure and learning 

algorithm, the most usually used and successful 

technique is the feed-forward and recurrent 

structure model using the BP learning algorithm.                                                                                                                    
On the other hand, according to the fuzzy model 

taken, two types of fuzzy models are merged with 

a neural network to form a neuro-fuzzy. These 
two models are familiar as Takagi and Sugeno 

model and the Mamdani-model. However, 

Mamdani-model based NNF represent more 
obvious neuro-fuzzy systems compared with TS-

model based NNF [7]. 

 A simple hybrid neural fuzzy controller is 

designed in this paper for human robotic leg 
model, this controller consist from single node 

neural integral derivative (NID) controller  and 
single input single output fuzzy proportional 
derivative (FPD) controller with nine rules. The 

details for this design will be explained in the 
sections of this paper. 

  
2. Human Robotic Leg Mathematical 
Model 

 
       The human robotic leg can by modeled 

depend on the relation between the input torque 
that generated by the muscle of the leg and the 

output of the angular rotation around the hip joint 

[8]. A simplified human robotic leg cylindrical 
model is shown in Fig. 1.  

                                                       
Fig. 1. Human a robotic leg cylindrical model [9].  

  
The parameters of Fig. 1 are defined by Table 1.  
 
Table 1, 

The parameters of human robotic leg model. 

 
The nonlinear equation of the dynamic model 

for the robotic human leg can be written as 

follows [9, 10]:   

� ������ � � ���� � �	 
� ��� � �����               … (1) 
    Where: Mg �� sinθ is the component of weight, 
D ��� 	is the damping torque and "�

��
��� # is the inertia 

torque. The state space for Eq. (1) is: 

Symbol Description values 

Tm torque supplied by DC 

motor 

 
D viscous damping 0.1Nms/ra

d 

J inertia around the hip joint 0.4 

kgm2/s2 

M mass of the leg 1 kg 

g acceleration due to gravity 

creates a nonlinear torque 

9.81 

L the length of the leg and the 

weight can be determine as 

L/2 

0.5m 


Ekhlas H. Karam                          Al-Khwarizmi Engineering Journal, Vol. 14, No. 1, P.P. 145- 155 (2018) 
  

147 

 
$%&'%�' ( � )
0 1

,� &-&	./
�0 ��%&� , "10 #2 3
%&%�4 � )

0&
0
2 ��	  

5 � 61				07 3%&%�4	                                            … (2) 
    Where: x1, x2 is robotic leg angular position and 
velocity respectively. Eq. (1) can be linearized for 

small angle approximation, the �	variation is 
small; therefore sinθ can assume equal � (i. 
e.	sinθ � �� so Eq. (1) becomes: 
� ������ � � ���� � �	 
�� � �����                   … (3) 
      The linear transfer function of Eq. (3) is given 

by: 

��8�
9�8� �

:
;

8�<=; 8<>?@�;
                                           … (4) 

    With parameter given by Table 1, Eq. (4) 

becomes: 
��8�
9�8� � �.B8�<C.C�B8<D.&E&                                    … (5) 
     This transfer equation has two complex poles 
(-0.0125+2.4761j, -0.0125-2.4761j) with damping 

ratio ζ=0.0050, the state space equations are: 

$%&'%�' ( � 3
0 1

,6.131 ,0.0254 3
%&%�4 � 3

0
2.54 ��	 

5 � 61				07 3%&%�4                                         … (6) 
     With unity step input, the time response of the 
leg linear and nonlinear model is shown in Fig. 2. 

 
Fig. 2. Time response for linear and nonlinear 

model.                                                                       
 

    This figure show that the leg model response is 
high oscillation under damped. In order to reduce 

the oscillation, a suitable velocity feedback gain 

(Kv=3.74) is adding to plant leg transfer function 
and hence this function becomes: 
��8�
9�8� � �.B8�<�C.C�B<�.BJK�8<D.&E& �

�.B
8�<L.M8<D.&E&…(7) 

    The damping ratio for linear model becomes   
ζ=1.76, so the response of unity step input for this 

equation and for the nonlinear model become over 
damped as shown in Fig. 3.                                  

 
Fig. 3. Time response for linear and nonlinear 

model with velocity feedback gain kv= 3.74 
 

3. Hybrid Neural Fuzzy Controller Design                  

     
    The block diagram for nonlinear robotic leg 
model with the suggested hybrid like neural fuzzy 

controller is shown in Fig. 4. 

 
Fig. 4. The block diagram for hybrid neural fuzzy 

controller for human robotic leg.                             
 

The suggested hybrid controller consists from 
SISO neural integral derivative (NID) and fuzzy 

proportional derivative (FPD) controller. The first 

step for design this controller is determine the 

proportional integral derivative (PID) controller 
for the robotic leg based on the linear model of 

the robotic leg.  

Generally, the equation of the ideal PID 
controller with ideal form is given as: 

N��� � �OP � JQ8 � O�����R���                   … (8) 
    Where: E(s) is the error signal between the 
desired input and the leg output position, while 
Kp, Ki, and Kd are proportional, integral and 

+  


Ekhlas H. Karam                          Al-Khwarizmi Engineering Journal, Vol. 14, No. 1, P.P. 145- 155 (2018) 
  

148 

 
derivative gain in respectively, the values of these 
parameters are determine by Launching PID tuner 

method that provide by matlab simulink with 

some manual modification. Eq. (8) can be written 
as: 

N��� � OP "1 � &9Q8 � ���# R���                  … (9) 
    Where:  Ti is integral or reset time, and Td 

is derivative or rate time.  

    In this paper, instead of ideal PID 

controller we use PI+2D and hence Eq. (9) 

becomes: 

N��� � OP "1 � &9Q8 � ��� � ���# R���						…	(10) 
Or 

N��� � OP T�1 � ���� � � &9Q8 � ����U R���                                                          
…                                                                 … (11) 
Eq. (11) can be written as: 

N��� � OP�1 � ����R��� � OP V 1�W� � ���X R��� 										� N&��� � N����	                            … (12)            
 

The steps for designing the suggested 

controller will be demonstrate in the following 
sub sections.   

    
3.1 Fuzzy Proportional Derivative 

Controller Design 
 

The first part of Eq. (12) is ideal PD controller 

as given by: 

N&��� � OP�1 � ����R���                         … (13) 
This equation is considered as input to the 

SISO fuzzy controller as shown in Fig. 5 after 

remove Kp as  given by: 

	YW��� � �Z��"1 � �� ���# [����                   … (14) 

 
Fig. 5. Fuzzy PD logic controller.  

 
The saturation function is used to limit any 

input signal to be between (N to –N), K] � KP ×O8 where Ks is selected gain such that the value of 
Kf  should be equal to magnitude of the input 

signal, for example if the input is step with 
magnitude 10, then Kf should be equal to10.  

Usually, fuzzy logic theory deals with 

uncertain or imprecise situation. A variable in 
fuzzy logic has sets of values which are 

characterized by linguistic expressions, such 

NEGATIVE, ZERO, POSITIVE, etc. These 
linguistic expressions are represented numerically 

by fuzzy set and it is characterized by 

membership function that varies from [0 to 1], 

which given element can be a member of any 
fuzzy set [11].  

In general, the fuzzy controller design consists 

from three parts: 

 
3.1.1. Fuzzification  
 

The input (crisp) data is fuzzified according to 

a selected membership functions. 
 The input and output membership are shown in 

Fig. 6.   

 
(a) 


Ekhlas H. Karam                          Al-Khwarizmi Engineering Journal, Vol. 14, No. 1, P.P. 145- 155 (2018) 
  

149 

 
(b) 
Fig. 6. Membership function for, (a) input variable, (b) output variable. 

 
3.1.2. Rule Base 

     
The knowledge base of the fuzzy logic consists 

of a set of fuzzy IF (the satisfied conditions set) 

THEN (the inferred consequence set) rules which 
themselves consist of linguistic set, associated 

variables with inputs, outputs and fuzzy operators 

like OR and AND [12]. 
The quantitative if-then rules of our fuzzy 

controller are described as: 

R1: if ui(t) is m1 then uf(t) is m1  

R2: if ui(t) is m2 then uf(t) is m2  
R3: if ui(t) is m3 then uf(t) is m3  

R4: if ui(t) is m4 then uf(t) is m4  

R5: if ui(t) is m5 then uf(t) is m5  
R6: if ui(t) is m6 then uf(t) is m6  

R7: if ui(t) is m7 then uf(t) is m7  

R8: if ui(t) is m8 then uf(t) is m8  
R9: if ui(t) is m9 then uf(t) is m9 

 
Where: m is linguistic terms of antecedent 

fuzzy set, they mean m1= mf1, …, m9=mf9. 
The universe of discourse from -1.2 to 1.2 and 

from –20 to 20 for the input and the output 

membership function in respectively as shown in 
Fig. 6.            

                                                       
3.1.3. Defuzzification  
 

    In this step, the Center of Mass (COM) formula 
is used to defuzzify the law of the fuzzy 

controller. 

 
3.2 Neural Integral Derivative Controller 

Design 
 

A neural network is an interconnected network 

of nodes, working manner similar neurons in the 
human brains. Each neurons contains a link 

collector that collects weighted with the shift 

income to form a numerical output of neuron, 
which is considered as lacking in movement with 

neural network fnn (x), where x …… ,R5.    

Multi-Layer Perception (MLP) and Radial 

Basis function (RBF) networks are the common 
traditional neural networks [13]. In this paper 

(MLP) network is used, which is consist from 

three layers (input layer, hidden layer and output 
layer) as shown in Fig. 7. 

 
Fig. 7. The single node of the MLP 

 
Where: i is the neuron number and xk is the 

input where k=1, …., K. (ni) is the result of 
multiplied the inputs by weights which is summed 

with each other with the bias term bi. This result 

becomes the input of the activation function (g). 
This function is considered to be a relay function. 

The sigmoid function or tangent hyberbolic (tanh) 


Ekhlas H. Karam                          Al-Khwarizmi Engineering Journal, Vol. 14, No. 1, P.P. 145- 155 (2018) 
  

150 

 
are widely used rather than the relay function 
[13]. The tangent function is given as: 

 
tanh�%� � &bcde&<cde                                      … (15) 
     In this paper our neural design is only single 

node of MLP networks with single input without 
delay, the integral derivative (ID) is consider as 

input to this neural controller as shown in Fig. 8, 

the output of neural network is multiply by 
proportional gain Kp, manual train is used to 

determine the value of the bias and weight.                

 
Fig.  8. Single input-single output NID    controller  

 
4. Simulation Results and Discussion 

 
     In this section, different simulations for the 

nonlinear robotic leg model with (PI+2D, 

PD+NID, FPD+ID, and the suggested FPD+NID) 

are carried out for step and multi-step input. The 
matlab simulink connection for the nonlinear leg 

model with the suggested controller is shown in 

Fig. 9. FPD+NID.                                                           

(a)            

 
                              (b) 

 
         (c) 

 
Fig. 9. Matlab simulink connection for the robotic 

leg with the suggested hybrid controller; (a): 

complete connection; (b): neural network 

connection; (c):  nonlinear leg model connection 

 
  The controller's parameters are given by Table 2.   

                          
Table 2, 

Controller parameters. 

Kp Ti Td Ki Kd wi bi 

14 2 0.0357 24 0.5 0.1 0.1 

 
The different simulations are presented as 
follows:  

i. Simulation (1): In this simulation, the 
controlled robotic leg is tested by step input 
with magnitude 2 and the results of this case 

(angular position, velocity, error, and control 

signal) which are given in Fig. 10 show that 
the position and velocity tracking is fairly good 

with nearly zero steady state error for all 

controller specially the our suggested 

FPD+NID controller. 

 
      (a) 

 
weight
1

Out

tansig
netsum

.1

bias

.1

 
1

In

th etad ot

the ta
Torque inp ut 

u(1 )

  u(2)

    u(3)

    u(4)

u(5)

u(6 )

2

Out2

1

Out1

-C-

M gL/2

.4

J

1

s

Integrator1

1

s

In tegrator

.01

D
Inte rpreted

M ATL AB Fcn

((-u(3)*u(4))-(u(2)*sin (u(5)))+u(6 ))/u(1)
1

In1


Ekhlas H. Karam                          Al-Khwarizmi Engineering Journal, Vol. 14, No. 1, P.P. 145- 155 (2018) 
  

151 

 
  (b) 

 
(c) 

 
 (d) 

 
Fig. 10. Simulation results for robotic leg controlled 

by (PI+2D, PD+NID, FPD+ID, FPD+NID) with step 

input of mag.2: (a) angular position; (b) angular 

velocity; (c) error signal; (d) control signal                

                                       
ii. Simulation (2): in this simulation, the 
controlled robotic leg is tested by unity step 
input with nonlinear sinusoidal disturbance 

(dis=0.1sin(20t)) in addition to 10% parameter 

uncertainty in J, D, and M parameters are 
introduce during the simulation period. The 

results of this case  are illustrate in Fig. 11, 

these results show that the robotic leg is 

remain stable even with disturbance and 

uncertainty with very small steady state error 
and the disturbance is remove from the 

response of the angular position while it is not 

rejected very well from the response of the 
velocity see Fig.11 b.  
 

(a)  

 
                             (b)   

(c) 

 
Ekhlas H. Karam                          Al-Khwarizmi Engineering Journal, Vol. 14, No. 1, P.P. 145- 155 (2018) 
  

152 

 
(d) 

Fig. 11. Unity step simulation results with nonlinear 

sinusoidal disturbance and parameter uncertainty: 

(a) angular position; (b) angular velocity; (c) error 

signal; (d) control signal.                   .                  

                                                                          
   iii. Simulation(3): in this simulation, the 
controlled robotic leg is tested by multi step 
input without  disturbance or parameter 

uncertainty as shown in Fig. 12, and the 

results for this simulation are shown in Fig. 

13, Fig.14, Fig.15, and Fig.16, these results 
show when sudden change occur in input 

signal and hence the mathematical model of 

robotic leg is nonlinear, the system become 
unstable with PI+2D, PD+NID, and FPD+ID 

controllers while it remain maintain the 

stability with efficient performance with the 
suggested FPD+NID controller (nearly zero 

steady state error with no overshoot and fast 

settling time). 

 
Fig. 12. Multi-step input of mag.2. 

  
      (a) 

  
    (b) 

Fig. 13. Simulation results for robotic leg controlled 

with PI+2D and multi-step input of mag.2: (a) 

angular position, (b) error signal.                                

     
(a)   

  
Ekhlas H. Karam                          Al-Khwarizmi Engineering Journal, Vol. 14, No. 1, P.P. 145- 155 (2018) 
  

153 

 
b)(  

Fig. 14. Simulation results for robotic leg controlled 

with PD+NID and multi-step input of mag.2: (a) 

angular position, (b) error signal.                          

     
(a)  

 
(b) 

Fig. 15 Simulation results for robotic leg controlled 

with FPD+ID and multi-step input of mag.2: (a) 

angular position, (b) error signal.                                

                       
(a) 

(b) 

Fig. 16. Simulation results for robotic leg controlled 

with FPD+NID and   multi-step input of mag.2: (a) 

angular position, (b) error signal. 

5. Conclusion 

 
A simple hybrid neural fuzzy controller is 

designed to improve the performance of human 
robotic leg model which is SISO. This controller 

consists from fuzzy proportion derivative (FPD) 

controller and single node neural integral 
derivative (NID) controller. The different 

simulation results with / without parameter 

uncertainty and nonlinear disturbance show that 
the suggested FPD+NID controller is better than 

PI+2D, PD+NID and FPD+ID controllers. 

 
Ekhlas H. Karam                          Al-Khwarizmi Engineering Journal, Vol. 14, No. 1, P.P. 145- 155 (2018) 
  

154 

 
6. References 
 
[1] Kenji Kaneko, Shuuji Kajita, Fumio                                 

Kanehiro, Kazuhito Yokoi, Kiyoshi                               

Fujiwara, Hirohisa Hirukawa, Toshikazu                      

Kawasaki, Masaru HIRATA, and Takakatsu                
Isozumi, Design of Advanced Leg Module                   

for Humanoid Robotics, Project of METI,                                                                      

International Conference on Robotics 

Automation, Washington, DC, May, 2002.            
[2] Alexander Schepelmann, Michael D. Taylor,                  

Hartmut Geyer, Development of a Testbed for  

Robotic Neuromuscular Controllers, Robotics:  
Science and System VIII, Jan 2012.                                                    

[3] A. Abraham et al., Neuro-Fuzzy Methods                   
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advances in intelligent paradigm and 
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2003.                                   

[4] Wei-Yen Wanga, Yih-Guang Leub, Tsu-Tian                
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systems using direct adaptive fuzzy-neural                   

controller, Fuzzy Sets and Systems 140, 341–
358, 2003.                                                                 

[5] Dr. Zs. J. Viharos, K. B. Kis, Survey on                         
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Advanced  measurement tools in technical                   

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805–829, 2013.                                                  

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[9] Abdur Raquib Ridwan, Md. Ibnea Sina Bony              
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[11] Nidhi K., Simulation Studies on Hybrid                                                                    

Fuzzy-PI Controllers for DC Motor                       

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[12] C. Yen, F. Wen, and M. Ouyang, Nonlinear                  
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[13] [Heikki N. Koivo, Neural Networks:                              
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 )2018(  144-154 ، صفحة1د، العد14دجلة الخوارزمي الهندسية المجلم                     اخالص حميد كرم                                    

155 

  
 تصميم مسيطر هجين من الشبكة العصبية مع المسيطر الضبابي لنظام ساق االنسان
 

 اخالص حميد كرم*      ايام محسن عباس**        نور صفاء عبد الجليل***
  *, ** قسم هندسة الحاسوب/ الجامعة المستنصرية
  *** قسم الهندسة الكهربائية/ الجامعة المستنصرية

  ekhlashameed@yahoo.co.uk* البريد االلكتروني: 
     ayammohsen@yahoo.com** البريد االلكتروني: 

  mail_ns1@yhoo.com*** البريد االلكتروني: 

  
  الخالصة
  

) SISOاحادي االخراج (- خطي احادي االدخالالطة النموذج التفاضلي غير سافي هذا البحث, الساق الروبوتية البشرية التي يمكن ان تمثل رياضيا بو
تم تصميم المسيطر الضبابي العصبي الهجين البسيط لتحسين اداء هذا الروبوت. هذا المسيطر يتكون من المسيطر ومع درجة واحدة من الحرية قد تم تحليله 

عقدة  يذNID)  ف مع المسيطر العصبي المشتق التكاملي () مع تسع قواعد تضاSISOاحادي االخراج (-احادي االدخال FDP)الضبابي النسبي المشتق (
نتائج المحاكاة بالماتالب لنموذج الساق الروبوتية مع المسيطر المقترح وضح كفاءة هذا المسيطر عند مقارنته مع نتائج ان واحدة مع دالة غير خطية. 

  PI+2D, .PD+NID, FPD-ID.المسيطرات