Thiết kế bộ điều khiển mạng neural thích nghi bền vững cho tay máy robot phá băng

rewritten as follows:
 * 0ˆT Tf z c z ec= + +! !! (20)
The function c! can perform in the form of Taylor 
series as follows:
1 2
ˆ
1 2
ˆ
, , ,
, , ,
n
n
g g
a a
g
a
cc cc g g g
cc c
a a a
=
=
é ¶ ù¶ ¶
= ê ú¶ ¶ ¶ë û
¶¶ ¶é ù
+ ê ú¶ ¶ ¶ë û
!
!
!
( )
1 2
ˆ
1 2
ˆ
, , ,
, , , , , ,
n
n H
p p
u u
cc c
p p p
cc c g a p uu u
p
uu
=
=
¶¶ ¶é ù
+ ê ú¶ ¶ ¶ë û
¶¶ ¶é ù
+  +ê ú¶ ¶ ¶ë û ! !
!
! !!
 (21)
Or
 ( ), , ,T T T TБ Hc g a p ug a p u= +G + ¡ +L +! ! ! !! ! ! !! (22)
Where the high-order composition vector is 
 ( ) nH , Rg a Î! !
Substitute (22) into (20), we have:
25
LIÊN NGÀNH ĐIỆN - ĐIỆN TỬ - TỰ ĐỘNG HÓA
Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, ISSN 1859-4190, Số 3 (70) 2020
( ) ( )
( ) ( )
( )
( )
( )
( )
( )
* *
* *
*
0
ˆ ˆ ˆ
ˆˆ
ˆ ˆ ˆ
ˆ
, , ,
ˆ
ˆ
, ,
ˆ
, ,
T T
T
e T T
T T T T
T
e
T T T T T
T T T T T
Бf D
Б
H D
Б
Б
W s
c g g a az p p u u
z g
z g a p u e
z c
z
g a p u
a p u
g a p u
g a p u
é ù
L
-
+ - +G -
+ =
+¡ - +L -
+ +G ¡ +L
+ + +
- -G ¡ -L
+
ê úê úë û
+
=
++G ¡ +
+
!
!
! !!
!
!
!
! !
!
!
! !!
Where ]1 2, , , T nnW W W W Ré=  Îë
( )
( )
( )( )
( )
( )
( )
* * *
*
0
* * * *
*
*
* *
*
0
*
*
0
*
, ,
ˆ ˆ ˆ
ˆ
ˆ
ˆ
,
T T T T T
T
T T T T T T
T T T T T
e
T T T T T
T T T T T
e
W Б
H
Б
Б D
Б
Б D
z g a
z g a p u e
z z g a
z c e
z c
p u
p u
g a p u
g a p u
g a p uz e
= +G ¡ +L
+ +
= - +G ¡ +L
+ - -G ¡ +L + +
= + +G ¡ +L
- +G ¡ +L + +
+
+
-
+
+
!
! ! !
!! !!
!
!
!
Since
* *
* *
* *
* *
ˆ ;
ˆ ;
ˆ ;
ˆ ;
ˆ
ˆ
ˆ
ˆ
T T T T
T T T T
T T T T
T T T T
Б Бz
u
z g
z z a
z
a
z p
z z u
g
p
£
G £ G
¡ £ ¡
L £ L
( )* * *
* *
*
* *
ˆ
ˆ
T T T T T
T T T T T
Б
Б
z g a
z g a
p u
p u
+G ¡ +L
£ ¡++ +L
+
G
Hence, we can infer:
( )*
* *
0
* *
* *
*
*
*
, , ˆ ˆ1, , ,
, , , ˆˆˆ , ,
T T T
e
T T T T T T
T T T T
T
W
D Б
Б
z e z g a
z z z p u z
c
g a p u
lj
£
+ + é ùê úG ¡ L ê úë û
+G ú¡ +
é ùê úê úê úê +ë ûL
£
! 
 (24)
Based on the above analysis, we recommend the 
sliding mode control components SMCt as following:
 ( )
2
2
2
T
SMC T
Z
Z
j lt j hl= + (25)
Where h is a positive scalar control gain:
 , (0) 0hh h h= -X >! (26)
With [ ]1 2 3 4 , , , Tj j j j j= is a bound of vector *j .
Based on (25) and (26). Adaptive sliding mode 
control components ˆASMCt is shown as follows: 
 ( )
2
2
2
ˆ ˆ ˆ
T
ASMC T
Z
Z
ljt j hl= + (27)
Where jˆ is the estimate of *j .
The proportional-integral controller PIt is designed by: 
 2 2
0
PI P IK Z K Z dt
t
t = + ò (28)
(23)
Fig 2. The architecture of the RM control system
26
NGHIÊN CỨU KHOA HỌC
Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, ISSN 1859-4190, Số 3 (70) 2020
Where PK and IK are proportional and integral term gains, respectively. Because PK and IK are adjustable adaptive parameters. For the 
convenience of presenting PIt in (28) it can be denoted adaptive proportional–integral controller 
 ˆAPIt in the form:
 ˆˆ TAPI PI PIK ht = 
Where 22 2 2( ) [ , ]PIh Z Z Z dt R= ò Î is a regressive 
vector and 2[ , ]PI P IK K K R= Î is the parameter 
vector that can be adjusted simultaneously with 
the system.
Applying (23) to (18), yields: 
( )
( )
( )
2
2 2 1
ˆ ˆ ˆˆ ˆ
ˆ
T T T T T
IRM
T T T T T
IRM SMC
T
PI
T
M Z Б
Б
C Z Z
E D
W
g a p u
g a
z c
z
µ t
t
p u
= - -G ¡ -L
+ +G ¡ +L +
- + - -
- - + F
-
+
Y
!
!
!
"
! !!
!
 (29)
Based on (16), (25) and (28). The online adaptive 
update laws of RAFNNs are designed as:
2
2
2
2
2
2
2
2
2
ˆ ˆ ˆ ˆ ˆˆ( )
ˆˆ
ˆˆ
ˆˆ
ˆˆ
ˆ
ˆ
ˆ
ˆ
T T T T
T
E E E
PI PI PI
T
T
T
T
T
Б Z
Б Z
Z
Z
Z
Z
E
K Z h
Z E Z
z
g
a
p
u
j
h
z c g a p u
g z
a z
p z
u z
j l
hh
n
ì
= X - -G - ¡ -Lïï = Xï
= X Gïï
= X ¡ïï
= X Líï
= Xïïïïïï
= -X
= X Y -X
= Xî
!
!
!
!
!
!
!
!
!
 (30)
Here ,, , , ,, ,, E PIz g a p u j hX XX X X X XX X are 
positive adaptation rates.
3.2. Stability Analysis
Theorem 1 
Consider a ARNNs adaptive control rule n-links 
IRM (1) designed in equation (16), robust control 
component SMCt in (25), the proportional-integral 
controller PIt is defined in (28), and adaptive parameters automatically adjusted corrected by 
Equation (30), the position error converges to zero 
as t approaches infinity.
Select the function lyapunov as follows:
2
2
2
2
2
2
2
2
2
ˆ ˆ ˆ ˆ ˆˆ( )
ˆˆ
ˆˆ
ˆˆ
ˆˆ
ˆ
ˆ
ˆ
ˆ
T T T T
T
E E E
PI PI PI
T
T
T
T
T
Б Z
Б Z
Z
Z
Z
Z
E
K Z h
Z E Z
z
g
a
p
u
j
h
z c g a p u
g z
a z
p z
u z
j l
hh
n
ì
= X - -G - ¡ -Lïï = Xï
= X Gïï
= X ¡ïï
= X Líï
= Xïïïïïï
= -X
= X Y -X
= Xî
!
!
!
!
!
!
!
!
!
 (31)
The derivative over time of ( )L t , we get:
1 2 1 1 2 2
2 2
1( ) ( ) 2
1 1ˆ ˆ
1 1 1ˆ ˆˆ
1 1ˆ
1 1ˆ ˆ( )
T T
IRM
T T T
IRM
T T T
T
T T
PI PI
E PI
L t Z Z Z Z M Z
Z M Z
tr E E K K
z g
a p u
j h
µ
x z g g
a a p p u u
j j h
= - +
+ - -X X
- - -X X X
- +X X
- -X X
" "
" "!" !
" ""! !!
"! "
" "! !
 (32) 
Substitute (29) into (32) and using property 2, 
we obtain:
1 2 1 1 2 2
2 2
1( ) ( ) 2
1 1ˆ ˆ
1 1 1ˆ ˆˆ
1 1ˆ
1 1ˆ ˆ( )
T T
IRM
T T T
IRM
T T T
T
T T
PI PI
E PI
L t Z Z Z Z M Z
Z M Z
tr E E K K
z g
a p u
j h
µ
x z g g
a a p p u u
j j h
= - +
+ - -X X
- - -X X X
- +X X
- -X X
" "
" "!" !
" ""! !!
"! "
" "! !
 (33)
Substituting the online adaptive update law (30) to 
(33), yields:
( ) (
) ( )
( )( )2
1 1 1 2 2 2 2
2
2 2
2ˆ
τ
T T T
T T T
SMC
T T
PI
P
PI
T T
D
I
L t Z Z Z Z Z W
Z E E
Z K Z h
tr D Z D Z
µ µ
t
j l h
aQ Q
Y
= - - + -
- - + -
- - -
- X -
F! !
!
!!
"
(34)
27
LIÊN NGÀNH ĐIỆN - ĐIỆN TỬ - TỰ ĐỘNG HÓA
Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, ISSN 1859-4190, Số 3 (70) 2020
By using (24), (25) and (28), it becomes:
( )
( )( )
2
1 1 1 2 2 2
2
2
ˆ 
ˆ 
ˆ
T
T T
T
T
E
T
ZL t Z Z Z Z Z
tr E Z Ev
lh j
µ µ h j hl
h
£ - - +
+
- + -F!
"
Because 2
2
ˆ 0ˆ 
T
T
Z
Z
h l
l
j hh j h - <+ , therefore (35) 
becomes
( )
( )( )( )
1 1 1 2 2 2
2
T
E
T T
T
L t Z Z Z Z
tr E Z E Ev
µ µ£ - -
+ - -F! !
" 
 (36)
By using
 ( ) ( ) 2 2,TtrE E E E E E E E E- = - £ -! ! ! ! ! !
and using the inequality (17) into (36) could be 
rewritten as follows:
 1 1 1 2 2 2 2
0 2 2E
T TL Z Z Z Z
c Z E v Z E
µ µ£ - -
+ -! !
" 
 (37)
With 0 Ec n Ev= + .
We see that to make sure 0L £! .
From the results show that the system is stable.
4. SIMULATION RESULTS
The structure of the n-links IRM is quite complicated 
in [19].
Fig 3. Architecture of three-link De-icing RM
According to practical model of three-link de-icing 
IRM, the parameters of this system are shown 
as follow: m1 = 3 (kg), m2 = 2 (kg), m3 = 2,5 (kg), 
l1 = 0,14 (m), l2 = 0,32 (m), and g = 9,81 (m/s2). 
The desired trajectories of joint for the three-link 
de-icing IRM are selected as follows:
 [ ]
( ) ( ) ( )
1 2 3
sin 1.5 0 ;.5sin 2 sin 1.5
T
d d d d
Tt t t
dQ = Q Q
= é ùë û
The ARNNs controller has the parameter values 
selected as follows:
, ; 
; ; 
( )1 22,2,2 ; (5,5,5);diag diagµ µ= =
( ) 60, 60, 60, 60, 60 ;diagzX = 0.001PIX =
( )0.001,0.001,0.001,0.001, 0.001 ;diagjX =
0.13gX = 0.12;hX = 0.1aX = 0.1pX =
0.1uX = 10EX = 0.2.Ev =
The initial condition is chosen as follows:
, , ( )0 1h = ( ) [ ] 0 1 1 1 1 l = ( )0 1.E =
Comparative results of the proposed ARNNs 
controller with the AF [3] and PID controllers are 
shown in Figure 4 and Table 1. We see that all three 
controllers achieve global stability, tracking error 
is very small around zero, the ability to respond 
quickly, the overshoot is insignificant. However, 
the proposed controller is capable of responding 
faster and with less overshoot than the AF and 
PID controllers. The errors that follow the desired 
trajectory of the proposed RANNs controller are 
smaller than the AF and PID controllers. That is, 
the proposed controller has the parameters that 
have been best adjusted based on the control 
law and update rules. The ability to approximate 
unknown functions of the ARNNs controller is also 
better. The durability of the SMC controller is also 
shown. Not only that, the PI controller also makes 
the overshoot of ARNNs improved compared to 
the two AF and PID controllers. In addition Fig 4 
also observes that the control force of the ARNNs 
is smoother and the vibration is smaller than that of 
the AF and PID controller even when the tracking 
error reaches a large value.
Table 1. Performance comparisons of proposed 
controller, PID and AF
Simulation Unit: radLink 1 Link 2 Link 3
Proposed 
controller 2.425×10-4 2.214×10-4 2.857 ×10-4
AF 5.756 ×10-4 5.548 ×10-4 5.945 ×10-4
PID 4.842 ×10-3 3.952 ×10-3 4.846 ×10-3
(35)
28
NGHIÊN CỨU KHOA HỌC
Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, ISSN 1859-4190, Số 3 (70) 2020
Figure 4. Trajectory, tracking errors, and control input of the AF, PID and proposed ARNNs system 
5. CONCLUSIONS
In this research, a sustainable adaptive controller 
to control the three links de-icing IRM on the basis 
of neural, ASMC, and API controllers has ensured 
stability and stability in disturbed and changing 
environments. By using the stability theory of 
Lyapunov, the authors have proved that the 
system is always stable throughout the workspace. 
Moreover, the effectiveness of the controller is also 
demonstrated through simulation and experiment 
results when comparing the proposed controller 
with AF and PID. The simulation results show that 
the convergence speed, braking ability, grip error, 
stability, fast response, overshoot of the proposed 
ARNNs controller are better than the AF controller 
and the PID control.
REFERENCES
[1] Jafarov, E.M., Parlakçı, M.N.A., and 
Istefanopulos. Y (2005), A New Variable 
Structure PID-Controller Design for Robot 
Manipulators, IEEE Trans. on control systems 
technology. 13 (1), pp 122-130.
[2] Al-Qahtani. H.M., Mohammed, Amin A., 
Sunar, M. (2017, Dynamics and control 
of a robotic arm having four links. Arabian 
journal for Science and Engineering, 42(5), 
pp. 1841-1852.
[3] Mohammad R S, Pooria O, Mohammad H K. 
(2015), Robust control strategy for electrically 
driven robot manipulators: adaptive fuzzy 
sliding mode, IET Sci. Meas. Technol. 9(3): 
322-334.
[4] Han, S., Lee, J. (2016), Finite-time sliding 
surface constrained control for a robot 
manipulator with an unknown deadzone and 
disturbance, ISA Transactions, vol. 65, pp. 
307-318.
[5] Cao L. J., Wang Y. C., Zhang S. X. et al. (2016), 
Robust Adaptive Backstepping Control for a 
Class of Uncertain Nonlinear System. Ieee.
[6] Lin X., Dong H. R., Yao X. M. (2018), Tuning 
function-based adaptive backstepping fault-
tolerant control for nonlinear systems with 
actuator faults and multiple disturbances, 
Nonlinear Dynamics. 91(4): 2227-2239.
[7] Yang H. J., Ye D. (2018), Fixed-time stabilization 
of uncertain strict-feedback nonlinear systems 
via a bi-limit-like strategy, International 
Journal of Robust and Nonlinear Control. 
28(17): 5531-5544.
[8] Khorashadizadeh S., Sadeghijaleh M. (2018), 
Adaptive fuzzy tracking control of robot 
manipulators actuated by permanent magnet 
synchronous motors, Computers & Electrical 
Engineering, vol. 72, pp. 100-111.
[9] Karamali Ravandi, Khanmirza E. and 
Daneshjou K. (2018), Hybrid force/position 
control of robotic arms manipulating in 
uncertain environments based on adaptive 
fuzzy sliding mode control, Applied Soft 
Computing, vol. 70, pp. 864-874.
[10] Peng J. and Dubay R. (2019), Adaptive fuzzy 
backstepping control for a class of uncertain 
nonlinear strict-feedback systems based on 
dynamic surface control approach, Expert 
Systems with Applications, vol. 120, pp. 
239-252. 
29
LIÊN NGÀNH ĐIỆN - ĐIỆN TỬ - TỰ ĐỘNG HÓA
Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, ISSN 1859-4190, Số 3 (70) 2020
[11] He J.,Luo M., Zhang Q., Zhao J. and Xu L. 
(2016), Adaptive Fuzzy Sliding Mode Controller 
with Nonlinear Observer for Redundant 
Manipulators Handling Varying External Forc, 
Journal of Bionic Engineering. vol. 13, pp. 
600-611, 2016.
[12] Chen D. D., Wang T. M., Yuan P. J. et al. 
(2019), A positional error compensation method 
for industrial robots combining error similarity 
and radial basis function neural network, 
Measurement Science and Technology. 30(12).
[13] Pham C. V., Wang Y. N. (2015), Robust Adaptive 
Trajectory Tracking Sliding mode control based 
on Neural networks for Cleaning and Detecting 
Robot Manipulators, Journal of Intelligent & 
Robotic Systems. 79(1): 101-114.
[14] Yen V. T., Nan W. Y., Cuong P. V. (2019), 
Robust Adaptive Sliding Mode Neural Networks 
Control for Industrial Robot Manipulators, 
International Journal of Control Automation 
and Systems, 17(3): 783-792.
[15] Wu Y., Huang R., Li X. et al. (2019), Adaptive 
neural network control of uncertain robotic 
manipulators with external disturbance 
and time-varying output constraints, 
Neurocomputing. 323: 108-116.
[16] Luan F. J., Na J., Huang Y. B. et al. (2019), 
Adaptive neural network control for robotic 
manipulators with guaranteed finite-time 
convergence, Neurocomputing. 337: 153-164.
[17] Vũ Thị Yến, Wang Yao Nan, Lê Thị Hồng 
Nhinh, Lương Thị Thanh Xuân (2017), Thiết 
kế bộ điều khiển thích nghi trượt bền vững 
trên cơ sở mờ nơron cho robot công nghiệp, 
Tạp chí Nghiên cứu khoa học – Đại học Sao 
Đỏ, Việt Nam.
[18] Vu D. H., Huang S., Tran T. D. et al (2019), 
A Robust Adaptive Control using Fuzzy Neural 
Network for Robot Manipulators with Dead-
Zone, International Journal of Computers, 
Communications & Control. 14(5).
[19] Van Tran, T., Wang, Y., Ao, H., & Khac Truong, 
T. (2015), Sliding mode control based on 
chemical reaction optimization and radial 
basis functional link net for de-icing robot 
manipulator, Journal of Dynamic Systems, 
Measurement, and Control, 137(5).
 Tran Thi Diep
- Summary of the training and research process (graduation time and training 
program, research):
+ In 2010: She received her B.S in Automation Engineering from Thai Nguyen 
University of Technology, Thai Nguyen Vietnam.
 + In 2013 : Graduated with Master degree in Automation from Hanoi University of 
Mining and Geology, Hanoi Vietnam.
+ In 2020: Graduated with a doctorate in electrical engineering from Hunan 
University, China.
- Summary of current work: Lecturer, Faculty of Electrical at Sao Do University.
- Areas of concern: Her current research interests include control nonlinear systems 
including SIMO and MIMO and control of distributed generation systems using 
renewable energy sources.
- Email: phuongdiep222@hnu.edu.cn.
- Phone number: 0374700015.
AUTHORS BIOGRAPHY