Utilizing P-Type ILA in tuning Hybrid PID Controller for Double Link Flexible Robotic Manipulator

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Utilizing P-Type ILA in tuning Hybrid PID
Controller for Double Link Flexible Robotic
Manipulator
A.Jamali
Department of Mechanical and
Manufacturing Engineering,
Faculty of Engineering,
Universiti Malaysia Sarawak
Sarawak, Malaysia
jannisa@unimas.my
Mat Darus I. Z.
Faculty of Engineering
Universiti Teknologi Malaysia
Johor, Malaysia
intan@mail.fkm.utm.my
M.O. Tokhi
London South Bank University
London, UK
o.tokhi@sheffield.ac.uk
A.S Z.Abidin
Department of Mechanical and
Manufacturing Engineering,
Faculty of Engineering,
Universiti Malaysia Sarawak
Sarawak, Malaysia
zaasakura@unimas.my
Abstract— The usage of robotic manipulator with multi-link
structure has a great influence in most of the current industries.
However, controlling the motion of multi-link manipulator has
become a challenging task especially when the flexible structure
is used. Currently, the system utilizes the complex mathematics
to solve desired hub angle with the coupling effect and vibration
in the system. Thus, this research aims to develop the controller
for double-link flexible robotics manipulator (DLFRM) with the
improvement on hub angle position and vibration suppression.
The research utilized DLFRM modeling based on NARX model
structure estimated by neural network. In the controllers’
development, this research focuses on adaptive controller. P-
Type iterative learning algorithm (ILA) control scheme is
implemented to adapt the controller parameters to meet the
desired performances when there are changes to the system. The
hybrid PID-PID controller is developed for hub motion and end
point vibration suppression of each link respectively. The
controllers are tested in MATLAB/Simulink simulation
environment. The performance of the controller is compared
with the fixed hybrid PID-PID controller in term of input
tracking and vibration suppression. The results indicate that the
proposed controller is effective to move the double-link flexible
robotic manipulator to the desired position with suppression of
the vibration at the end of the double-link flexible robotic
manipulator structure.
Keywords—robotic manipulator, flexible, Iterative learning
algoritmn , vibration suppression
I. INTRODUCTION
The advancements in various field of life inclusive of
domestic and industries create a great demand for flexible
robot manipulator. Many robot manipulator applications are
categorized as multiple-input-multiple-output (MIMO)
systems due to multi-link structure. The design and tuning of
multi-loop controllers to meet certain specifications are often
the pullback factor because there are interactions between the
controllers. The system must be decoupled first to minimize
the interaction or to make the system diagonally dominant.
Moreover, the reduction of vibration on flexible structure of
robot manipulator must be treated at the same time. The
continuous stress produced by the vibration can lead to
structural deterioration, fatigue, instability and performance
degradation. Thus, the reduction of vibration on flexible
structure of robot manipulator is of paramount importance.
Though many researchers have successfully produced the
controllers for multi-link flexible manipulator, the control
scheme developed involves complex mathematics to solve the
coupling effect and vibration simultaneously. As a result, it
consumes a lot of time in numerical computation which leads
to higher computational cost. Thus, the drawback received
substantial attention to cater recent industries demand in
various applications. On-going researches focused on
improving the control methods to fulfill all the conflicting
requirements.
The study of adaptive controller in flexible manipulator
remained until today due to its significant contribution in
actual plant. Among them, a new Nonlinear Adaptive Modal
Predictive Controller on two link flexible manipulator with
various payload was carried out [1]. The controller could
generate appropriate adaptive torque to control tip trajectory
tracking and fast suppression of tip deflection. Besides,
indirect control of Self-Tuning PI controller of two link
flexible manipulator tune by Neural Network was proposed
[2]. Simulation results showed that the tuning parameters
obtain could suppress the vibration and track the desired joint
angles effectively. E. Pereira et al. have investigated the use of
adaptive input shaping using an algebraic identification for
single-link flexible manipulators with various payloads [3].
Experiment results proved that the proposed control managed
to follow tip trajectories in shorter time. Another research on
adaptive controller was comprised of a fast on-line closed-
loop identification method combined with an output-feedback
controller for single link flexible manipulators [4].
Experimental results showed that the controller manage to
follow the trajectory tracking.
Another type of adaptive controller that is iterative learning
algorithm (ILA) has been implemented in different control

scheme in the flexible manipulator system. For example, two
phase ILA controllers to carry out the ideal input and output
signals of iterative learning control (ILC) where the error is
used to calculate the parameters of the proportional-derivative
(PD) controller by using standard least squares (LS) algorithm
for the SLFM [5] which the controller is effective in tracking
the desired trajectory over interval time. Zhang and Liu
employed an adaptive iterative learning control scheme based
on Fourier basis function for single-link flexible manipulator
(SLFM) [6] whereby the controller portrayed successfully
tracks the actual trajectory. Besides, genetic algorithm was
applied to tune three combinations of controller for single link
flexible manipulator in vertical plane motion that is PID, PID-
PID and PID-ILC controller [7]. Simulation demonstrated that
the PID-ILC parameter obtained in the optimization
outperform other controllers and allow the system to perform
well in reducing the vibration at the end-point of the
manipulator. However, none of the research based on iterative
learning algorithm (ILA) was implemented on DLFRM.
Apart from that, ILA have been used in different control
engineering problems such as robot manipulator for industry
and healthcare, machining machine, process plant, power
plant, nanotechnology area etc. Among them, Jain and Garg,
have proposed ILC for the nano-positioning system to reject
disturbances [8]. Besides, a back-stepping adaptive iterative
learning control incorporating fuzzy neural network was
implemented to approximate the unknown and robust learning
term to compensate the uncertainty for robotic systems with
repetitive task [9]. Mola et al. presented a new intelligent
robust control method based on an active force control (AFC)
strategy for anti-lock brake system (ABS) [10]. Another
research employed PID active vibration controller using ILA
for marine riser whereby ILA was used to optimize the value
of PID parameters based on the error portray in the system
[11]. A novel method to control mobile manipulator was
developed where ILA is combined with active force control
(AFC) and PID scheme to compensate the dynamic effect of
the disturbances that includes impact force and vibratory
excitation applied to each wheel and joint of mobile
manipulator [12].
The variety of application of ILA shown in literatures
review has proven the competency of ILA especially in
dealing with non-linear system.
In this paper, P-Type ILA in tuning the hybrid PID
controller was developed. The dynamic model of the system
was established through system identification using Neural
Network. NARX model structure based on multi-layer
perceptron was employed to obtain the non-parametric
modeling networks of DLFRM. The control structure of PID
controllers optimized by P-Type ILA was proposed for
position tracking and end point vibration suppression.
Performances of the proposed controllers were implemented
through simulation in MATLAB/Simulink environment.
This paper is organized as follows; Section 2 presents the
modeling and system identification of the system; Section 3
describes the control scheme applied to the system; and
Section 4 discusses the obtained results and draws the
conclusions.
II. MODELING AND SYSTEM IDENTIFICATION
A. Experimental Data
The planar DLFRM was developed and fabricated to
perform the angular movement of manipulator as shown in
Fig. 1. The schematic diagram of the system was illustrated in
Fig. 2.
A bang-bang signal with ± 0.7 V amplitude and ± 0.5 V
amplitude were used to provide required torque to excite the
double-link simultaneously. Four outputs were collected from
two encoders and two accelerometers which represent the hub
angles and end point acceleration of each link respectively.
The experiment was carried out for the duration of 9 s with
sampling time of 0.01 s.
Fig. 1. Double Link Flexible Robotic Manipulator rig
Fig. 2. Schematic Diagram of DLFR
B. Modeling Estimation
The DLFRM is categorized under highly non-linear, thus
non-parametric modeling is preferred to model it. Among non-
parametric model, NARX have the simplest structure. NARX
model is the nonlinear generalization of the well-known ARX
model, which constitute a standard tool in linear black-box
identification. For estimating the nonlinear part of the ARX

structure, the neural network was utilized. The research utilized
back propagation for multi-layer perceptron (MLP) neural
network and Elman neural networks (ENN) for modeling four
set of a Single input Single output (SISO) DLFRM system.
The developed model was validated by Mean Squared Error
(MSE) and Correlation Test. The details of the modeling is
elaborated in previous study [13].
III. CONTROL SCHEME
The control scheme is shown in Fig.3 and 4. The PID
i1
controller is developed for hub angle motion while PID
i2
controller is applied for flexible body motion. The entire PID
controllers are tuned by P-Type ILA. The two loops of each
link (i=1,2) are combined together to give control inputs to the
double link flexible robotic manipulator system.
A. Controller Design
In this work, the intelligent PID controllers are utilized to
ensure the hub follows the reference trajectory and the
vibration of the system is eliminated simultaneously through
end point acceleration feedback.
Fig. 3. Block diagram of control rigid body motion
For the hub angle motion,
di
θ
, and
)(t
i
θ
represents
reference hub angle and actual hub angle of the system
respectively. By referring to the block diagram in Fig. 3, the
close loop signal of U
mi
can be written as;
() () ()()
[]
tetCAtU
mimimimi
=
21,i =
(1)
where U
mi
is PID control input, A
mi
is motor gain and C
mi
is
PID controller. The controller gains are K
Pi
, K
Ii
and K
Di
. And;
()
mii
Ht =
θ
(2)
DtUH
mimi
+= )(
(3)
The error function of the system is defined as in Eq. (4);
() () ()
[]
tθGtθte
imidimi
−=
21,i =
(4)
Therefore, the closed loop transfer function obtained as in Eq.
(5);
[]
[]
mimimimi
mimimi
di
i
HGAC
HAC
θ
θ
+
=1 (5)
Fig. 4. Block diagram of control flexible body motion
For the flexible motion as illustrated in Fig. 4, the control
input is given by;
() () ()
[
]
tetCAtU
pipipipi
=
21,i =
where U
pi
is PID control input, A
pi
, are piezoelectric gain, C
pi
is PID controller as derived in Eq. 5.1. The controller gains are
K
Pi
, K
Ii
and K
Di
. The deflection output represents by y
i
and the
desired deflection y
di
is set to zero. And;
()
pii
Uty =
(7)
()
DtUH
pipi
+=
(8)
Thus, the error e
pi
is defined as;
() ()
[
]
tyGte
ipipi
−= 0
21,i =
(9)
Therefore, the closed loop transfer function obtained as;
[
]
[]
pipipipi
pipipi
di
i
HGAC
HAC
y
y
+
=1 (10)
All the parameters of K
Pi
, K
Ii
and K
Di
were tuned so that U
mi
and U
pi
provide acceptable performance of DLFRM. The
performance of the PID controller was based on minimizing
the MSE value.
B.
P-type ILA
Iterative learning algorithm is a scheme that uses
information in previous repetitions to improve the control
signal which ultimately enabling a suitable control action. In
this work, ILA is used to improve the performance of PID
control structure. The schematic diagram of the ILA tuner
with PID controller is shown in Fig. 5.
In this scheme, the ILA performed a self-tuning to the PID
controller parameters to minimize the overall system error so
that the performance iteratively gets improved as presented in
the following equations [14]:
( ) () ()
( ) () ()
() () ()
kek
K
k
K
kek
K
k
K
kek
K
k
K
DD
II
PP
×+=+
×+=+
×+=+
ϕ
ϕ
ϕ
3
2
1
1
1
1
(11)

where K (k) is the stored value from the previous iteration
(from memory), K(k+1) is the updated value (to memory), Φ
1
is the proportional learning parameter, Φ
2
is the integral
learning parameter, Φ
3
is the derivative learning parameter
and e(k) is the system error.
Fig. 5. P-type ILA with PID controller
ILA computes successive approximations such that the system
output approaches a suitable value as the time increases.
However, the over learning might occur during the learning
processes as the time increased continuously. This condition
might lead to system instability when it enters a dangerous
zone [14]. Thus, a stopping criterion is implemented into the
ILA to overcome this drawback.
In this study, there are two errors are considered that is to
minimize the error from the hub angles and the error from the
end point acceleration. For hub angle, the smaller value
indicates precision in positioning the link to desire position.
Meanwhile, the smaller value of end point acceleration
implies that the vibration in the system is very much reduced.
The system error is calculated as:
() () ()
kykyke
d
−=
(12) (6.2)
where e(k), y
d
(k) and y(k) is the system error, desired input and
actual output respectively.
The new signals K
P
(k+1), K
I
(k+1) and K
D
(k+1) are
calculated based on Eq. (11) if the error is larger than the set
stopping criterion error. However, if the error is smaller than
the stopping criterion error, then the new signals are calculated
by using the following equations:
() ()
() ()
() ()
kKkK
kKkK
kKkK
DD
II
PP
=+
=+
=+
1
1
1
(13)
(6.3)
IV.
RESULTS AND DISCUSSION
Simulation was carried out to study the effectiveness of the
PID-ILA controller in trajectory tracking and vibration
suppression control of DLFRM with no payloads. The
simulation was implemented and tested within
MATLAB/Simulink environment. The Simulink models were
based on block diagram shown in Fig. 6 and 7. Step signals
were employed as input reference with magnitude of ± 2.1 rad
and ± 1.1 rad for links 1 and 2 respectively. The learning
parameters were tuned through trial and error method. The
simulations were run for 9 s with sampling rate of 0.01 s.
During simulation, the controller stores information of
parameter gains. These values are used as references in the
next parameter gains’ computation which is identified by error
difference.
Fig. 6. Block diagram of self-tuning control scheme based on ILA for hub
angles 1 and 2
Fig. 7. Block diagram of self-tuning control scheme based on ILA for end
point accelerations 1 and 2
A.
Hub angle Motion
During the simulation, the learning process was executed
to find new controller parameters based on the learning
parameters. The learning parameters presented in Eqs. (11)
were tuned through trial and error method. During simulation,
the controller stores information of parameter gains and uses
these values as references to compute the next parameter gains
which is identified by error difference. The control parameters
of K
P
, K
I
, and K
D
converge when it reached the constant
values. At this point the minimum output error is reached. The
time taken for the controller parameters K
P
, K
I
, and K
D
of both
links to settle at those constant values are about 2.81 s and
2.65 s respectively.
0100 200 300 400 500 600 700 800 900
-0.5
0
0.5
1
1.5
2
2.5
Tim e (ms)
Hub Angle 1 (rad)
Target Output
PID-ZN
PID-PSO
PID-ILA
Fig. 8. Comparison between PID-ZN, PID-PSO and PID-ILA of hub angle 1

0100 200 300 400 500 600 700 800 900
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Time (ms)
Hub Angle 2 (rad)
Target Output
PID-ZN
PID-PSO
PID-ILA
Fig. 9. Comparison between PID-ZN, PID-PSO and PID-ILA of hub angle 2
The intelligent PID-ILA controller was compared with the
fixed controller, PID-PSO. PID-ZN worked as the control
benchmark. The results for closed-loop hub angle 1 and 2 of
PID-ILA controller were shown in Fig. 8 and 9 respectively.
The stopping criterion is 0.02 rad which was obtained through
heuristic method. The performance of self-tuning PID-ILA
control structure is observed in terms of rise time, tr (s),
settling time, ts (s), maximum overshoot, Mp (%) and steady
state error, Ess (rad).
The numerical results are tabulated in Table 1. It can be
noted that PID-ILA control structure for link 1 and 2 were
able to track the desired hub-angle of DLFRM. There are
significant improvements observed on PID-ILA. The
percentage of improvement achieved by PID-ILA controller
compared with PID-PSO controller for t
r
, t
s
and M
p
are 86.2
%, 44.94 % and 86.21 % for link 1 and 80.95 %, 16.95 % and
17.91 % for link 2.
TABLE
1 P
ERFORMANCE OF CONTROLLERS FOR HUB ANGLE
Controller Parameters of controllers
Φ
1
Φ
2
Φ
3
K
P
K
I
K
D
HUB 1
P-Type ILA 3 1 10 13.8 8.30 40.9
PID-PSO - - - 3.7 57.8 3.4
PID-ZN - - - 2.1 0.54 2.0
HUB 2
P-Type ILA 3 1 10 21.3 7.01 60.5
PID-PSO - - - 2.19 88.2 0.79
PID-ZN - - - 4.15 1.29 3.32
Controller
Rise
Time
(s), t
r
Settling
Time (s), t
s
Over shoot
(%), M
p
SSE,
E
ss
HUB 1
P-Type ILA 0.008 0.49 0.16 0
PID-PSO 0.058 0.89 1.16 0.003
PID-ZN 2.965 7.147 4.69 0.68
HUB 2
P-Type ILA 0.008 0.49 1.10 0
PID-PSO 0.042 0.59 1.34 0.002
PID-ZN 1.460 5.45 5.45 0.21
B.
Flexible Motion
The same simulation process applied to the end-point
acceleration control. The learning process to find the new
controller parameters is executed based on the learning
parameters. The parameters value become constant once the
minimum output error reached the set stopping criterion error
that is 0.0015 m/s
2
. This value is obtained through heuristic
method. The time taken for the controller parameters K
P
, K
I
,
and K
D
of both links to settle at those constant values are
about 7.34 s and 8.27 s respectively.
The intelligent PID-ILA controller was compared with the
conventional controller, and PID-PSO. The results show that
PID tuning through ILA managed to improve the performance
of vibration suppression than those obtained by the PSO
method. These can be observed from Fig. 10 and 11
respectively.
0100 200 300 400 500 600 700 800 900
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
Time (ms)
End point acceleration (m/s2)
Uncont rolled Signal
PID-ZN
PID-PSO
PID-ILA
Fig.10. Comparison between controllers for end-point acceleration 1
0100 200 300 400 500 600 700 800 900
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
Tim e (ms )
End poin acc eleration 2 (m/s2)
Uncontrol led Signal
PID-ZN
PID-PSO
PID-ILA
Fig. 11. Comparison between controllers for end-point acceleration 2
T
ABLE
2 P
ERFORMANCE OF CONTROLLERS FOR END
-
POINT ACC ELERATION
Controller Parameters of controllers MSE
Φ
1
Φ
2
Φ
3
K
P
K
I
K
D
Link 1
PID-ILA 3 1 5 7.38 21.24 1.81 1.810 × 10
-8
PID-PSO - - - 2.07 498.1 2.33 3.948 ×10
-8
PID-ZN - - - 7.2 21.18 0.61 2.822 ×10
-6
Link 2
PID-ILA 3 1 5 16.11 55.12 3.05 4.054 × 10
-8
PID-PSO - - - 8.06 817.9 1.03 4.315 × 10
-8
PID-ZN - - - 4.16 55.08 1.28 7.564 ×10
-7

This could be further investigated from frequency domain
result as shown in Fig.12 (a) and (b).
510 15 20 25 30 35
-350
-300
-250
-200
-150
-100
X: 1.594
Y: -150.2
Frequency (Hz )
X: 0.996
Y: -105.9
X: 1.594
Y: -162.7
Magnitude (dB )
Uncontrolled S ignal
PID-PSO
PID-ILA
(a) Link 1
510 15 20 25 30 35
-320
-300
-280
-260
-240
-220
-200
-180
-160
-140
-120
X: 1.793
Y: -122.9
Frequency (Hz)
Magnitude (dB)
X: 1.594
Y: -158.7
X: 1.594
Y: -161
Uncontrolled Si gnal
PID-PSO
PID-ILA
(b) Link 2
Fig. 12. Spectral density of the system output not label axes with a ratio of
quantities and units
.
PID-ILA control provides higher attenuation value for link
1 that is 56.8 dB as compared to PID-PSO that is 44.3 dB. The
attenuation value of PID-ILA for link 2 shows the same
pattern is that is 38.1 dB as compared to PID-PSO that is 35.8
dB. The comparison focused on mode 1 since the first mode is
dominant and contributes substantial effect to the system.
V.
C
ONCLUSIONS
In this work, the proposed P-Type ILA to tune the PID
controller in tracking the desired hub-angle and suppress the
vibration of DLFRM was investigated and compared with
corresponding fixed control structure that is conventional PID
and PID-PSO. It was noted that PID-ILA control structure
performed well as compared to those fixed PID control
structure specifically PID-PSO manages to give a good
response. For the hub angle, the percentage of improvement
achieved by P-Type ILA controller compared with PID-PSO
controller for t
r
, t
s
and M
p
are 86.2 %, 44.94 % and 86.21% for
link 1 and 80.95 %, 16.95 % and 17.91 % for link 2.
Meanwhile, the percentage of improvement for flexible body
control achieved by PID-ILA controller compared to PID-PSO
controller for MSE is 54.15 % and 6.05 % for link 1 and 2
respectively. It can be concluded from this observation that the
performance of the proposed adaptive PID-ILA control
scheme is better than the fixed PID controller
.
A
CKNOWLEDGMENT
The authors would like to express their gratitude to
Minister of Education Malaysia (MOE), Universiti Teknologi
Malaysia (UTM) and Universiti Malaysia Sarawak (UNIMAS)
for funding and providing facilities to conduct this research
R
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