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International Journal of Advanced Robotic Systems
Composite Fuzzy Logic Control Approachto a Flexible Joint ManipulatorRegular Paper
Mohd Ashraf Ahmad1,*, Mohd Zaidi Mohd Tumari1 and Ahmad Nor Kasruddin Nasir1
1 Control & Instrumentation (COINS) Research Group, Faculty of Electrical Engineering, University of Malaysia Pahang, Pekan, Malaysia* Corresponding author E-mail: [email protected]
Received 18 Jun 2012; Accepted 21 Aug 2012
DOI: 10.5772/52562
© 2013 Ahmad et al.; licensee InTech. This is an open access article distributed under the terms of the CreativeCommons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract The raised complicatedness of the dynamics
of a robot manipulator considering joint elasticity
makes conventional model‐ based control strategies
complex and hard to synthesize. This paper presents
investigations into the development of hybrid
intelligent control schemes for the trajectory tracking
and vibration control of a flexible joint manipulator. To
study the effectiveness of the controllers, a collocated
proportional‐derivative (PD)‐type Fuzzy Logic
Controller (FLC) is first developed for the tip angular
position control of a flexible joint manipulator. This is
then extended to incorporate a non‐collocated Fuzzy
Logic Controller, a non‐collocated proportional‐
integral‐derivative (PID) and an input‐shaping scheme
for the vibration reduction of the flexible joint system.
The positive zero‐vibration‐derivative‐derivative
(ZVDD) shaper is designed based on the properties of
the system. The implementation results of the response
of the flexible joint manipulator with the controllers
are presented in time and frequency domains. The
performances of the hybrid control schemes are
examined in terms of input tracking capability, level of
vibration
reduction
and
time
response
specifications.
Finally, a comparative assessment of the control
techniques is presented and discussed.
Keywords Elastic Joint, Vibration Control, Fuzzy Logic,
Input‐Shaping, Collocated and Non‐Collocated Control
1. Introduction
Currently, elastic joint manipulators have received a great
deal of attention due to their light weight, high
manoeuvrability, flexibility, high power efficiency and
large number of applications. However, controlling such
systems still faces numerous challenges that need to be
addressed. The
control
issue
of
the
flexible
joint
is
to
design the controller so that the link of the robot can track
a prescribed trajectory precisely with minimum vibration
to the link. In order to achieve these objectives, various
methods using different techniques have been proposed.
Yim [1], Oh and Lee [2] proposed an adaptive output‐
feedback controller based on a backstepping design. This
technique is proposed in order to deal with parametric
uncertainty in a flexible joint. The relevant work also
being done by Ghorbel et al. [3]. Lin and Yuan [4] and
Spong et al. [5] introduced a nonlinear control approach
using the feedback linearization technique and the
integral manifold
technique
respectively.
A
robust
control
design was reported by Tomei [6] by using simple PD
1Mohd Ashraf Ahmad, Mohd Zaidi Mohd Tumari and Ahmad Nor Kasruddin Nasir:
Composite Fuzzy Logic Control Approach to a Flexible Joint Manipulator
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ARTICLE
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control and Yeon and Park [7] by applying robust H∞
control. An open‐loop optimal control approach for
generating the optimal trajectory of the elastic robotic
arms in point‐to‐point motion is proposed by Korayem et
al. [8]. This method is based on Pontryagin’s minimum
principle which considers the mobility of the elastic
manipulator.
In recent years, tools of computational intelligence ‐such
as artificial neural networks and fuzzy logic controllers ‐
have been credited in various applications as powerful
tools capable of providing robust controllers for
mathematically ill‐defined systems. This has led to recent
advances in the area of intelligent control [9, 10]. Various
neural network models have been applied in the control
of flexible joint manipulators which have led to
satisfactory performances [11]. H. Chaoui et al. [12] used
a sliding mode control approach that learns the system’s dynamics through a feed‐forward neural network. A
time‐delay neuro‐fuzzy network was suggested in [13],
where a linear observer was used to estimate the joint
velocity signals and eliminated the need to measure them
explicitly. Subudhi et al. [14] presented a hybrid
architecture composed of a neural network to control the
slow dynamic subsystem and an H∞ to control the fast
subsystem. A feedback linearization technique using a
Takagi‐Sugeno neuro‐fuzzy engine was adopted in [15].
Lin and Chen [16] propose a combined rigid model‐ based
the computed torque and fuzzy control of flexible‐ joint
manipulators.
As to another aspect, an acceptable system performance
with reduced vibration that accounts for system changes
can be achieved by developing a hybrid control scheme
that caters for the rigid body motion and vibration of the
system independently. This can be realized by utilizing
control strategies consisting of either non‐collocated with
collocated feedback controllers or feed‐forward with
feedback controllers. In each case, the former can be used
for vibration suppression and the latter for the input
tracking of a flexible manipulator. A hybrid collocated
and non‐collocated controller has been widely proposed
for the control of flexible structures [17, 18, 19]. The works
have shown that the control structure gives a satisfactory
system response with significant vibration reduction as
compared to a response with a collocated controller. A
feedback control with a feed‐forward control for
regulating the position of a flexible structure has been
proposed previously [20, 21]. A control law partitioning
scheme which uses the end‐point sensing device has also
been reported [22]. The scheme uses an end‐point
position signal in an outer loop controller to control the
flexible modes, whereas the inner loop controls the rigid
body motion independently of the flexible dynamics of
the
manipulator.
However,
to
the
best
of
our
knowledge,
there is still no research which adopts intelligent schemes
‐ especially the fuzzy logic approach ‐ for both collocated
and non‐collocated feedback schemes. Moreover, there is
still no article focusing on a comparison study between
the non‐collocated control and feed‐forward control of an
elastic joint manipulator.
This paper presents an investigation into the development of hybrid intelligent control schemes for the
trajectory tracking of the tip angular position and the
vibration control of a flexible joint manipulator. Control
strategies are investigated based on a collocated PD‐type
FLC with non‐collocated control and a collocated PD‐type
FLC with a feed‐forward scheme. For non‐collocated
control, a deflection angle is fed back through a fuzzy
logic control configuration. In order to evaluate the
performance of the non‐collocated fuzzy logic scheme, it
will be compared with the non‐collocated PID scheme.
For the feed‐forward scheme, an input‐shaping strategy is
utilized
for
reducing
a
deflection
effect.
The
positive
zero‐
vibration‐derivative‐derivative (ZVDD) shaper is
designed based on the properties of the flexible joint
manipulator. In this study, we will provide a comparative assessment of the performances of the composite
strategies which are evaluated in terms of input tracking
capability, level of vibration reduction in the frequency
domain and time response specifications. The
implementation environment is developed within
Simulink and Matlab for the evaluation of the
performance of the control schemes. The rest of the paper
is structured as follows: Section 2 provides a brief
description of the single‐link flexible joint manipulator
system considered in this study. Section 3 describes the
modelling of the system derived using Euler‐Lagrange
formulation. The composite collocated PD‐type FLC with
a Fuzzy Logic Control, PID control and input‐shaping
scheme are described in Section 4. The simulation results
and a comparative assessment are presented in Section 5
and the paper is concluded in Section 6.
2. The Flexible Joint Manipulator System
In this study, the joint flexibility of the robot is
represented by a linear spring, as shown in Figure 1. The
rotary
flexible
joint
module
provided
by
the
Quanser
system [23] includes a servomotor in the high gear ratio
configurations and a free arm attached to two identical
springs. The springs are mounted to an aluminium
chassis which is driven by the servomotor. Rotating the
base of the arm causes the entire arm to oscillate due to
the joint flexibility introduced by the springs. An optical
encoder attached to the shaft of the DC motor is used to
measure the angular position of the shaft θ(t). The joint
deflection α(t) is measured by an encoder located at the
motor end of the arm.
In
Figure
2,
is
the
tip
angular
position
and
is
the
deflection angle of the flexible link. The base of the FJM
which determines the tip angular position of the FJM is
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driven by a servomotor. The deflection of the link will be
determined by the flexibility of the spring as their
intrinsic physical characteristics.
Figure 1. Rotary flexible joint manipulator
Figure 2. Description of the flexible joint manipulator system
3. The Modelling of the Flexible Joint Manipulator
This section
provides
a brief
description
on
the
modelling
of the FJM system as a basis of a simulation environment
for the development and assessment of the proposed
control techniques. The Euler‐Lagrange formulation is
considered in characterizing the dynamic behaviour of
the system.
The linear model of the uncontrolled system can be
represented in a state‐space form [23] as shown in
equation (1), that is:
,
x Ax Bu
y Cx
(1)
where the vector T
x and the matrices A ,
B and C are given by:
2
2
0 0 1 0
0 0 0 1
0 0
0 0
0 0 , 1 0 0 0 .
stiff m g t m g eq m
eq eq m
stiff eq arm m g t m g eq m
eq arm eq m
m g t g m g t g
eq m eq m
K η η K K K B R A
J J R
K (J J ) η η K K K B R
J J J R
η η K K η η K K B C
J R J R
(2)
In equation (1), the input u is the input voltage of the
servomotor mV which determines the FJM base
movement. In this study, the values of the parameters are
defined in Table
1.
Symbol Quantity Value
Rm Armature Resistance (Ω) 2.6
K m Motor Back‐EMF Constant (V.s/rad) 0.00767
K t Motor Torque Constant (N.m/A) 0.00767
J link Total Arm Inertia (kg.m2) 0.0035
J eq Equivalent Inertia (kg.m2) 0.0026
K g High gear ratio 14:5
K stiff Joint Stiffness (N.m/rad) 1.2485
Beq Equivalent Viscous Damping (N.m.s/rad) 0.004
η g Gearbox Efficiency 0.9
ηm Motor Efficiency 0.69
Table 1. System Parameter of FJM
4. Control Algorithm
In this section, control schemes for the rigid body motion
control and vibration suppression of a flexible joint
manipulator are proposed. Initially, a collocated PD‐type
FLC controller is designed. Then, a non‐collocated fuzzy
logic, non‐collocated PID and input‐shaping schemes are
incorporated in the closed‐loop system for the control of
vibration of the system.
4.1 PD‐type fuzzy logic controller (PD‐FLC)
A PD‐type FLC utilizing tip angular position error and a
derivative of tip angular position error is developed to
control the rigid body motion of the system. The hybrid
fuzzy control system proposed in this work is shown in
Figure 3, where ( )r t , ( )t and ( )t are the desired angle,
tip angular position and deflection angle of the FJM,
whereas k1 , k2 and k3 are scaling factors for two inputs and
one output of the FLC used with the normalized universe
of discourse for the fuzzy membership functions. For a
PD‐type FLC, triangular membership functions are
chosen for the tip angle error, tip angle error rate and
input voltage with 50% overlap. Normalized universes of
discourse are used for both the tip angle error and its
error rate and input voltage. Scaling factors k1 and k2 are
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chosen in such a way as to convert the two inputs within
the universe of discourse and activate the rule base
effectively, whereas k3 is selected such that it activates the
system to generate the desired output. Initially, all these
scaling factors are chosen based on trial and error. To
construct a rule
base,
the
tip
angle
error,
tip
angle
error
rate and input voltage are partitioned into five primary
fuzzy sets as:
Tip angle error E = {NM NS ZE PS PM},
Tip angle error rate V = {NM NS ZE PS PM},
Voltage U = {NM NS ZE PS PM},
where E , V and U are the universes of discourse for tip
angle error, tip angle error rate and input voltage,
respectively. The nth rule of the rule base for the FLC,
with the angle error and angle error rate as inputs, is
given by:
Rn: IF ( e is Ei) AND ( e is V j) THEN (u is U k),
where , Rn , n=1, 2,…N max , is the nth fuzzy rule, Ei , V j and
U k for i , j , k = 1,2,…,5, are the primary fuzzy sets.
A PD‐type FLC was designed with 11 rules as a closed
loop component of the control strategy for maintaining
the angular position of the FJM. The rule base was
extracted based on the underdamped system response
and is shown in Table 2. The three scaling factors, k1 , k2
and k3 were chosen heuristically to achieve a satisfactory
set of time domain parameters. These values were recorded as k1 = 0.552, k2 = 0.073 and k3 = ‐985.
Figure 3. PD‐type fuzzy logic control structure
No. Rules
1. If ( e is NM) and ( e is ZE) then (u is PM)
2. If ( e is NS) and ( e is ZE) then (u is PS)
3. If ( e is NS) and ( e is PS) then (u is ZE)
4. If ( e is ZE) and ( e is NM) then (u is PM)
5. If ( e is ZE) and ( e is NS) then (u is PS)
6. If ( e is ZE) and ( e is ZE) then (u is ZE)
7. If ( e is ZE) and ( e is PS) then (u is NS)
8. If ( e is ZE) and ( e is PM) then (u is NM)
9. If ( e is PS) and ( e is NS) then (u is ZE)
10. If ( e is PS) and ( e is ZE) then (u is NS)
11. If ( e is PM) and ( e is ZE) then (u is NM)
Table 2. Linguistic Rules of the PD‐type Fuzzy Logic Controller
4.2 PD‐type fuzzy logic with a non‐collocated fuzzy logic
controller (PD‐FLC‐FLC)
A combination of PD‐type fuzzy logic and a non‐collocated
fuzzy logic control scheme for the control of the tip angular
position
and
the
vibration
suppression
of
the
system ‐
respectively ‐ is presented in this section. The use of a non‐
collocated control system, where the deflection angle of the
flexible joint manipulator is controlled by measuring its
angle, can be applied to improve the overall performance as
more reliable output measurement is obtained. The control
structure comprises two feedback loops: (1) The hub angle as
an input to the PD‐type FLC for tip angular position control.
(2) The deflection angle as an input to a separate non‐
collocated control law for vibration control. These two loops
are then summed together to give a torque input to the
system. A block diagram of the composite fuzzy logic
control scheme is shown in Figure 4.
For tip angular position control, the PD‐type FLC strategy
developed in the previous section is adopted whereas for
the vibration control loop, the deflection angle feedback
through a non‐collocated fuzzy logic control scheme is
utilized. In designing the non‐collocated fuzzy logic
control, basic triangular and trapezoidal forms are chosen
for the input and output membership functions. Figure 5
shows the membership functions of the fuzzy logic
controller for vibration control. It consists of Negative Big
(NB), Negative Small (NS), Zero (Z), Positive Small (PS)
and Positive Big (PB), as shown in the diagram. The
universes of
discourses
of
the
deflection
angle,
deflection
angle rate and input voltage are from 1.2 to ‐1.2 rad, ‐
0.015 to 0.015 rad/s and ‐447 to 447 V respectively.
Table 3 lists the generated linguistic rules for vibration
control. The rules are designed based on the condition of the
deflection angle and the deflection angle rate, as illustrated
in Figure 6. Consider that the joint of the manipulator rotates
in an anti‐clockwise direction and that the link deflects in a
clockwise direction. As illustrated in Figure 6(a), under this
condition – and intuitively ‐ the torque should be applied in
a clockwise direction in order to compensate the deflection.
In
this
case,
the
relation
between
the
input
voltage
and
the
torque per inertia is shown in equation (3):
m m g t g
m
V η η K K
R (3)
Figure 4. PD‐type FLC with a non‐collocated fuzzy logic control
structure
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Figure 5. Membership functions of the input and output signals Deflection angle
rate
Deflection angle
PB PS Z NS NB
PB PB PB PB NB NB
PS PB PS PS NS NB
Z PB PS Z NS NB
NS PB PS NS NS NB
NB PB PB NB NB NB
Table 3. Linguistic rules for non‐collocated fuzzy logic control
Figure 6. Rules generation based on the motion condition Meanwhile, if the joint rotates in a clockwise direction, as
shown in Figure 6(b), and the link deflects in an anti‐
clockwise direction,
the
torque
should
be
imposed
in
an
anti‐clockwise direction to suppress the deflection
motion. In the case where there is no deflection, no torque
should be applied. Furthermore, the proposed fuzzy logic
control adopts the well‐known Mamdani min‐max
inference and centre of area (COA) methods.
4.3 PD‐type fuzzy logic with a non‐collocated PID Controller
(PD‐FLC
‐PID)
A combination of a PD‐type FLC and non‐collocated PID
control scheme for the control of the rigid body motion
and vibration suppression of the system is presented in
this section. The control structure of the PD‐FLC‐PID is
not very different from the PD‐FLC‐FLC and a block
diagram of the control scheme is shown in Figure 7.
For the rigid body motion control, the PD‐type FLC
control strategy developed in the previous section is
adopted whereas, for the vibration control loop, the
deflection angle feedback through a PID control scheme
is utilized. The PID controller parameters were tuned
using the Signal Constraint blockset of MATLAB via a
closed‐loop technique. At this moment, the PID controller
is optimized by considering the following desired
specifications:
Overshoot ≤10%
Settling time ≤0.75 sec
Rise time ≤0.55 sec
The initial parameters for PID controllers must be
specified before the Signal Constraint blockset executes the
tuning and optimizing process. The initial controller
parameters can be obtained either by trial and error or
else given as a default by the Signal Constraint blockset.
From the results of a Signal Constraint tuning process, the
values were recorded as k p = 602.5128, ki = ‐43.8895 and kd
= ‐19.7696.
Figure 7. PD‐type FLC with a non‐collocated PID control
structure
4.4 PD‐type fuzzy logic with input‐shaping (PD‐FLC‐IS)
A control structure for the control of the rigid body
motion and deflection angle reduction of the flexible joint
manipulator based on a PD‐type FLC and input‐shaping
scheme is proposed in this section. The positive input‐
shapers are
proposed
and
designed
based
on
the
properties of the system. In this study, the input‐shaping
control scheme is developed using a Zero‐Vibration‐
-400 -300 -200 -100 0 100 200 300 400
0
0.5
1
Input voltage (V)
NB NS Z PS PB
D e g r e e o f m e m b e r s h i p
-0.015 -0.01 -0.005 0 0.005 0.01 0.015
0
0.5
1
Deflection angle rate (rad/s)
D e g r e e o f m e m b e r s h i p
NB NS Z PS PB
1 0.8 0.6 0.4 0.2 0 -0.2 - 0.4 - 0.6 - 0.8 -1
0
0.5
1
Deflection angle (rad)
NB NS Z PS PB
D e g r e e o f m e m b e r s h i p
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Composite Fuzzy Logic Control Approach to a Flexible Joint Manipulator
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Derivative‐Derivative (ZVDD) input‐shaping technique
[21]. Previous experimental studies with a flexible
manipulator have shown that significant vibration
reduction and robustness is achieved using a ZVDD
technique [24]. A block diagram of the PD‐type FLC with
an input
‐shaping
control
technique
is
shown
in
Figure
8.
The input‐shaping method involves convolving a desired
command with a sequence of impulses known as input‐
shapers. The design objectives are to determine the
amplitude and time location of the impulses based on the
natural frequencies and damping ratios of the system.
The positive input‐shapers have been used in most input‐
shaping schemes. The requirement of positive amplitude
for the impulses seeks to avoid the problem of large
amplitude impulses. In this case, each individual impulse
must be less than one in order to satisfy the unity
magnitude
constraint.
In
addition, the
robustness
of
the
input‐shaper to errors in the natural frequencies of the
system can be increased by solving the derivatives of the
system vibration equation. This yields a positive ZVDD
shaper with a parameter as:
t1 = 0, t2 =
d
, t3 =
2
d
, t4 =
3
d
1 2 3
1
1 3 3 A
H H H
, 2 2 3
3
1 3 3
H A
H H H
2
3 2 331 3 3
H AH H H
,
3
4 2 31 3 3H A
H H H
(4)
where:
21H e
,
n and represent the natural frequency and damping
ratio respectively. For the impulses, t j and A j are the time
location and amplitude of impulse j respectively.
Figure 8. PD‐type FLC with an input‐shaping control structure
5. Implementation and Results
In this section, the proposed control schemes are
implemented and tested within the simulation
environment of the flexible joint manipulator and the
corresponding results are presented. The manipulator is
required to
follow
a trajectory
of
50º.
System
responses
‐namely the tip angular position and the deflection angle ‐
are observed. To investigate the vibration of the system in
the frequency domain, the power spectral density (PSD)
of the deflection angle response is obtained. The
performances of the control schemes are assessed in
terms of vibration suppression, trajectory tracking and
time response specifications. Finally, a comparative
assessment of
the
performance
of
the
control
schemes
is
presented and discussed.
(a) Tip angular position
(b) Deflection angle
(c)
Power
spectral
density
Figure 9. Response of the flexible joint manipulator using PD‐
FLC
21 nd
0 0.5 1.0 1.5 2.0 2.5 3.00
10
20
30
40
50
60
Time (s)
T i p a n g u l a r p o s i t i o n ( d e g )
0 0.5 1.0 1.5 2.0 2.5 3.0-20
-15
-10
-5
0
5
10
15
20
Time (s)
D e f l e c t i o n a n g
l e ( d e g )
0 2 4 6 8 10 12 14 16 18-100
-80
-60
-40
-20
0
20
40
Frequency (Hz)
P o w e r S p e c t r a l D e n s i t y ( d B )
8.83 Hz
2.94 Hz
14.52 Hz
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Figure 9 shows the responses of the flexible joint
manipulator to the reference input trajectory using the
PD‐FLC in a time‐domain and a frequency domain (PSD).
These results were considered as the system response
under rigid body motion control and will be used to
evaluate the
performance
of
the
non
‐collocated
fuzzy
logic control and input‐shaping scheme. The steady‐state
tip angular trajectory of 50º for the flexible joint
manipulator was achieved within the rise and settling
times and an overshoot of 0.222 s, 0.565 s and 1.78 %
respectively. It is noted that the manipulator reaches the
required position within 1 s, with little overshoot.
However, a noticeable amount of vibration occurs during
the movement of the manipulator. It is noted from the
deflection angle response that the vibration of the system
settles within 3 s with a maximum residual of 15º.
Moreover, and from the PSD of the deflection angle
response, the
vibrations
at
the
flexible
joint
are
dominated
by the first three vibration modes, which are obtained as
2.94 Hz, 8.83 Hz and 14.52 Hz with a magnitude of 32.38
dB, ‐12.08 dB and ‐26.52 dB respectively.
The tip angular position, deflection angle and power
spectral density responses of the flexible joint
manipulator using PD‐FLC‐FLC, PD‐FLC‐PID and PD‐
FLC‐IS are shown in Figure 10. It is noted that the
proposed control schemes are capable of reducing the
system vibration while maintaining the trajectory
tracking performance of the manipulator. A similar tip
angular
position,
deflection
angle
and
power
spectral
density of the deflection angle responses were observed
as compared to the PD‐FLC. The steady‐state tip angular
trajectory of non‐collocated fuzzy logic was achieved
within the rise and settling times and overshoot of 0.215 s,
0.613 s and 9.68 %, respectively and 0.222 s, 0.501 s, and
9.40 %, respectively for PID control.. Meanwhile, with
PD‐FLC‐IS, the manipulator reached the rise, settling
times and overshoot of 0.469 s, 0.857 s and 0.16 %
respectively. It is notable that the settling time of PD‐FLC‐
FLC is much faster as compared to the case of PD‐FLC‐
PID and PD‐FLC‐IS. However, the percentage overshoot
of
PD‐
FLC‐
IS
is
much
lower
than
both
cases
of
PD‐
FLC
with non‐collocated control. Besides this, the results also
demonstrate a significant amount of deflection angle
reduction at the tip angle of the manipulator with the
proposed composite controllers. The vibration of the
system using PD‐FLC‐FLC and PD‐FLC‐PID settle within
1 s, which is much faster as compared to PD‐FLC‐IS.
However, in terms of the maximum residual of the
deflection angle, the PD‐FLC‐IS produces almost a four‐
fold improvement as compared to the PD‐FLC scheme.
This result is slightly higher than with both cases of PD‐
FLC‐PID and PD‐FLC‐FLC, with only a twofold
improvement
over
the
PD‐
FLC
scheme.
In
terms
of
the
power spectral density of the deflection angle response,
the magnitudes of vibrations using PD‐FLC‐FLC, PD‐
FLC‐PID and PD‐FLC‐IS were reduced to [1.87, ‐41.95, ‐
48.25] dB, [‐2.55, ‐33.53, ‐45.55] dB and [17.59, ‐25.28, ‐
36.69] dB respectively for the first three modes of
vibration. It is noted that both the PD‐FLC‐PID and PD‐
FLC‐FLC schemes produce a higher level of vibration
reduction as
compared
to
PD
‐FLC
‐IS.
(a) Tip angular position
(b) Deflection angle
(c) Power spectral density
Figure 10. Response of the flexible joint manipulator using
composite PD‐FLC‐FLC, PD‐FLC‐PID and PD‐FLC‐IS
0 0.5 1.0 1.5 2.0 2.5 3.00
10
20
30
40
50
60
Time (s)
T i p a n g u l a r p o s i t i o n ( d e g )
PD-FLC-FLC
PD-FLC-PID
PD-FLC-IS
0 0.5 1.0 1.5 2.0 2.5 3.0-15
-10
-5
0
5
10
Time (s)
D e f l e c t i o n a
n g l e ( d e g )
PD-FLC-FLC
PD-FLC-PID
PD-FLC-IS
0 2 4 6 8 10 12 14 16 18-100
-80
-60
-40
-20
0
20
40
Frequency (Hz)
P o w e r S p e c t r a l D e n s i t y ( d B )
PD-FLC-FLC
PD-FLC-PID
PD-FLC-IS
2.94 Hz
8.83 Hz
14.52 Hz
7Mohd Ashraf Ahmad, Mohd Zaidi Mohd Tumari and Ahmad Nor Kasruddin Nasir:
Composite Fuzzy Logic Control Approach to a Flexible Joint Manipulator
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Table 4 and Figure 11 summarize the magnitude of the
vibration and the level of the vibration reduction of
deflection, respectively, for the proposed composite control
schemes. It is seen that a high performance in the reduction
of the vibration of the system is achieved using both non‐
collocated fuzzy
logic
and
PID
control
as
compared
to
feed
‐
forward control based on an input‐shaping technique. This
is observed and compared to the PD‐FLC for the first three
modes of vibration. In addition, as demonstrated in the tip
angular trajectory response, a slightly faster response with a
higher overshoot is obtained using both non‐collocated
fuzzy logic and PID control scheme as compared to the
input‐shaping technique. Comparisons of the specifications
of the tip angular trajectory responses are summarized in
Table 5. In addition, and as demonstrated in the tip angular
trajectory response with PD‐FLC‐FLC and PD‐FLC‐PID, the
minimum phase behaviour of the manipulator is unaffected.
In terms
of
the
design
complexity,
the
implementation
of
the
input‐shaper technique is much easier as compared to both
non‐collocated controls as a large amount of design effort is
required in order to determine the controller parameters,
such as the range of the membership function in the fuzzy
logic design and k p , ki and kd gains in the PID design.
However, the input‐shaper strategy is very sensitive to the
system parameter variation and could not compensate for
any effect of disturbance as compared to the non‐collocated
control.
Controller Mode 1 Mode 2 Mode 3
Magnitude of
vibration (dB) PD
‐
FLC‐
FLC 1.87 ‐
41.95 ‐
48.25
PD‐FLC‐PID ‐2.55 ‐33.53 ‐45.55
PD‐FLC‐IS 17.59 ‐25.28 ‐36.69
Table 4. Magnitude of the vibration and level of vibration
reduction of the deflection angle
Controller Settling time (s) Rise time (s) Overshoot (%)
PD‐FLC‐FLC 0.613 0.215 9.68
PD‐FLC‐PID 0.501 0.222 9.40
PD‐FLC‐IS 0.857 0.469 0.16
Table 5. Time response specifications of tip angular position
Figure 11. Level of the vibration reduction of the deflection angle
6. Conclusions
The development of composite fuzzy logic schemes for
the trajectory tracking and vibration suppression of a
flexible joint manipulator has been presented. The control
schemes
have
been
developed
based
on
a
PD‐
type
FLC
with non‐collocated fuzzy logic control, a PD‐type FLC
with non‐collocated PID control and a PD‐type FLC with
an input‐shaping scheme. The proposed composite
control schemes have been implemented and tested on a
flexible joint manipulator. The performances of the
control schemes have been evaluated in terms of input
tracking capability and vibration suppression for the
resonance modes of the manipulator. An acceptable
performance in input tracking and vibration control has
been achieved with the proposed control strategies. A
comparative assessment of the control schemes has
shown that the PD‐FLC with non‐collocated strategies
performs better
than
the
PD
‐FLC
with
a
feed‐forward
technique in respect of the deflection angle reduction of
the elastic joint. Moreover, in terms of the speed of
responses, PD‐FLC with non‐collocated PID and FLC
results in a faster settling time response with high
overshoot as compared to PD‐FLC with a feed‐forward
scheme. The work thus developed and reported in this
paper forms the basis of the design and development of
composite control schemes for the input tracking and
vibration suppression of multi‐degree of freedom robotic
arms with flexible links and joints.
7. Acknowledgments
This work was supported by the Faculty of Electrical &
Electronics Engineering, University of Malaysia Pahang,
and especially the Control & Instrumentation (COINS)
Research Group.
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8 Int J Adv Robotic Sy, 2013, Vol. 10, 58:2013 www.intechopen.com
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9Mohd Ashraf Ahmad, Mohd Zaidi Mohd Tumari and Ahmad Nor Kasruddin Nasir:
Composite Fuzzy Logic Control Approach to a Flexible Joint Manipulator
www.intechopen.com