Modelling and Control of a Worm-Like Micro Robot with ... · with control volumes (CV pneumatic...
Transcript of Modelling and Control of a Worm-Like Micro Robot with ... · with control volumes (CV pneumatic...
Abstract— In this paper, a pneumatic worm-like micro robot
with active force control (AFC) capability is modelled and
simulated in a constrained environment (pipe). A mathematical
model that represents the dynamic characteristics of the
worm-like micro robot is first presented. Then, the dynamic
response of the robot system subjected to different input
excitations is investigated. A proportional-integral-derivative
(PID) controller is applied to the micro robot system to follow
the desired trajectory while an AFC controller is utilized to
reject the unwanted disturbances which may be created due to
frictional forces or fluid viscosity in the pipe. The control system
is tuned so that an accurate trajectory tracking is possible. The
performance of the control system under different types of
disturbances is evaluated through a rigorous simulation study.
The obtained results clearly demonstrate an effective trajectory
tracking capability of the worm-like micro robot in spite of the
negative effects of the external disturbances.
Index Terms—Active Force Control, Micro Robot, PID
Controller, Robust Tracking, In-pipe.
I. INTRODUCTION
Micro robotics is a field that has generated much interest
amongst researchers and robot engineers alike due to its
potentials operating in adverse working conditions and
constrained environments. Examples can be seen in micro
robots performing various tasks such as exploration and
inspection in industrial pipes that can be associated with
petroleum piping installations, chemical plants, heat
exchangers, and gas or water supply systems; a much smaller
scale robotic system may be applicable to carry out
endoscopic procedure in vessels of the human body. An
in-pipe inspection micro robot is useful to inspect the state
and conditions of the pipe to detect leaks, cracks or
modification of cross section in pipe lines. The robot is able
to move effectively in the pipe and transport exteroceptive
sensors that give different results such as finding or detecting
the position/location and type of problem and measurements
about the environment.
Some basic research on mobile micro robotic mechanisms for
use in pipes have been reported, such as those that are driven
by piezoelectric actuators [1, 2, 3], by giant magnetostrictive
actuators [4] by pneumatic actuators [5, 6], or by
Manuscript received April 14, 2010.
M. Mailah is with the Universiti Teknologi Malaysia (UTM), 81310
Skudai, Johor, Malaysia (phone: 607-5534562; fax: 607-5566159; e-mail:
Y. Sabzehmeidani is with the Universiti Teknologi Malaysia (UTM),
81310 Skudai, Johor, Malaysia (e-mail: yaser7002@ gmail.com).
M. Hussein is with the Universiti Teknologi Malaysia (UTM), 81310
Skudai, Johor, Malaysia (e-mail: [email protected]).
electromagnetic actuators [7].
However, most of these robots are still in the
developmental stage and certain problems still have to be
addressed and solved before they become practical. Such
micro robots for small pipes have low pulling force and have
difficulty negotiating curved pipes or vertical pipes. Besides,
commercial charge-coupled device (CCD) cameras are too
big to mount on these robots.
Lim et al. invented an inchworm like micro robot by using
only one pneumatic line [8]. It is based on drilling
different-sized micro holes in two plates among three
chambers. The rear clamp, the elongation module, and the
front clamp work sequentially as the air flows to each
chamber. It enables the robot not only to generate inchworm
like locomotion, but also to allow significant reduction of the
stiffness of pneumatic lines and the drag force due to one
pneumatic line. In order to operate the robot efficiently, the
stroke according to the supplied pneumatic pressure is
investigated.
In another design, a pneumatic flexible robot prototype for
in-pipe inspection was designed and experimented as
described in [9]. A dynamic model which takes into account
the flexibility, damping and friction was developed. A
number of experiments were carried out in order to
characterize the robot and provide the input for the numerical
model. The model was validated by comparing the
experimental and numerical robot gait in time domain. The
robot motion for different pipes network geometry is also
presented in the research. The works described above mostly
focus on the principle of actuation and assume an open loop
control configuration that does not include sensory feedback
information and control algorithm for critical task
applications.
In the proposed research, we incorporate a robust feedback
control mechanism into a pneumatically actuated micro robot
taking into account the robust tracking performance in a
constrained environment in pipe. The strategy used is based
on active force control (AFC) technique that has been
successfully applied to many dynamical systems [10-13].
Pioneering AFC work applied to robotic manipulator was
presented by Hewit and Burdess (1981), in which an efficient
disturbance rejection technique was established to facilitate
the robust motion control of the dynamical system in the
presence of disturbances, parametric uncertainties and
changes that are commonly prevalent in the real-world
environment [10]. Mailah et al. investigated the usefulness of
the AFC method by introducing intelligent mechanisms to
approximate the mass or inertia matrix of the dynamic system
to trigger the compensation effect of the controller. It was
Modelling and Control of a Worm-Like Micro
Robot with Active Force Control Capability
Yaser Sabzehmeidani, Musa Mailah, Member, IAENG, Mohamed Hussein, Member, IAENG.
Proceedings of the World Congress on Engineering 2010 Vol II WCE 2010, June 30 - July 2, 2010, London, U.K.
ISBN: 978-988-18210-7-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
WCE 2010
recognized that the AFC was rob
theory as well as in
AFC method is extended to correct the accuracy, stroke and
reach point of
tracking performance
and later simulated with the active force control mode
incorporated.
II.
A
specifically
produces
five phases illustrated by schematic drawings in
(a)
(c)
Figure
part: The rear bladder expands and pushes onto the inner pipe
wall, holding the robot fixed (b) Second part: The robot body
stretches (c) Third part: The front bladder expands (d) Fourth
part: The rear bladder
deflates executing the net gait
B
chambers
with control volumes (CV
pneumatic resistance is
��Where,
the
mass
terms of the pneumatic capacitances
expressed as:
�� �Where,
��and
��
By
recognized that the AFC was rob
theory as well as in
AFC method is extended to correct the accuracy, stroke and
reach point of the
tracking performance
and later simulated with the active force control mode
incorporated.
. MODELING AND
A. Mechanism of Robot Movement
The proposed study considers that the
specifically intended
produces a worm
five phases illustrated by schematic drawings in
(a)
(c)
(e)
Figure 1: Mechanism of micro robot movement, (a) First
part: The rear bladder expands and pushes onto the inner pipe
wall, holding the robot fixed (b) Second part: The robot body
stretches (c) Third part: The front bladder expands (d) Fourth
part: The rear bladder
deflates executing the net gait
B. Mathematical Formulation
For the given dynamic system
chambers and bladders
with control volumes (CV
pneumatic resistance is
� �� � �� Where, is defined in terms of the mass rate of flow
the input pressure,
mass flow rate of
terms of the pneumatic capacitances
expressed as:
� � ��� � � ��� �Where,
� � ��� � � �� �
���
and
� � �� �
By inserting Eq. (1) into Eq. (2), we have
recognized that the AFC was rob
theory as well as in practice [1
AFC method is extended to correct the accuracy, stroke and
the micro robot
tracking performance. The m
and later simulated with the active force control mode
ODELING AND SIMULATION OF
Mechanism of Robot Movement
The proposed study considers that the
intended for in-pipe
worm-like locomotion. The gait cycle consists of
five phases illustrated by schematic drawings in
(d)
(e)
Mechanism of micro robot movement, (a) First
part: The rear bladder expands and pushes onto the inner pipe
wall, holding the robot fixed (b) Second part: The robot body
stretches (c) Third part: The front bladder expands (d) Fourth
part: The rear bladder deflates (e) Fifth part: The robot body
deflates executing the net gait
Mathematical Formulation
For the given dynamic system
and bladders in a cylindrical space
with control volumes (CV1 and CV
pneumatic resistance is given as
� �� � ������
is defined in terms of the mass rate of flow
input pressure, �� is the output pressure, and
rate of the fluid. The differential mass flow rate in
terms of the pneumatic capacitances
� ��� �����
���
inserting Eq. (1) into Eq. (2), we have
recognized that the AFC was robust and effective both in
[12, 13]. In this research, the
AFC method is extended to correct the accuracy, stroke and
micro robot, all pertaining to robust
micro robot shall be
and later simulated with the active force control mode
IMULATION OF MICRO R
Mechanism of Robot Movement
The proposed study considers that the
pipe application
like locomotion. The gait cycle consists of
five phases illustrated by schematic drawings in
(b)
(d)
Mechanism of micro robot movement, (a) First
part: The rear bladder expands and pushes onto the inner pipe
wall, holding the robot fixed (b) Second part: The robot body
stretches (c) Third part: The front bladder expands (d) Fourth
deflates (e) Fifth part: The robot body
Mathematical Formulation
For the given dynamic system comprising
in a cylindrical space
and CV2) as shown in Fig. 2,
given as:
is defined in terms of the mass rate of flow
output pressure, and
The differential mass flow rate in
terms of the pneumatic capacitances (C1 and
inserting Eq. (1) into Eq. (2), we have:
ust and effective both in
In this research, the
AFC method is extended to correct the accuracy, stroke and
, all pertaining to robust
icro robot shall be modelled
and later simulated with the active force control mode
ROBOT SYSTEM
The proposed study considers that the robot is
application and that it
like locomotion. The gait cycle consists of
five phases illustrated by schematic drawings in Fig. 1 [8].
Mechanism of micro robot movement, (a) First
part: The rear bladder expands and pushes onto the inner pipe
wall, holding the robot fixed (b) Second part: The robot body
stretches (c) Third part: The front bladder expands (d) Fourth
deflates (e) Fifth part: The robot body
comprising a series of air
in a cylindrical space (inside pipe)
own in Fig. 2, the
(1)
is defined in terms of the mass rate of flow, �� i
output pressure, and �� is the
The differential mass flow rate in
and C2) can be
(2)
(3)
ust and effective both in
In this research, the
AFC method is extended to correct the accuracy, stroke and
, all pertaining to robust
modelled
and later simulated with the active force control mode
YSTEM
robot is
it
like locomotion. The gait cycle consists of
Mechanism of micro robot movement, (a) First
part: The rear bladder expands and pushes onto the inner pipe
wall, holding the robot fixed (b) Second part: The robot body
stretches (c) Third part: The front bladder expands (d) Fourth
deflates (e) Fifth part: The robot body
air
(inside pipe)
the
(1)
is
the
The differential mass flow rate in
can be
(2)
(3)
������� ��
Using Eq. (1)
�� � � �����
Figure
Eq. (3) can also be expressed������� � ��
Similar to CV
CV2 and CV������� � ��
������� � ��
Figure
By using
�� � �����
From Eq. (
� � �! �For the displacement of
�"#" � $"Substituting
����
� %�! ���& � ��'�
�����
For the above condition, since
and rear bladder
displacement is
friction) and
not change,
�� � � ��� � ��Eq. (1), the following expression can����
Figure 2: Free body diagram
can also be expressed������ � ��� � �
Similar to CV1 and referring to Fig. 3, the expressions for
and CV3 are given as follows: ������ � ���& � �
��( � ��( � �����
Figure 3: Free body diagram
By using Eq. (5), �� can be written
�� %����� �
Eq. (8), � can be determined
� !���( � ��( �displacement of
")" ��*�� �
�*'*
�
Substituting Eqs. (8) and (����� %����� �� !���( � ��( � �'� + ����
���
e above condition, since
and rear bladders is assumed to sufficiently
displacement is relatively
and that the lengths of the
change, Eq. (12) could be simplif
�� �����
, the following expression can
ree body diagram related to
can also be expressed as:
��� �����
and referring to Fig. 3, the expressions for
are given as follows:
��& � �����
ree body diagram related to
can be written as:
��� �,��� � ���can be determined as:
�����
displacement of section, it is given as��*�� ��� � - � .�/�0
) and (9) into Eq. (6)
� � ��� ��'������ �
��'�
����� 1 � �� �
e above condition, since the movement of
assumed to sufficiently
relatively small enough
that the lengths of the front and rear bladder
could be simplified
, the following expression can be written as:
related to CV1 and CV
and referring to Fig. 3, the expressions for
related to CV2 and CV
as:
�� � ��!1
as:
it is given as:
0
Eq. (6), we have:
��� � ��!1 �� � !��! � �
the movement of the
assumed to sufficiently quick while
small enough (neglecting the
front and rear bladder
ied as:
(4)
be written as:
(5)
and CV2
(6)
and referring to Fig. 3, the expressions for
(7)
(8)
and CV3
1 (9)
(10)
(11)
1 �!���& � (12)
the front
while the
(neglecting the
front and rear bladders do
Proceedings of the World Congress on Engineering 2010 Vol II WCE 2010, June 30 - July 2, 2010, London, U.K.
ISBN: 978-988-18210-7-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
WCE 2010
�+ �
Using Laplace transformation, the
displacemen
2
For testing
tracking the desired locomotion accurately,
input sources
functions
determine
namely the PID and AFC controllers shall be applied and
incorporated into the mi
A
most commonly used control algorithm in industry and has
been universally accepted in industrial control
popularity of PID controllers can be attributed partly
robust performance in a wide range of operating conditions
and partly to their functional simplicity, which allows
engineers to operate them in a simple, straightforward
manner
controller
The basic idea behind a PID controller is to read a sensor,
then compute the desired actuator output by calculating
proportional, integral, and derivative responses and summing
those three components to com
controller calculation (algorithm) involves three separate
parameters;
The
3�45where
derivative gains, respectively. In this study, the
Ziegler
parameters. The final gains
$4the gains can be seen in Fig. 5
throughout the simulation study.
������� 6��� ��������
Using Laplace transformation, the
displacement can be found as:
27 87 �9:;����
For testing the
tracking the desired locomotion accurately,
input sources in the form of
functions via feedback control techniques
determine the system responses.
namely the PID and AFC controllers shall be applied and
incorporated into the mi
A. PID control
Proportional
most commonly used control algorithm in industry and has
been universally accepted in industrial control
popularity of PID controllers can be attributed partly
robust performance in a wide range of operating conditions
and partly to their functional simplicity, which allows
engineers to operate them in a simple, straightforward
manner. A schematic diagram of system
controller is shown in
Figure
The basic idea behind a PID controller is to read a sensor,
then compute the desired actuator output by calculating
proportional, integral, and derivative responses and summing
those three components to com
controller calculation (algorithm) involves three separate
parameters; the proportional,
The PID control algorithm is
�45 � $� � �<= �
here $� , $4 , and
derivative gains, respectively. In this study, the
Ziegler–Nichols
parameters. The final gains
� >.?, $5 �the gains can be seen in Fig. 5
throughout the simulation study.
��!@ � !�!
Using Laplace transformation, the
t can be found as:
ABC�C�C�BC�D
���EFG�
H� IGJKL
H�M�;�
III. CONTROL
the system effectiveness in producing and
tracking the desired locomotion accurately,
in the form of step
via feedback control techniques
system responses.
namely the PID and AFC controllers shall be applied and
incorporated into the micro robot
PID control
Proportional-Integral-Derivative (PID) control is the
most commonly used control algorithm in industry and has
been universally accepted in industrial control
popularity of PID controllers can be attributed partly
robust performance in a wide range of operating conditions
and partly to their functional simplicity, which allows
engineers to operate them in a simple, straightforward
chematic diagram of system
is shown in Fig. 4.
Figure 4: Schematic diagram of system
The basic idea behind a PID controller is to read a sensor,
then compute the desired actuator output by calculating
proportional, integral, and derivative responses and summing
those three components to com
controller calculation (algorithm) involves three separate
proportional, i
control algorithm is given as follows:
� $5N
and $5 are the proportional, integral and
derivative gains, respectively. In this study, the
method is employed to tune the PID
parameters. The final gains were determined as
� >0. The resultant tracking control based on
the gains can be seen in Fig. 5
throughout the simulation study.
� �!�, �
�� �
Using Laplace transformation, the transfer function based on
D�H�M�A
C�C�C�BC����DO
ONTROL SCHEMES
effectiveness in producing and
tracking the desired locomotion accurately, we applied
step, square and sin
via feedback control techniques
system responses. Two types of controllers,
namely the PID and AFC controllers shall be applied and
cro robot system.
Derivative (PID) control is the
most commonly used control algorithm in industry and has
been universally accepted in industrial control
popularity of PID controllers can be attributed partly
robust performance in a wide range of operating conditions
and partly to their functional simplicity, which allows
engineers to operate them in a simple, straightforward
chematic diagram of system employing a PID
Schematic diagram of system
The basic idea behind a PID controller is to read a sensor,
then compute the desired actuator output by calculating
proportional, integral, and derivative responses and summing
those three components to compute the output. The PID
controller calculation (algorithm) involves three separate
integral and derivative
given as follows:
are the proportional, integral and
derivative gains, respectively. In this study, the
method is employed to tune the PID
were determined as
The resultant tracking control based on
and these gains shall be used
throughout the simulation study.
� ���
��'�
����� �
(13)
transfer function based on
DO (14)
effectiveness in producing and
we applied three
sinusoidal input
via feedback control techniques in order to
Two types of controllers,
namely the PID and AFC controllers shall be applied and
Derivative (PID) control is the
most commonly used control algorithm in industry and has
been universally accepted in industrial control [14]. The
popularity of PID controllers can be attributed partly to their
robust performance in a wide range of operating conditions
and partly to their functional simplicity, which allows
engineers to operate them in a simple, straightforward
employing a PID
Schematic diagram of system
The basic idea behind a PID controller is to read a sensor,
then compute the desired actuator output by calculating
proportional, integral, and derivative responses and summing
pute the output. The PID
controller calculation (algorithm) involves three separate
derivative terms
given as follows:
(15)
are the proportional, integral and
derivative gains, respectively. In this study, the
method is employed to tune the PID
were determined as $� � P?The resultant tracking control based on
hese gains shall be used
(13)
transfer function based on
(14)
effectiveness in producing and
three
input
in order to
Two types of controllers,
namely the PID and AFC controllers shall be applied and
Derivative (PID) control is the
most commonly used control algorithm in industry and has
. The
to their
robust performance in a wide range of operating conditions
and partly to their functional simplicity, which allows
engineers to operate them in a simple, straightforward
employing a PID
The basic idea behind a PID controller is to read a sensor,
then compute the desired actuator output by calculating
proportional, integral, and derivative responses and summing
pute the output. The PID
controller calculation (algorithm) involves three separate
terms.
(15)
are the proportional, integral and
derivative gains, respectively. In this study, the
method is employed to tune the PID
P?,
The resultant tracking control based on
hese gains shall be used
Figure 5:
B. Active Force Control
The research on active force control (AFC) is initiated by
Johnson (1971) and later Davison (1976) based on the
principle of invariance and the classic
of motion
to design a feedback controller that will ensure the system
setpoint remains unchanged even in the presence of the
disturbances or adverse operating and loading conditions
provided that the actual disturbances can be modelled
effectively. Hewit and Burdess (1981) proposed a more
complete package of the system such that the nature of
disturbances is oblivious to the system and that it is readily
applied to multi
Thus, an effective
robust motion control of dynamical systems in the presence
of disturbances
commonly
et al. extended the usefulness of the method by intro
intelligent mechanisms to approximate the mass or inertia
matrix of the dynamic system to trigger the compensation
effect of the controller
technique that relies on the appropriate estimation of the
inertial or mass
measurements of the acceleration and force signals induced
by the system
For theoretical simulation, it is normal that perfect modelling
of the sensors is assumed and
totally neglected.
subjected to a number of disturbances remains stable and
Performance of
wave and (c
Active Force Control
The research on active force control (AFC) is initiated by
Johnson (1971) and later Davison (1976) based on the
principle of invariance and the classic
of motion [15, 16]. It has been demonstrated
to design a feedback controller that will ensure the system
setpoint remains unchanged even in the presence of the
disturbances or adverse operating and loading conditions
provided that the actual disturbances can be modelled
y. Hewit and Burdess (1981) proposed a more
complete package of the system such that the nature of
disturbances is oblivious to the system and that it is readily
applied to multi-degree of freedom dynamic systems
Thus, an effective method
robust motion control of dynamical systems in the presence
of disturbances, parametric
commonly prevalent in the real
extended the usefulness of the method by intro
intelligent mechanisms to approximate the mass or inertia
matrix of the dynamic system to trigger the compensation
effect of the controller
technique that relies on the appropriate estimation of the
inertial or mass parameters of the dynamic system and the
measurements of the acceleration and force signals induced
by the system if practical implementation is ever considered.
For theoretical simulation, it is normal that perfect modelling
of the sensors is assumed and
totally neglected. In AFC, it is shown that the system
subjected to a number of disturbances remains stable and
(a)
(b)
(c)
Performance of PID controller
c) square input
Active Force Control
The research on active force control (AFC) is initiated by
Johnson (1971) and later Davison (1976) based on the
principle of invariance and the classic
. It has been demonstrated
to design a feedback controller that will ensure the system
setpoint remains unchanged even in the presence of the
disturbances or adverse operating and loading conditions
provided that the actual disturbances can be modelled
y. Hewit and Burdess (1981) proposed a more
complete package of the system such that the nature of
disturbances is oblivious to the system and that it is readily
degree of freedom dynamic systems
method has been es
robust motion control of dynamical systems in the presence
, parametric uncertainties
in the real-world environment.
extended the usefulness of the method by intro
intelligent mechanisms to approximate the mass or inertia
matrix of the dynamic system to trigger the compensation
[11, 12, 17]. The AFC method
technique that relies on the appropriate estimation of the
parameters of the dynamic system and the
measurements of the acceleration and force signals induced
if practical implementation is ever considered.
For theoretical simulation, it is normal that perfect modelling
of the sensors is assumed and that noises in the sensors are
In AFC, it is shown that the system
subjected to a number of disturbances remains stable and
PID controller for (a) step,
input functions
The research on active force control (AFC) is initiated by
Johnson (1971) and later Davison (1976) based on the
principle of invariance and the classic Newton’s second law
. It has been demonstrated that it is possible
to design a feedback controller that will ensure the system
setpoint remains unchanged even in the presence of the
disturbances or adverse operating and loading conditions
provided that the actual disturbances can be modelled
y. Hewit and Burdess (1981) proposed a more
complete package of the system such that the nature of
disturbances is oblivious to the system and that it is readily
degree of freedom dynamic systems
has been established to facilitate
robust motion control of dynamical systems in the presence
uncertainties and changes
world environment.
extended the usefulness of the method by intro
intelligent mechanisms to approximate the mass or inertia
matrix of the dynamic system to trigger the compensation
The AFC method
technique that relies on the appropriate estimation of the
parameters of the dynamic system and the
measurements of the acceleration and force signals induced
if practical implementation is ever considered.
For theoretical simulation, it is normal that perfect modelling
that noises in the sensors are
In AFC, it is shown that the system
subjected to a number of disturbances remains stable and
for (a) step, (b) sine
The research on active force control (AFC) is initiated by
Johnson (1971) and later Davison (1976) based on the
second law
that it is possible
to design a feedback controller that will ensure the system
setpoint remains unchanged even in the presence of the
disturbances or adverse operating and loading conditions
provided that the actual disturbances can be modelled
y. Hewit and Burdess (1981) proposed a more
complete package of the system such that the nature of
disturbances is oblivious to the system and that it is readily
degree of freedom dynamic systems [10].
to facilitate
robust motion control of dynamical systems in the presence
and changes that are
world environment. Mailah
extended the usefulness of the method by introducing
intelligent mechanisms to approximate the mass or inertia
matrix of the dynamic system to trigger the compensation
The AFC method is a
technique that relies on the appropriate estimation of the
parameters of the dynamic system and the
measurements of the acceleration and force signals induced
if practical implementation is ever considered.
For theoretical simulation, it is normal that perfect modelling
that noises in the sensors are
In AFC, it is shown that the system
subjected to a number of disturbances remains stable and
Proceedings of the World Congress on Engineering 2010 Vol II WCE 2010, June 30 - July 2, 2010, London, U.K.
ISBN: 978-988-18210-7-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
WCE 2010
robust via the compensating action of the control strategy. A
more detailed description on the mathematical trea
related to the derivation of important equations and stability
criterion, can be found in
concept of AFC applied to
presented with reference to Fig.
The notations used in
The
following expression:
F can be readily measured by means of a
using an accelerometer.
perfect model
[11]
give the ultimate AFC signal command to be embedded with
an outer control loop. This creates a two degree
controller that could provide excellent overall system
performance provided that the measurement and estimated
parameters were appropriately acquired. The outer control
loop can be a proportional
controller, resolved mo
intelligent controller or others deemed suitable. It is apparent
that a
cause the output to
disturbances
G
A
open loop system, by first generating the world coordinate
error vector, which would then be processed through a
controller function,
that maybe represented by Eq (15).
burden in AFC is the multiplication of the estimated inertia
parameter
component
Mailah
demonstrated the effectiveness of the AFC scheme applied to
rigid robot arms.
robust intelligent AFC method that is capable of controlling a
vehicle suspension system
introduced
Desired
Position
robust via the compensating action of the control strategy. A
more detailed description on the mathematical trea
related to the derivation of important equations and stability
criterion, can be found in
concept of AFC applied to
presented with reference to Fig.
Figure 6: A schematic diagram
The notations used in
G(s) :
Ga(s) :
Gc(s) :
KAFC :
H(s) :
F :
F* :
m :
a :
he estimated disturbance
following expression:
F* =
can be readily measured by means of a
using an accelerometer.
perfect model, crude approximation
[11]. F* is then passed through a
give the ultimate AFC signal command to be embedded with
an outer control loop. This creates a two degree
controller that could provide excellent overall system
performance provided that the measurement and estimated
parameters were appropriately acquired. The outer control
loop can be a proportional
controller, resolved mo
intelligent controller or others deemed suitable. It is apparent
that a suitable choice of
cause the output to
disturbances such that:
Ga(s)H(s) = 1
A set of outer
open loop system, by first generating the world coordinate
error vector, which would then be processed through a
controller function,
that maybe represented by Eq (15).
burden in AFC is the multiplication of the estimated inertia
parameter with the angular acceleration of the
component before being fed into the AFC feedforward loop.
Mailah et al. [18]
demonstrated the effectiveness of the AFC scheme applied to
rigid robot arms.
robust intelligent AFC method that is capable of controlling a
vehicle suspension system
introduced disturbances.
Gc(s)
Desired
PositionController
+
-
robust via the compensating action of the control strategy. A
more detailed description on the mathematical trea
related to the derivation of important equations and stability
criterion, can be found in [10]
concept of AFC applied to a dynamic rotational system is
presented with reference to Fig.
A schematic diagram
The notations used in Fig. 6 are as follows:
Dynamic system transfer function
Actuator transfer function
Outer loop controller
AFC constant
Weighting function
Applied force
Estimated force
Estimated mass
Linear acceleration
estimated disturbance is
following expression:
= F – m a
can be readily measured by means of a
using an accelerometer. m may be obtained by assuming a
crude approximation
passed through a
give the ultimate AFC signal command to be embedded with
an outer control loop. This creates a two degree
controller that could provide excellent overall system
performance provided that the measurement and estimated
parameters were appropriately acquired. The outer control
loop can be a proportional
controller, resolved motion acceleration controller (RMAC),
intelligent controller or others deemed suitable. It is apparent
suitable choice of H(s) needs to be obtained that
cause the output to be made invariant with respect to the
such that:
outer control loop control
open loop system, by first generating the world coordinate
error vector, which would then be processed through a
controller function, Gc(s), typically a classic P
that maybe represented by Eq (15).
burden in AFC is the multiplication of the estimated inertia
with the angular acceleration of the
before being fed into the AFC feedforward loop.
], Mailah [11] and Pitowarno
demonstrated the effectiveness of the AFC scheme applied to
rigid robot arms. Gigih et al.
robust intelligent AFC method that is capable of controlling a
vehicle suspension system and
disturbances.
Ga(s)
KAFC
F
Actuator
H(s)
+
+
robust via the compensating action of the control strategy. A
more detailed description on the mathematical trea
related to the derivation of important equations and stability
[10]. For brevity, the underlying
a dynamic rotational system is
presented with reference to Fig. 6.
A schematic diagram of an AFC scheme
are as follows:
ynamic system transfer function
Actuator transfer function
Outer loop controller
AFC constant
Weighting function
force
force
mass
acceleration
is obtained by considering the
can be readily measured by means of a force
may be obtained by assuming a
crude approximation or intelligent methods
passed through a weighting function
give the ultimate AFC signal command to be embedded with
an outer control loop. This creates a two degree
controller that could provide excellent overall system
performance provided that the measurement and estimated
parameters were appropriately acquired. The outer control
loop can be a proportional-integral-derivative (PID)
tion acceleration controller (RMAC),
intelligent controller or others deemed suitable. It is apparent
needs to be obtained that
be made invariant with respect to the
control is applied to the above
open loop system, by first generating the world coordinate
error vector, which would then be processed through a
typically a classic P
that maybe represented by Eq (15). The main computational
burden in AFC is the multiplication of the estimated inertia
with the angular acceleration of the
before being fed into the AFC feedforward loop.
and Pitowarno
demonstrated the effectiveness of the AFC scheme applied to
. [20] have equally shown a
robust intelligent AFC method that is capable of controlling a
and effectively suppressing the
G(s)
Disturbances
m
F ++
+ -
Force
Sensor
Accelero
meter
Dynamic
System
Estimated MassF*
robust via the compensating action of the control strategy. A
more detailed description on the mathematical treatment
related to the derivation of important equations and stability
. For brevity, the underlying
a dynamic rotational system is
of an AFC scheme
ynamic system transfer function
obtained by considering the
(16
force sensor and a
may be obtained by assuming a
or intelligent methods
function H(s) to
give the ultimate AFC signal command to be embedded with
an outer control loop. This creates a two degree-of-freedom
controller that could provide excellent overall system
performance provided that the measurement and estimated
parameters were appropriately acquired. The outer control
derivative (PID)
tion acceleration controller (RMAC),
intelligent controller or others deemed suitable. It is apparent
needs to be obtained that can
be made invariant with respect to the
(2)
is applied to the above
open loop system, by first generating the world coordinate
error vector, which would then be processed through a
typically a classic PID controller
The main computational
burden in AFC is the multiplication of the estimated inertia
with the angular acceleration of the dynamic
before being fed into the AFC feedforward loop.
and Pitowarno et al. [19] have
demonstrated the effectiveness of the AFC scheme applied to
have equally shown a
robust intelligent AFC method that is capable of controlling a
ffectively suppressing the
1/s2
Actual
Position
AFC
a
robust via the compensating action of the control strategy. A
tment
related to the derivation of important equations and stability
. For brevity, the underlying
a dynamic rotational system is
obtained by considering the
6)
a
may be obtained by assuming a
or intelligent methods
to
give the ultimate AFC signal command to be embedded with
freedom
controller that could provide excellent overall system
performance provided that the measurement and estimated
parameters were appropriately acquired. The outer control
derivative (PID)
tion acceleration controller (RMAC),
intelligent controller or others deemed suitable. It is apparent
can
be made invariant with respect to the
(2)
is applied to the above
open loop system, by first generating the world coordinate
error vector, which would then be processed through a
ller
The main computational
burden in AFC is the multiplication of the estimated inertial
dynamic
before being fed into the AFC feedforward loop.
have
demonstrated the effectiveness of the AFC scheme applied to
have equally shown a
robust intelligent AFC method that is capable of controlling a
ffectively suppressing the
A useful point to note is that, the constant
can effectively serve as a
scheme (AFC
by simply setting the
between value of
effect of percentage
this study.
IV
For th
MATLAB
robot are
Parameter
��!$!#!
The applied disturbance considered in the study is a harmonic
force that emulates a constant vibratory excitation with a
magnitude of 40 N and frequency, 10
the following function, 40 sin 10
disturbance shall act as a test for the robustness of the system
performance via observation of the response obtained.
Figure 7:
For simulating th
PID plus AFC, a number of input
that are related to
functions. The responses to these inputs are shown in Figs.
and 9.
Actual
Position
A useful point to note is that, the constant
effectively serve as a
scheme (AFC – OFF) or PID plus AFC method (AFC
by simply setting the K
between value of KAFC can also be experimented to show the
effect of percentage KAFC
this study.
IV. SIMULATION
For the proposed simulation study of the
MATLAB and Simulink was used
are shown in Table
Table I: Parameters of micro robot
arameter Value
� ?7P
� ?70Q! ?7.! ?7>� RS
! ?7?0�T �>?�
The applied disturbance considered in the study is a harmonic
force that emulates a constant vibratory excitation with a
magnitude of 40 N and frequency, 10
the following function, 40 sin 10
disturbance shall act as a test for the robustness of the system
performance via observation of the response obtained.
The applied harmonic
For simulating the proposed control schemes, i.e., PID and
PID plus AFC, a number of input
related to step, sinusoidal and
functions. The responses to these inputs are shown in Figs.
A useful point to note is that, the constant
effectively serve as a mode switch between the PID only
OFF) or PID plus AFC method (AFC
KAFC to 0 or 1 respectively.
can also be experimented to show the
AFC which however is not covered in
IMULATION RESULTS AND
e proposed simulation study of the
Simulink was used. The
shown in Table I.
arameters of micro robot
alue Parameter
P �
0Q U
. 2
++S V
���+� m
The applied disturbance considered in the study is a harmonic
force that emulates a constant vibratory excitation with a
magnitude of 40 N and frequency, 10 rad/s
the following function, 40 sin 10t as shown in Fig.
disturbance shall act as a test for the robustness of the system
performance via observation of the response obtained.
harmonic disturbance considered in the
study
e proposed control schemes, i.e., PID and
PID plus AFC, a number of input sources
, sinusoidal and
functions. The responses to these inputs are shown in Figs.
(a)
A useful point to note is that, the constant KAFC in Fig. 6
switch between the PID only
OFF) or PID plus AFC method (AFC
to 0 or 1 respectively.
can also be experimented to show the
which however is not covered in
ESULTS AND DISCUSSION
e proposed simulation study of the
The parameters of micro
arameters of micro robot
arameter Value
>???� WX+
?7?YZQ�>?�� +
/??[�\ ]� ^_�+[\ ?7>Q�WX
The applied disturbance considered in the study is a harmonic
force that emulates a constant vibratory excitation with a
rad/s, i.e., according to
as shown in Fig.
disturbance shall act as a test for the robustness of the system
performance via observation of the response obtained.
disturbance considered in the
e proposed control schemes, i.e., PID and
sources were considered
, sinusoidal and square wave
functions. The responses to these inputs are shown in Figs.
in Fig. 6
switch between the PID only
OFF) or PID plus AFC method (AFC – ON)
to 0 or 1 respectively. The in
can also be experimented to show the
which however is not covered in
ISCUSSION
e proposed simulation study of the system,
parameters of micro
alue
WX+!
?YZQ� T+�
\� +!
[\
WX
The applied disturbance considered in the study is a harmonic
force that emulates a constant vibratory excitation with a
, i.e., according to
as shown in Fig. 7. The
disturbance shall act as a test for the robustness of the system
performance via observation of the response obtained.
disturbance considered in the
e proposed control schemes, i.e., PID and
were considered
square wave forcing
functions. The responses to these inputs are shown in Figs. 8
Proceedings of the World Congress on Engineering 2010 Vol II WCE 2010, June 30 - July 2, 2010, London, U.K.
ISBN: 978-988-18210-7-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
WCE 2010
Figure
Figure
plus
From
perform
the responses to
Figure 8: Effect of
for PID controller only (AFC
Figure 9: Effect of harmonic force on the p
plus AFC scheme
From Fig. 8, it can be seen that the
perform the trajectory tracking task
the responses to converge to the reference
(b)
(c)
Effect of harmonic disturbance on system response
for PID controller only (AFC
conditions
(a)
(b)
(c)
Effect of harmonic force on the p
AFC scheme (AFC – ON)
it can be seen that the
the trajectory tracking task
converge to the reference
(b)
(c)
disturbance on system response
for PID controller only (AFC – OFF) for various input
conditions
(a)
(b)
(c)
Effect of harmonic force on the performance of
ON) for various input conditions
it can be seen that the PID controller is able to
the trajectory tracking task satisfactorily by bringing
converge to the reference positions
disturbance on system response
OFF) for various input
erformance of PID
for various input conditions
PID controller is able to
satisfactorily by bringing
positions but at the
disturbance on system response
PID
for various input conditions
PID controller is able to
satisfactorily by bringing
at the
expense of relatively large track
ripples or oscillation
disturbance (vibratory)
shown through the
clearly demonstrated that the PID
ON) manages to accurately and readily track the desired
responses. This shows that the latter system is much more
robust than its counterpart
disturbance at relatively high frequency
pneumatically actuated micro
effectively
with the given loading and operating
In this study a pneumatic worm
modelled
the PID incorporated with the AFC was employed to ensure
an accurate
under the presence of
operating environment
tuned using the typical
achieve satisfactory performance
the proposed schemes
of the closed
with AFC method (AFC
the rigorous study on sensitivity analysis related to the effects
of other loading and operating conditions. The possibility of
performing practical
system should
The authors would like to thank the Universiti Teknologi
Malaysia (UTM) for their continuous support in the research work.
[1] S. Aoshima et al.,
mobility in a thin tube.
270-278.
[2] T. Idogaki et al.,
for an in
Micro Machine and Human Sciences. pp.
[3] T. Matsumoto
mobile machine with piezoelectric driving force actuator.
IEEE 5th Int. Symp. Micro Machine and Human Sciences. pp. 47
[4] T. Fukuda
magnetostrictive alloy (GMA) applications to micro mobile robot as a
micro actuator without power supply cables.
Workshop Micro Electro Mechanical Systems (MEMS). pp. 210
[5] Suzumori, K. and Abe T.,
pipeline inspection robots.
Int. Symp. Robotics and Manufacturing Systems. pp. 515
[6] M. Takahashi,
in-pipe microrobot applying the motion of an earthworm.
5th Int. Symp. Micro Machine and Human Sciences. pp. 35
[7] S. Iwashita
in-pipe operation micro robots.
Machine and Human Sciences. pp. 41
[8] Lim, J.,
line based inchworm
2008, Mechatronics, pp. 315
[9] A. Manuello Bertetto and M. Ruggiu,
flexible robot.
Conference on Advanced Intelligent Mechatronics. pp. 1226
[10] J.R. Hewit, J.S. Burdess, Fast
Robotics using Active Force Control
Theory, 16(5), 1981, pp. 535
expense of relatively large track
ripples or oscillation, largely due to the nature of the applied
disturbance (vibratory).
shown through the second set of graphs
clearly demonstrated that the PID
manages to accurately and readily track the desired
responses. This shows that the latter system is much more
robust than its counterpart
disturbance at relatively high frequency
ically actuated micro
effectively based on the
with the given loading and operating
V.
In this study a pneumatic worm
and simulated. A hybrid control strategy including
the PID incorporated with the AFC was employed to ensure
an accurate and robust trajectory trac
under the presence of
operating environment. The PID
using the typical
achieve satisfactory performance
the proposed schemes clearly demonstrated the effectiveness
closed-loop control algorithm
with AFC method (AFC
the rigorous study on sensitivity analysis related to the effects
of other loading and operating conditions. The possibility of
performing practical experimenta
system should also be explored and investigated.
VI. A
The authors would like to thank the Universiti Teknologi
Malaysia (UTM) for their continuous support in the research work.
S. Aoshima et al., A miniature mobile robot using piezo vibration
mobility in a thin tube.
278.
T. Idogaki et al.,Characteristics of piezoelectric locomotive mechanism
for an in-pipe micro inspection machine.,
Micro Machine and Human Sciences. pp.
Matsumoto, H. Okamoto, and M. Asano
mobile machine with piezoelectric driving force actuator.
IEEE 5th Int. Symp. Micro Machine and Human Sciences. pp. 47
T. Fukuda, H. Hosokai, H. Ohyama, H. Hashimoto,
magnetostrictive alloy (GMA) applications to micro mobile robot as a
micro actuator without power supply cables.
Workshop Micro Electro Mechanical Systems (MEMS). pp. 210
Suzumori, K. and Abe T.,
pipeline inspection robots.
Int. Symp. Robotics and Manufacturing Systems. pp. 515
Takahashi, I. Hayashi,
pipe microrobot applying the motion of an earthworm.
5th Int. Symp. Micro Machine and Human Sciences. pp. 35
Iwashita, I. Hayashi, N.
pipe operation micro robots.
Machine and Human Sciences. pp. 41
Lim, J., Park, H., An, J.,
line based inchworm-like micro robot for half
2008, Mechatronics, pp. 315
A. Manuello Bertetto and M. Ruggiu,
flexible robot. Como, Italy
Conference on Advanced Intelligent Mechatronics. pp. 1226
J.R. Hewit, J.S. Burdess, Fast
botics using Active Force Control
Theory, 16(5), 1981, pp. 535
expense of relatively large tracking errors
, largely due to the nature of the applied
. This is in stark contrast
second set of graphs
clearly demonstrated that the PID with AFC scheme
manages to accurately and readily track the desired
responses. This shows that the latter system is much more
robust than its counterpart in compensating the harmonic
disturbance at relatively high frequency
ically actuated micro robot is able to operate
based on the closed-loop control
with the given loading and operating conditions.
. CONCLUSION
In this study a pneumatic worm-
and simulated. A hybrid control strategy including
the PID incorporated with the AFC was employed to ensure
trajectory tracking of the robot system
under the presence of the prescribed
. The PID controller was
using the typical Ziegler-Nichols
achieve satisfactory performance. The simulation results
clearly demonstrated the effectiveness
ontrol algorithms, particularly th
with AFC method (AFC – ON). Future works
the rigorous study on sensitivity analysis related to the effects
of other loading and operating conditions. The possibility of
experimentation on the micro robot
also be explored and investigated.
ACKNOWLEDGEMENT
The authors would like to thank the Universiti Teknologi
Malaysia (UTM) for their continuous support in the research work.
REFERENCES
A miniature mobile robot using piezo vibration
mobility in a thin tube. 1993, ASME J. Dynam. Syst, Vol. 115, pp.
Characteristics of piezoelectric locomotive mechanism
pipe micro inspection machine.,
Micro Machine and Human Sciences. pp.
, H. Okamoto, and M. Asano
mobile machine with piezoelectric driving force actuator.
IEEE 5th Int. Symp. Micro Machine and Human Sciences. pp. 47
, H. Hosokai, H. Ohyama, H. Hashimoto,
magnetostrictive alloy (GMA) applications to micro mobile robot as a
micro actuator without power supply cables.
Workshop Micro Electro Mechanical Systems (MEMS). pp. 210
Suzumori, K. and Abe T., Applying a flexibl
pipeline inspection robots. The Netherlands
Int. Symp. Robotics and Manufacturing Systems. pp. 515
Hayashi, and N. Iwatsuki
pipe microrobot applying the motion of an earthworm.
5th Int. Symp. Micro Machine and Human Sciences. pp. 35
, N. Iwatsuki, and K.
pipe operation micro robots. 1994. IEEE 5th Int. Symp. Micro
Machine and Human Sciences. pp. 41–45.
, J., Hong, Y-S., Kim, B.,
like micro robot for half
2008, Mechatronics, pp. 315–322.
A. Manuello Bertetto and M. Ruggiu, In
Como, Italy : s.n., 2001. IEEVASME International
Conference on Advanced Intelligent Mechatronics. pp. 1226
J.R. Hewit, J.S. Burdess, Fast Dynamic Decoupled Control for
botics using Active Force Control, Trans.
Theory, 16(5), 1981, pp. 535-542.
ing errors with substantial
, largely due to the nature of the applied
This is in stark contrast to the results
second set of graphs (Fig. 9) in which it is
with AFC scheme
manages to accurately and readily track the desired
responses. This shows that the latter system is much more
in compensating the harmonic
disturbance at relatively high frequency. The proposed
robot is able to operate
loop control configuration
conditions.
ONCLUSION
-like micro robot was
and simulated. A hybrid control strategy including
the PID incorporated with the AFC was employed to ensure
ing of the robot system
the prescribed disturbances
controller was
Nichols method so as to
. The simulation results
clearly demonstrated the effectiveness
s, particularly th
. Future works may include
the rigorous study on sensitivity analysis related to the effects
of other loading and operating conditions. The possibility of
tion on the micro robot
also be explored and investigated.
CKNOWLEDGEMENT
The authors would like to thank the Universiti Teknologi
Malaysia (UTM) for their continuous support in the research work.
A miniature mobile robot using piezo vibration
1993, ASME J. Dynam. Syst, Vol. 115, pp.
Characteristics of piezoelectric locomotive mechanism
pipe micro inspection machine., 1995. IEEE 6th Int. Symp.
193–198.
, H. Okamoto, and M. Asano, A prototype model of micro
mobile machine with piezoelectric driving force actuator.
IEEE 5th Int. Symp. Micro Machine and Human Sciences. pp. 47
, H. Hosokai, H. Ohyama, H. Hashimoto, and F. Arai
magnetostrictive alloy (GMA) applications to micro mobile robot as a
micro actuator without power supply cables., 1991. IEEE Int.
Workshop Micro Electro Mechanical Systems (MEMS). pp. 210
Applying a flexible microactuators to
The Netherlands : s.n., 1993. IMACS/SICE
Int. Symp. Robotics and Manufacturing Systems. pp. 515–520.
Iwatsuki, The development of an
pipe microrobot applying the motion of an earthworm. 1994. IEEE
5th Int. Symp. Micro Machine and Human Sciences. pp. 35–
and K. Nakahara, Development of
. IEEE 5th Int. Symp. Micro
45.
, B., Yi, B-J, One pneumatic
like micro robot for half-inch pipe inspection.
In-pipe inch-worm pneumatic
: s.n., 2001. IEEVASME International
Conference on Advanced Intelligent Mechatronics. pp. 1226
Dynamic Decoupled Control for
, Trans. Mechanism and Machine
with substantial
, largely due to the nature of the applied
the results
in which it is
with AFC scheme (AFC –
manages to accurately and readily track the desired
responses. This shows that the latter system is much more
in compensating the harmonic
The proposed
robot is able to operate
configuration
like micro robot was
and simulated. A hybrid control strategy including
the PID incorporated with the AFC was employed to ensure
ing of the robot system
disturbances and
controller was initially
method so as to
. The simulation results of
clearly demonstrated the effectiveness
s, particularly the PID
may include
the rigorous study on sensitivity analysis related to the effects
of other loading and operating conditions. The possibility of
tion on the micro robot
The authors would like to thank the Universiti Teknologi
Malaysia (UTM) for their continuous support in the research work.
A miniature mobile robot using piezo vibration for
1993, ASME J. Dynam. Syst, Vol. 115, pp.
Characteristics of piezoelectric locomotive mechanism
1995. IEEE 6th Int. Symp.
A prototype model of micro
mobile machine with piezoelectric driving force actuator., T 1994.
IEEE 5th Int. Symp. Micro Machine and Human Sciences. pp. 47–54.
and F. Arai, Giant
magnetostrictive alloy (GMA) applications to micro mobile robot as a
, 1991. IEEE Int.
Workshop Micro Electro Mechanical Systems (MEMS). pp. 210–215.
e microactuators to
: s.n., 1993. IMACS/SICE
520.
The development of an
1994. IEEE
–40.
Development of
. IEEE 5th Int. Symp. Micro
One pneumatic
inch pipe inspection.
m pneumatic
: s.n., 2001. IEEVASME International
Conference on Advanced Intelligent Mechatronics. pp. 1226-1331.
Dynamic Decoupled Control for
Mechanism and Machine
Proceedings of the World Congress on Engineering 2010 Vol II WCE 2010, June 30 - July 2, 2010, London, U.K.
ISBN: 978-988-18210-7-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
WCE 2010
[11] M. Mailah, Intelligent Active Force Control of a Rigid Robot Arm
Using Neural Network and Iterative Learning Algorithms, University
of Dundee, UK: Ph.D Thesis, 1998.
[12] M. Mailah, Ong, M.Y., Intelligent Adaptive Active Force Control of A
Robot Arm With Embedded Iterative Learning Algorithms , Jurnal
Teknologi (A), No. 35, 2001, pp. 85-98.
[13] S.B.Hussein, A.M.S. Zalzala, H. Jamaluddin, M. Mailah, An
Evolutionary Neural Network Controller for Intelligent Active Force
Control, Evolutionary Design and Manufacture, Ed. I.C. Parmee,
Springer Verlag, London, 2000, pp 352-362.
[14] Fu, K.S., Gonzales, R.C., and Lee, C.S.G. Robotics: Control, Sensing,
Vision, and Intelligence. New York: McGraw-Hill Inc., 1987. [15] Johnson, C.D., Accomodation of external disturbances on linear
regulator and servomechanism problems, IEEE Trans. Automat.
Control, 1971, AC-16, No. 6, pp. 635-644.
[16] Davison, E.J., Multivariable Tuning Regulators: The Feedforward and
Robust Control of a General Servomechanism Problem, 1976, IEEE
Trans. Automat. Control, AC-21, pp. 35-47.
[17] M.Mailah, E. Pitowarno, H.Jamaluddin, Robust Motion Control for
Mobile Manipulator Using Resolved Acceleration and
Proportional-Integral Active Force Control, International Journal of
Advanced Robotic Systems, Vol. 2, No. 2, 2005, pp. 125-134.
[18] Mailah, M., Hewit, J.R., Meeran, S., Active Force Control Applied to
A Rigid Robot Arm, Jurnal Mekanikal, Vol.2, No.2, 1996, pp. 52-68.
[19] Endra Pitowarno, Musa Mailah and Hishamuddin Jamaluddin,
Knowledge-Based Trajectory Error Pattern Method Applied to An
Active Force Control Scheme, International Journal of Engineering
and Technology, Vol. 2, No.1, 2002, pp. 1-15.
[20] Gigih Priyandoko, Musa Mailah, Simulation of A Suspension System
With Adaptive Fuzzy Active Force Control, International Journal on
Simulation Modelling, Vol. 6, No.1, 2007, pp. 25-36.
Proceedings of the World Congress on Engineering 2010 Vol II WCE 2010, June 30 - July 2, 2010, London, U.K.
ISBN: 978-988-18210-7-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
WCE 2010