A Numerical Analysis on Double Acting Telescopic Pneumatic Cylinder Motion Characteristics.
2010 IACSIT 2nd INTERNATIONAL CONFERENCE ON MECHANICAL AND
AEROSPACE ENGINEERING (CMAE 2010), CHENGDU, CHINA
A Numerical Analysis on Double Acting Pneumatic Telescopic
Cylinder Motion Characteristics
1
I.
Abdul Talib Din (Author)
INTRODUCTION
1
Faculty of Mechanical Engineering,
Universiti Teknikal Malaysia Melaka, UTeM,
Melaka, Malaysia
e-mail : talib@utem.edu.my
Abstract - This paper presents the design and
development of a mathematical model of dynamic
motion of pneumatic telescopic cylinder. The aim of
the research is to develop a telescopic pneumatic
system that can handle variable load at constant
forward and retracting speed. The design analysis
carried out is focused and based mainly on
identifying the characteristics of the pneumatic
cylinder using force-feedback control system. A
conceptual model was made and the limitations were
identified and further studied on nonlinear behavior
and the solutions to improve its characteristics were
sought in the process of designing and developing
the telescopic cylinder. The control system contained
combination of proportional and on-off valve in
controlling the telescopic cylinder movement. The
determination of the displacement of each stage of
the telescopic cylinder, velocity and acceleration
were optimized using multi-order PI controller.
Method of research is performed by simulation
studies using Matlab Simulink to prove the dynamic
mathematical modeling of the cylinder. During the
last stage of the research, a scale down model of the
telescopic cylinder was fabricated incorporating all
design aspects derived from the theoretical and
simulation analysis. After that an experimental
study was conducted on the scale down cylinder in
order to validate the data obtained. The validated
data shall be used in the design of the full scale of the
telescopic cylinder. It is found that from the
numerical analysis, the designed system can achieve
a constant speed although loaded with varied axial
force.
Keywords - telescopic cylinder; motion
characteristic ; force-feedback ; pneumatic
Telescopic is design and applied in hydraulic or
pneumatic cylinders in order to minimize the length
of the stroke when in retracted position. It can be
found in several applications such as telescoping
fluid actuator that useful in industries for localized
applications of considerable forces in areas that lack
sufficient space, in agricultural tools or on vehicle
for use in construction and maintenance work on
overhead system as the telescopic cylinder were
mounted on the platform and can be lifted enough to
reach the uppermost parts of the structure [10],[11].
2
Roslina Aida Rahimi (Co-author)
2
Faculty of Mechanical Engineering,
Universiti Teknikal Malaysia Melaka, UTeM,
Melaka, Malaysia
e-mail : roslina_ra@utem.edu.my
Pneumatic telescopic cylinder is applied in this
research and more particularly to a compact
apparatus which is of simple construction,
inexpensive, easy to manufacture and use in a
variety of ways. The benefit of this actuator
compared to hydraulic type were its simple
construction that minimize the production cost on
material construction and maintenance while at the
same time reducing the overall length of the
pneumatic cylinder when retracted and to maximize
the effective length when extended. [9]
Pneumatic cylinder is one of most common type of
industry actuators. Compared to conventional
electric and hydraulic actuators, it offers better
alternative in certain types of applications.
Pneumatic actuators provide the enumerated
qualities at low cost and suitable for clean
environments as it safer and easier to work with [1],
[2]. Furthermore, the pneumatic actuator has a lower
specific weight and a higher power rate (torquesquared to inertia ratio) than an equivalent
electromechanical actuator. In some cases, a
pneumatic system may provide a significant weight
advantage [4].
The objective of this paper is to propose a control
system for telescopic cylinder using pneumatic
medium. The actuator model is a double acting type
2010 IACSIT 2nd INTERNATIONAL CONFERENCE ON MECHANICAL AND
AEROSPACE ENGINEERING (CMAE 2010), CHENGDU, CHINA
and controlled using force-feedback of system that
will also control the nonlinearities obtained from
the compressibility of air. The behavior of the
actuator is then controlled by multi order
Proportional-Integral (PI) that will control the
error in displacement, velocity and acceleration of
the cylinder motion. Simulation results were
presented to obtain the idea of the telescopic
cylinder behavior.
II.
TELESCOPIC CYLINDER
MODEL
III.
PNEUMATIC ACTUATOR MODEL
The pneumatic system that is used in this research
consists of double acting telescopic cylinder that
reacts as force in its motion and connected to the
valve. In this study, a combination of 5/3 way valve
and proportional regulator has been applied. The
combination of the on-off valve and pressure
regulator is needed in controlling the speed of each
stage and at the same time to avoid shock when the
telescopic cylinder retract or extend from stage to
stage. The schematic figure can be seen in figure 2.
Telescopic pneumatic cylinder consists of several
segments of cylinder which could shorten and
lengthen by mean of tightly slide-on hollow
cylindrical shape high pressure containers as
shown in Figure 1 below.
Figure 2. Schematic representation of the pneumatic
telescopic cylinder-valve system.
Figure 1. Pneumatic Telescopic cylinder.
(source : Vatel. B,1994)
The cylinder was designed by providing a
telescopic cylinder having several stages with
each having a hollow piston and piston rod
opening toward an inlet end of the cylinder and
substantially contained therein when retracted. An
inner sealed bushing on the opposite end of the
piston rod is used as a cylinder face cap. Air
opening serving as exhaust ports are aligned to
vent the voids between piston rods when
sequentially extending the several stages. [9]
The mathematical model considers the dynamics of
the piston and pressure of the chamber in extended
and retracted motion. The system model consist of
several equations as follows [1],[2] :-
M ẍ +B ẋ+F f +F=A ( P1 −P2 )
(1)
Ṗ1=
C f R √T
A
(
1
L+ x
2
)
[ α in Ā υ1 in Ps ṁ r ( Ps , P̄1 )
−α ex Āυ 1 ex P1 ṁr ( P1 , P̄a )]−α
(2)
P1 A
ẋ
1
A ( L+ x )
2
2010 IACSIT 2nd INTERNATIONAL CONFERENCE ON MECHANICAL AND
AEROSPACE ENGINEERING (CMAE 2010), CHENGDU, CHINA
C f R √T
[ α in Ā υ2 in Ps ṁr ( P s , P̄2 )
1
A
L+ x
2
P2 A
−α ex Āυ 2 ex P2 ṁ r ( P2 , P̄a )]−α
ẋ
1
A( L+ x )
2
Ṗ2=
(
)
(3)
C2
Pd
Pu
1/ k
C1
√
Pd
1−
Pu
¿
ṁ r =¿ { ¿ ¿ ¿
¿
( )
( k−1 ) / k
( )
Pd
≤P cr
Pu
P
if d >Pcr
Pu
if
(4)
Figure 3. Control structure of Pneumatic
Telescopic Cylinder Motion
B. Inner Loop Control
IV.
THE CONTROL STRUCTURE
A. Overall Control Structure
The control structure of the pneumatic telescopic
cylinder can be seen in figure 3. It is aim to
obtain the same velocity value for extended
movement of each stage of the telescopic cylinder.
The telescopic cylinder used in this experiment
consists of three stages with different value of
surface area.
Proportional-Integral-Derivative
(PID) was applied in this study to control the error
measurement from the pneumatic system [3].
However the measurement of the multi-order
value of displacement, velocity and acceleration
of this study were only using Proportional-Integral
and usually be called PI controller. There were
several studies on control strategies such as
(Jihong et al., 1999) that using combination of
modified PID controller to a pusher mechanism in
the packaging of confectionary products that give
accurate positioning and time accuracy [5]. In
other cases, PID control shown good control level
of speed for radial piston air motor and both speed
and direction control of motor is feasible in real
time (Takhi et al., 2001).
The inner loop control was simulated using PI
controller whereby the proportional makes change
to the output that is proportional to the current error
value while integral function was to reset magnitude
and the duration of the error by summing the
instantaneous error over time. The inner loop
schematic can be seen in figure 4.
Figure 4 . Position feedback varied with
load disturbance
The optimum value of the Multi-order ProportionalIntegral (PI) controller employed in this paper is
adopted [8]. The optimum value of the real time
desired force for the pneumatic actuator is given by
∑ F=e z
[
K P+
KI
s
] [
z
+ e ż K P +
KI
s
] [
ż
+e z̈ K P +
KI
s
]
z̈
(5)
Whereby,
e z , e ż
e
z̈
and
is the displacement error,
velocity error, and acceleration error respectively.
KP and KI are the proportional constant and the
integral constant of the PI controller respectively.
2010 IACSIT 2nd INTERNATIONAL CONFERENCE ON MECHANICAL AND
AEROSPACE ENGINEERING (CMAE 2010), CHENGDU, CHINA
Single order of PI controller namely known as
zero-order PI controller, first-order PI controller,
and the second-order PI controller. The optimum
value of the real time desired force for the
pneumatic actuators given by the zero-order PI,
first-order PI, and second-order PI controller
given in Eq. (6), (7), and (8).
[
K P+
[
K P+
[
K P+
∑ F=e z
s
]
z
KI
s
]
ż
KI
]
KI
(6)
∑ F=e ż
Figure 5a. Velocity at 5 kg in sinusoidal line
(7)
∑ F=e z̈
s
z̈
(8)
(8)
Where
Pout : Proportional term of output
Kp : proportional gain, a tuning parameter
Ki : Integral gain, a tuning parameter
e
: Error = SP-PV
t
: Time or instantaneous time(the present)
Figure 5b. Velocity at load 5 kg in quadratic line
V.
SIMULATION RESULTS
Figure 5 and 6 show the simulation results of the
telescopic cylinder movement using certain given
load.
Simulation of the multi order velocity and
acceleration were obtained using Simulink and
compared with the theoretical calculation. Graphs
shown are the results of the actual condition while
the theoretical calculation represents the desired
value of the zero, first and second order for the
telescopic movement.
2010 IACSIT 2nd INTERNATIONAL CONFERENCE ON MECHANICAL AND
AEROSPACE ENGINEERING (CMAE 2010), CHENGDU, CHINA
reduce jerk condition in motion changing stage to
stage that proves the functionality of on-off and
proportional regulator valve combination.
VII.
REFERENCES
[1] Richer, E. and Hurmuzlu, Y. , A high performance
pneumatic force actuator system Part I - Nonlinear
mathematical model. Journal of Dynamic Systems,
Measurement and Control, ASME, Vol.122, No.3,
2000, pp 416–425.
Figure 6a. Acceleration at load 5 kg in sinusoidal
line
[2] Richer, E. and Hurmuzlu, Y., A high performance
pneumatic force actuator system Part II – Nonlinear
controller design. Journal of Dynamic Systems,
Measurement and Control, ASME, Vol.122, No.3,
2000 , pp 426–434.
[3]
Lai, J.Y., Menq, C.H. and Singh, R., Accurate
Position Control of a Pneumatic
Actuator,
Journal of Dynamic Systems, Measurement and
Control, ASME, Vol.112, No.4, 1990, pp 734-739.
[4] Hazem I. Ali, Mohd Noor, S.B., S. M. Bashi, M. H.
Marhaban , A Review of Pneumatic Actuators
(Modeling and Control), Australian Journal of Basic
and Applied Sciences, Vol 3(2), 2009, pp 440-454.
[5] Xiang, F., Block Oriented Nonlinear Control of
Pneumatic Actuator Systems, PhD thesis, Royal
Institute of Technology, KTH. , 2001
[6]
Figure 6b. Acceleration at load 5 kg in quadratic
line
VI.
CONCLUSION
The differential value of displacement, velocity
and acceleration has been developed by
minimizing the error from the position and force
feedback control structure. The simulation results
shown that the telescopic cylinder system able to
achieve desired performance of the pneumatic
actuator compared to the theoretical calculation
that has been made. In conclusion, the simulation
results manage to obtain good agreement with the
expected experimental value where the motion of
each telescopic stage moving in constant velocity
even though the surface area is different from each
telescopic stage. Besides that, the cylinder able to
Kamman, J. W. and Jennings, A. System
Identification and Control of a Pneumatic Cylinder.
Western Michigan University.Technical Report
Number: MAE-05-07. 2005
[7] Wang, J., Kotta, U. and Ke, J., Tracking control of
nonlinear pneumatic actuator systems using Static
state feedback linearization of the input–output
map . Proc. Estonian Acad. Sci. Phys. Math., Vol 56,
1, 2007, pp 47–66.
[8] Imaduddin, F., Hudha, K., Ubaidillah and Jamaluddin
, H., Simulation and Experimental Evaluation of
Multi-order Proportional-Integral Control for
Pneumatically Actuated Active Suspension System.
2008, Universiti Teknikal Malaysia Melaka.
[9] Vatel, B. Pneumatic Telescoping Cylinder and
Method. US005341724A(Patent). 1994
[10] Franco Telescopic Extensible Rod.,
0666019A1(Patent). 1994
[11]
Miller,G.L.Telescoping
Fluid
US2007/0074964A1
(Patent),2007
Actuator.
AEROSPACE ENGINEERING (CMAE 2010), CHENGDU, CHINA
A Numerical Analysis on Double Acting Pneumatic Telescopic
Cylinder Motion Characteristics
1
I.
Abdul Talib Din (Author)
INTRODUCTION
1
Faculty of Mechanical Engineering,
Universiti Teknikal Malaysia Melaka, UTeM,
Melaka, Malaysia
e-mail : talib@utem.edu.my
Abstract - This paper presents the design and
development of a mathematical model of dynamic
motion of pneumatic telescopic cylinder. The aim of
the research is to develop a telescopic pneumatic
system that can handle variable load at constant
forward and retracting speed. The design analysis
carried out is focused and based mainly on
identifying the characteristics of the pneumatic
cylinder using force-feedback control system. A
conceptual model was made and the limitations were
identified and further studied on nonlinear behavior
and the solutions to improve its characteristics were
sought in the process of designing and developing
the telescopic cylinder. The control system contained
combination of proportional and on-off valve in
controlling the telescopic cylinder movement. The
determination of the displacement of each stage of
the telescopic cylinder, velocity and acceleration
were optimized using multi-order PI controller.
Method of research is performed by simulation
studies using Matlab Simulink to prove the dynamic
mathematical modeling of the cylinder. During the
last stage of the research, a scale down model of the
telescopic cylinder was fabricated incorporating all
design aspects derived from the theoretical and
simulation analysis. After that an experimental
study was conducted on the scale down cylinder in
order to validate the data obtained. The validated
data shall be used in the design of the full scale of the
telescopic cylinder. It is found that from the
numerical analysis, the designed system can achieve
a constant speed although loaded with varied axial
force.
Keywords - telescopic cylinder; motion
characteristic ; force-feedback ; pneumatic
Telescopic is design and applied in hydraulic or
pneumatic cylinders in order to minimize the length
of the stroke when in retracted position. It can be
found in several applications such as telescoping
fluid actuator that useful in industries for localized
applications of considerable forces in areas that lack
sufficient space, in agricultural tools or on vehicle
for use in construction and maintenance work on
overhead system as the telescopic cylinder were
mounted on the platform and can be lifted enough to
reach the uppermost parts of the structure [10],[11].
2
Roslina Aida Rahimi (Co-author)
2
Faculty of Mechanical Engineering,
Universiti Teknikal Malaysia Melaka, UTeM,
Melaka, Malaysia
e-mail : roslina_ra@utem.edu.my
Pneumatic telescopic cylinder is applied in this
research and more particularly to a compact
apparatus which is of simple construction,
inexpensive, easy to manufacture and use in a
variety of ways. The benefit of this actuator
compared to hydraulic type were its simple
construction that minimize the production cost on
material construction and maintenance while at the
same time reducing the overall length of the
pneumatic cylinder when retracted and to maximize
the effective length when extended. [9]
Pneumatic cylinder is one of most common type of
industry actuators. Compared to conventional
electric and hydraulic actuators, it offers better
alternative in certain types of applications.
Pneumatic actuators provide the enumerated
qualities at low cost and suitable for clean
environments as it safer and easier to work with [1],
[2]. Furthermore, the pneumatic actuator has a lower
specific weight and a higher power rate (torquesquared to inertia ratio) than an equivalent
electromechanical actuator. In some cases, a
pneumatic system may provide a significant weight
advantage [4].
The objective of this paper is to propose a control
system for telescopic cylinder using pneumatic
medium. The actuator model is a double acting type
2010 IACSIT 2nd INTERNATIONAL CONFERENCE ON MECHANICAL AND
AEROSPACE ENGINEERING (CMAE 2010), CHENGDU, CHINA
and controlled using force-feedback of system that
will also control the nonlinearities obtained from
the compressibility of air. The behavior of the
actuator is then controlled by multi order
Proportional-Integral (PI) that will control the
error in displacement, velocity and acceleration of
the cylinder motion. Simulation results were
presented to obtain the idea of the telescopic
cylinder behavior.
II.
TELESCOPIC CYLINDER
MODEL
III.
PNEUMATIC ACTUATOR MODEL
The pneumatic system that is used in this research
consists of double acting telescopic cylinder that
reacts as force in its motion and connected to the
valve. In this study, a combination of 5/3 way valve
and proportional regulator has been applied. The
combination of the on-off valve and pressure
regulator is needed in controlling the speed of each
stage and at the same time to avoid shock when the
telescopic cylinder retract or extend from stage to
stage. The schematic figure can be seen in figure 2.
Telescopic pneumatic cylinder consists of several
segments of cylinder which could shorten and
lengthen by mean of tightly slide-on hollow
cylindrical shape high pressure containers as
shown in Figure 1 below.
Figure 2. Schematic representation of the pneumatic
telescopic cylinder-valve system.
Figure 1. Pneumatic Telescopic cylinder.
(source : Vatel. B,1994)
The cylinder was designed by providing a
telescopic cylinder having several stages with
each having a hollow piston and piston rod
opening toward an inlet end of the cylinder and
substantially contained therein when retracted. An
inner sealed bushing on the opposite end of the
piston rod is used as a cylinder face cap. Air
opening serving as exhaust ports are aligned to
vent the voids between piston rods when
sequentially extending the several stages. [9]
The mathematical model considers the dynamics of
the piston and pressure of the chamber in extended
and retracted motion. The system model consist of
several equations as follows [1],[2] :-
M ẍ +B ẋ+F f +F=A ( P1 −P2 )
(1)
Ṗ1=
C f R √T
A
(
1
L+ x
2
)
[ α in Ā υ1 in Ps ṁ r ( Ps , P̄1 )
−α ex Āυ 1 ex P1 ṁr ( P1 , P̄a )]−α
(2)
P1 A
ẋ
1
A ( L+ x )
2
2010 IACSIT 2nd INTERNATIONAL CONFERENCE ON MECHANICAL AND
AEROSPACE ENGINEERING (CMAE 2010), CHENGDU, CHINA
C f R √T
[ α in Ā υ2 in Ps ṁr ( P s , P̄2 )
1
A
L+ x
2
P2 A
−α ex Āυ 2 ex P2 ṁ r ( P2 , P̄a )]−α
ẋ
1
A( L+ x )
2
Ṗ2=
(
)
(3)
C2
Pd
Pu
1/ k
C1
√
Pd
1−
Pu
¿
ṁ r =¿ { ¿ ¿ ¿
¿
( )
( k−1 ) / k
( )
Pd
≤P cr
Pu
P
if d >Pcr
Pu
if
(4)
Figure 3. Control structure of Pneumatic
Telescopic Cylinder Motion
B. Inner Loop Control
IV.
THE CONTROL STRUCTURE
A. Overall Control Structure
The control structure of the pneumatic telescopic
cylinder can be seen in figure 3. It is aim to
obtain the same velocity value for extended
movement of each stage of the telescopic cylinder.
The telescopic cylinder used in this experiment
consists of three stages with different value of
surface area.
Proportional-Integral-Derivative
(PID) was applied in this study to control the error
measurement from the pneumatic system [3].
However the measurement of the multi-order
value of displacement, velocity and acceleration
of this study were only using Proportional-Integral
and usually be called PI controller. There were
several studies on control strategies such as
(Jihong et al., 1999) that using combination of
modified PID controller to a pusher mechanism in
the packaging of confectionary products that give
accurate positioning and time accuracy [5]. In
other cases, PID control shown good control level
of speed for radial piston air motor and both speed
and direction control of motor is feasible in real
time (Takhi et al., 2001).
The inner loop control was simulated using PI
controller whereby the proportional makes change
to the output that is proportional to the current error
value while integral function was to reset magnitude
and the duration of the error by summing the
instantaneous error over time. The inner loop
schematic can be seen in figure 4.
Figure 4 . Position feedback varied with
load disturbance
The optimum value of the Multi-order ProportionalIntegral (PI) controller employed in this paper is
adopted [8]. The optimum value of the real time
desired force for the pneumatic actuator is given by
∑ F=e z
[
K P+
KI
s
] [
z
+ e ż K P +
KI
s
] [
ż
+e z̈ K P +
KI
s
]
z̈
(5)
Whereby,
e z , e ż
e
z̈
and
is the displacement error,
velocity error, and acceleration error respectively.
KP and KI are the proportional constant and the
integral constant of the PI controller respectively.
2010 IACSIT 2nd INTERNATIONAL CONFERENCE ON MECHANICAL AND
AEROSPACE ENGINEERING (CMAE 2010), CHENGDU, CHINA
Single order of PI controller namely known as
zero-order PI controller, first-order PI controller,
and the second-order PI controller. The optimum
value of the real time desired force for the
pneumatic actuators given by the zero-order PI,
first-order PI, and second-order PI controller
given in Eq. (6), (7), and (8).
[
K P+
[
K P+
[
K P+
∑ F=e z
s
]
z
KI
s
]
ż
KI
]
KI
(6)
∑ F=e ż
Figure 5a. Velocity at 5 kg in sinusoidal line
(7)
∑ F=e z̈
s
z̈
(8)
(8)
Where
Pout : Proportional term of output
Kp : proportional gain, a tuning parameter
Ki : Integral gain, a tuning parameter
e
: Error = SP-PV
t
: Time or instantaneous time(the present)
Figure 5b. Velocity at load 5 kg in quadratic line
V.
SIMULATION RESULTS
Figure 5 and 6 show the simulation results of the
telescopic cylinder movement using certain given
load.
Simulation of the multi order velocity and
acceleration were obtained using Simulink and
compared with the theoretical calculation. Graphs
shown are the results of the actual condition while
the theoretical calculation represents the desired
value of the zero, first and second order for the
telescopic movement.
2010 IACSIT 2nd INTERNATIONAL CONFERENCE ON MECHANICAL AND
AEROSPACE ENGINEERING (CMAE 2010), CHENGDU, CHINA
reduce jerk condition in motion changing stage to
stage that proves the functionality of on-off and
proportional regulator valve combination.
VII.
REFERENCES
[1] Richer, E. and Hurmuzlu, Y. , A high performance
pneumatic force actuator system Part I - Nonlinear
mathematical model. Journal of Dynamic Systems,
Measurement and Control, ASME, Vol.122, No.3,
2000, pp 416–425.
Figure 6a. Acceleration at load 5 kg in sinusoidal
line
[2] Richer, E. and Hurmuzlu, Y., A high performance
pneumatic force actuator system Part II – Nonlinear
controller design. Journal of Dynamic Systems,
Measurement and Control, ASME, Vol.122, No.3,
2000 , pp 426–434.
[3]
Lai, J.Y., Menq, C.H. and Singh, R., Accurate
Position Control of a Pneumatic
Actuator,
Journal of Dynamic Systems, Measurement and
Control, ASME, Vol.112, No.4, 1990, pp 734-739.
[4] Hazem I. Ali, Mohd Noor, S.B., S. M. Bashi, M. H.
Marhaban , A Review of Pneumatic Actuators
(Modeling and Control), Australian Journal of Basic
and Applied Sciences, Vol 3(2), 2009, pp 440-454.
[5] Xiang, F., Block Oriented Nonlinear Control of
Pneumatic Actuator Systems, PhD thesis, Royal
Institute of Technology, KTH. , 2001
[6]
Figure 6b. Acceleration at load 5 kg in quadratic
line
VI.
CONCLUSION
The differential value of displacement, velocity
and acceleration has been developed by
minimizing the error from the position and force
feedback control structure. The simulation results
shown that the telescopic cylinder system able to
achieve desired performance of the pneumatic
actuator compared to the theoretical calculation
that has been made. In conclusion, the simulation
results manage to obtain good agreement with the
expected experimental value where the motion of
each telescopic stage moving in constant velocity
even though the surface area is different from each
telescopic stage. Besides that, the cylinder able to
Kamman, J. W. and Jennings, A. System
Identification and Control of a Pneumatic Cylinder.
Western Michigan University.Technical Report
Number: MAE-05-07. 2005
[7] Wang, J., Kotta, U. and Ke, J., Tracking control of
nonlinear pneumatic actuator systems using Static
state feedback linearization of the input–output
map . Proc. Estonian Acad. Sci. Phys. Math., Vol 56,
1, 2007, pp 47–66.
[8] Imaduddin, F., Hudha, K., Ubaidillah and Jamaluddin
, H., Simulation and Experimental Evaluation of
Multi-order Proportional-Integral Control for
Pneumatically Actuated Active Suspension System.
2008, Universiti Teknikal Malaysia Melaka.
[9] Vatel, B. Pneumatic Telescoping Cylinder and
Method. US005341724A(Patent). 1994
[10] Franco Telescopic Extensible Rod.,
0666019A1(Patent). 1994
[11]
Miller,G.L.Telescoping
Fluid
US2007/0074964A1
(Patent),2007
Actuator.