The Real-time Tracking Servo Control of a Rodless Pneumatic

Actuator System under an Asymmetrical Load via the Feedback

Measurement System

Hao-Ting Lin

Department of Mechanical and Computer-Aided Engineering, Feng Chia University,

No. 100, Wenhwa Road, Seatwen, Taichung 40724, Taiwan, ROC

Keywords: Rodless Pneumatic Cylinder, Asymmetrical Load, Feedback Measurement System, Real-time Control, Path

Tracking Servo Control.

Abstract: Due to the nonlinear and time-varying characteristics, pneumatic servo control systems are difficult to

realize real-time path tracking control, especially for the rodless pneumatic cylinder which has relative

larger friction force. An asymmetrical vertical load resulting from the gravity makes the motion control in

the vertical direction more difficult. This study develops a rodless pneumatic actuator system for the real-

time tracking servo control with an asymmetrical vertical load. First, the dynamic models of the rodless

pneumatic actuator system will be established and simulated by the Matlab software. Then, the test rig

layout will be proposed and experimented under the asymmetrical load via the feedback measurement

system. Finally, the experimental results show that a rodless pneumatic actuator system with the

asymmetrical vertical load is successfully implemented for the path tracking profile.

1 INTRODUCTION

The pneumatic system is one of the power sources to

perform in the industry. Due to its reliability, low

cost, cleanness, simplicity, easy maintenance, and

safety in operation, the pneumatic system has

gradually been widely adopted in the industrial

automation. In recent years, pneumatic actuators

have been used to work on positioning and motion

tasks, and quite suitable for applying in the robotics

fields. However, compared with electrical motors

with equal power, pneumatic actuators are still not

competitive in a few applications which demand

accuracy, versatility and flexibility. Although

pneumatic actuators have disadvantages such as high

nonlinearity, low natural frequency due to low

stiffness of air compressibility, and control

complexity, researches on robots with the pneumatic

actuator system are still popular in the automation

industry.

Because pneumatic system is a highly nonlinear

system and does not easily get accurate

mathematical models, it is difficult and complicated

to accomplish the pneumatic servo control (Oyama

et al, 1990). To resolve the above problems, some

researcher adopted the model reference control

scheme (Gyeviki et al, 2005). In additional, Chiang

and Lin proposed a Fourier series-based adaptive

sliding-mode controller with H-inf tracking

performance for the rodless pneumatic cylinder

system (Chiang and Lin, 2011). The proposed

method can not only be effective in preventing

approximation errors, disturbance, and un-modeled

dynamics, but it also guarantees a desired H-inf

tracking performance for the overall system.

In this paper, the rodless pneumatic actuator is

set up in the vertical direction to be an asymmetrical

load mechanism system. For this system, the

properties of mass, flow and pressure between two

chambers of the pneumatic actuator are totally

different while the pneumatic actuator works. These

properties affect the overall system dramatically and

the real-time control for the path tracking servo

control is more difficult. In this research, the Matlab

simulation will be establish to simulate the proposed

system via the mathematical models and control

methods. Finally, the test results indicate that the

rodless pneumatic actuator system with an

asymmetrical vertical load can follow the desired

path profiles and achieve the required accuracy.

Lin, H-T.

The Real-time Tracking Servo Control of a Rodless Pneumatic Actuator System under an Asymmetrical Load via the Feedback Measurement System.

DOI: 10.5220/0005950603990403

In Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2016) - Volume 1, pages 399-403

ISBN: 978-989-758-198-4

Copyright

c

2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

399

2 DESCRIPTION OF THE

SYSTEM

Figure 1 photographically shows the test rig of the

rodless pneumatic servo system with an

asymmetrical vertical load. The test rig layout is

shown in Figure 2. In Figure 2, the real-time control

of the rodless pneumatic actuator system mainly has

five parts which are an air source unit, a rod-less

pneumatic actuator, a proportional servo valve,

signal processing cards and a PC-based controller

unit. The air pressure for the experiments is set as

0.5 MPa. The rod-less pneumatic actuator and the

proportional servo valve are manufactured by

FESTO. The type of the rod-less pneumatic actuator

is DGC-25-500-KF-YSR-A and the model of the

pneumatic proportional servo valve is MPYE-5-M5-

010-B. An optical linear encoder has a resolution of

0.1 μm for the feedback measurement system. The

PC-based controller is a feedback measurement

control unit which handles the control signals for the

pneumatic proportional servo valve by an AD/DA

interface card and gathers the feedback measuring

signals for itself via a counter card. The control

software of the overall system is computed by a 32-

bit Open Watcom C program and the sampling

frequency is 1000 Hz.

Figure 1: Rodless pneumatic actuator system.

Figure 2: Test rig layout.

3 DYNAMIC MODELS AND THE

CONTROL STRATEGY OF A

RODLESS PNEUMATIC

ACTUATOR SYSTEM WITH AN

ASYMMETRICAL VERTICAL

LOAD

In this research, the rodless pneumatic actuator is

arranged in the vertical direction for the path

tracking servo control. In this case, the gravity effect

plays an important role in the rodless pneumatic

actuator system with a vertical load. Therefore, the

proposed system is an asymmetrical system when

the block shifts dynamically in the rodless

pneumatic actuator. The block motion in the

pneumatic cylinder can dramatically influence the

air flow rates and pressure changes between two

cylinder chambers. In this chapter, the nonlinear

mathematical models of the asymmetrical rodless

pneumatic actuator system is derived inclusive of the

dynamics of pneumatic servo valve, the mass flow

rate equation of the pneumatic cylinder, the

continuity equation and the motion equation. To

implement the real-time servo control of a rodless

pneumatic actuator system under an asymmetrical

load, a Fourier series-based adaptive sliding mode

controller with H-inf tracking performance

(FSBASMC+Hinf) [3] is used for the overall

feedback measurement system in this study.

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

400

3.1 The Dynamics of the Pneumatic

Servo Valve

A proportional directional flow control valve is used

in this experiment. The main feature of this type of

valve is that its input control signal and the valve

spool position is in the linear relationship. Hence,

the dynamics of the valve can be described by the

following relation:

() ( () ())

vn

Xt K ut u t=−

(1)

where

()

X

t

is the valve spool displacement of the

pneumatic servo valve,

v

K

represents the

displacement-voltage gain,

)(tu

is the control input

and

()

n

ut

is the neutral voltage.

3.2 The Mass Flow Rate Equation of

the Pneumatic Cylinder

The mass flow rate of the air is dependent on the

orifice area, temperature and pressure difference

across the orifice, when the air flows through an

orifice. In Figure 2, considering the mass flow rate

of pneumatic cylinder chambers A and B, the

following equation can be expressed as

0

() () ( ())

()

dur

u

CCwX tP t f p t

mt

T

=

(2)

where

d

C

is the discharge coefficient (

0.8

d

C =

),

0

C

is

the mass flow parameter,

w

is the port width (m),

()

u

P

t

is the up-stream pressure (N/m

2

),

u

T

is the up-

stream temperature,

()

()

()

d

r

u

P

t

pt

P

t

=

is the ratio between

the down-stream and up-stream pressure,

)(tP

d

is the

down-stream pressure (N/m

2

), and

1

21

2

1, ( )

()

(())

() () , () 1

atm

rr

u

r

k

kk

kr r r r

P

pt C

Pt

fpt

Cpt p t C pt

+

⎧

<<

⎪

⎪

=

⎨

⎡⎤

⎪

−<<

⎢⎥

⎪

⎣⎦

⎩

(3)

For air,

k

=1.4 is the specific heat constant,

r

C

=0.528 and

k

C

=3.864. In order to simplify the

analysis, the following functions can be derived as

()

() ( )

()

ˆ

( ( ), ( ), ( ))

()

() ( )

()

a

s

s

s

ase

e

a

a

a

P

t

Ptf

P

t

T

fPt Pt Pt

P

t

Ptf

P

t

T

⎧

⎪

⎪

⎪

⎪

=

⎨

⎪

⎪

⎪

⎪

⎩

(4)

()

() ( )

()

ˆ

( ( ), ( ), ( ))

()

() ( )

()

e

b

b

b

bse

b

s

s

s

P

t

Ptf

P

t

T

fPtPtPt

P

t

Ptf

P

t

T

⎧

⎪

⎪

⎪

⎪

=

⎨

⎪

⎪

⎪

⎪

⎩

(5)

where

s

P

=5×10

5

(N/m

2

) is the supply pressure,

e

P

=1

×10

5

(N/m

2

) is the exhaust pressure,

a

P

and

b

P

are

the pressure values of the chamber A and B,

s

T

=293K is the supply temperature,

a

T

and

b

T

are

the temperature values in the chamber A and B.

3.3 The Continuity Equation

We assume that the air into the cylinder is an

adiabatic process of an ideal gas, the change in

energy can be shown as

( () ) () () ()

vc s Ps

d

cVtT mtCTPtVt

dt

ρ

=−

(6)

where

v

c

is the specific heat of air at constant

volume,

c

ρ

is the air density of the cylinder,

()Vt

is

the volume of the cylinder,

()mt

is the mass flow

rate,

P

C

is the specific heat of air at a constant

pressure and

()Pt

is the pressure of the chamber.

Assuming an ideal gas

( () ) () ()

()

() () () () () ()

vc s

Ps

ssPs

d

cVtT PtVt

dt

mt

CT

P

tV t PtV t PtV t

kRT kRT C T

ρ

+

=

=++

(7)

where

P

v

C

k

c

=

is the ratio of the specific heat for air

at the temperature

s

T

. For an ideal gas

111

P

R

CkR

=+

(8)

where R=287 (J/kg*K) is the universal gas constant.

Then

() () () ()

()

ss

P

tV t PtV t

mt

kRT RT

=+

(9)

For the chamber A and B, the following equations

hold:

() () () ()

()

aa aa

a

ss

P

tV t P tV t

mt

kRT RT

=+

(10)

() () () ()

()

bb bb

b

ss

P

tV t P tV t

mt

kRT RT

=+

(11)

The Real-time Tracking Servo Control of a Rodless Pneumatic Actuator System under an Asymmetrical Load via the Feedback

Measurement System

401

where V

a

and V

b

are the volumes of the chamber A

and B. Combining Eqs. (2)-(5), (10) and (11) as

0

ˆ

() ( (), (), ()) () ()

()

()

sd a s e a a

a

a

kRTCCwXtfPtPtPt kPtVt

Pt

Vt

−

=

(12)

0

ˆ

() ( (), (), ()) () ()

()

()

sd b s e b b

b

b

kRTCCwXtfPtPtPt kPtVt

Pt

Vt

−

=

(13)

3.4 The Motion Equation

Applying the Newton’s second law of motion, the

asymmetric pneumatic cylinder’s motion can be

described as

(() ())sgn(()) ()

( ( )) ( ( ), ( ), ( )) ( )

ab f

Sc a b

AP t AP t x t K x t

KxtSxtPtPt MgMxt

−

−−

−−=

(14)

where

A

denotes the piston area (m

2

),

M

is the mass

(kg), Mg indicates the asymmetrical vertical

payload,

f

K

is the viscous friction coefficient, and

()

Sc

Kx

−

is the combination of static and Coulomb

friction forces which are position and velocity

dependent. Function is expressed as

( ( )) ( ( ), ( ), ( ))

Sc a b

KxtSxtPtPt

−

() (),

0()()(())

( ( )) ( ( ), ( ), ( ))

( ( ))sgn( ( )),

0()()(())

ab

abS

Sc a b

c

abS

AP t AP t

as x and AP t AP t K x t

KxtSxtPtPt

Kxt xt

as x or AP t AP t K x t

−

−

⎧

⎪

=−≤

⎪

=

⎨

⎪

⎪

≠−>

⎩

(15)

where

(())

S

Kxt

is the position-dependent static

frictions,

(())

c

Kxt

is the variable position-dependent

load via friction effects.

Furthermore,

()

a

Vt

and

()

b

Vt

are defined as

() ( () )

a

Vt Axt=+Δ

(16)

() ( () )

b

Vt Al xt=−+Δ

(17)

where

l

is the stroke (m),

Δ

is an equivalent extra

length to the cylinder.

3.5 Control Strategy

The block diagram of the overall scheme is shown in

Figure 3. To realize the real-time path tracking servo

control for the rodless pneumatic actuator system

under an asymmetrical load, the FSBASMC-Hinf is

adopted in this study. Define the output error as

)()()( tytyte

m

−=

(18)

where

)(ty

m

is a given bounded reference signal. The

sliding surface is described as

)(...)()(

)1(

21

teteateas

n−

+++=

(19)

where

i

a

are chosen such that

∑

=

−

n

i

i

i

a

1

1

λ

is a Hurwitz

polynomial. In this paper, the FSBASMC-Hinf

controller is proposed to solve the high non-linearity

and time-varying problems of the rodless

pneumatics servo system under the asymmetrical

load. Therefore, the control input is chosen as

3

1 2 21 22

2

ˆ

() ()

2

ˆ

()

T

FF m

T

GG

s

t aeaepe peyt

u

t

ρ

−−−−−+−

=

Wq

Wq

iii i

(20)

where the sliding surface defined as

540

s

ee e=+ +

,

initial values of Fourier coefficients

ˆ

F

W

and

ˆ

g

W

are

111

[0,0, , 0]

×

and

111

[20000,0, ,0]

×

, respectively,

1

a

is

40,

2

a

is 5 and

ρ

=

0.2.

Figure 3: The block diagram of the overall scheme.

4 SIMULATIONS AND

EXPERIMENTS

First, the simulation of the overall rodless pneumatic

actuator system is established by the Matlab

software. Next the experiments of path tracking

servo control in a rodless pneumatic system under an

asymmetrical load are implemented. In the

experiments, the desired path trajectory, namely a

fifth-order polynomial function is chosen for the

real-time path tracking servo control in the vertical

direction.

4.1 Simulations of Path Control

The simulation of the path tracking servo control of

a fifth order polynomial with stroke of 200 mm in

2 sec controlled by FSBASMC+Hinf is

implemented, as shown in Figure 4, where the

position control response, the control error and the

control input are schematically described. The

simulation responses by FSBASMC+Hinf are shown

in Figure 4(a). From Figure 4(b), the tracking error

is bounded and well converged. Figure 4(c) shows

the control signal of FSBASMC+Hinf.

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

402

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

50

100

150

200

250

(a)

position (mm)

Time (sec)

Target

Experiment

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-2

0

2

(b)

error(mm)

Time (sec)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-10

-5

0

5

10

(c)

Voltage(V)

Time (sec)

Figure 4: Simulation results of the rodless pneumatic

actuator system under an asymmetrical load for a fifth

order polynomial path with stroke of 200 mm in 2 sec: (a)

position control response (b) control error (c) control

input.

4.2 Experiments of Path Control

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

50

100

150

200

Time (sec)

position (mm)

(a)

Target

Experiment

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-1

-0.5

0

0.5

1

(b)

error(mm)

Time (sec)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-5

0

5

(c)

Voltage(V)

Time (sec)

Figure 5: Experimental results of the rodless pneumatic

actuator system under an asymmetrical load for a fifth

order polynomial path with stroke of 200 mm in 2 sec: (a)

position control response (b) control error (c) control

input.

In the experiments, the position responses, tracking

errors and control inputs for the rodless pneumatic

actuator system under an asymmetrical load by a

fifth order polynomial with stroke of 200 mm in

2 sec are shown in Figure 5. Figure 5(b) shows the

maximum tracking error can reach about 0.9mm.

The control inputs are shown in Figure 5(c). From

Figure 5(c), control input signals fluctuate form +5

volts to -5 Volts. Therefore, the desired tracking

performance can be achieved.

5 CONCLUSIONS

In this study, a rodless pneumatic actuator system

under an asymmetrical load has been developed and

successfully implemented for real-time path tracking

servo control by the feedback measurement system.

The dynamic models and the control strategies are

built in Matlab software. The real-time control

measurement system is established by PC-based

system. For further confirming the proposed system,

the 5-th order polynomial path is implemented.

Finally, the simulation and experimental results

demonstrate that the proposed method is validated to

apply in the real-time path tracking control of the

pneumatic servo system under the asymmetrical

vertical load.

ACKNOWLEDGEMENTS

This research was sponsored by Ministry of Science

and Technology, Taiwan under the grant MOST

104-2218-E-035 -017.

REFERENCES

Oyama, O. et al, 1990. Model reference adaptive control

for a pneumatic cylinder servo system. Journal of the

Japan Hydraulic Pneumatic Society, Vol. 21, pp. 182-

186.

Gyeviki, J. et al, 2005. Sliding Modes Application in

Pneumatic Positioning. Proceedings of the 2005 IEEE

International Conference on Mechatronics, Taipei,

Taiwan, pp. 964-969, July 10-12.

Chiang, M. H., Lin, H. T., 2011. Development of a 3D

parallel mechanism robot arm with three vertical-axial

pneumatic actuators combined with a stereo vision

system. Sensors, Vol. 11, pp. 11476-11494.

The Real-time Tracking Servo Control of a Rodless Pneumatic Actuator System under an Asymmetrical Load via the Feedback

Measurement System

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