Identification and Control of Pneumatic
Servodrives
Željko Šitum, Branko Novaković and Joško Petrić

Abstract-- This paper deals with the control of an electropneumatic servodrive for translational task. In order to obtain
approximate model of the pneumatic servosystem the off-line
identification procedure in closed-loop from experimental
measured data has been made. The real discrete-time control
system has been presented with pseudo-continuos-time (PCT)
system for the sake of the simplification of the dynamic
synthesis. The simulation results from the identified model
and PCT system are compared with experimental measured
system output on varying reference signal.
Index Terms-- electropneumatic servodrive, identification,
position control
I. INTRODUCTION
Pneumatic servo-technology have an important role in
applications of modern industrial mechatronic systems,
offering in many cases a cost-effective solutions for a wide
range of intelligent motion applications. Pneumatic
actuators give suitable solutions for quickly transporting
materials between workstations and for movements in
automatic control and flexible manufacturing systems. The
advantages of pneumatic actuators are their high loadvolume ratios, high speed action capabilities, high amount
of available forces, cleanliness, simple working mechanism.
Because of that pneumatic plants have been designed for a
variety of applications in industrial environment. However,
the application of pneumatic drives is limited in practice by
the problems in controlling these plants. Pneumatic
actuators are characterized by high-order, time-variant
dynamics, nonlinearities due to compressibility of air,
internal and external disturbances and wide range of supply
pressure and payload variations. These problems originate
mainly from the phenomena of using compressible working
fluid, which results in nonlinearities of pressure-flow
characteristics. For many applications of pneumatic
servodrives, fast moving in operation and good position
accuracy without overshoot in response are often a
prerequisite. This implies that the motion controller should
be able to operate on various types of motion task.
However, it is very difficult to get an accurate dynamic
model for describing pneumatic servodrives behavior. The
classical approach to position control of pneumatic drives is
based on the linearization of the nonlinear dynamic of the
system around the desired set point. Such models are valid
only for small deviations about an operating point [1].
The authors are with Department of Automatic Control, Faculty of
Mechanical Engineering and Naval Architecture, University of Zagreb,
I. Lučića 5, 10000 Zagreb, Croatia
6
5
4
3
2
1
(a)
(b)
1 - Linear potentiometer,
3 - Pressure sensor,
5 - Filter-regulator unit,
2 - Pneumatic rodless cylinder
4 - Proportional 5/3 valve
6 - Control computer
Fig. 1. The experiment system setup (a) photo of the laboratory
model, (b) schematic diagram of the control system
In this work the off-line identification procedure for
pneumatic servodrive in closed-loop using least-squares
method from sampled data of input-output measurements
has been made.
A. Schematic representation of the system
In Fig. 1. the photo and the schematic representation of the
experimental
electropneumatic
servosystem
for
translational positioning is shown. The physical model is
composed of a pneumatic rodless cylinder, SMC
CDY1S15H-500 with inertial load and proportional 5/3
electropneumatic valve, FESTO MPYE-5-1/8. A horizontal
linear potentiometer fixed on the cylinder is used for
measuring the position of the piston and for providing the
position feedback. All signals are sending to a
microcomputer via an 12 bit A/D converter board. The
computer can accomplish a control algorithm based on
these signals and set an output value of voltage via a D/C
converter. The input signal of the valve is the control
voltage from the computer. The change of input voltage
produces the change of valve flow through the valve and
also faster or slower motion of the piston of the cylinder.
The position of the piston is a controlled variable.
necessary to comparing the degree of compatibility between
the estimated model and the system. First 400 values of the
input and the output is shown in Fig. 2.
II. IDENTIFICATION PROCEDURE
The suitable model which gives the best fit for the reference
set is four order model with four poles, without zeros and
single time delay, i.e. [ na nb d ] = [ 4 1 1 ].
The polynomial parameters (with estimated standard
deviations) of the ARX model structure (1) are estimated
using the least-squares method, and they are listed below in
table I:
where u (k ) and y(k ) are the control signal and the
measured process output at sample instant k ,
a1 ,..., ana ; b1 ,..., bnb are model parameters and d is the
discrete dead time.
From equation (1) the z-transfer function becomes:
Gp ( z ) 
b z 1  ....  bnb z nb d
y( z ) B( z 1 ) d
(2)

z  1
z
u( z ) A( z 1 )
1  a1 z 1  ...  ana z na
An ARX (autoregressive with external input) model to
pneumatic actuator system was used. It is assumed that the
level of external noise in the servomechanism is negligible,
and modeling of noise is not necessary. To get a good
mathematical model it is very important how to select the
data, so that they are as informative as possible. The
considered system was excitated to a pseudo random binary
signal input of varying amplitudes (APRBS). In order to
obtain more information about the system dynamics, the
input signal has been designed that it varies over the entire
admissible region (from 0 to 10 V). The identification
procedure was used with a period of 10 ms. The input
signal of the process is the voltage from the computer and
the output of the process is the position of the piston,
measured in volts by a linear potentiometer. The system
off-line identification example described in this section are
based on measured input-output data obtained during the
experiment. From the process 800 input-output data points
were collected and loaded into MATLAB in ASCII form.
The data was split into two halves: first 400 data points
were used for building (estimation) a mathematical model
of the system and the other 400 data points were used for
model-validation test. A validation procedure is generally
y [V]
8
6
4
2
0
0
50
100
150
200
250
300
350
400
250
300
350
400
INPUT
u [V]
10
8
6
4
2
0
0
50
100
150
200
k
Fig 2. Portion of the input-output data used for model estimation
TABLE I
LEAST-SQUARES PARAMETER ESTIMATION OBTAINED DURING OFF-LINE
IDENTIFICATION METHOD
b1
0.0125
(0.0011)
a1
a2
a3
a4
2.4478
(0.0500)
2.1352
(0.1264)
0.7742
(0.1209)
0.0995
(0.0436)
To find how good is this model, we have been simulated it
and compared the model output with measured system
output on a portion of the original data that was not used to
the estimation of the model (from sample 400 to 800). The
agreement of the model and the measured output is shown
in Fig. 3.
10
Input s ignal
Measured output
Model output
9
8
7
6
[V]
System identification deals with the problem of building
mathematical models of dynamic systems based on
observed data from the systems [2,3]. The discrete time
model of the process can be described by a linear difference
equation:
y (k )  a1 y (k  1)  ...  ana y (k  na ) 
(1)
b1u (k  d  1)  ...  bnbu (k  d  nb )
OUTPUT
10
5
4
3
2
1
0
0
50
100
150
200
k
250
300
350
400
Fig. 3. Model validation test
The plots of the auto-correlation function for the residuals
and the cross-correlation between the input and the
residuals for 99 percent confidence levels are given in
Fig.4.
control purposes. System is a natural integrator, i.e. the
output (the position of the piston) is proportional to the
integral of the output (control voltage from the computer).
The velocity gain K v is determined from the open-loop
response, where the output is the speed of the cylinder's
piston x(t ) and the input is the unit step of electric voltage
Correlation f unct ion of residuals
1
0.5
0
-0.5
0
5
10
15
20
25
Cross correlation f unct ion between input and residuals
ui (t ) applied on the spool of the valve, Fig. 6. The gain
(5)
K v can be approximated: K v  0.7 m / V s
0.2
0.1
0
1
-0.1
-20
-15
-10
-5
0
lag
5
10
15
20
0.8
Fig. 4. Auto-correlation function of residuals and cross-correlation
function between input and residuals
III. CONTROL OF THE PNEUMATIC SERVODRIVE
GR ( z )
x R (z )
Controller
ur ( z )
Cylinder +
proportional valve
ZOH
KR
ur ( s )
xm ( s )
K AD
ui ( s )
Kv
s (02 s 2  20 01 s  1)
ux( s )
x( s )
Km
Fig. 5. (a) Block sheme of digital control of pneumatic
servosystem, (b) Block diagram of PCT system
An usual approach to position control of pneumatic drives
are based on linearization of the nonlinear dynamics around
an equilibrium state. A simplified model which still reflects
essential characteristic of pneumatic drive controlled by
proportional valve can be shown:
Kv
x( s )
(3)
G p ( s) 

ui ( s) s(0 2 s 2  201s  1)
where x(s) is the position of the load, ui (s) is the input to
the proportional valve, 0 is the natural frequency of the
loaded cylinder drive,  is its damping ratio, K v is the
velocity gain. The natural frequency, and damping ratio of
the cylinder can be expressed as [5]:
4  A2    p ,
M  Vc

Vc
1
k f 
2
4  p  A2    M
0.1 0.2
0.3 0.4 0.5 0.6 0.7 0.8
0.9 1
Time [s]
K DA
K
1  e T s
(6)

 DA
Ts
T / 2 s  1 T0 s  1
In order to simplify the synthesis of the control system the
nondominant time constant of the sampler and the zero
order hold can be added to process time constant:
(7)
Ts  T / 2  T0
The closed-loop transfer function as the ratio of measured
piston position to applied reference value can be expressed:
x ( s)
K0
(8)
Go ( s)  m

x R (s) s (Ts2 s 2  2 0 Ts s  1)
GDA (s)  K DA
(b)
0 
0
The transfer function of the D/A converter is approximated
using the first-order Padé approximation, as follows:
Process
K DA
T 2 s 1
0.1
Fig. 6. Open-loop step response
(a)
xR ( s )
0.4
0.2
x( s )
Linear
potentiometer
Control computer
0.5
0
Gm ( s )
T
xm ( z )
0.6
0.3
Gp( s )
T
Kv
0.7
The real discrete-time control system can be approximated
with the pseudo-continuous-time equivalent control system
(PCT system), [4], shown in Fig. 5.
input
experiment
simulation
Ts
25
Velocity [m/s]
-0.2
-25
0.9
(4)
The symbols are defined in the Table II.
In general, the bandwidth of electropneumatic proportional
valves is much higher than that of the cylinder with load, so
it is assumed that the valve dynamics can be neglected for
where the gain K0 is product of all system gains: the
controller gain K R , the D/A converter gain K DA , the
velocity gain K v , the gain of linear potentiometer K m and
the A/D converter gain K AD , i.e.:
(9)
K 0  K R  K DA  K v  K m  K AD
Applying Hurwitz stability criterion on the transfer function
from (8), we get the following condition for the stability of
closed-loop system:
2 0 Ts  0
20 Ts  K0 Ts2  0
(10)
K0 (2 0 Ts  K0 Ts2 )  0
Hence, the system will be stable for the condition:
(11)
K0  20 / Ts
and the stable system behavior is guaranteed for the
controller gain:
K0
KR 
(12)
K DA K v K m K AD
IV. EXPERIMENTAL RESULTS
The experimental system used is shown in Fig. 1. with
system parameters listed in Table II.
The control program is written in the C language, and the
control algorithm is implemented with a sampling period of
10 ms. The program for simulating PCT system has been
developed in Matlab/Simulink environment.
Figure 7. show the output of the identified transfer function,
the output of the PCT system and measured responses of
the system for applied reference signal.
400
Reference signal
Identified model
PCT system
Measured output
360
320
Position [mm]
280
240
pneumatic drives with classical controllers are not so
effective, because high order system tend to became
unstable if the gains are high in order to achieve steadystate accuracy. In practical positioning applications the
procedures for tuning controller parameters require an
accurate model of the process. To get an appropriate model
of the electropneumatic servodrives it is not easy because of
the nonlinearities and parameter variations in the system
dynamics. One way to get an approximated model of the
system is the identification procedure based on
experimental sampled data. For the task of classical control
synthesis a linear pseudo-continuous-time system can be
used. These model's can be useful for preliminary study of
the closed-loop control system , on which can be built more
complex structure in order to get better performance of the
system.
200
160
APPENDIX
120
Experiments and simulations
parameters listed in table below.
80
are
performed
using
40
0
0
5
10
15
TABLE II
NUMERICAL VALUES OF SYSTEM PARAMETERS
20
Time [s]
Fig. 7. Simulated and measured output of the system
The errors in the responses of the simulated and identified
model compared with experimental measured output are
caused by unmodeled effects like static friction, varying of
the supply pressure, servovalve deadband, air leakage. It
can be seen that the system with only proportional gain is
able to track the reference value, but with large steady-state
error. In order to improve closed-loop characteristic a PD
controller is applied. Zero of the controller is settled near
the system's time constant Ts , compensating thus its
influence and achieving better responses of the system,
Fig.8.
450
xR ( t )
d  15 mm
Cross-sectional area
A  1.767  10 4 m 2
Volume of the cylinder
Vc  8.835  10 5 m 3
Supply pressure
p  5  10 5 Pa
M  0.91 kg
Initial load
Friction coefficient
k f  65 Ns / m
Spec. heat ratio of air
D/A converter gain
  1.4
A/D converter gain
K AD  204.8 1 / V
K DA  2.44  10 3 V
Controller gain
K R  1 V /V
350
Forward gain
K v  0.7 m / Vs
300
Measuring system gain
K m  20 V / m
250
Natural frequency
200
Damping ratio
Process time constant
0  32.97 rad / s
  1.1
x( t )
400
Position [mm]
L  500 mm
Cylinder stroke length
Cylinder diameter
150
100
Sampling time
T0  30 ms
T  10 ms
50
0
0
1
2
3
4
5
6
7
8
9
10
Tim e [s]
Fig. 8. Experimental results of pneumatic cylinder positioning
using PD controller
V. CONCLUSION
Pneumatically powered drives are characterized by high
order dynamics, they usually have poor damping and low
stiffness, significant friction effects and limited bandwidth.
In such conditions, the accuracy and repeatability of
REFERENCES
[1]
[2]
[3]
[4]
[5]
Richard, E., Scavarda, S., "Comparison Between Linear and
Nonlinear Control of an Electropneumatic Servodrive", Journal of
Dynamic Systems, Measurement and Control, Vol.118, June 1996,
Astrom, K.J., Wittenmark,B., "Computer Controlled Systems:
Theory and Design", Prentice-Hall, Englewood Cliffs, 1984,
Ljung, L., "System identification: Theory for the User", PrenticeHall, Englewood Cliffs, 1987,
Šitum, Ž., "Electropneumatic Servodrives Control for Positioning
Task", 5th International Scientific Conference on Prod. Eng. CIM'99,
Opatija, 1999.
Eschmann, R., "Modellbildung und Simulation pneumatischer
Zylinderantriebe", Dissertation, RWTH Aachen, 1994.