Modelling of Actuators in Active Mechanical Vibration Reduction
System
JANUSZ KOWAL, ROMAN KORZENIOWSKI, JAROSLAW BULKA*
Department of Process Control
* Department of Automatics
AGH - University of Science and Technology
Av. Mickiewicza 30, 30-059 Cracow
POLAND
Abstract: - The paper is focused on modelling of active vibration isolation systems utilising electropneumatic
units. Unlike the models employed to date, the presented model involves all the relationships describing the
pneumatic supply system performance and takes into account all possible leaks in the pneumatic amplifier in
the servovalve. The main focus is on modelling friction forces in the structural nodes of the actuator unit. The
dynamic model of friction was selected. Results of numerical experiments run in MATLAB-Simulink
environment were most promising and the selected model proved adequate.
Key-Words: - vibroisolation, modeling, simulation
1. Introduction
One of the basic methods of vibroisolation is
stopping the propagation from the source to the
object. From a practical perspective, two methods
are used: force vibroisolation and displacement
vibroisolation [2]. The principle of the former is the
isolation of the dynamic force generated by the
object and transmitted onto the ground. In
displacement vibroisolation, the vibration reducing
system has to isolate the object from the source of
undesired dynamic displacement coming from the
ground. From the point of view of energy supply,
control mechanisms and technical measures applied
in any specific implementation, two groups of
vibration reducing systems are additionally
distinguished, like: passive methods group and active
methods group.
In passive methods group the tasks leading to the
reducing vibration have the following features:
 the prevention of vibration reasons,
 parameter modification,
 structural modification,
 vibration isolation.
In case of these methods energy scattering or
periodical storage and producing energy occur.
Passive methods are limited by little effectiveness of
reducing vibration in the range of low frequencies,
sensibility to operating condition changes etc.
Better results can be achieved using the active
methods, which amount to structural or parametric
changes using external source of power. These
methods allow to solve the problem of contradictory
demands such us high machine efficiency, low
vibration level, dynamic stability and rigidity. In
active methods properly controlled source of external
power can deliver or absorb energy, in a specific
way, from different parts of the machine. The drive
(hydraulic, pneumatic, electric) added to the
vibroisolated object generates opposite force to the
harmful dynamic displacement force. The control
strategy of the force generator set by controller is
based on information about the system coming from
measurement system. The measurement system
includes transducers, amplifiers and pre-equalization
elements. From the point of view of energy supply in
active methods, a number of vibration reducing
systems are additionally distinguished, like passive,
semiactive, hybrid and adaptive systems. From the
point of view of the drive, pneumatic, hydraulic,
electromagnetic and hybrid active vibration isolation
systems are distinguished. In the following part of
the paper active systems based on fluid and electrofluid drives are described.
2. Examples of active fluid vibration
isolation system in automotive vehicles
Among
well-known
solutions
of
active
vibroisolation systems, which have been applied,
most of them are based on fluid, and electro-fluid
drives. The most interesting solutions are presented
in the suspensions of different vehicles. To assure
appropriate comfort of driving is the main reason of
their evaluation. Usage of suspension springs and
shock absorbers in conventional suspensions is
constrained as result of contradictory relations
among stability and drive comfort and the inability to
The design of the active vibration isolation system
shown in Fig. 3 utilises the electropneumatic
servodrive configuration. It has electric components:
electronic control systems, displacement transducers
5 and 6. The servodrive employed here consists of a
piston-type cylinder 3 with a single-action rod and a
flow control servovalve 4. Application of
electropneumatic
servovalves
ensures better
flexibility of the system as it allows for programming
any control algorithms. Other advantages of the
applied method are simplicity of pneumatic system
design and continuous control of its motion
parameters, which may vastly improve the functional
quality of the whole system. For the purpose of
numerical tests a mathematical model of the
vibration isolation system was developed. It utilises
partial models describing system components and
units. Models of a pneumatic cylinder, a servovalve
and the pneumatic supply unit are taken into account.
M
5
y2
3
4

2
4
x
6

3 1 5
1
Control
System
y1
reducing vibration low frequency as well as high
one. From now on many suspensions models have
been improved and developed but with the existing
suppressions. Suspension systems have been
revolutionized by the active suspensions reconciling
comfort and drive stability. Among such examples,
based on fluid drives suspension systems applied in
cars of such companies as Citroen, Nissan,
Mitsubishi, Toyota, Mercedes can be specified.
Some of the companies use electropneumatic
systems, some others electrohydraulic and electropneumo-hydraulic systems as well.
The suspensions, drown up in Nissan Company,
operates as “skyhook damper” together with
damping in the function of vibration frequency.
Functional scheme of suspension and its equivalent
model is presented in Fig 1. An actuator and
electrohydraulic proportional pressure regulator are
included in the system. Hydraulic cylinder, throttling
valve and hydraulic accumulator in the lower part of
the cylinder belong to the actuator. Apart from
vibration reduction coming from the road
irregularity, this suspension compensates settlement
in accelerating and braking as well as car body
rolling. It also enables unequal balance of the mass
arranged inside the car together with stable body car
position. The advantages of the active systems versus
the passive ones are illustrated by frequency
characteristics presented on Fig 2.

2
Vz
Fig. 3. Fully active electropneumatic vibration
isolation system: M - isolated mass, 1 - source of
mechanical vibration, 2 - pneumatic supply source, 3
- pneumatic cylinder, 4 - pneumatic servovalve, 5
and 6 - displacement transducers
2.1. Model of the pneumatic supply unit
Fig. 1 Structure of Nissan suspension
Transmision T [dB]
10
0
Characteristic without
“skyhook damper”
-10
Characteristic with
“skyhook damper”
-20
1
2
3
4
5
6
7
10
Frequency [Hz]
Fig. 2 Passive and Nissan active suspension
attenuation diagram
2.1. Description of the system
The efficiency of a real pneumatic supply unit is
limited and compressed air pressure depends on the
capacity of the supply line, on the type of pressure
control elements and absorbing capacity of the
receiver as well as the nature of its loading. In a
pneumatic system where cylinder loading changes
dynamically, the pressure at the servovalve inlet is
lower or higher than pressure generated by the
source of pneumatic energy. The magnitude of this
pressure depends on the direction and rate of the
working medium flow. It means that apart from the
“natural” flow direction, the compressed air may
flow from the cylinder chamber to the supplying
source. A schematic diagram of the pneumatic unit
for compressed air supply and its computational
model taking into account all the factors mentioned
previously is shown in Fig. 4.
a)
b)
p1
PR
pz
p1 T1
q2
q1z
PR
Vz
p3
qz3
3. Examples of laboratory systems
Vz pz Tz
q2z p2 T2
qz2
Fig. 4 Pneumatic supply unit: a) schematic diagram,
b) throttling model; PR – pressure regulator
Application of the rule of energy conservation for the
adopted computation algorithm yields the system of
equations defining the state of gas in a constant –
volume tank:
 dpz  
  1 dQz 
 dt  V  RT1q1z  T2q2 z  Tz qz 3  qz 2    dt 

z 


 dTz  Tz  R q  T  Tz   q  T  Tz   q  q  T  Tz      1 dQz 
 dt pzVz   1z  1   2 z  2   z 3 z 2  z     dt 



(1)
The mass flow rate formula, as set forth in the
standard ISO 6358, is written as:
qij  Cij  pi   0
T0
 r 
Ti
(2)
where: Cij - conductance of the flow channel ij, 0 air density in the standardised reference conditions,
T0 - reference temperature, R – universal gas
constant, Qz – heat flux transfer with environment.
The auxiliary function (r) and pressure ratio r are
given by the formulas:
2

 1   r  b 
 r   
 1 b 

1

r
for
b  r 1
for
0r b
pi
wher i  1, z, j  z, 3, i  j
pj
compensated through substitution of a variant
polytropic exponent n in place of an adiabate
exponent .
(3)
(4)
Several simplifications were made on the basis of
laboratory tests and results published in literature on
the subject [7, 8]. It is assumed that compressed air
temperature is constant and that there is no heat
exchange with environment. The error involved is
The experimental researches, particularly in the area
of practical realization, belong to the most important
conditions of the development of the active vibration
reduction methods. Estimating the experiments
meaning, the long-lasting, laboratory and ranging
research program has been undertaken, together with
simulation research. Most of them are operated on
the specially designed laboratory stand [5], which is
shown in Fig. 5. It is mainly accommodated to the
researches of the active reduction vibration systems,
which are based on electrohydraulic and
electropneumatic elements and sets, but other
systems are also taken into consideration. It can be
used for general purposes because of the
characteristics of the elements and sets applied in the
laboratory stand. Consequently, there are wide
opportunities of the stand, which allow researches of
various mechanic structures systems. The laboratory
stand enables rapid attenuation diagram tracing, the
parameter choice of excitation setting, various
algorithms control system testing, system structure
modification.
Here the most important parts of the laboratory stand
are presented: supporting frame 1, leveling platforms
2 and 3, electrohydraulic vibrator 4. Vibration
reduction system 5 is placed among the leveling
platforms. Additionally, hydraulic or pneumatic
pressure supplies cooperate with the laboratory
stand. There are two independent data acquisition
systems applied in the research. The first one, using
the dSPACE computer with the DSP processor,
operates with electrohydraulic vibrator. The second
system, cooperating with the vibration isolation
system, includes PC computer equipped with the
PCL 818HG ADVANTECH data acquisition
adapter. The data storage, operation and
measurement opportunities are widened by the set of
MATLAB/Simulink RTW toolbox. The laboratory
stand is also equipped with the set of dislocation,
accelerator and pressure transducers.
Load
M

1
x
2
3

5
Source of
vibration
Ground
Levelling
actuator
Electropneumatic vibroisolation
data aquition system
PCL 818
HG
Electrohydraulic excitator
control system
x

4
E
rn e
the
Fig. 7 Physical model of semiactive system
t
PCL 818
..x
..x
M



x

dSPACE


PSV
HSV
Hydraulic
pressure
supply
Spring

Pneumatic
pressure
supply

x
Terminal strip

x
Adjustable
damper
Fig. 5. Laboratory stand for testing vibration
isolation system
x


In the prepared research program there are specified
mainly active systems groups, based on
electropneumatic, proportional and servovalve
technique. Driving elements as actuators together
with the proportional valves and servovalves are
included in these systems. Basing on the elements
above different structures of active reduction
vibration systems has been constructed. The
pneumatic schemes as well as physical models of a
few chosen solutions are shown in Fig. 6, 7, 8, 10, 11
and 12.
Electropneumatic semiactive vibration isolation
systems have the simplest structure. Their pneumatic
schema has been shown in the Fig 6 as well as their
physical model in the Fig 7. Bellows actuator 1 and
proportional electropneumatic pressure valve 2 are
main elements of this system. Among other, during
investigation [3] in laboratory stand has been
observed that this system and passive ones have very
similar characteristic. Usage of proportional
electropneumatic pressure valve allows changing
working conditions according to force excitations.
Fig. 8. Pneumatic fully active system
In the Fig 8, 9 and 10 electropneumatic fully active
mechanical vibration reduction system has been
presented. The most important elements in this
system are piston actuator equipped with low friction
sealing and pneumatic servovalve 5/3. This
pneumatic servodrive operates fully active in wide
range of force excitation because high frequency
switching servovalve has been used.

..x

PCL 818
..x
M
Fig. 6. Semiactive system
Fig. 9. View of fully active vibration isolation
system in laboratory stand
x
Accelerometer

..
M

F
There are also conduct research on electrohydraulic
vibration isolation systems. For the sake of
references where the laboratory hydraulic systems
has been wide described this paper does not present
it.
Load
Servodrive
x
Accelerometer

..
Source of
vibration
Ground
4. Conclusion
Fig. 10. Physical model of fully active system
The pneumatic adaptive vibration isolation system
gives
greater
possibility
of
transmission
characteristic modifying and has been presented in
Fig 11 and 12. As a pneumatic spring 1 pneumatic
piston actuator equipped with low friction has been
used. For pressure control in actuator chamber has
been used electropneumatic proportional pressure
valve 3 as well as pneumatic servovalve 4 to control
flow rate between actuator chamber 1 and
accumulator 5. Leveling of the actuator together with
system stiffens characteristic and vibration
elimination in low frequency range is possible
because working pressure control. Flow rate control
causes pneumatic spring stiffness characteristic and
attenuation ones changes.
M


1
4
5

..x
x

PCL 818
..x
2
The technology usage of vehicles active control is
becoming more and more common. Until now it has
been proved that active vehicles suspensions enables
eliminating the compromise among the load and
spring stiffness as well as the compromise among
roadholding and drive comfort, reduction of
uncomfortable body car behavior changes during
steering and surmount disturbances coming from the
road. In spite of this, the reasonable application
amount is too low. Almost all of the well-known
active vibration reduction solutions in vehicles are
based on the fluid or electro-fluid elements, mostly
electrohydraulic sets. Studies of the development and
implementation of new solutions of such systems are
currently under way. The development of
electropneumatic and electrohydraulic proportional
technique as well as microprocessor technique favor
the research program it as well. This technique gives
new possibility to develop new solutions in active
vibration reduction systems. This new hybrid
technology as a new tendency, joins together
pneumatic power transmission with the precision,
speed and flexibility of electronic control. Till now
application of vibration reduction systems are based
on proportional electrohydraulic valves. There is no
such systems using electropneumatic proportional
valves or servovalves. Draw up examples of
laboratory electropneumatic systems is an attempt to
new solutions of active vibrations reduction systems.
3
Fig. 11. Structure of pneumatic adaptive system

..x
Accelerometer
Load
M
Spring
Multi-Setting
Damper
..
x

Source of
vibration
Leveling
actuator
Accelerometer
Ground
Fig. 12. Physical model of adaptive system
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