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JOURNAL of AUTOMATION, MOBILE ROBOTICS& INTELLIGENT SYSTEMS
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CONTENTS
Angle Measuring by MEMS AccelerometersKamil Zidek, Miroslav Dovica, Ondrej Liska
Modeling of Circulatory System with CoronaryCirculation and the POLVAD Ventricular Assist DeviceAlicja Siewnicka, Bartlomiej Fajdek, Krzysztof
Janiszowski
PI Control of Laboratory Furnace for Annealing of
Amorphous Alloys CoresJerzy E. Kurek, Roman Szewczyk, Jacek Salach and Rafa
Kloda
Surface Topography Parameters Important in ContactMechanicsPawe Pawlus, Wiesaw Zelasko, Jacek Michalski
Behavior Based Co-ordination of a Troop ofVehicles Targeted to Different Goals in an UnknownEnvironmentSourish Sanyal, Ranjit Kumar Barai, Pranab Kumar
Chattopadhyay, and Rupendranath Chakrabarti
About Evaluation of Multivariate MeasurementsResultsZygmunt L. Warsza
Positioning and Control of Nozzles and Water Particlesin Decorative Water Curtain and Water ScreensMahdi Hajiheydari, Sasan Mohammadi
Stable Gait Synthesis and Analysis of a 12-degree ofFreedom Biped Robot in Sagittal and Frontal PlanesA.P. Sudheer, R. Vijayakumar, K.P. Mohandas
Intelligent Utilization of Waste of Electrical and
Electronic Equipment (WEEE) with Robotized ToolJakub Szalatkiewicz, Roman Szewczyk
Influence of PWM to Trajectory Accuracy in MobileRobot MotionRyszard Beniak, Tomasz Pyka
Robot for Monitoring Hazardous Environments as aMechatronic ProductLeszek Kasprzyczak, Stanislaw Trenczek, Maciej Cader
Analysis of Influence of Drive System Configurationsof a Four Wheeled Robot on its MobilityMaciej Trojnacki
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Articles 3
Angle Measuring by Mems Accelerometers
Kamil Zidek, Miroslav Dovica, Ondrej Liska
Submitted: 26thJune 2011; accepted 23rdSeptember 2011
Abstract:This article contains the description of MEMS acceler-
ometers implementation to device which is able to meas-
ure danger tilt. We can find out actual tilt in two basic
axes X and Y, from -90 to +90. Z Axis can only detect
fall of device or in vehicle system very fast downhill grade
during movement. For testing of the solution we select
small mobile robotic carriage. Hardware and software
part of solution are described. Because data from sensorare in raw format from analog MEMS Accelerometer, we
use free C# library with Kalman Filter implementation
to remove signal error. We can acquire next information
from sensor data for example movements trajectory in
X/Y axis (Cartesian system) and actual speed in all three
axes. Fast alarm is provided by RGB led diode (red color
is dangerous tilt.
Keywords: mems, Kalman filter, control.
1. Introduction to MEMS SensorsShortcut MEMS means micro electromechanical sys-
tems, marks mechanical and electromechanical construc-
tion of very small dimensions, and technologies used
for their preparation too. MEMS technology is based
on many tools and methods, which are used for creating
very small structure with dimension of couple microm-
eters. An important part of technology was takeover from
production of Integrated circuit (IC technology). Almost
all of these devices are based on a silicon substrate.
MEMS structures are realized from thin layer. There are
produced by photo lithographic methods. Some other
methods also exist, but they arent derivate straight from
technology of IC. There are three basic steps of operation
in MEMS technology for layer applying to silicon mate-
rial to substrate. Process of MEMS is usually a structured
sequence of this operation for creating real application.
Real device, then, contains central unit for processing of
data (microprocessor), and some other mechanical part
which compose unit named micro sensor too [4].
2. MEMS accelerometersOne of usual application for MEMS is sensor for
measuring of acceleration. This MEMS sensor is usually
named Accelerometer. They are divided to one-, two- or
three Axes. Measuring of acceleration is possible to use
in electronics and robotics for measuring: acceleration,deceleration, tilt, rotation, vibration, collision (crash) or
gravitation. Accelerometers are used in many devices,
special equipment and personal electrotechnics, for ex-
ample:
robots and automated devices with balancing func-
tion (segway),
controls with tilt measuring,
Auto pilots of aeroplanes,
car alarm systems,
car crash detection (used in airbag system),
monitoring of human movements (virtual reality
gloves).
Example of MEMS microstructure sensor magniedby microscope is displayed in Fig. 1 on the left side, right
is displayed measuring principle.
Fig. 1. MEMS sensor and principle of microstructures
Older accelerometers had big dimension and werevery expensive. The construction was created from stan-
dard metal parts, springs and PCB. That was reason why at
that time accelerometers were not used in electronics nor
robotics. This situation was changed thanks to progress in
MEMS technology. MEMS technologies reduce the price,
energetic consumption and dimensions. Main usability
is measuring of acceleration in three Axes: X forward/
backward, Y left/right, Z up/down. For mobile robot-
ics we can use this sensor for measuring acceleration or
deceleration by movement front and back, second Axis for
change direction of movement right or left, and third Axis
for fall detection of device. Second method of usability
is measuring of device tilt based on simple mathematics.
Figure 2 shows MEMS Axis conguration and principle of
tilt measuring with this sensor along y axis.
Fig. 2. MEMS sensor: axis conguration, principle of tilt
measuring
Output information from accelerometer is voltagewhich depends on movement or tilt of sensor in space.
A static characteristic of sensor is not exactly linear. For
common application we can this nonlinearity omit. The
acceleration is usually in MEMS application measured
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in G unit. Expression 1 g = 9,80665 m/s2 means, that
for every second, which passed the speed change will be
9,80665 meters for second. That is approximately speed
35.30394 km/h. The three Axis accelerometer can get
null G on every Axis, if is in ballistic trajectory known
as inertial or free fall. If we turn the accelerometer to
90 the output from one Axis will be exactly +1 g. In
this situation, accelerometer measuring gravitation Forceand can be in static position. Described characteristics for
analogue MEMS sensor is depicted in Fig. 3. [1]
Fig. 3. Characteristics of MEMS accelerometer sensor
with nonlinearity [2]
Example of block scheme sensor connection to user
application is displayed in the Fig. 4. Additional LCD
display connected straight to microcontroller enabling
testing of application without Computer necessity.
Fig. 4. Block scheme of complete application based on
MEMS accelerometer sensor
Sensitivity of measured values depends on sensor G
range (most precise we acquire if sensor is set to 1g). A
disadvantage is that we cannot measure the higher values
of acceleration. Common sensors are produced to 5g
and it is possible to switch between ranges during appli-
cation activity. Computations of tilt angles are realized
thru basic mathematics and goniometric function. V_out
is actual value of voltage; V_offset is voltage by 0 g. Sen-
sitivity of sensor is dened by technical documentation.
In math is necessary nd out positive or negative accel-
eration according to offset value. Datasheet math count
according this:
V_OUT=V_OFF+ V/g*1g*sin (1)
=arcsin(V_OUT- V_OFF)/(V/g) (2)
where:
V_OUT output of accelerometer (V) from ADCVOFF acceleration 0 g offset
V/g sensitivity
1 g world gravitation
tilt angle
Our values are counted according changed math,
because we dont know max and min values for actual
accelerometer. This math get extreme values during ac-
celerometer operation.
incr = 180 * (H_max - H_min) (3)
= incr * (H_nam - H_min) (4)
where:H_max, H_min initial value of accelerometer extreme
H_nam actual accelerometer value
3. Tested hardware platformIntroduced solution was tested on mobile com-
puter with open source application in programming
language C#. A prototype board contains Accelerom-
eter MMA7341L (analog) and accelerometer MMA7455
(digital) from Freescale. Currently there is active only
analog Accelerometer. Microcontroller computes values
of voltage for all Sensor Axis with help of three 10 bits
ADC converters. Data are coded to frames (9 bytes as
string $XXYYZZ1310). Every axis has value coded totwo bytes (Low and High 8 bites).
First method of accelerometer communication is only
for debug the application. Sensor is connected straight
to PC. Data are sent thru serial line to serial port of PC.
For implementation to mobile robot is used USART
interface without UART/RS232 Transducer and com-
municate straight with High Level control system based
on AT91 control board with Linux Embedded OS. These
serial data are transferred to TCP packet thru ser2net
command line application. Data are sent next thru wife
interface to C# application. Block diagram of testing de-
bug solution and mobile control system implementation
is displayed in Fig. 5. Figure 6 shows is rst prototype ofsensor without RS232/USB transducer.
Fig. 5. Block diagram of connection sensor to testing
mobile control system
Fig. 6. Hardware of accelerometer. 1 microcontroller;2 accelerometer MMA7341L (analog); 3 accelerome-
ter MMA7455 (digital); 4 voltage regulator LF33CDT;
5 I2C bus for LCD BO1602D; 6 USB connector; 7
RGB LED diode.
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4. Software platform implementationSoftware solution is based on an open source C# ap-
plication, which is currently implemented to mobile solu-
tion Graphical Interface of solution is displayed in Figure
7. Left is displayed 2D graphics, tilt in x-Axis, left 3D
graphics tilt in all three axis X,Y,Z. All values of real time
tilt are displayed in graphical interface in text edit boxes.
Basic value of danger tilt is set to value bigger than40. This value starts critical routine and block move-
ment of mobile device to actual direction. Danger tilt
value can be changed through graphical interface from
090.
Fig. 7. C# application, 3D tilt X,Y Axis and conguration
panel
5. Kalman flter implementation to smoothraw dataThe Kalman lter is an efcient recursive lter that
estimates the internal state of a linear dynamic system
from a series of noisy measurements. The Kalman lter
is used in sensor fusion and data fusion. Typically real
time systems produce multiple sequential measurementsrather than making a single measurement to obtain the
state of the system. These multiple measurements are
then combined mathematically to generate the systems
state at that time instant. Acquired data from MEMS sen-
sor are in raw form with many disturbances, white noise
etc. For testing solution we implement free C# Math.
NET Neodym (Signal Processing) [8] with Kalman lter
function to desktop application. Graphical interface pro-
vides settings of three basic values of Kalman ltering
r, T, q which is necessary for customizing lter for real
application.
r Measurement covariance
T Time interval between measurements
q Plant noise constant
Discrete Kalman Filter consists of two parts: predic-
tion and update.
prediction:
x(k|k-1) = F(k-1) * x(k-1|k-1) (5)
P(k|k-1) = F(k-1)*P(k-1|k-1)*F(k-1) + G(k-1)*Q(k-
1)*G(k-1) (6)
update:
S(k) = H(k)*P(k|k-1)*H(k) + R(k) (7)
K(k) = P(k|k-1)*H(k)*S^(-1)(k) (8)
P(k|k) = (I-K(k)*H(k))*P(k|k-1) (9)
x(k|k)=x(k|k-1)+K(k)*(z(k)-H(k)*x(k|k-1)) (10)
where:
S Measurement covariance,
K Kalman gain,
P Covariance update,
x State update,
F State transition matrix,
G Noise coupling matrix,
Q Plant noise covariance matrix,
H Measurement model,
R Covariance of measurements,I Matrix identify,
z Measurements of the system.
Figure 8 shows graph of actual values when MEMS
sensor is stand statically on the ground (blue plotline).
Black plotline shown ltered value cleared from errors
and noise from ADC transduction. There is used for test-
ing application only 1D Kalman lter for ltering only
actual acceleration value. Next extension will be imple-
mentation of 2D or 3D lter for all three Axes.
Fig. 8. Kalman ltering for raw accelerometer data in
static position
In the Fig. 9 is displayed data from accelerometer
during tilt to 90 to one side, next to static position andthen tilt to opposite side. Reference signal is red plotline.
Black line is Kalman ltered value.
Fig. 9. Dynamic data from MEMS Accelerometer sensor
with Kalman ltering
We experimentally nd out constants for kalman l-
ter with compromise of minimal displace during dynamic
and static operation: r = 30.0, T = 2.0, q = 0.1.
There is one problem in setup lter, when there is
very fast acceleration and deceleration. This situation can
occur when the real device fall or crash to the obstacle.We can avoid this situation by setting adequate value to
danger alarm tilt and implementation of obstacles sensor
detection (infra or ultrasonic) to mobile solution.
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6. ConclusionIntroduced measuring solution is implemented to
mobile device. Actual possibilities are measuring of tilt
device 90 to 90. You can select bound angle for start
indication of danger device tilt with next visual or sound
alarm. We can improve precision data from MEMS sen-
sor by using 12 bit ADC but then is necessary change themicrocontroller. Next idea can be change of Accelerom-
eter with digital I2C output, which removes error gener-
ated by ADC conversion. We are computing next values
from acquired data for example: trajectory, deceleration,
average and actual speed.
Next work on this solution will be an implementation
of Kalman lter to program of MCU rmware and dis-
play actual angle value and alarm on LCD display. This
remove testing mobile computer from actual solution and
application will be small and compact device. This re-
searched accelerometer device will be used in rehabilita-
tion system as safety circuit to monitor extreme accelera-
tion and deceleration for fast action to stop device.
AcknowledgementsThe research work is supported by the Project of the
Structural Funds of the EU, Operational Program Re-
search and Development, Measure 2.2 Transfer of knowl-
edge and technology from research and development into
practice: Title of the project: Research and development
of the intelligent non-conventional actuators based on ar-
tificial muscles ITMS code: 26220220103
AUTHORSKamil Zidek*, Ondrej Liska, Miroslav Dovica
Technical University of Kosice, Faculty of mechanical
engineering, Department of Biomedical engineering au-
tomation a measuring, Koice, 042 00, Slovakia, kamil.
[email protected], [email protected], miroslav.dovica@
tuke.sk
*Corressponding author
References[1] Tuck K., Tilt Sensing Using Linear
Accelerometers, Application Note, AN3461, Rev
2, 06/2007.http://www.freescale.com/les/sensors/
doc/app_note/AN3461.pdf
[2] Clifford M., Gomez L., Measuring Tilt with Low-g
Accelerometers, Application Note, AN3107, Rev
0, 05/2005,http://www.freescale.com/les/sensors/
doc/app_note/AN3107.pdf
[3] What is MEMS Technology? https://www.
memsnet.org/mems/what-is.html, Online, cit.
8.2.2010
[4] Johnson C. D., Accelerometer Principles,Process
Control Instrumentation Technology, Apr 14, 2009,0-13-441305-9.
[5] Zidek K: Open robotics control system, Technical
University Kosice, Online, www.orcs.sebsoft.com
[6] Saloky T., Pite J., Vojtko I., Control systems design
with reliability dened in advance. In:Proceedings
of the 1st IFAC Workshop on New Trends, Design
of Control Systems, Smolenice, Slovakia, 7th10th
September 1994, pp. 404407.
[7] Zidek K., MEMS Accelerometer SVN, Google
code, 2010. http://code.google.com/p/orcs/source/browse/#svn/MEMS_Accelerometer_SVN2
[8] Christoph Regg, Math.NET Neodym 2008 February
Release, v2008.2.2.364, http://www.mathdotnet.
c o m / d o w n l o a d s / N e o d y m - 2 0 0 8 - 2 - 2 - 3 6 4 .
ashx?From=NeodymCurrentRelease
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Articles 7
Modeling of Circulatory System With Coronary
Circulation and the POLVAD Ventricular Assist Device
Alicja Siewnicka, Bartlomiej Fajdek, Krzysztof Janiszowski
Submitted: 26thJune 2011; accepted 23rdSeptember 2011
Abstract:This paper presents an application of a numerical pack-
age for modeling and simulation of human circulatory
system. The model includes a coronary circulation and
the parallel heart assistance. The cases of the simulation
of the proper and the pathology circulation conditions,
such as left or right heart failure are shown. A descrip-
tion of the coronary circulation system is presented and
obtained coronary sinus occlusion simulation results areincluded. An implementation of the whole package as a
part of PExSim application is contained. The identifica-
tion experiment for the ventricular assist device has been
described and different methods of the artificial ventricle
modeling are presented. An example of use of a fuzzy
logic to presentation the dynamics of the POLVAD de-
vice is also included. Advantages of developed simula-
tion platform are discussed.
Keywords: PExSim, modeling of the circulatory system,
modeling of the coronary system, modeling of the ven-
tricular assist device, POLVAD.
1. Introduction
The continuous development of technology enabled
for the more common use of its achievements in medical
applications. Therefore, in recent years many scienticprojects were run to allow the use of technology to save
human life and health. One of the biggest bio-engineer-
ing projects in Poland is the Polish Articial Heart Pro-gram, whose aim is to develop of the construction and
control algorithms for the heart assist device. Application
of the developed solutions requires accurate testing. For
this purpose the modeling methods are widely used. In
recent years some different models of the human circula-
tory system were developed, both numerical and physical
ones, for example electrical or hydraulic [1, 2]. All of
them are widely used to reproduce hemodynamic condi-
tions of circulation system. Besides this, they can be ap-
plied for the testing of medical devices such as the blood
pumps or assist devices. For this purposes also models of
the same new devices are created. This way the possibil-
ity of simulating of the inuence of the heart support canbe obtained without carrying out experiments on living
organisms. This paper contains description of the devel-
oped circulatory model with the possibility of connec-
tion of the simply models of the extracorporeal ventricleassist device. In our case, the main aim of development
the mathematical description of circulatory system was
to create a research platform, for general purpose, which
could be easily adopted to solve different problems. For
example it could be used for determination and testing
of a Polish Ventricular Assist Device (POLVAD) control
and diagnostic algorithms.
2. Model of the circulatory system
The main part of the developed research platform
is the mathematical model of the circulatory system. It
is based on the description proposed by Ferrari [3] and
implemented as a part of the PExSim application [4].This software consists of predened function blocks thatrepresent basic mathematical and logic relationships, dy-
namic and static elements or support an input and out-
put operations. The possibility of easy extension with
user-written objects makes it a exible tool that can beused for emulation of complex dynamic system. For the
simple and clear presentation of circulation system and to
ensure the ability of easy parameters changes, each of the
blocks is responsible for reproducing behavior of differ-ent part of human circulatory system. They are grouped
in Human Circulatory System library, which consists
such elements and systems as:
left and right ventricle (LH, RH), systemic arterial circulation (SAC),
systemic venous circulation (SVC),
pulmonary arterial circulation (PAC),
pulmonary venous circulation ( PVC).
The model is based on a Starling`s law [3], which de-
nes the conditions for a balance between the lling andejection characteristics of the ventricle. The basic rela-
tion is a function that makes it possible to calculate theventricular pressure [3, 5]:
0 max max
( ) ( )
( ) ( ( ) ( )) ( ( ), ( ), ( ))v v v v v v
k Vv t j Vv t
P t V t V t E f V t V t V t
A e B e C
=
+ + +
(1)
where: Pv(t) the ventricle pressure, V
v(t) the ventricle
volume, Vv0
the ventricle rest volume, Ev(t) the nor-
malized elastanse function, Emax
the maximum value
of the elastance (end-systolic), max( ( ), ( ), ( ))v v vf V t V t V t the
correction function dependent on the ventricle volume
and ejection rate, and A, B, C, j, k constant parameters.The values of the flows are calculated as the ratio of
the proper pressure difference and the vascular resist-
ance. The rest of the pressures values arecalculated asthe solution of the differential equation which defines the
pressure derivative as the quotient of the sum of flowsand the capacity of the system. In the PExSim modeling
platform, the simple model of ventricular assist device
(VAD), based on the ventricle activity description, was
added. The parameters values were adopted to ensure
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work consistent with the theoretical data. The model ofthe ventricular assist device is included into the system
between the atrium and the arterial system, creating a by-
pass of the model of the natural ventricle. The mathemat-
ical equations in the circulation blocks were respectivelyadopted to join the parallel ventricle support. The proper
connection of all elements creates a complete model ofcirculatory system with the external assist device (Fig. 1).
Fig. 1. The circulatory model in PExSim application with
the parallel connection of ventricular assist device
A full description of structure and function of the
blocks one can nd in [6]. As a result of this work wereceived a useful tool, that yields an investigation of the
proper and pathological circulation conditions and the in-
uence of the ventricle assistance for the hemodynamicconditions. For example, Fig. 2 presents the inuence ofthe left heart support on the atrium (P
la) and arterial (P
as)
pressures.
Fig. 2. The modeled waveforms of the atrium (Pla) and ar-
terial (Pas) pressures for normal, pathological and patho-
logical with left ventricle assistance (LVAD) conditions
In the ventricular failure state the blood accumulates
in atrium causing the rise of the pressure volume. At the
same time the pressure in arteries is low due to insuf-cient stroke volume of the heart. In simulation we canobserve the reduction of the atrium pressure value and
increase of the arterial pressure as a result of left ventricle
support which conrms medical observations.
3. The coronary circulation model
The system described above did not contain the coro-
nary circulation model. As the extension of functionality
of the developed platform, the coronary circulation mod-
el was developed and included. This way a possibility of
simulating the caval occlusion was achieved. The applied
mathematical description is the combination of the mod-els proposed in [7] and [8]. The schematic representation
of this, as an analogy to electric circuit diagram, is shown
in Fig. 3. It was added to the mentioned PExSim applica-
tion as a new CC (Coronary Circulation) element.
The driving pressure for the coronary circulation
(Psqz
) is taken as a proportional to left ventricle pressure.According to this, the input values for the model are:
pressure values in aorta, left ventricle and right atrium
(Pil, P
lv, P
ra). The others pressures are obtained by the
equations:
( ) ( ) ( )lca il lca art P t P t R Q t= (2)
( )( ) ( )lcxlcx sqz
lcx
V tP t P t
C= +
(3)
( )( ) ( )ladlad sqz
lad
V tP t P t
C= +
(4)
0
( )( ) exp[ ( ( ) )]venven ven ven
ven
V tP t V t V
=
(5)
where:
Plca
the pressure in bifurcation of coronary arteries, Pil
the aortic pressure, Qart
the coronary arterial flow, Plcx
and Plad
the coronary capillaries pressures (lad left
anterior descending artery, lcx
left circumflex artery),
Rlca
the arterial resistance, Clcx
and Clad
the coronary
capillaries compliances, Vlcx
and Vlad
the coronary cap-
illaries volumes, Vven
the coronary veins volume, ven
, ,V
ven0 the parameters for venous compliance.
The coronary arterial ow value (Qart
) is obtained as a
sum of the capillaries input ows (Qlcx1
, Qlad1
). Input and
output ows are calculated based on pressures differenceand blood vessels volumes as follows:
ows in direction to the coronary capilares system
(PlcaPlcx, PlcaPlad, PvenPlcx, PvenPlad, PraPven):
1
1
( ) ( )( ) lca lcxlcx
lcx
P t P tQ t
R
=
(6)
Fig. 3. The electric analogue of the coronary circulation
system
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1
1
( ) ( )( ) lca lad lad
lad
P t P tQ t
R
=
(7)
2
2
( ) ( )( ) lcx venlcx
lcx
P t P tQ t
R
=
(8)
2
2
( ) ( )
( ) lad ven
ladlad
P t P t
Q t R
=
(9)
( ) ( )( ) ven raven
ven
P t P tQ t
R
=
(10)
where:
Qlcx1
and Qlad1
the capillaries input flows, Rlcx1
and Rlad1
the capillary resistances, Qlcx2
and Qlad2
the capillary
output flows, Rlcx2
and Rlad2
the capillary resistances,
Qven
the flow supplying the right atrium, Pra the right
atrium pressure, Rven
the coronary venous resistance.
ows in direction from the coronary capilares sys-tem (P
lca
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Determination of the coefcients is performed mostlyin an indirect way of parametric identication method.On the base of sampled data the discrete transfer func-
tions )( zGQoutVj are determined in such a way that the
modeled signal, )(~
kQout , where is the sampling step,should be as closely as possible to the measured one. We
get a description consisting of a vector of inputs to the
model v(k
), containing the signals measured in the re-spective moments of time, and the vector of unknowncoefcients of the investigated transfer functions.
( ) ( )Q k v k out
=
(22)
Vector of transfer function coefcients can be esti-mated using various methods, for example, by the small-
est sum of squared errors (LS). The dynamic model de-
termined in this way usually accurately reproduces the
dynamics of the process but is very local. This means
that the change of supply parameters makes it necessaryto re-selection transfer function coefcients. That why,
the fuzzy modeling is very useful method. For the samestructure of the system (22) vector of coefcients isdependent on some fuzzy variables, dened by member-ship functions. For example, separate models can be de-
termined for the value of low, medium and high value
of the fuzzy variable. The model is the weighted sum of
the partial models and the corresponding membership
function values. General fuzzy model can be determined
as a linear combination of several local models set for
the different intervals of membership function. Estima-
tion algorithms of partial models coefcient vectors aremore complex and require the simultaneous calculation
of the vectors for all the partial models. The basic dif-
culty is also the designation of the proper shape andnumber of membership functions. In our case, in order
to obtain a general description of the dynamic properties
of the device, as a fuzzyfying variables were used two
signals: output ow value Qout
and a set pressure differ-
ent P. The rst signal determines different valve states(Fig. 9a): positive ow (ejection, valve open), backwardow (closing of the valve) and the closed valve phase (noow). For the second variable the membership functionwas divided for three areas (Fig. 9b): low, medium and
high values of pressure.
Fig. 9 The membership functions for the fuzzy variables:
a) output ow value, b) pressure difference
As a result of the presented fuzzy modeling method
the nine partial models had to be determined. The mea-
surements were carried out for ve values of pressuredifference. For the estimation of the models the measure-
ment data for maximum, medium and low pressure dif-
ferential were used. To verify the obtained model, the re-
maining series were used. The sample waveforms of the
modeled and measured output ow are shown in Fig. 10.
Fig. 10 Sample measured and modeled ow waveform
for the verication data set
The estimated parametric fuzzy model reproduces
output ow value relatively well both, for the data onwhich he was appointed and the verication series. Ityields a good representation of the dynamics of the
POLVAD articial ventricle. The extended description ofthe fuzzy modeling applied to determine the assist device
model one can nd in [11].
5. Summary
The paper presents a new numerical library for mode-ling and simulation of human circulatory system with the
extension of coronary circulation model and possibility
of the parallel assist device connection. The main result
of the coronary model addition was to allow simulation
and verification of the influence of the left ventricle as-
sistance on the coronary flow conditions. The whole li-
brary was implemented as a part of PExSim application.
Modular construction of the plugin ensures flexibility
because it can be easily modified to solve different prob-
lems within modeling and support of the human circula-
tory system. The modeling methods of the ventricular as-
sist device were presented. We received an approximate
representation of the output flow value dependent on the
supply pressure. Method based on fuzzy modeling made
it possible to achieve better results. However, in the caseof even small modification of the device construction,
the measurements and the whole modeling procedure
will have to be carried again. Also, we do not receive the
direct dependence of the output signal from the power
supply parameters. Work on the determination of a bettermodel of the mechanical construction of the ventricular
assist device is still carried out. However, as a result ofpresented work we have the useful tool, which gives theopportunity to study functions of individual components
of the human circulatory system as well as the system aswhole. It enables a simulation of the proper and the pa-
thology circulation conditions, such as left or right heart
failure. Implemented model of the ventricle assist device
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gives the opportunity for modeling the influence of the
heart assistance on the hemodynamic co
Acknowledgements
This work was partially supported by the NationalCentre for Research and Development (NCBiR) in Po-
land under Project Development of metrology, informa-tion and telecommunications technology for the prosthet-ic heart as part of the Polish Artificial Heart Program.
AUTHORSAlicja Siewnicka*, Bartomiej Fajdek, Krzysztof Jani-
szowski Warsaw University of Technology, Faculty of
Mechatronics,Institute of Automatic Control and Robotics,
ul. w. Andrzeja Boboli 8, 02-525, Poland,
E-mail: [email protected], b.fajdek@mchtr.
pw.edu.pl, [email protected]
*Corresponding author
References
[1] M. Korda, S. Leonardis, J. Trontelj, An electricalmodel of blood circulation, Medical and Biologi-cal Engineering and Computing, vol. 6, 1968, pp.449451.
[2] M. Sharp, R. Dharmalingham, Development ofa hydraulic model of the human systemic circula-
tion,ASAIO J., vol. 45, 1999, pp. 535540.[3] G. Ferrari, Study of Artero-ventricular Interaction
as an Approach to the Analysis of Circulatory Phys-
iopathology: Methods, Tools and Applications,Ph. D. dissertation, Consiglio Nazionale delle Ri-cerche, Rome, Italy.
[4] K. Janiszowski, P. Wnuk, A novel approach to theproblem of the investigation of complex dynamic
systems in an industrial environment,MaintenanceProblems, vol. 4, 2006, pp. 1736.
[5] De Lazzari C., Darowski M., Ferrari G., ClementeF., Guaragno M., Computer simulation of haemo-
dynamic parameters changes with left ventricle as-sist device and mechanical ventilation, Computersin Biology and Medicine, vol. 30, 2000, pp. 5569.
[6] B. Fajdek, A. Golnik, Modelling and simulation ofhuman circulatory system.,Methods and Models in
Automation and Robotics (MMAR), vol. 15, 2010,
pp. 399404.
[7] W. Shreiner, F. Neumann, W. Mohl, The RoleOf Intramyocardial Pressure During Coronary Si-
nus Interventions: A Computer Model Study,IEEE Transactions on Biomedical Engineering, vol.
37, 1990, pp. 956967.[8] K. M. Lim, I. S. Kim, S. W. Choi, B. G. Min, Y.
S Won, H. Y. Kim, E. B. Shim, Computationalanalysis of the effect of the type of LVAD ow oncoronary perfusion and ventricular afterload, The
Journal of Physiological Sciences, vol. 59, 2009,
pp. 307316.[9] A. Siewnicka, B. Fajdek, K. Janiszowski, Appli-
cation of a PExSim for modeling a POLVAD arti-
cial heart and the human circulatory system withleft ventricle assistance,Polish Journal of Medical
Physics and Engineering, vol. 16, no. 2, 2010, pp.107124.
[10] M. Stachura, Application of the PExSim packagein identication of multi-dimensional model of a
waste water treatment plant,Pomiary AutomatykaKontrola, vol. 55, no. 3, 2009, pp. 156159.
[11] K. Janiszowski, Fuzzy identication of dynamicsystems used for modeling of hearth assisting
device POLVAD,Pomiary Automatyka Robotyka,11/2010, pp. 9095.
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Articles 13
PI Control of Laboratory Furnace for Annealing
of Amorphous Alloys Cores
Jerzy E. Kurek, Roman Szewczyk, Jacek Salach, Rafal Kloda
Submitted: 29th May 2012; accepted: 21stJune 2012
Abstract:There are presented theoretical and practical aspects of
automatic control of resistive furnace for thermal anneal-
ing of magnetic cores made of amorphous alloys. Process
of annealing requires specific conditions both from the
point of view of temperature and its changes. Solutions
presented in the paper create possibility for low value of
error as well as fast achievement of set value.
Keywords:PI controller, resistive furnace, temperature
control.
1. Introduction
New soft magnetic materials amorphous alloys based
on iron, nickel and cobalt gives new possibilities for de-
sign of inductive components [1], magnetic field sensors
[2], magneto-mechatronic sensors [3], and heat transpor-
tation devices [4]. However, production of amorphous
alloys cores requires precise thermal relaxation (cores
annealing) [5]. This process is usually realized in 1 hour
in argon protective atmosphere in order to avoid quickcorrosion of cores surface. The relaxation improves cores
magnetic permeability and reduces its coercive force.
Thermal relaxation in amorphous alloys, if performed
correctly, enables fabrication cores with relative perme-
ability magnitude greater than 2106. This makes the
amorphous alloys one of the best magnetic materials,
with highest magnetic permeability.
This paper describes a control system for resistive
furnace for annealing of amorphous alloys cores in the
laboratory of Institute of Metrology and Biomedical En-
gineering, Warsaw University of Technology.
2. The furnace, measurement system andcontrol system equipment
The thermal relaxation process of cores is realized in a
small laboratory resistive furnace which mass is approxi-
mately 3 kg. The furnace has canal winding, installed
in chamotte corpus covered by thermal isolation with
mineral wool. Inside the furnace there is a long quartz
pipe with 40 mm diameter, which is filled by argon with
pressure slightly higher than atmosphere pressure during
the relaxation stage. Argon atmosphere protects the core
during relaxation process.
The relaxation process begins with heating the furnace
to the relaxation temperature. Then, there is inserted cap-sule with room temperature having inside the annealed
core and it is heated in the furnace during required time
in the relaxation temperature. The temperature of amor-
phous alloys cores relaxation is equal to 345C and the
relaxation time is equal to 60 minutes. When the relax-
ation is finished the capsule is taken out of the furnace
and it is cooled inside the cold part of the quartz pipe.
Therefore, also cooling in argon protective atmosphere
is performed.
The controlled output signals are the furnace tempera-
ture measured by thermocouple type K and then the cap-
sule temperature measured by thermocouple type J. Ther-
mocouples are connected with temperature transducersAR-580 of Apar firm. Temperature measured range is
from 0 to 500C and transducers output range is voltage
from 0 to 10 V. Both sensors have linear characteristics.
The furnace is powered by pulse wide modulation
power controller EJ1P50E of Carlo Gavazzi firm. Con-
trol output of the controller is voltage from 0 to 10 V and
full pulse control period is 3 sec.
The furnace, temperature transducers and power con-
troller are connected with PC computer by data acquisi-
tion card NI-USB-6361 of National Instruments firm.
The control of the furnace temperature is realized by
computer controller implemented on the connected PC
computer. The controller program was prepared using theLabView software and implementing the PI controller.
Block diagram of the laboratory furnace for annealing
of amorphous alloys cores with measurement and control
system is presented in Fig. 1, and the furnace laboratory
stand is shown in Fig. 2, where 1 capsule with core,
2 furnace, 3 quartz pipe, 4 temperature transducer,
5 argon inlet, 6 data acquisition card and 7 PWM
power controller.
PCComputer
Transducer
AR-580
Transducer
AR-580
Thermocouple
type J
Thermocouple
type K
PWM Power
ControllerResistive
Furnace
Annealed
CoreNI Card
USB-6361
Fig. 1. Block diagram of the installation for annealing
of amorphous magnetic cores
Fig. 2. Laboratory stand of furnace for cores annealing
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3. Requirements of the control process
As mentioned before, the controlled process consists
of (i) heating stage of the empty furnace and (ii) core re-
laxation stage in the relaxation temperature. The control
input is a voltage of power controller and the output sig-
nal is in the first stage temperature inside the quartz pipe
and in the second stage the annealed core temperature.
For the furnace heating stage it is only required rela-tively short heating time and limitation of control input
magnitude and change speed because of furnace proper-
ties, step response time for the furnace is approximately
3 hours.
Then, for the annealing stage it is required
1. annealing temperature equal to 345C,
2. annealing temperature errors should be less than
5C,
3. time of core heating from temperature 320C
to 345C no longer than 15 min,
4. no overshoots in the core heating stage to 345 C.
The third requirement is rather important since usu-
ally annealing process starts in temperature 320C and ifcore stay too long in the annealing temperature but less
than required annealing temperature its properties are
different to the required ones.
4. Identication of control plant
Model of the furnace has been calculated based on step
response of the furnace for change of voltage of power
controller from 0 to 0.7 V in the form
0( )
1
=+
T sG s e
Ts (1)
where kis model gain, Ttime constant and T0time delay.In the identification we have found the following val-
ues of the parameters
k= 500 [C/V], T= 3450 [sec], T0= 840 [sec]
In Fig. 3 there are presented response of the furnace
and response of the model. It is easy to see that the calcu-
lated model is quite good.
It should be however noted that because relatively big
mass of the capsule with core (0.25 kg) with respect to
mass of the furnace (3 kg) insertion of the core in room
temperature approximately 22C into warm furnace with
temperature 345C really inuent temperature of the fur-
nace.
Fig. 3. Furnace step response: measured temperature
and model response
5. Control algorithm
Accordingly to the requirements indicated in Section
3, two stages of the process were identied: heating stage
and annealing stage. Considering step response time for
the furnace (which is approximately 3 hours) two control
algorithms were proposed:
1. linear control of the furnace heating stage, and
2. linear control for annealing of the core with nonlin-ear phase after insertion of capsule with core into the
furnace.
In both cases we have used PI linear controller
+=
sTksR
I
P
11)(
(2)
Settings of the controller were chosen based on the
calculated model (1) of the furnace. Calculating the set-
tings in such a way that overshooting of the process is
equal to zero, =0, one obtains [6]
0
0
0.6 0.0049, 0.8 0.5 2397 (s)= = = + =P I
Tk T T T
kT
Next, we have modeled control system [Fig. 4] with PI
controller and calculated settings.
Furnace
PI Controller+
+ +
Tz
u Tr
Fig. 4. Block diagram of furnace temperature control
system, T furnace temperature, u control input volt-
age, Tr reference temperature, z disturbance
Unfortunately, in the contradiction to setting base we
have obtained small overshooting for step change refer-
ence temperature Tr, Fig. 5. However, overshooting for
the disturbance which modeled insertion of capsule with
core into the furnace was quite small. Therefore, we have
decided to apply for control of the furnace the PI control-
ler with calculated settings.
0 5000 10000 15000 20000 25000 300000
100
200
300
400
500
t (s)
T(oC)
Tr
T
0 5000 10000 15000 20000 25000 30000-0.5
0
0.5
1.0
1.5
2.0
2.5
t (s)
U(
V)
z
u
Fig. 5. Furnace model control response with PI controller
PI controller has been used for control of the furnace
and core temperature for (i) shortening of the furnace heat-
ing and (ii) control of the furnace heating after insertion of
0
50
100
150
200
250
300
350
400
0 5000 10000 15000
T ( oC)
t (s)
model
measurements
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the capsule with core and (iii) control of the core tempera-
ture in the annealing process.
The nonlinear phase of control algorithm after insertion
of the capsule with core into furnace was as follows:
1. before insertion of the capsule with core automatic con-
trol was changed into manual control with constant
control input voltage,
2. after insertion of the capsule into furnace there was add-ed one triangle control input impulse with magnitude
0.6 V and time 600 sec (10 min) to constant control in-
put; the triangle input was designed based on practical
experiments and in the control process it was automati-
cally generated by the controller software LabView,
3. after the triangle impulse the control was changed from
manual mode into automatic mode with PI controller
with calculated settings but also with annealing core
temperature as the controlled output signal.
In the control we do not use PID controller because in
the control system we have quick measurement distur-
bances which generate quite big control input changes cal-
culated by PID controller since derivative action D of PIDcontroller implemented in the software has big dynamic
derivative gain.
6. Experimental results
Designed control system has been applied for control of
the furnace for annealing of cores in the Institute of Me-
trology and Biomedical Engineering of Warsaw Univer-
sity Technology. In Fig. 6 there are presented temperature
of the furnace, temperature of the core and control input
voltage obtained by PI controller and triangle impulse in
the insertion of capsule with core into the furnace. Con-
troller settings were as we calculated before.
It is interesting to note that the core temperature is lower
than the furnace temperature in the annealing process.
In the annealing process we have obtained maximal core
temperature error 2C. The core heating time from 320C
to 345C was 12 min, less than it was maximal allowed
value 15 min and annealing time in temperature equal to
345C was 60 min.
7. Concluding remarks
Proposed PI control system allows conducting an-
nealing process according to requirements quickly and
in the required temperature without overshooting and
without presence of operator, operator action was only
required for short time in the moment of insertion of cap-
sule with core into furnace.
In laboratory conditions the proposed control system
has shorten the annealing time about 70% comparing
with annealing process in the manual mode and also im-
proved quality of the annealing because less annealing
temperature errors. Moreover, the annealing was auto-
matic and no operator assistance was required.Presently we work on improving the automatic anneal-
ing process and shortening assistance of the operator.
The research on magnetic cores was founded in 2010-
2012 as a research project.
AUTHORS
Jerzy E. Kurek* Institute of Automatic Control and
Robotics, Warsaw University of Technology, Warsaw,
Poland, [email protected].
Roman Szewczyk Industrial Research Institute for
Automation and Measurements, Warsaw, PL 02-486, Po-
land.Jacek Salach and Rafal Kloda- Institute of Metrol-
ogy and Biomedical Engineering, Warsaw University of
Technology, Warsaw, Poland.
*Corresponding author
References
[1] OHandley R., Modern magnetic materials prin-
ciples and applications. John Wiley & Sons, 2000.
[2] Ripka P., Magnetic Sensors and Magnetometers.
Artech, Boston, 2001.
[3] Bienkowski A., Szewczyk R., The possibility of
utilizing the high permeability magnetic materials in
construction of magnetoelastic stress and force sen-
sors, Sensors and ActuatorsA113, 2004, p. 270.
[4] Kolano-Burian A., Kowalczyk M., Kolano R.,
Szymczak R., Szymczak H., Polak M., Magnetoca-
loric effect in Fe-Cr-Cu-Nb-Si-B amorphous materi-
als.J. Alloys Comp.vol. 479, 2009, p. 71.
[5] Biekowski A., Szewczyk R., Salach J., Kolano R.,
Kolano-Burian A., Influence of thermo-magnetic
treatment on magnetoelastic properties of Fe81S-
i4B14 amorphous alloy,Journal of Physics Con-
ference Series 144, 2009, 012070. (http://iopscience.iop.org/1742-6596/144/1/012070)
[6] Puaczewski J., Ukady regulacji z regulatorami typu
PID, Poradnik Inyniera Automatyka, WNT, War-
saw 1973, pp. 571635. (in Polish)
Fig. 6. Heating and annealing process with PI controller
and triangle impulse control input: a) furnace and core
temperature b) control input voltage
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Articles16
Surface Topography Parameters Important in Contact
Mechanics
Pawel Pawlus, Wieslaw Zelasko, Jacek Michalski
Submitted: 2012; accepted: 2012
Abstract:The random surface models are important to many sta-
tistical peak-based contact models of rough surfaces.
Statistics of 3D surface topographies and 2D profiles
are compared and their interrelationship examined for
generated and measured common random engineering
surfaces. The applicability of the spectral moments ap-
proach to random surface specification is checked. Pa-
rameters important in contact mechanics, like summitdensity, summit curvature and summit height obtained by
their definitions and predicted by the spectral moment
approach, as well as calculated directly from profiles are
compared. Also, the values of plasticity index are com-
puted using various methods. Good agreement is found
between theory and measurement.
Keywords: surface topography, contact mechanics,
spectral moments.
1. IntroductionAll engineering surfaces are rough and their descrip-
tion is important to the study of many interfacial phe-
nomena, such as friction, wear, electric al and thermal
contact resistance, etc. Surface topography is recognized
as being an important factor in determining the nature
and extent of contact. Because surfaces are rough, the
true area of contact, which is much smaller than the
nominal area of contact must support very large pressure.
Two types of parameters were advocated for contact and
wear prediction: parameters based on peak (summits)
and parameters based on plots of material ratio.
The pioneering contribution to this field was made by
Greenwood and Williamson [1], who developed a basic
contact model (GW model) of isotropic surface. Chang
et al.[2] put forward an elastic-plastic contact model for
rough surfaces on the basis of volume conservation of
plastically deformed asperities. These models have been
extended by many researchers. Parameters connected
with peak as peak radius, peak height and peak curvature
were used. These parameters are based on a 2D profile.
However the statistic of the areal (3D) surface and the
statistics of a 2D profile of the surface are not the same.
It is necessary to distinguish a peak on a profile from
a summit on the surface. A detailed comparison was made
by statistical approach. Rough surfaces were modeled as
two dimensional, isotropic, Gaussian random surface byNayak [3]. Dependencies between profile spectral mo-
ments and parameters important in contact mechanics
were also developed by Bushet al.[4]. They were pre-
sented by McCool [5]. Surface and profile measurement
and their resultant statistics were compared and their in-
terrelationship examined for several common engineer-
ing surfaces [6]. Good agreement was found between
theory and measurements over a large range of sampling
intervals. Yu and Polycarpou [7] compared the summit
density and summit radius obtained from numerically
generated isotropic Gaussian surfaces.
2. Connections between summit parametersand spectral momentsSpectral moments m
0, m
2and m
4can be obtained from
profiles. They are equivalent to the mean square height,
rms. slope square and second derivative of profile.
The areal (3D) surface summit density is given by [5]:
4
2
1( )
6 3=
p
mSpd
m. (1)
The mean summit curvature averaged over all summit
heights is [5]:
48
3 =
mSpc . (2)
The variance of the summit height is [5]:
2
0
0.8968(1 )= s
as m . (3)
The distance between the mean of the summit height
distribution and the surface mean plane is [5]:
04 mys =
, (4)
where:0 4
2
2
=am m
m. (5)
3. Calculation procedureIsotropic surfaces of Gaussian ordinate distribution
were generated, using the procedure developed by Wu [8].
Each surface of this type is characterized by correlation
distance (in which the autocorrelation function decays to
0.1 value) and standard deviation of height. In addition,
some measured isotropic Gaussian surface topographies
were analyzed. The values of their texture parameterStrwere higher than 0.8. These surfaces were measured by
stylus 3D Talyscan 150 equipment with nominal radius
of tip 2 m. The initial numbers of the measured points
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were between 401 x 401 to 601 x 601. The sampling in-
tervals were 5 and 10 micrometers. However in order to
decrease correlation length sampling interval sometimes
increased and the number of points was reduced. For
each of measured surfaces, the form was eliminated by
a polynomial of the 2nddegree. Digital filters were not
used. For each surface, parameter connected with sum-
mits were calculated. For areal measurements, the meanradius of each summitRwas computed as reciprocal of
mean arithmetic average curvature in orthogonal direc-
tions. Summit curvature was calculated on the basis of
three-point formula [9]. The summit identification is
a real problem. Usually surface point is a summit if its
ordinate was higher than ordinates of four or eight near-
est neighbors (see Figure 1). The second possibility was
accepted by the present authors. This criterion was based
on works of Greenwood [10] and Sayles and Thomas [6]
as well as our previous research.
Areal density of asperitiesSpd, standard deviation of
summits heights sand distance between the mean of as-
perity heights and that of surface ordinatesys(see Figure2) were obtained from their definitions directly from ar-
eal surfaces. The parameters characterized summits were
also determined on the basis of 2D profiles. Sets of paral-
lel profiles were obtained from measured surfaces and
average profile spectral moments m0, m
2 and m
4 were
calculated according to procedure presented in paper
[11]. Parameters characterized summits were obtained
using equations (1) (5).
It is also possible to estimate parameters characterizing
summits from profile peaks analysis (summits are local
maxima on the surface, as distinct from peaks, which are
local maxima on a profile). Therefore peak density, aver-
age peak curvature, standard deviation of peak heightsand distance between the mean of line of peak heights
and mean profile line were calculated for set of parallel
profiles and mean values were taken into consideration.
As recommended by Nayak [3] sum-
mit density was computed as square
of peak density multiplied by 1.2.
The well-known plasticity index
postulated by Greenwood and Wil-
liamson (GW) [1] in 1966 is wide-
ly applied in studying the contact of
rough surfaces. The basic assump-
tions were adopted in GW model:
asperities are spherical near their
peaks (summits),
there is no interaction between as-
perities,
Fig. 1. Various summit identications
Fig. 3. Modeled isotropic surface topography (a), prole from this surface (b)
a) b)
Fig. 2. Scheme of contact of two rough surfaces
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only the asperities deform during contact,
all peaks (summits) have the same radiusR.
The contact between two rough surfaces is modeled
by contact of single rough surface with a smooth plane.
Figure 2 shows the geometry model of contacting rough
surfaces, zdenotes the height of asperity, d separation
of the surfaces measured from the summits mean plane,
but his the separation of the surfaces based on surfaceheights (ordinates). The plasticity index postulated by
Greenwood and Williamson was defined as:
'0.5( )=
sy s
E
H R, (6)
whereHis the hardness of the softer contacting materi-
als, and
2 2' 11 2
1 2
1 1( )
= +
n n
EE E
(7)
Eiand
i(i = 1, 2) are Youngs moduli and Poissons ra-
tios for the two contacting elements.
In this work the plasticity index wascalculated for various methods of com-
puting contact parameters. The following
material properties were selected (con-
tact of steel-on-steel elements)E1=E
2=
2.07 x 105MPa, Brinell hardnessH= 200
(1960 MPa), 1=
2= 0.29. These proper-
ties were also used in paper [2].
Figure 3 shows example modeled sur-
face M1 of correlation = 0.85 between
neighboring points and profile from this
surface.
4. Results and discussionThe results of calculations of selected
surface topographies are listed in Table 1.
Index smeans calculation of contact pa-
rameters from the areal (3D) surface, m
using profile spectral moment andp
basing on the profile peaks analysis. Sur-
faces 1-5 were modeled, 6-10 measured.
means average value of correlation
between neighboring points (ordinates)
obtained from 6 profiles.
It is evident from the analysis of the
simulated and measured surfaces that
high values of the parameter (not small-
er than 0.85) correspond to large errors
of summit density Spdprediction using
spectral moment approach. The errors
were bigger than 100%; summit density
was overestimated. So the error in ob-
taining summit density on the basis of
profile measurement can be large. For
values between 0.25 and 0.77 the devia-
tions of summit density was smaller than
10%; for non-correlated neighboring
points ( between 0.1 and 0.12) applica-
tion of spectral moments method causedunderestimation of summit density
errors were between 15 and 18%. For
high correlation between neighboring or-
dinates the errors of summit density was also high based
on profile peaks analysis. For the other cases application
of this method led to overestimation of density; howev-
er it was found that summit density should be equal to
square of peak density on profile, in this case the error of
summit density was smaller than 6% for the coefficient
not higher than 0.77.
Mean radius of summit curvature was accurately pre-dicted by spectral moments approach, independently on
the value. The errors were smaller than 10%, only for
highly correlated points case ( = 0.99) deviation was
24%. Estimated value was usually smaller than that
obtained by definition. However the analysis of profile
peaks led to overestimation of mean summit radius; the
errors were in the range: 1635%.
Relative difference between standard deviation of
summit height was usually smaller than 5% but not
higher than 10% when spectral moments approach was
used. Higher errors occurred for measured surface topog-
Table 1. Surface topography parameters and plasticity indices calculated using
different methods
Surface , m s, m Spd, 1/m2 R, m y
s, m
M1s
M1m
M1p
0.85 0.176
0.174
0.174
0.158
0.164
0.169
0.00104
0.00211
0.00231
157.6
161.5
208.3
0.17
0.15
0.07
1.85
1.84
1.64
M2s
M2m
M2p
0.4 0.176
0.174
0.174
0.132
0.137
0.152
0.000191
0.000187
0.000235
1024.5
976.6
1351.4
0.25
0.25
0.12
0.65
0.68
0.61
M3sM3
m
M3p
0.12 0.1760.174
0.174
0.1230.13
0.142
0.0000610.000052
0.000077
3076.52816.9
4000.1
0.2540.269
0.14
0.360.39
0.34
M4s
M4m
M4p
0.91 0.93
0.91
0.91
0.82
0.87
0.91
0.000232
0.00047
0.000531
177.3
176.8
232.5
0.70
0.56
0.28
3.92
4.04
3.61
M5s
M5m
M5p
0.65 0.93
0.91
0.91
0.81
0.83
0.87
0.000063
0.000061
0.000074
714.2
713.9
952.4
0.95
1.06
0.48
1.94
1.92
1.74
M6s
M6m
M6p
0.5 0.66
0.64
0.64
0.46
0.5
0.51
0.000046
0.000042
0.000052
1383.1
1220.2
1724.0
0.79
0.89
0.45
0.99
1.18
0.99
M7s
M7m
M7p
0.25 0.82
0.8
0.8
0.49
0.56
0.61
0.000026
0.000024
0.000029
1666.7
1538.4
2173.9
1.1
1.24
0.64
0.99
1.13
0.97
M8s
M8m
M8p
0.99 0.57
0.56
0.56
0.56
0.56
0.56
0.00038
0.00081
0.0007
436.7
333.5
512.8
0.134
0.15
0.061
2.07
2.44
1.91
M9s
M9m
M9p
0.77 2.28
2.23
2.23
1.78
1.81
1.99
0.000019
0.0000199
0.000022
714.2
746.3
833.3
3.17
3.07
1.75
2.88
2.84
2.82
M10sM10
m
M10p
0.1 1.07
1.05
1.05
0.64
0.69
0.79
0.000017
0.000014
0.000019
1897.5
1724.13
2380.9
1.45
1.72
0.83
1.03
1.15
1.05
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raphies. When the sparameter was calculated directly
from profile based on its peaks, the deviations were usu-
ally higher (up to 24%). Estimation of summit standard
deviation height on the basis of profile analysis using
2 applied methods led usually to overestimation of s.
For highly correlated points ( = 0.99) no difference was
found after application of three analysed methods. In this
case standards deviation of summit height was equal orvery close to standard deviation of ordinates.
When spectral moments method was used, the pre-
dicted ysdistance was higher than value obtained from
the analysis of simulated and measured surfaces for cor-
relation smaller than 0.77, however for larger values
it was usually smaller (except for M8 surface) but dif-
ferences were not higher than 20%. Calculation of the
ysparameter directly from the profile peaks caused its
underestimation (1.7-2.5 times).
Generally when spectral moments were used, good
agreement was found between the theory and the results
of the areal (3D) surface topography analysis except for
summit density which could be overestimated by theoryfor comparatively high values. However these param-
eters cannot be calculated on the basis of profile peaks
analysis; the errors were higher, particularly for theyspa-
rameter. Only summit density can be calculated without
large errors as the square of peaks density on the profile
when correlation between neighboring points was not too
high. Therefore when summit contact parameters are es-
timated from profile spectral moments, values higher
than 0.85 should be avoided.
Application of spectral moments method led to correct
estimation of plasticity index for modeled surfaces; the
errors were not higher than 8%. Differences were larger
for measured surfaces (up to 20%). However plasticityindex can be determined on the basis of profile peak anal-
ysis the errors were not larger than 10% and for meas-
ured surfaces they were smaller than those obtained after
using spectral moments approach. The reason of such
low deviations is that as a result of application of profile
peak analysis both sandRvalues were overestimated.
Decrease of correlation length causes increase in the
distance between the mean of asperity heights and that
of surface ordinatesysand decrease in standard deviation
of summit height s. Mean value of standard deviation
of ordinates is a little smaller than standard deviation of
height of areal surface; differences were a few percents.
5. ConclusionApplicability of the profile spectral moment approach
to areal random surface specification was checked. Good
agreement between the analysis of modeled and meas-
ured surfaces and theory was generally found. The er-
rors of calculation of parameter important for contact
mechanics after the analysis of profile peaks, particularly
for the distance between the mean of asperity heights and
that of surface ordinates ys, were higher than those af-
ter using profile spectral moments. However the errors
of computing the plasticity index on the basis of profile
peaks analysis was small, especially for small correlationbetween ordinates. Summit density can be overestimat-
ed by the profile analysis (using both applied methods)
for comparatively high correlation between neighboring
points . Therefore when summit contact parameters are
estimated from 2D profiles, values higher than 0.85
should be avoided. Summit density can be calculated
as the square of peaks density on the profile when sum-
mit was identified based on its eight neighbors for not
too high correlation between ordinates. Decrease in the
parameter by increase in the sampling interval caused
increase in the distance between the mean of asperity
heights and that of surface ordinates ysand decrease instandard deviation of summit height
s.
AUTHORSPawe Pawlus*, Jacek Michalski Rzeszow Univer-
sity of Technology, Faculty of Mechanical Engineer-
ing and Aeronautics, Al. Powstancow Warszawy 8, 35-
959 Rzeszw, Poland. E-mails: [email protected],
Wiesaw elasko - Upper-Secondary Technical School
Complex in Lezajsk, ul. Mickiewicza 67, 37-300 Leza-
jsk, Poland. E-mail: [email protected]
*Corresponding author
References
[1] J. A. Greenwood and J. B. P. Williamson, Contact
of nominally at surfaces, Proc. Roy. Soc. (Lon-
don), A295, 1966, pp. 300-319.
[2] W. R. Chang, I. Etsion and D. B. Bogy, An elastic-
plastic model for the contact of rough surfaces,
ASME Journal of Tribology, 109, 1987, pp. 257-
263.
[3] P. R. Nayak, Random process model of rough sur-
faces,ASME Journal of Lubrication Technology,93, 1971, pp. 398-407.
[4] A. W. Bush, R. D. Gibson and G. P. Keogh, The
limit of elastic deformation in the contact of rough
surfaces,Mech. Res. Commun.3, 1976, pp. 169-
174.
[5] J. I. McCool, Comparison of models for the con-
tact of rough surfaces, Wear, 107, 1986, pp. 3760.
[6] R. S. Sayles, T. R. Thomas, Measurements of the
statistical properties of engineering surfaces,
ASME Journal of Lubrication Technology, 1979,
101, pp. 409-417.
[7] N. Yu and A. A. Polycarpou, Extracting summit
roughness parameters from random surfaces ac-
counting for asymmetry of the summit heights,
ASME Journal of Tribology, 126, 2004, pp. 761-
766.
[8] J. J. Wu, Simulation of rough surfaces with FFT,
Tribology International, 33, 2000, pp. 47-58.
[9] D. J. Whitehouse, The digital measurement of
peak parameters on surface proles,Journal Me-
chanical Engineering Science IMechE, 20/4, 1978,
pp. 221-226.
[10] J. A. Greenwood, A unied theory of surface
roughness,Proc. Roy. Soc. (London), A393, 1984,
pp. 133-157.[11] J. I. McCool, Finite difference spectral moments
estimation for proles: the effect of sample spacing
and quantization error, Precision Engineering,
vol. 4, no. 4,1982, pp. 181-184.
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Articles20
Behavior Based Co-ordination of a Troop of Vehicles
Targeted to Different Goals in an Unknown Environment
Sourish Sanyal, Ranjit Kumar Barai, Rupendranath Chakrabarti, Pranab Kumar Chattopadhyay
Submitted 26thJanuary 2012; accepted 16thAugust 2012
Abstract:The issue of coordinated operation of multi-vehicle for
a variety of tasks is getting increasing attention day by
day and standing as a major research field due to their in-
creased capacity and flexibility they can offer as a team.
This paper presents a novel algorithm for multi-vehicle
navigation, based on exhaustive search to avoid a set
of randomly generated obstacles, predict the approxi-
mate position of other vehicles and thus keeping a safedistance to avoid collision and to maintain a formation
amongst them while targeted towards the assigned goals.
The proposed algorithm uses two optimizing functions
in deriving drive commands, direction and turning, for
a troop of vehicles. This particular algorithm is similar
to the artificial potential field (APF) method which is
widely used for autonomous mobile robot path planning
due to its simplicity and mathematical elegance. In this
work we have taken a behavior based reactive scheme
together with artificially generated perturbation as the
vehicles are running in a real time environment. Simula-
tions have been carried out for a group of four vehicles,
paired in two groups, approaching two different targetsavoiding eight randomly generated obstacles, and keep-
ing proper coordination between the members of intra
and inter groups. The effectiveness of the proposed ap-
proach has been shown by some simulation results.
Keywords: behavior-based collision avoidance, rando-
mized obstacles, multi-vehicle coordination, particle
swarm optimization.
1. Introduction
The challenge that a troop of multiple uninhabited au-
tonomous vehicles (UAVs) would be able to adaptively
react to their environment, whether known, unknown or
uncertain, and learn about their surroundings while fol-
lowing either an individual or a communal agenda is an
intriguing field of research. Achieving such a degree of
control and producing such sophisticated behavior re-
mains an elusive goal that demands considerable atten-
tion and this is inherently a complex task. The problem
of multi-vehicle coordination and control has been re-
ceiving an exquisite amount of attention during the past
few years due to critical importance of the field in wide-
ranging applications [8].In many practical applications of autonomous vehicles
multiple teams are to be used. Such teams have many po-
tential benefits, including faster completion through par-
allelism and increased robustness through redundancy.
Further, teams of vehicles can increase the application
domain of autonomous vehicles by providing solutions
to tasks that are inherently distributed, either in time, or
in space, or in functionality. Since the 1980s, researchers
have addressed many issues in multi-vehicle, or multi-
robot teams or automated guided vehicles (AGVs) [12],
such as control architectures, communication, task al-
location, swarm robots, learning [25]. A critical issue
in these mobile robot teams is coordinating the motionsof multiple vehicles interacting in the same workspace.
Regardless of the mission of the vehicles, they must be
able to effectively share the workspace to prevent inter-
ference between the team members. Solutions to the mo-
tion coordination problem are approached in a variety of
ways, depending upon the underlying objectives of the
vehicle team. In some cases, the paths of the robots are
explicitly planned and coordinated in advance, as might
be needed in a busy warehouse management application.
In other cases, planning is relaxed and emphasis is placed
on mechanisms to avoid collision, applicable for tasks
such as automated hospital meal deliveries. In yet other
situations, the robots could have mechanisms with littlepre-planning that focus on coordinating vehicle motions
in real-time using reactive, behavior-based, or control-
theoretic approaches, such as would be used in a convoy-
ing or formation-keeping application.
Existing work on multi-vehicle control focuses reced-
ing-horizon planning (an optimization method) and hier-
archical structures. The receding-horizon trajectory plan-
ner based on Mixed Integer-Linear Programming (MILP)
is capable of planning planner-based trajectories directed
to a goal [14,15,16]. The goal is constrained by no-fly
areas, or obstacles, and is free from leader-follower ar-
chitecture which is adopted by model predictive control
(MPC) [17]. Game-theoretic approach is also adopted by
different co-ordination schemes for decision making of
the multi-vehicle problem [18,19,20]. A disjoint path al-
gorithm for a reconfiguration of multi-vehicle was also
proposed [21]. A class of triangulated graphs for alge-
braic representation of formations have been introduced
to specify a mission cost for a group of vehicles [22].
The present work focuses on simultaneous movement of
a troop of vehicles from their initial locations towards
different targets in such an environment where obstacles
are generating stochastically based on the Artificial Po-
tential Field (APF) approach. The basic idea of the APF
approach is to fill the robots workspace with an artificialpotential field in which the robot is attracted to its target
position and is repulsed away from the obstacles [4]. This
method is particularly attractive because of its elegant
mathematical analysis and simplicity. The application of
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Articles 21
APF for obstacle avoidance was first developed by Kha-
tib [3]. In the past decade this method has been studied
extensively for autonomous mobile robot path planning
by many researchers [5-7].This is a new approach where
the troops are divided into two groups and set out for
their own targets, maintaining a formation amongst them.
This work is an extension of the work done by KevinPassino [2] on obstacle avoidance of a single vehicle in
presence of a number of fixed obstacles.
2. Problem description
A. Cooperation of multi-vehiclesThe word cooperation means interaction or integra-
tion of multiple vehicles [11]. In a cooperative team the
vehicles have to communicate, exchange information or
interact in some way to achieve an overall mission. The
term cooperation has been widely discussed in different
scientific community and different definitions have been
proposed.
B. Multi-vehicle path planning problemIt is defined as follows: given a set of mvehicles in
k-dimensional workspace, each specified with an initial
starting configuration (e.g., position and orientation) and
a desired goal configuration, determine the path each ve-
hicle should take to reach its goal, while avoiding colli-
sions with obstacles and other vehicles in the workspace.
More formally, let A be a rigid vehicle in a static work-
space W =k
[18,19], where k = 2 or k = 3. The work-
space is populated with obstacles. A configuration q is
a complete specification of the location of every point on
the robot geometry. The configuration space C represents
the set of all the possible configurations of A with respectto W. Let O W represent the region within the work-space populated by obstacles. Let the close set A(q) Wdenote the set of points occupied by the vehicle when it
is in the configuration qC. Then, the C-spaceobstacle
region,obs
C , is defined as [1]:
{=obsC q | ( ) C A q } (1)
The set of configurations that avoid collision (called
thefree space) is:
\=free obs
C C C . (2)
Afree pathbetween two obstacle-free configurations
initC and goalC is a continuous map:
[0,1] freeC (3)
such that (0) = initc and .(1) = goalc .For a team of m vehicles, define a state space that con-
siders the configurations of all the robots simultaneously:
1 2 ...= mX C C C . (4)
Note that the dimension of X is N, where =N1dim( )
=m i
iC The C-space obstacle region must now be
redefined as a combination of the configurations leading
to a robot-obstacle collision, together with the configura-
tions leading to vehicle to vehicle collision. The subset
of X corresponding to robotiA with the obstacle region
O, is
{ | ( ) }= i i iobsX x X A q (5)
The subset of X corresponding to robot Ai in collision
with robotjA is
{ | ( ) ( ) }= ij i i j iobsX x X A q A q (6)
The obstacle region in X is then defined as the combi-
nation of Equations (5) and (6), resulting in
1 ,
( ) ( )=
= m
i i
obs obs obs
i ij i j
X X X (7)
With these definitions, the planning process for multi-
vehicle system treats X the same as C, andobs
X the same
asobs
C ,whereinit
C represents the starting configuration of
all the robots, and goalC represents the desired goal con-
figurations of all the vehicles.
The APF uses two types of potential field, namely a re-pulsive potential field to force a robot away from obsta-
cles or forbidden regions and an attractive potential field
to drive the robot to its goal. The rob