Journal of
Computer Science and Control Systems
University of Oradea Publisher
Vol. 6, Nr. 2, October 2013
Academy of Romanian Scientists
University of Oradea, Faculty of Electrical Engineering and Information Technology
S
C S
JC
S
C
S
- J
ou
rn
al
of
C
om
pu
te
r S
cie
nc
e a
nd
C
on
tro
l S
ys
te
m
s,
V
ol.
6
, N
r. 2
, O
cto
be
r 2
01
3
University of Oradea Publisher
ISSN: 1844-6043
Journal of Computer Science and Control Systems
http://electroinf.uoradea.ro/reviste/default.htm
J
C
S
C
S
J
o
u
r
n
a
l
o
f
C
o
m
p
u
te
r
S
c
ie
n
c
e
a
n
d
C
o
n
tr
o
l
S
y
s
te
m
s
,
V
o
l.
6
,
N
r.
2
,
O
c
to
b
e
r
2
Journal of
Computer Science and Control Systems
Vol.
6
, Nr.
2
,
October
201
3
University of Oradea Publisher
University of Oradea, Faculty of Electrical Engineering and Information Technology
S
EDITOR IN-CHIEF
Eugen GERGELY - University of Oradea, Romania EXECUTIVE EDITORS
Gianina GABOR - University of Oradea, Romania Daniela E. POPESCU - University of Oradea, Romania Helga SILAGHI - University of Oradea, Romania Viorica SPOIALĂ - University of Oradea, Romania
ASSOCIATE EDITORS
Mihail ABRUDEAN Technical University of Cluj-Napoca, Romania Angelica BACIVAROV University Politehnica of Bucharest, Romania Valentina BALAS “Aurel Vlaicu” University of Arad, Romania Dumitru Dan BURDESCU University of Craiova, Romania
Toma Leonida DRAGOMIR "Politehnica" University of Timisoara, Romania János FODOR Szent Istvan University, Budapest, Hungary Voicu GROZA University of Ottawa, Canada
Štefan HUDÁK Technical University of Kosice, Slovakia Geza HUSI University of Debrecen, Hungary Ferenc KALMAR University of Debrecen, Hungary Jan KOLLAR Technical University of Kosice, Slovakia Anatolij MAHNITKO Technical University of Riga, Latvia Ioan Z. MIHU “Lucian Blaga” University of Sibiu, Romania Constantin POPESCU University of Oradea, Romania
Dumitru POPESCU University Politehnica of Bucharest, Romania Alin Dan POTORAC "Stefan cel Mare" University of Suceava, Romania Ioan ROXIN Universite de Franche-Comte, France
Ioan SILEA "Politehnica" University of Timisoara, Romania Lacramioara STOICU-TIVADAR "Politehnica" University of Timisoara, Romania Lorand SZABO Technical University of Cluj Napoca, Romania Janos SZTRIK University of Debrecen, Hungary
Honoriu VĂLEAN Technical University of Cluj-Napoca, Romania
ISSN 1844 - 6043
CONTENTS
BÎRTE Ovidiu, RUSU Tiberiu, SZABÓ Loránd, MAR IŞ Claudia Stelu a - Technical University of Cluj-Napoca, Romania
Script Controlled Model of a Synchronous Reluctance Machine for Rapid Design Optimization ...5
BODOLAI Tamás1, VÁRADINÉ SZARKA Angéla2 - 1University of Miskolc, Hungary, 2University of Debrecen, Hungary
Solving the Big Data Problem in Area of High-Speed Optical Vibration Measurement ...9
HUANG Yuan, CHEN Yanqi, LIU Xingwei - Xihua University, China
Local Minimax Probability Machine Forecasting of Wireless Network Traffic...13
INOAN Iulia, ABRUDEAN Mihail - Technical University of Cluj-Napoca, Romania
Design of NARMA-L2 Neural controller for an Induction Motor’s Speed Control...18 LAKHOUA Mohamed Najeh - University Tunis el Manar, Tunisia
Novel Approach for the Analysis and the Optimization of the Cereal Stock Mobility ...22
Mohd Nazri Ismail1, Mohd Hafizh Mohamed2 - 1National Defence University of Malaysia, Malaysia, 2University of Kuala Lumpur, Malaysia
File Transfer over Dual-Stack IPv6 Tunnelling in Real Network Environment: Router to Router Performance
Script Controlled Model of a Synchronous Reluctance Machine
for Rapid Design Optimization
BÎRTE Ovidiu, RUSU Tiberiu, SZABÓ Loránd, MAR I
Ş
Claudia Stelu a
Department of Electrical Machines and Drives, Technical University of Cluj-Napoca 28 Memorandumului str., 400114 Cluj-Napoca, Romania
E-mail: Ovidiu.Birte@emd.utcluj.ro
Abstract – In the last years several methods for design optimization of the synchronous reluctance motors were suggested in the literature. The main concern is to find the ideal rotor geometry for the best performance of the machine. To achieve this, finite element method analysis, a powerful tool widely used in the design and optimization of electrical machine, is used. The model of the machine is built up by using scripts. The automated parametric modeling enables the designer to perform changes in the geometry very quickly, thus considerably shortening the design and optimization time.
Keywords: synchronous reluctance machine, design optimization, parametric model, scripting.
I. INTRODUCTION
The synchronous reluctance machine (SyncRel) is a singly salient machine in which the rotor is built up so as to employ the principle of reluctance torque to produce electromechanical energy conversion. It produces torque by the tendency of its rotor to move to a position where the inductance of the excited winding and also the corresponding magnetic flux are maximized. They do not need field windings or permanent magnets on the rotor. The stator of the SyncRel has a cylindrical inner surface and is typically wound in an identical manner to an induction machine. This means that the stator of these machines has uniform slots with concentrated or with distributed multiphase singly or doubly windings. The rotor is made of conventional or axial laminations with or without cage winding and usually without permanent magnets [1].
The SyncRel can have very high power density at low costs, being ideal for many advanced industrial and automotive applications. Supplementary it can work at high speeds and temperatures [2], [3].
The main disadvantages of the machine is its high torque ripple when operated at low speed, and the noise caused by this torque ripple.
Until the 90's their use was limited by their complex design and complicated control. All these were overcame by the technological advances in sophisticated computer aided design tools and by the wide spreading use of the low-cost embedded systems for control.
The torque development capability of the motor is
highly dependent on the ratio (Md Mq) and the
difference ( ) of the direct-axis ( ) and
quadrature-axis ( ) magnetizing inductances. The
inductance ratio and difference strongly depends on the design of the rotor [
q
d M
M Md
q
M
1].
Thus, it is very important to design the optimal barrier and segment structure of the rotor, which is strongly related with the d-axis and q-axis inductances.
When performing the optimal design of the SyncRel, there are several design variables related to the shape of a stator and rotor that must be taken into account [4].
In this paper a parameterized model of the SyncRel is presented, which is very useful in the rapid optimal design of the machine by allowing to simply modifying the geometry by only changing some earlier defined geometrical parameters.
II. THE SYNCREL MODEL
The SyncRel to be designed has a transversally laminated anisotropic (TLA) rotor (see Fig. 1).
Figure 1. The cross-section of the SyncRel with TLA rotor.
This topology of the rotor has several advantages: the better suitability for industrial manufacturing, smaller torque ripple and iron losses, the possibility of skewing the rotor, etc. [5].
The main steps to be performed during a FEA in JMAG are: creating the geometry, setting the materials, creating a circuit, setting the conditions, generating the mesh, running the analysis and displaying the results.
The preprocessor (for defining the problem to be solved), postprocessor (data processing and graphical visualization) and the solver all can be controlled using scripts. This allows all procedures from creating a model to displaying the results to be run automatically. This can be used to either automate commonly performed operations or link JMAG to other software, such as optimizers, which need to control JMAG programmatically.
The following scripting languages are supported by JMAG's Geometry Editor: Python, VBScript and Jscript.
The 2D model of the motor is realized by using a VBS program with the simple GUI (graphical user
interface), shown in Fig. 2, where the geometrical
parameters of the machine can be introduced. All the dimensions that have to be given in are in millimeters. The geometry data can also be imported from a text file.
Figure 2. The user interface.
The geometrical dimensions that can be modified in this window are:
the stator outer diameter
the stator inner diameter
the air-gap length
the number of slits in the rotor
the width of one slit
the width of the segments
the diameter of the shaft.
Other dimensions, like the width of the stator tooth or the depth of the slot can be modified inside the script.
The windings, the stator and the rotor cores are each drawn separately as individual parts.
Two types of slot designs (shown in Fig. 3) for the stator core can be chosen.
Figure 3. Design models for the stator slots.
This slot is then copied in a circular pattern for the number of instances introduced by the user, this way a full model of the stator being built up.
In order to draw the rotor, first a one-pole slice (as that in Fig. 4) has to be constructed. This instance is then multiplied to obtain the entire rotor.
Figure 4. Rotor geometrical parameters
The rotor design can be realized with ribs of same or with different thickness (see Fig. 5).
a) different segment thickness b) same segment thickness Figure 5. Rotor design models.
Two models were created in this study for a comparative analysis. The parameters of the models were set up by using the GUI of the program.
The two built up models are shown in Fig. 6.
Figure 6. The two rotor topologies.
Materials used in the simulation are copper for the coils and 50A230 soft magnetic steel for the iron core of the stator and rotor. These materials can be found in the JMAG material library.
The windings of the stator are star connected and supplied from a 5 A, 50 Hz current source. For both models the rotor is considered as stationary.
III. SIMULATION RESULTS
Next the most important results obtained via simulations for the two models are detailed.
A. Results for the First Model
The first step when running the simulation is the generation of the mesh. The mesh created automatically by the program is given in Fig. 7.
Figure 7. The mesh generated for the first model.
The simulation results of most interest are the flux lines and the flux density plots for the d and q-axis directions. The obtained flux lines are given in Fig. 8.
a) d-axis position
b) q-axis position Figure 8. Flux lines obtained for the first model (q-axis position).
The reluctance torque of SyncRel is highly dependent of the d-axis and q-axis inductances [6]:
Ld Lq
idiqp
T
2 2 3
(1)
To maximize the d-axis inductance the flux guides
should ideally have the same shape as the flux path
shown in Fig. 8a. And to minimize the q-axis magnetic
flux the flux barriers should be perpendicular to the flux lines, as it is shown in Fig. 8b.
In the case of this type of electrical machine the risk of self-saturation occurring on the d-axis direction is
quite high [7]. The flux barriers reduce the q-axis
magnetic flux, so that the risk of saturation on the q-axis direction is lower.
For these reasons it is of maximum interest to study the saturation level of the machine taken into study on the two orthogonal directions.
The magnetic flux density of the first model taken into study for two positions of rotor is shown in Fig. 9.
a) d-axis position
b) q-axis position
Figure 9. Flux lines and flux density plot for the first model.
q-axis position, the rib is saturated and the segments are not saturated at all, in contrast to the d-axis position.
IV. CONCLUSIONS
B. Results for the Second Model
The magnetic flux density maps for this case are given in Fig. 10.
This study presents a fast and comfortable way to perform the numeric field computation for different designs of the SyncRel by means of the script editor of JMAG.
The results of the study can be interpreted and then is easy to intervene on the initial parameters in order to optimize the model.
Also, by using scripting language, JMAG Designer can be further linked to other software products.
ACKNOWLEDGMENT
This work was supported by the Romanian Executive Agency for Higher Education, Research, Development and Innovation Funding (UEFISCDI) under the Automotive Low-Noise Electrical Machines and Drives
Optimal Design and Development (ALNEMAD) Joint
Applied Research Project (PCCA) in the frame of "Partnerships" projects (PN II – National Plan for
Research, Development and Innovation) and the DEsign,
MOdelling and TESTing tools for Electrical Vehicles
powertrain drives (DeMoTest_EV) in the frame of FP7
IAPP Marie Curie Actions.
a) d-axis position
REFERENCES
[1] G. Henneberger, I.A. Viorel, Variable Reluctance Electrical Machines. Aachen (Germany): Shaker Verlag, 2001.
[2] M. Sanada, K. Hiramoto, S. Morimoto, Y. Takeda, "Torque ripple improvement for synchronous reluctance motor using an asymmetric flux barrier arrangement,"
IEEE Transactions on Industry Applications, vol. 40, no. 4, pp. 1076-1082, 2004.
[3] N. Bianchi, S. Bolognani, D. Bon, M. Dai Pré, "Rotor flux-barrier design for torque ripple reduction in synchronous reluctance and PM-assisted synchronous reluctance motors," IEEE Transactions on Industry Applications, vol. 45,no. 3, pp. 921-928, 2009.
[4] A. Vagati, "The synchronous reluctance solution: a new alternative in AC drives," in Proceedings of the 20th International Conference on Industrial Electronics, Control and Instrumentation (IECON '94), Bologna (Italy), 1994, pp. 1-13.
b) q-axis position
Figure 10. Flux density plot and flux lines for the second model.
As it can be observed in the figure, for the d-axis position the flux lines are more evenly distributed in the rotor and the flux density is more uniform. However, on
the q-axis the number of barriers in the flux path is
decreased, thus implying an increase of the q-axis
inductance, which is to be avoided.
[5] R.R. Moghaddam, "Synchronous reluctance machine (SynRM) design," M.S. Thesis, Royal Institute of Technology (KTH), Stockholm (Sweden), 2007.
[6] K.C. Kim, "Magnetic saturation effect on the rotor core of synchronous reluctance motor," Journal of Electrical Engineering & Technology, vol. 6, no. 5, pp. 634-639, 2011.
Therefore, the design parameters should consider the saturation on both d- and q-axis, in order to obtain the optimal inductance ratio.
Solving the Big Data Problem in Area of High-Speed Optical
Vibration Measurement
Tamás BODOLAI
1, Angéla VÁRADINÉ SZARKA
21
University of Miskolc, Hungary
Department of Electrical and Electronic Engineering, Faculty of Mechanical Engineering and Informatics Egyetemváros A/3., 3515 Miskolc, Hungary, elkbodo@uni-miskolc.hu
2
University of Debrecen, Hungary
Department of Experimental Physics, Faculty of Science and Technology Bem tér 18., 4032 Debrecen, angela.varadi@science.unideb.hu
Abstract– In industrial applications using contact vibration measurement method is often not possible, therefore contactless methods has more and more importance. This is one of the most important reasons why laser distance sensors are widely used for vibration measurement. Although the sampling rate of these sensors is still lower than the speed of the industrial contact vibration sensors. In order to increase the performance of contactless measurement, development of new methods is required. One of the possibilities is to use line scan cameras, as its resolution and speed enable the application for high-speed vibration measurement. The application of the method is not widespread because of the huge amount of collected data. The article demonstrates a realized one of the possible solutions for the described problem.
Keywords: big data; optical vibration; FPGA; vibration measurement; data reduction.
I. REVIEWOF OPTICAL MEASUREMENT
METHODS
Cameras are widely used in industrial measurement technologies. Pictures taken by cameras can be processed on the basis of three different theories.
1) In case of product inspection the most widespread
method is identifying the specific, easy-to-distinguish points in the picture, then on the basis of these performing the necessary measurements. This method applied also in AOIs (Automated Optical Inspection) of electronic industry for several phases of the production process, including paste printing, pick and place machines or inspection after soldering of parts.
2) Another group of camera applications is projecting
a pattern on the surface of the measured object. On the basis of the picture taken by the camera and the projected pattern, the surface deformations of the object can be determined. Product reproduction or Moire-photography for measuring scoliosis in Medicine is such an example.
Procedures using different ways of lighting, for example contour light for identifying the points of the object belong to the border of the two methods mentioned above.
3) Procedures placing some pattern on the surface of
the objects to be measured belong to the third group. In mass-production except for barcodes this is not an efficient method, however it may be a well-applicable method in the fields of contactless vibration measurement, mainly in vibration measurement of manufacturing equipment.
II. BIG DATA PROBLEM IN AREA OF
CONTINOUS OPTICAL MEASUREMENT
In the fields of optical measurement techniques the main disadvantage of the area scan cameras applications is their low speed. Nowadays high-speed digital cameras are available, suitable for taking 100 000 pictures/second [1]. Nevertheless this speed can be only reached in case of extremely small sensors containing ~128x64 pixels. This resolution is not enough for most measurement applications. Although by increasing the size of sensor the obtainable speed is decreasing. For example in case of a sensor containing 640x480 pixels the speed is only 36 000 fps (frame per second). The other great problem is the amount of data. The high-speed cameras even in case of small sensor size produce so huge amount of data, that it is impossible to transmit them to a computer online. That is the reason why the time of the continuous (no interruption) record of these cameras depends on the capacity of their caches (integrated memory inside of the sensor). In practice most high-speed cameras are capable of taking 5-7 second pictures continuously.
practical applicability of these cameras in the field of contactless vibration measurement.
III. THE APPLIED MEASUREMENT METHOD
Figure 1. Demonstrating the theory of measurement.
A specially designed pattern containing well-defined black and white areas is attached onto the surface of the object to be measured. The camera is placed in a way that the line sensed by the camera entirely includes the black areas in the pattern (Figure 1). In the picture taken by the camera the crucial data regarding the measurement result are carried by the positions of the black-white and white-black transitions. That is the reason why the value of the pixels' intensity is not needed for measurement. The theory of data reduction described in details is that a pre-processing hardware detects each transition in the pixel line in real time and sends only their positions to the computer. The reduced data amount can be calculated by the following formula:
(1) where
fs means sampling frequency,
nl means number of transitions in the pattern,
dtype is the bit number of the data type necessary for describing the positions of the transitions.
Regarding line scan cameras available at present 16 bit unsigned data type is necessary for the application (dtype=16).
The original amount of data of the black-white line scan camera can be calculated by the following formula:
(2) where
fs means sampling frequency,
np means the number of pixels in the pixel line, nbit means the number of bits describing pixel intensity.
The measure of data reduction (R) can be calculated from the quotient of the reduced amount of data (Dr) and the original amount of data (Do) by the following formula:
(3) In the practice a camera containing 8 192 pixels
with 80 kHz line rate with 8 bit resolution produces 5 000 Mbit data/second. Our specially developed pattern contains 20 transitions, so in case of 80 kHz line
frequency the reduced amount of data is 25 000 kbit/second. Using this reduction method we have only ~0.49% of the original data amount, so approximately only 200th part of the produced data amount is required for measurement.
IV. REALISATION OF DATA REDUCTION
Line scan cameras are developed for taking pictures of moving products (for example on conveyor). The aim of these applications is definitely to transmit each value of pixel intensity of each pixel line to the computer. In these cases the entire amount of data provided by the camera is needed. Each data is considered to be relevant information.
On the basis of the described measurement theory it is known that information is not directly hidden in pixel intensity values but in the positions of transitions.
As we see the method of data reduction includes a data pre-processing hardware detecting positions of transitions in each pixel line and sending arrays of the positions of each lines to the computer for further data processing.
Regarding the fact that the pattern attached to the surface to be measured contains black and white areas, in case of homogeneous and well-balanced lighting it is enough to examine only the most significant bit (MSB) of each pixel. There are transitions in the picture when this bit of consecutive pixels changes from low-level to high-level or vice versa.
This method is implemented in our newly developed data reduction unit.
Figure 2. Structure of the test environment.
There have been several development possibilities for realisation of the reduction method but flexibility provided by FPGA (field-programmable gate array) made us to use to realize data reduction by FPGA, in LabVIEW development environment.
with NI-PXI-7852R FlexRIO data acquisition card not designed specially for this purpose.
In order to realize the simple prototype we did not intend to implement the communication ways (necessary for adjusting the camera properties). That is the reason why it seemed to be efficient to keep the opportunity of the original using of the system. This has been made by
an adapter module paralleling the LVDS (low voltage differential signalling) channels arriving from the camera. This way makes possible the parallel operation of the systems. DS90CR288 type decoder integrated circuit produces the digital signals for the FPGA measuring card. The sketch of the developed system can be seen on Figure 2.
Figure 3. LabVIEW programme on FPGA.
V. SOFTWARE IMPLEMENTATION OF DATA
REDUCTION
The controlling programme of the measuring card wired to FPGA has been developed in LabVIEW environment. The Dalsa camera uses two ports (taps) for
digital values can be read. Clock frequency is 40 MHz in the test camera.
For the exact determination of the high level of CLK signal FPGA is operated on 160 MHz, four times higher than the original clock signal (Figure 3).
The four important digital lines are read in each iteration of the FPGA (Figure 3 Point 1.). The programme part marked with Point 2 on Figure 3. detects the raising edge of the CLK line and at the same time it checks the validity of LVAL line. The switching possibility of the inspections is built into the programme only to make it suitable for testing. The programme part marked with Point 3 on Figure 3. detects the beginning of a new pixel line. This happens when the value of line LVAL changes from low to high level. Case structure ensures the examination of LVAL line’s value only in case of valid CLK signal. When a new pixel line starts, the select node after the case structure sets the pixel counter to zero.
In case of CLK and LVAL lines are validated programme part 4 compares the MSB value of the second pixel of the previous iteration with the MSB value of the first pixel of the on-going iteration, and the MSB value of the two pixels of the on-going iteration. If there is a change in any of these comparisons because of a changing from black area to white or vice versa, FIFO register marked with Point 5 is becoming activated for writing. Depending on the actual pixel of a defined transition the value or the incremented value of the pixel counter is written into the FIFO memory. The value of the pixel counter increases with two in each valid iteration. Data stored in FIFO memory is read and processed by host application running on the computer.
The "Time Out?" indicator had a significant role in development phase, providing information on the full state of the memory. The warning can be accepted by pressing "New data" button. This programme part is not necessary for the normal operation of the data reduction unit.
VI. OPPORTUNITIES OF FURTHER
DEVELOPMENT
Although the test results have proved the efficiency of the new method, in order to develop a system for practical use, further developments are required.
The accuracy of the present system depends on the clearness of the transitions, which means that no repeated MSB value changing is sensed for one transition. This accuracy depends on several parameters in the practice e.g. lighting, calibration of the camera, resolution of the pattern, etc. Handling of not clear transitions should be solved inside of the reduction unit.
Consecutive transitions causing unreliability can be filtered on the basis of the transitions frequency that can be calculated from the shape of the used pattern.
Though the hardware and software products on the market provide a magnificent environment for the development of the system, our final aim is to create a stand alone unit which can be connected to the computer without a special measuring card.
VII. CONCLUSIONS
Using a Dalsa P2k40 line camera with 6 144 pixel
with maximum of 12.3 kHz line rate in the data
reduction tests, no error was detected in continuous data acquisition. In this case the unit reduced data amount from ~72 MByte to 480 kByte in every second. The amount of reduced data can be saved and processed by an up-to-date computer without any difficulties.
REFERENCES
Local Minimax Probability Machine Forecasting of Wireless
Network Traffic
HUANG Yuan, CHEN Yanqi, LIU Xingwei
School of Mathematics and Computer Engineering, Xihua University,
610039 Chengdu, China, lxwphd@139.com
Abstract –With the growing application of wireless networks, there are increasing security issues. The forecasting technologies for network traffic are effectively used to deal with these emerging problems. However, because the wireless network traffic has several characteristics such as nonlinearity and bursty, the classical methods could be scarcely applied to the increasingly complicated wireless network traffic problems. Minimax Probability Machine (MPM) is a recently intelligent algorithm used to deal with model for wireless network traffic. Like global SVM, global MPM has the same shortcomings on the forecast accuracy and computational complexity. Therefore, a local MPM algorithm, LMPM, is proposed in this paper, and experimental results show that forecasting accuracy and real-time computing capability of LMPM are much better than that of global MPM.
Keywords: wireless network traffic; forecasting algorithm; local Minimax Probability Machine; Ki strategy.
I. INTRODUCTION
With the growing application of wireless networks, there are increasing security issues. Except access control technology based on key management and certification authority, the forecasting and anomaly detection technologies for network traffic are effectively used to deal with these emerging problems.
Forecasting technology is the process of making statements about events which have not yet been observed. Forecasting algorithms have been investigated for decades along with the development of Time Series Analysis (TSA), and generally could be categorized as classical algorithms and intelligent algorithms. Classical algorithms include Auto-Regressive (AR), Moving Average (MA) and Auto-Regressive and Moving Average (ARMA), Auto-Regressive Integrated Moving Average (ARIMA), Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) [1], as well as Bayesian model and Karlman Filtering. However, because the wireless network traffic has several characteristics such as nonlinearity and bursty, the classical methods could be scarcely applied to the increasingly complicated wireless network traffic
problems [2]. Recently intelligent algorithms, such as Wavelet Analysis, Artificial Neural Networks (ANN) [3], Support Vector Machine (SVM) [4], Local SVM (LSVM) based on Chaos Theory [5], and Minimax Probability Machine (MPM) [6], have come prevailing.
LSVM, which combines the advantage of traditional local prediction methods and support vector machines, is an effective method to deal with model for wireless network traffic. The key of LSVM is to search out some feature points from network traffic dataset for constituting a Nearest Neighbor Points Set (NNPS) by calculating Euclidean Distance. Then, the NNPS is used as training dataset to input SVM regression. Experimental results show that LSVM can improve the forecast accuracy and the real-time computing capability for spatiotemporal chaotic time series. The main disadvantage of Euclidean Distance in measuring similarity between two points is not always accurate. In [7], an improved LSVM algorithm, LSVM-DTW-K, is introduced for wireless network traffic forecasting, of which Dynamic Time Wrapping (DTW) is used to replace Euclidean Distance and “Dynamic K” strategy is used to kick the bursty points out from the NNPS. Experimental results show that the advantage and accuracy of LSVM-DTW-K are clear and generally satisfactory. However, we find that the selection of the number of the nearest neighbor points and the bursty points kicked out from the NNPS is so experience-relied. In addition, the time complexity of DTW algorithm is higher than that of Euclidean Distance. To further improve the forecast accuracy and the real-time computing capability of LSVM-DTW-K, Hannan-Quinn information criterion (HQ) [8-9] is used to calculate the number of the nearest neighbor points, and Symbolic Aggregate Approximation (SAX) [10] is used to symbolic the time series for reducing the computational complexity. The improved algorithm, LSVM-HQ-SAX-DTW-K, has favorable forecasting accuracy and real-time computing capability [11]. However, the selection of the bursty points kicked out from the NNPS is still experience-relied.
II. LOCAL MINIMAX PROBABILITY MACHINE
MPM is a recently intelligent algorithm used to deal with model for wireless network traffic. MPM makes use of the “kernel trick” to transform a linearly inseparable problem into a higher dimensional space where the problem may be linearly separable. In [12], an evaluation of SVM and MPM for prediction is presented, and experimental results show that the accuracy of MPM is better than that of SVM. Like global SVM, global MPM forecasting algorithms of wireless network traffic use all original data as the training dataset. Therefore, global MPM and global SVM have the same shortcomings on the forecast accuracy and computational complexity [5]. In this paper, a local MPM algorithm, LMPM, is proposed, and the key steps of LMPM are summarized as follows:
Suppose a time series is defined as .
}
,
,
,
,
{
x
1x
2x
n 1x
nT
Step 1: Estimate time delay
by Mutual Informationalgorithm [5].
Step 2: Estimate embedding dimension
m
by Cao’smethod [5].
Step 3: Reconstruct Phase Space , by
t i
Xi}, 1,2,...,
{ , , , 2 , 1 )}, ) 1 ( ( , ), ( ), (
{xi xi xi m i t
Xi
1
,
1
1
,
)
1
(
m
n
t
m
n
t
(1)Step 4: Calculate the number of the nearest neighbor points using AICi information criterion. Several information criterion criteria are used for calculate the number of the nearest neighbor points [13], such as Akaike information criterion (AIC) [14, 15], Bayesian information criterion (BIC) [16], the Hannan-Quinn information criterion (HQ) and an improved variant of the Akaike information criterion (AICi) [17]. Considering the limitations of AIC, BIC and HQ criteria, in this paper, the number of the nearest neighbor points is calculated by AICi information criterion.
Step 5: k-d tree algorithm is used to construct the NNPS [18].
Step 6: Ki strategy is proposed in this paper and used to kick the bursty points out from the NNPS. Ki strategy is an improved “Dynamic K” strategy which is used in LSVM-DTW-K and LSVM-HQ-SAX-DTW-K. The key steps of Ki strategy are described as follows. Suppose the range of cosine of the angle is set to [-1, 1], and the
number of the nearest neighbor points is
t
. Firstly,cosine of the angle between each point in NNPS with
target point is calculated, which is defined
as . Then a threshold
i
X
2
cos(
),
...,
cos(
)}
),
1
{cos(
t
p
isset, such as
p
0
.
05
%
. Ifp t t % )} )} cos(
)
4
(
n
2Dn
D
2n
O
O
(Lm
)
i cos( ..., ), 2 cos( max{cos( ..., ), 2 cos( ), 1 ) cos( 100 ), 1 max{cos( ,
then the point
i
is kicked out from the NNPS. Afterlimited iteration, a pruned NNPS is obtained.
Step 7: Constitute MPM model, where the pruned NNPS is used for the training dataset.
Step 8: Tune the parameters of MPM model, and figure out the forecast value.
Analyzing the time complexity of LMPM taken on
any input of size
n
in single-step mode, it can bedefined as
))
log(
(
n
n
O
)
(
Lm
+ + +
+
O
O
((
2
P
1
)(
1
))
))
1
L
+
(
2
log(
L
2
P
O
)
(
2
(
P
K
+ + , (2)
))
2
(
(
P
m
P
O
))
K
P
(
O
where is the number of valuation of embedding
dimension ,
D
m
L
n
(
m
1
)
,L
m
,P
is theamount of the points in NNPS,
L
P
,K
is theamount of the points kicked out from NNPS,
P
K
.In [7], the time complexity of LSVM-DTW-K taken
on any input of size
n
in single-step mode is describedas
))
)
P
3log(
(
n
n
O
)
1
((
L
m
2(
(
Nsv
3O
+ + +
+ +
+ , (3)
)
4
(
n
2Dn
D
2n
O
))
1
(
(
P
L
O
)
(
)
Nsv
2m
P
K
K
)
(Lm
O
(
KPm
O
)
Nsv
O
)
where is the amount of the support vector.
Comparing LMPM with LSVM-DTW-K in the time complexity, the first three steps are the same. In order to analysis, the time complexity of the after four steps of LSVM-DTW-K can be further abbreviated as
, where ,
Nsv
(
O
)
)
(
L
Nsv
O
L
m
L
P
, andK
P
. Obviously, the time complexity of LMPM islower than that of LSVM-DTW-K.
In [11], the time complexity of
LSVM-HQ-SAX-DTW-K taken on any input of size
n
in single-stepmode is described as
))
)
2
(
O
log(
(
n
n
O
)
1
2
((
L
w
(
(
Nsv
3
P
+ + +
+ + +
, (4)
)
4
(
n
2Dn
D
2n
O
O
(
Lm
)
O
O
))
1
(
(
P
L
O
O
(
)
(
)
Nsv
2w
P
K
Nsv
K
)
KPw
)
where . Comparing LMPM with
LSVM-HQ-SAX-DTW-K in the time complexity, the first three steps are the same. In order to analysis, the time complexity of the after four steps of LSVM-HQ-SAX-DTW-K can be further abbreviated as
+ + + , where ,
w
m
L
)
2Lw
PL
)
w
m
L
(
O
O
(
KPw
)
O
(
Nsv
3)
P
L
, andP
K
))
(
m
P
P
. At the same time, the time complexity of the after four steps of LMPM can be further abbreviated as
+ + +
)
Lm
O
(
)
(
O
PL
O
(
P
log L
)
O
(
+III. EXPERIMENTS
A. Traffic datasets
The dataset of wireless network traffic used in our experiments is directly downloaded from the Community Resource for Archiving Wireless Data at Dartmouth (CRAWDAD), which is a wireless network data resource for the research community. The dataset is collected by Simple Network Management Protocol (SNMP) with polling each Access Point (AP) in every 5 minutes at Dartmouth wireless campus network from the autumn in 2002 to the winter in 2004. Through parsing these SNMP packets, we can obtain 287 points for everyday, and each point measured in Kilobyte (KB) denotes the cumulative bulk of IP traffic in 5 minutes. Analyzing the characteristics of the dataset from CRAWDAD, we find that the traffic always shows a certain self-similarity.
B. Performance indicators
actual forecasted actual
y
y
y
error
forecast
100
%
(5)
n
i iactual
i actual i y forecasted y y n error forecast mean
1 ( )
) ( ( ) 1 % 100 (6)
In this paper, the amount of training data vs. average training time is used to analyze on real-time computing capability of algorithms.
C. Experimental results
We use all of the real data from CRAWDAD to compare forecast accuracy among LMPM, global MPM, LSVM-DTW-K, and LSVM-HQ-SAX-DTW-K. The experimental results are shown in Table 1. To make the figure look more clearly, we merely display a little proportion of experimental results in Fig. 1.
TABLE 1. Comparison of forecast accuracy among four algorithms.
Forecast Error Algorithm
<5% 5%-10%
10%-20% >20%
Mean Forecast
Error
LMPM 32632 27193 5439 2719 6.89% global
MPM 5439 10877 29912 21755 25.13%
LSVM-DTW-K 26105 18383 14650 8845 15.29%
LSVM-HQ-SAX- DTW-K
31157 21375 12039 3412 9.67%
Figure 1. Comparison of forecast accuracy among four algorithms.
Comparing among LMPM, global MPM, LSVM-DTW-K and LSVM-HQ-SAX-LSVM-DTW-K, the proportions of forecasting points fallen into 5% error regions are 48.00%, 8.00%, 38.40% and 45.83%, respectively, as well as the proportions of forecasting points fallen into below 20% error regions are 96.00%, 68.00%, 86.99% and 94.98%, respectively. Moreover, the mean forecast error of LMPM is also smaller than those of global MPM, LSVM-DTW-K and LSVM-HQ-SAX-DTW-K. It is can be seen that the improved algorithm, LMPM, has favorable forecasting accuracy.
Through traversing all of the real data from CRAWDAD, the amount of training data vs. average training time is used to analyze on real-time computing capability of LMPM. The parameters of computer used for our experiments are as follows: operation system is Windows XP, CPU is Intel (R) Pentium (R) D for 2.80 GHz, and memory is 1GB. To make the table look more clearly, we merely list a little proportion of experimental results in Table 2, and the all results are shown in Fig. 2.
2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14
Amount of Training Data (Days)
A v er a ge T raining T im e ( S ec onds ) LMPM LSVM-DTW-K LSVM-HQ-SAX-DTW-K
Figure 2. Comparison of real-time computing capability among three algorithms.
are the upper limit required by real-time computing. In Fig. 2, with the increasing of the amount of training data, the average training times of all three algorithms increase gradually. The estimation of the embedding dimension is the main factor that influences the real-time computing capability of LMPM or LSVM based on algorithms. Comparing the real-time computing capability among four algorithms, LMPM is satisfactory.
TABLE 2. Comparison of real-time computing capability among four algorithms.
Average Training Time (Seconds) Amount
of Training
Data (Days)
LMPM global MPM
LSVM-DTW-K
LSVM-HQ-
SAX-DTW-K
1 0.0513 3.8273 0.0805 0.0451
2 0.1541 36.8750 0.2205 0.1202
3 0.2878 120.7500 0.4563 0.2521
4 0.4253 422.9844 0.5920 0.3403 5 0.5919 - 0.9098 0.4214
6 0.8659 - 1.3671 0.8020
7 1.1508 - 1.8545 0.9700
8 1.5071 - 2.3127 1.2425
9 1.9336 - 2.8456 1.5820
10 2.2991 - 3.6279 1.7906 11 2.7976 - 3.7382 2.2342
12 3.3399 - 4.2413 2.4951
13 3.9441 - 5.2929 2.8523
14 4.7117 - 6.0380 3.3405
15 5.15 - 7.0573 3.6238
16 6.2601 - 8.2800 4.0329
17 7.0441 - 9.3071 4.7806
18 7.9537 - 10.5502 5.3724
19 9.0629 - 11.6622 5.8422
20 9.3577 - 12.8510 6.9803
IV. CONCLUSIONS
In this paper, the number of the nearest neighbor points is calculated by AICi information criterion, which is an improved variant of the Akaike information criterion , and the issue that the selection of the number of the nearest neighbor points is experience-relied in LSVM-DTW-K has been resolved.
Ki strategy is proposed in this paper and used to kick the bursty points out from the NNPS. Ki strategy is an improved “Dynamic K” strategy which is used in LSVM-DTW-K and LSVM-HQ-SAX-DTW-K, and the issue that the selection of the bursty points kicked out
from the NNPS is still experience-relied in LSVM-HQ-SAX-DTW-K has been resolved.
In a word, LMPM is an effective method to deal with model for wireless network traffic. The key of LMPM is to search out some feature points from network traffic dataset for constituting a NNPS. Then, the NNPS is pruned by Ki strategy and used as training dataset to input MPM model. Experimental results show that forecasting accuracy and real-time computing capability of LMPM are much better than that of global MPM.
ACKNOWLEDGMENTS
This research was partly supported by the Key Technology Research and Development Program of Sichuan Province under grant No. 13ZC2178, and the Applied Research Fund of Chengdu Municipality under grant No. 12DXYB127JH. The authors are grateful to all the anonymous referees.
REFERENCES
[1] G. E. P. Box, G. M. Jenkins and G. C. Reinseleds., "Time Series Analysis: Forecasting and Control”, Prentice Hall, 1999.
[2] I. W. C. Lee and A. O. Fapojuwo, “Analysis and modeling of a campus wireless network TCP/IP traffic”, Computer Networks, vol.53, no.15, 2009, pp.2674-2687. [3] Gowrishankar and P. S. Satyanarayana, “Neural Network
Based Traffic Prediction for Wireless Data Networks”, International Journal of Computational Intelligence Systems, vol.1, no.4, 2008, pp.379-389.
[4] N. Cristianini and J. Shawe-Tayloreds, “An Introduction to Support Vector Machines”, Cambridge University Press, 2000.
[5] Jia Shu Zhang, Jian Liang Dang and Heng Chao Li, “Local support vector machine forecasting of spatiotemporal chaotic time series”, Acta physica sinica, vol.56, no.3, 2007, pp.67-77.
[6] R. G. L. Gert, E. G. Laurent, B. Chiranjib and I. J. Michael, “Minimax Probability Machine, in Advances in Neural Information Processing Systems 14”, Cambridge: MITPress, 2002.
[7] Xing Wei Liu, Xu Ming Fang, Zhen Hua Qin, Chun Ye and Miao Xie, “A Short-Term Forecasting Algorithm for Network Traffic Based on Chaos Theory and SVM”, Journal of Network and Systems Management, vol.19, no.4, 2011, pp.427-447.
[8] E. J. Hannan and B. G. Quinn, “The determination of order of an autoregression”, Journal of the Royal Statistical Society. Series B (Methodological), vol.41, no.2, 1979, pp.190-195.
[9] Hong Zhi An, Zhao Guo Chen and E. J. Hannan, “Autocorrelation, autoregression and autoregressive approximation”, Annals of Statistics, vol.10, no.3, 1982, pp.926-936.
[10]Yi Liu, De Pei Bao, Ze Hong Yang, Yan Nan Zhao, Pei Fa Jia and Jia Qin Wang, “Research of new similarity measure method on time series data”, Application Research of Computers, vol.24, no.5, 2007, pp.112-114. [11]Xing Wei Liu, Hua Li, Lei Chen and Xu Chen, “An
[12]S. Sullivan, “Evaluation of support vector machines and minimax probability machines for weather prediction”, 2008.
[13]S. O. I and A. M. J, “Comparison of criteria for estimating the order of autoregressive process: a Monte Carlo approach”, European Journal of Scientific Research, vol.30, no.3, 2009, pp.409-416.
[14]H. Akaike, “Autoregressive model fitting for control”, Annals of the institute of statistical mathematics, vol.23, no.1, 1971, pp.163-180
[15]R. Shibata, “Selection of the order of an autoregression model by Akaike information criterion”, Biometrika, vol.63, no.1, 1976, pp.117-126.
[16]H. Akaike, “A Bayesian analysis of the minimum AIC procedure”, Annals of the Institute of Statistical Mathematics, vol.30, no.1, 1978, pp.9-14.
[17]T. Bengtsson and J. E. Cavanaugh, “An improved Akaike information criterion for state-space model selection”, Computational Statistics & Data Analysis, vol.50, no.10, 2006, pp.2635-2654.
Design of NARMA-L2 Neural controller for an Induction Motor’s
Speed Control
INOAN Iulia, ABRUDEAN Mihail
Technical University of Cluj – Napoca, Romania,
Department of Automation, Faculty of Automation and Computer Science, 26-28 Baritiu, 400027 Cluj-Napoca, Romania,
iulia.inoan@aut.utcluj.ro mihai.abrudean@aut.utcluj.ro
Abstract – This paper presents a design method for an induction motor’s (IM) speed control using a neural network controller. The role of the motor is to rotate the hearth of a rotary hearth furnace (RHF) in a jerky regime, to ensure the proper loading and unloading of billets. The neural controller in use is the NARMA-L2 controller given in MATLAB® since the model of the IM is nonlinear. After training the neural network with a set of input output pairs the neural controller results. Since simulating the neural closed loop control structure results in chattering of the plant’s output signal the authors propose the usage of a filter for smoothing the controlled motor’s speed.
Keywords: neural controller, NARMA-L2 controller, induction motor, speed control.
I. INTRODUCTION
The main procedure used for manufacturing seamless tube pipes is the hot rolling process. The hot rolling process is very complex and it involves several stages. The basic stage consists in heating up blocks of billets from the ambient temperature to the rolling temperature. The scope of the heating is to lead the billets material from the elastic domain to the plastic one. The billet heating process is carried out inside the rotary hearth furnace (RHF), thus the RHF is the basic aggregate for the hot rolling process [1].
The RHF has a continuous functioning in the technological flow of the rolling line. The furnace has five regulating temperature areas that have a total of 48 burners and consists of a sector for loading billets, two sectors for heating, a sector for preheating, and a sector for unloading billets [2, 3]. The supply and evacuation of billets is carried out with the help of a loading machine and an unloading one that work only when the heart is stopped [4].
The furnace’s hearth is rotated by two action mechanisms placed at the exterior of the furnace in reverse direction. The rotation regime of the hearth is jerky with stops at fixed angles and the acting system is reversible, meaning that the hearth can be rotated in both directions. The measurement of the rotation is done with an incremental encoder. The billet’s loading on to the
hearth is being done uniformly on the entire sitting circle. In order to ensure the entrance of the loading or unloading clipper’s jaws and also for an optimum heating of the billets a minimum distance between two adjacent billets, measured on the sitting circle, is left. This distance equals at least with the diameter of the billet and will not be below 100 mm [5].
Under the metal frame that supports the furnace’s hearth sits a rack with 597 teeth, with a width of 300 mm, used for the rotation of the hearth. The toothed rim
has 34 sectors of 10˚ 15’14’’ each, and a sector of 11˚
29’26’’. The internal diameter of the rim is 11640 mm at the centre of the hearth and 11940 mm at the exterior of the furnace [6]. The rim conjugates with two pinions of 17 teeth each, placed at opposite direction. The two pinions are activated by reducers with three steps, by two electric engines. The two electric engines are induction motors (IM) with the coiled rotor, each one having the power of 37 KW [6].
The command of the motors is being done manually by an operator with the help of a command key.
In practice only two different diameters are used for billets: 150 mm and 180 mm, thus for each diameter the step of rotation of the hearth is calculated in [6]. Further work will treat the case of a 150 mm in diameter billet, thus for this diameter resulted a loading capacity of 192 billet and a rotation step of 1.75 degrees. The number of IM rotation needed in order to complete a full rotation step is 49.82 rotations [6].
A. Problem statement
Currently all the above described operations that represent a full cycle of loading and unloading are done manually, since the mounted furnace control system failed to ensure the accuracy needed.
For precise control of the hearth’s rotation step a modern drive is required in order to meet high precision requirements. Thus a noiseless start and stop of the furnace hearth by using a speed control system is impetuous.
through the appliance of intelligent control. The type of control proposed in this paper is a NARMA-L2 neural network controller.
II. INDUCTION MOTOR MATHEMATICAL MODEL
This section describes the nonlinear mathematical model for an induction motor. The model is the fifth-order model that gives the dynamics of an IM with one pole pair in a fixed frame a – b, attached to stator [7]. The model is defined by the following equations [8].
1 1 1 aa b M a
b
b b M a
a a
a s a s
b b
b s b s
f
M R
a b b a r d L i dt d L i dt di d
u R i dt dt L
di d
u R i dt dt L
K
L M
d
i i
dt J L J J
(1)
In the model described above the state variables are
the rotor speed, the rotor fluxes a, b, and the stator
currents ia, ib. The stator voltages ua, ub constitute the
control signals and their form is given in (2). LM represents the mutual inductance, while Ls, Lr are the stator and the rotor inductances, Rs, Rr are the stator and the rotor windings resistances, J is the moment of inertia, Kf is the friction coefficient and MR is the load torque.
220 2 sin(2 ) 2 220 2 sin(2 )
a b u f u f t t (2)
where f represents the frequency of the stator
voltages and t represent time.
For concision the following notation were used: 2
1
; ; 1
r M
r s r
R L L
L L L L
M .
s rL
(3)
The induction motor used for the rotation of the hearth has one pair of stator poles and it is designed at a nominal power of 37kW, a rated speed of 2940 rpm, respectively a nominal frequency of 50 Hz. The
constants used in (1) are as follows: J = 0.4 Kg·m2, Kf=
0.1115, Rr = 0.156 Ω, Rs = 0.294 Ω, Lr = 0.0417 H, Ls =
0.0424 H, LM = 0.041 H. The values of α, and
coefficients result immediate by using the parameters described above [9, 10].
III. NEURAL NETWORK CONTROLLER
Intelligent control systems such as neural network controllers have the ability to approximate nonlinear systems [11].
NARMA-L2 controller, also known as feedback linearization controller when the plant model has a particular form, is first trained using input output data
pairs and then reconfigured to form a controller that suppresses the nonlinearity of the system very efficiently [12]. This type of control transforms nonlinear systems dynamics into linear dynamics by canceling the nonlinearities [13].
The first step in using the NARMA-L2 controller is to identify the plant model [14].
Figure 1. NARMA-L2 control structure [14].
The model of the plant is determined by two neural networks approximation functions f and g, after the controller is trained offline by using a set of input output data pairs [15]. The f and g functions are the functions of the past values of both the output (y) and the control effort (u), values recorded by tapped delay lines (TDL), as shown in Fig. 1 [14].
The second step is obtaining the neural controller which is simply the rearrangement of the two
sub-networks f and g trained offline, thus the computation
time is reduced [16].
A. NARMA-L2 controller design for the IM’s speed control
For the induction motor’s speed control the authors
used the NARMA-L2 neural controller from MATLAB®
neural network toolbox [14]. In order to design the controller one needs to use the plant model, in this case the induction motor’s model. For a proper training of the network the model of the plant must have one input and one output. Thus in this case the plant input is consider to be the frequency of the stator voltages and the plant output is consider to be the induction motor’s speed, obtained from the following dependence on the rotor
speed .
30
n
(4)
Figure 2. The plant input signal used for the network training.
Figure 3. The plant output signal used for the network training.
Figure 4. The validation error signal.
The set of data presented in Fig. 2 and Fig. 3 is divided into a training set and a validation set. The validation error signal presented in Fig. 4 is achieved after 6 epochs.
IV. SIMULATION RESULTS
The obtained NARMA-L2 controller is simulated
using MATLAB® Simulink in a closed loop control
structure. The speed control system must achieve the motor starting, constant maintenance of speed at a desired value, and also the motor braking. The induction motor speed resulted from the neural control closed loop system is presented in Fig. 5. As shown in this figure a drawback of this controller is that it results in chattering of the output signal, in this case the induction motor’s speed.
In Fig. 6 the control signal generated by the NARMA-L2 controller is depicted. The control signal is applied to the induction motor’s model and it is processed in order to represent the frequency of the stator voltages. It may be noted that the command signal is very oscillating.
In order to smooth the IM speed the authors propose the usage of a first order filter (Hf) on the portion designed for the constant maintenance of speed.
Figure 5. NARMA-l2 controlled induction motor’s speed.
Figure 6. The NARMA-L2 control signal.
Figure 7. The NARMA –L2 smoothed speed for the induction motor.
Figure 8. The smoothed NARMA-l2 control signal.
( ) 1
8 1
f
H s
s
(5)
of filter for the constant maintanence of speed to the usage of saturation element for braking. The obtained IM’s speed is presented in Fig. 7 and the corresponding control signal for the NARMA-L2 controller in this case is shown in Fig. 8. The switch block shifts at 5.7 s. One can observe the control signal and the motor speed improvements, namely their smoothing.
It was prior specified that the rotation of a complete step requires a number of 49.82 rotations from the motor. Next, the authors calculate the number of rotations made by the motor in the case presented above. In order to calculate the number of motor’s rotation the authors have divided the motor’s speed curve given in Fig. 7 in several sections. The sections corresponding to starting and braking of the motor from the chart are approximated by ramps. The average speed (n) of each section is calculated and the number of rotations (r) results from the following formula:
rotations 60
n t
r (6)
where t represents the time interval fot the given section. The first section corresponds to the selection between t1=1.30 s and t2=2.37 s, from a motor speed of 0 rpm to 403.41 rpm. The motor’s average speed is 201.7 rpm and the corresponding number of rotations is 3.59. The second section is the curve between t2=2.37 s and t3=3.97 s. The motor’s average speed for this section is 626.59 rpm and the number of rotations is 16.709. The third section is the selection between t3=3.97 s and t4=5.7 s. The motor’s average speed for this section is considered to be 850 rpm and the corresponding number of rotations is 24.5. The last section is between t4=5.7 s and t5=6.4 s with an average speed of 425 rpm and a number of rotations of 5.02.
The total number of rotations is 49.819 which is close enough to the number of rotations needed in order to complete a step in the rotation of the rotary hearth.
V. CONCLUSIONS
This paper presents the design of a NARMA-L2 controller for the speed control of an induction motor used to rotate the hearth of a rotary hearth furnace. The NARMA-L2 control structure is simple and it has the advantage of reducing computation time since the controller is simply a rearrangement of a neural network plant model, trained offline.
A shortcoming of this controller is that it results in chattering of the plant output signal. In order to smooth the IM speed the authors propose the usage of a first order filter for the constant maintenance of speed and a saturation element for the motor braking. A switch allows shifting from one element to another. The usage of the proposed solution brings a major improvement in both the control signal and the plant’s output signal.
REFERENCES
[1] I. Inoan, D.C. Dumitrache, and T. Szelitzky, A control system design for the positioning system for a billets
unloading machine, 2012 IEEE International Conference on Automation, Quality and Testing, Robotics, Cluj-Napoca, Romania, 24-27 May, 2012.
[2] V. Muresan, Mathematical modelling and numerical simulation of the temperature control system in a furnace with rotary hearth, IEEE International Joint Conferences on Computational Cybernetics and Technical Informatics Proceedings, Timisoara, pp. 203-208, 2010.
[3] V. Muresan, Temperature control in the furnace with rotary hearth, IEEE International Conference on Automation, Quality and Testing, Robotics, Cluj-Napoca, Romania, vol. 1, Cluj-Napoca, Romania, pp. 1-6, 28 May, 2010.
[4] I. Inoan, D.C. Dumitrache, and T. Szelitzky, Parametric identification of a positioning system for a billets unloading machine, 14th IFAC Symposium on Information Control Problems in Manufacturing, vol. 14, no. 1, Bucuresti, Romania, pp. 1722-1726, 2012.
[5] V. Muresan and M. Abrudean, Control System Optimization of Rotary Hearth Furnace Charging / Dischargin, 5th International Symposium on Applied Computational Intelligence and Informatics Proceedings, Timisoara, pp. 277-282, 2009.
[6] V. Muresan and M. Abrudean, The Control of the step for the furnace with rotary hearth in the technologic flow for manufacturing pipes without welding, IEEE International Conference on Automation, Quality and Testing, Robotics Proceedings, Cluj-Napoca, pp.258-261, 2008.
[7] R. Yazdanpanah, J. Soltani and G.R. Arab Markadeh,
Nonlinear torque and stator flux controller for induction motor drive based on adaptive input-output feedback linearization and sliding mode control, Energy Conversion and Management, vol. 49, pp. 541-550, 2008.
[8] C. Aurora, and A. Ferrara, Sensorless speed and flux regulation of induction motors: a sliding mode approach, Proceedings of 16th IFAC World Congress, vol. 16. Part 1,
Prague, 2005.
[9] V. Muresan, Industrial processes control, UTPress Publisher, Cluj-Napoca, 2011.
[10]I. Inoan, M. Abrudean, Control of an induction motor using the relay method approach, unpublished.
[11]S. S. Mokri, H. Husain, W. Martono and A. Shafie, Real time implementation of NARMA-L2 control of a single link manipulator, American Journal of Applied Sciences, vol. 12, no. 5, pp. 1642-1649, 2008.
[12]K. Srakaew, J. Kananai, and R. Chancharoen, Trajectory control of a nonlinear dynamical system using NARMA L2 neurocontroller, Journal of Computer and Information Technology.
[13]A. Pukrittayakamee, O. De Jesus, and M. Hagan,
Smoothing the control action for NARMA-L2 controllers, The 45th Midwest Symposium on Circuits and Systems, vol.3, pp. III 37- III 40, 4-7 Aug. 2002.
[14]H. Demuth and M. Beale, Neural network toolbox user guide – For use with Matlab®, MathWorks, Inc., 1992-2002.
[15]F. Chetouane and S. Darenfed, Neural network NARMA control of a gyroscopic invertum pendulum, Engineering Letters, vol. 16, no. 3, 2008.
