Induction Motor Identification Using Elman Neural Network

Transcription

1 Poceedings of the 5th WSEAS Int Conf on Signal Pocessing, Robotics and Autoation, Madid, Spain, Febuay 15-17, 2006 (pp ) Induction Moto Identification Using Elan Neual Netwok AA AKBARI 1, K RAHBAR 2 and MJ MOHAMMADI AGHIABAD 3 1 Mechanical Engineeing Depatent, Faculty of Engineeing, Fedowsi Univesity of Mashhad 2 Young Reseaches Club, Islaic Azad Univesity, Mashhad Banch 3 NN Co Mashhad Islaic Republic of IRAN Abstact In this pape, we study an induction oto identification in all states and conditions whethe tansient o steady using Elan neual netwok Induction otos have highly nonlinea dynaic behavious whee the paaetes vay with tie and opeating conditions hese nonlinea dynaic behavious ake difficult the identification of induction oto While any applications such as contol [1] need an accuate identification of induction oto, theefoe having an appopiate identification sees to be necessay Hee a ecuent neual netwok intoduced by Elan [2] which has the ability of leaning tepoal pattens as well as spatial ones is eployed fo induction oto identification Ou expeients show that using Elan ecuent neual netwok fo identification could achieve high degee of accuacy in all states and conditions Keywods: Induction Moto, Syste Identification, Elan Neual Netwok, Nonlinea Dynaic Behaviou 1 Intoduction Now a days fo induction otos identifications any ethodologies have been eployed aong which Koubaa [3], Fang et al [4] ay eceive futhe consideation Fang et al [4] descibes an autoatic pocedue fo induction oto using PI contolle whee the tansfe function of a oto at stand still is used to obtained linea paaetic he pobles aise hee ae: a) tansient states ae ignoed, and b) the odel which is obtained within liited ange can not be genealized Koubaa [3] applied an identification ethodology based on RS algoith Hee again as he hi self pointed out the wok was in a peliinay and the soe deficiencies whee obseved that is tansient state and load vaiations ae ignoed Hee we ae going to intoduce a new ethod of induction oto identification using Elan neual netwok which has the ability of leaning tepoal pattens as well as spatial ones We fist descibe an induction oto using its echanical equation hen by ceating leaning dataset in an infinite ange of possible loads, we tain the Elan neual netwok Finally we test the netwok using testing dataset ceated in a siila way hough ou expeiental esults, we found that the identification of induction oto could be done accuately using Elan neual netwok his pape is oganized as follows: Section 2 and 3 oveviews the induction oto echanical equation and Elan neual netwok, espectively Section 4 descibes how Elan neual netwok identify induction oto Section 5 gives the esult obtained fo saple induction oto and finally section 6 gives the conclusion of this pape 1

2 Poceedings of the 5th WSEAS Int Conf on Signal Pocessing, Robotics and Autoation, Madid, Spain, Febuay 15-17, 2006 (pp ) 2 Induction oto echanical equation As in, Fu and sai entioned in [5], in geneal, the echanical equation of an induction oto can be witten as: (1) J ϖ + Bϖ + = e Whee J and B ae the inetia constant and the viscous fiction coefficient of the induction oto syste, espectively; is the extenal load, ϖ is the oto echanical speed in angula fequency and denotes the geneated e toque of an induction oto defined as: e = ( ψ d iqs ψ q ids ) 2 (2) Whee ψ d and ψ q ae the oto-flux linkages; iqs and i ae the stato cluste, and p is the ds pole nubes It is noting that and ae utual inductance and oto self-inductance, espectively Using the field-oientation contol pinciple the cuent coponent is aligned in the diection i qs of the oto flux vectoψ, and the cuent coponent i qs _ is align in the diection pependicula to it In this condition, it is satisfied that: _ (3) ψ = 0, ψ = ψ q d heefoe, taking into account the pevious esults, the equation of induction oto toque (2) is siplified to: (4) e = ψ d iqs = K iqs 4 K Whee is the toque constant, and defined as follow: (5) K = ψ d 4 Whee ψ denotes the coand oto flux d u[k] 3 Elan Neual Netwok Contay to othe feed-fowad neual netwoks, Elan neual netwok has the capability of pesenting tie ie in applications whee tie is integated, it has dynaic behavios, Elan neual netwok ay be used fo identifying, appoxiating, and classifying by having the least siplified conditions Based on Elan intoduced in [2], the Elan netwok coonly is a ecuent neual netwok with thee layes: input laye, hidden laye and output laye Input laye is consisted of two diffeent goups of neuons: input neuons and context neuons A thee-laye Elan netwok is shown below Context neuons Input neuons Hidden laye x[k] Output laye Input laye Fig1 Elan neual netwok In geneal, in feed fowad netwoks eploying hidden units and a leaning algoith, the hidden units develop intenal epesentations fo the input pattens which ecode those pattens in a way that enable the netwok to poduce the coect output fo a given input In the Elan achitectue, the context units eebe the pevious intenal state hus, the hidden units have the task of apping both an extenal input and also the pevious intenal state to soe desied output Because the pattens on the hidden units ae those which ae saved on context, the hidden units ust accoplish this apping and at the sae tie develop epesentations which ae useful encodings of the tepoal popeties of the sequential input hus, the intenal epesentations that ae developed ae sensitive to tepoal context; the effect of tie is iplicit y[k] 2

3 Poceedings of the 5th WSEAS Int Conf on Signal Pocessing, Robotics and Autoation, Madid, Spain, Febuay 15-17, 2006 (pp ) in these intenal states Note, howeve, that these epesentations of tepoal context need not be liteal hey epesent a eoy which is highly task and stiulus dependent So the netwok can stoe infoation fo futue efeence, it is also able to lean tepoal pattens as well as spatial pattens heoetically, an oiginal Elan neual netwok with all feedback connections fo the hidden laye to the context neuons can epesent an abitay n th ode syste, whee n is the nube of context units 4 Induction oto identification he ability of Elan neual netwok studied in section 3 is to be tained fo identifications plant as induction oto echanical equation descibed in section 2 As illustated in Figue 2, a sequence of input signals u [k], ( k = 0,1,) is fed to both the plant and the Elan neual netwok he output signals y p [ k +1] fo the plant and y [ k +1] fo th e Elan neual netwok ae copaed and the diffeences e[ k + 1] = y p [ k + 1] y[ k + 1] ae coputed he MSE of all e [ k +1] fo the whole sequence is used as a easue of the goodness of identification u[k] Fig2 Induction oto identification using Elan neual netwok 5 Expeiental Results he induction oto used in this case study is a50 HP, 460 V, two poles, 60 Hz oto having the following paaetes: R = 0 087Ω, R = 0 228Ω, s s = 35 5H, = 86 01H, and = 82 59H Plant ( Induc tion Moto) Elan Neual Netwok y [k+1] y p [k+1] - + eo he syste has the following 2 echanical paaetes: J = 1662kg and B = Ns he Elan netwok has hypebolic tangent sigoid tansfe function (Figue 3) neuons in its hidden (ecuent) laye, and linea tansfe function (Figue 3) neuons in its output laye his cobination is special in that two-laye netwoks with these tansfe functions can appoxiate any function (with a finite nube of discontinuities) with abitay accuacy he only equieent is that the hidden laye ust have enough neuons Moe hidden neuons ae needed as the function being fit inceases in coplexity Fig3 ansfe functions use in Elan neual netwok Hypebolic tangent sigoid tansfe function inea tansfe function By assuing = sind(t) cosd(3t) as input, i qs as output, and using an Elan neual netwok oganized as 70 hidden units (1 input, and 1 output) afte 1000 epochs on leaning dataset containing 2400 saples we achieved MSE = 043e-3 on testing dataset Figue 4 shows a step function assuing fo testing load his is vey natual fo induction oto identification, if the condition in which the load falls fo the load handle o added to it siultaneously is consideed In this condition load inceases o deceases as a step function Figue 4 shows i qs calculated using atheatical foulae vs the one which is obtained fo Elan neual netwok As we see hee the Elan neual netwok sees oe ealistic in pactical condition whee i qs neve follows the load siultaneously 3

4 Poceedings of the 5th WSEAS Int Conf on Signal Pocessing, Robotics and Autoation, Madid, Spain, Febuay 15-17, 2006 (pp ) Fig4 esting step load esting load i qs calculated fo atheatic foulas (dash line) vs which was obtain fo Elan neual netwok (solid line) Figue 5 shows the above step load which is infected by a peiodic noisy signal In contast to i qs, calculated fo atheatical foulae which is affected by noisy signal, as in figue 5 the one which is calculated fo Elan neual netwok is oe obustness in noisy conditions his obustness could be contolled though the nube of hidden neuons in the way that when the nube of hidden neuon inceases, the netwok obustness deceases in the cast of loosing accuacy and vice vesa So in eal application we need to find tadeoffs between syste accuacy and obustness Fig5 esting step load infected by peiodic load esting load i qs calculated fo atheatic foulas (dash line) vs which was obtain fo Elan neual netwok (solid line) Figue 6 shows anothe possible condition whee the test load is assued as an ipulse Hee Elan neual netwok esults (figue 6) sees to be oe ealistic copaing with i qs calculated fo atheatical foulae which is oe siila to ipulse signal 4

5 Poceedings of the 5th WSEAS Int Conf on Signal Pocessing, Robotics and Autoation, Madid, Spain, Febuay 15-17, 2006 (pp ) identification An identification ethodology based on the Elan neual netwok was successfully applied in this wok fo induction oto identification he expeients show that Elan ecuent neual netwok fo identification could achieve easonable accuacy and obustness Acknowledgent he authos acknowledges the text editing of M M Rahba, acadeic ebe of Islaic Azad Univesity, Quchan, Ian Fig6 esting ipulse load esting load i qs calculated fo atheatic foulas (dash line) vs which was obtain fo Elan neual netwok (solid line) heefoe, the calculations esulted fo Elan neual netwok is oe natual and ealistic copaing with the calculations esulted fo atheatical foulae in pactice his is because of the siplifications and ignoance of soe nonlinea and dynaic behaviou while calculating using atheatical foulae which in tun leads to having an uneal esponse in eal wold copaing with Elan neual netwok Refeences [1] RJ Wai, HH ine and FJ in Hybid contolle using neual netwok fo identification and contol of induction sevo oto, Neuocoputing, Vol 35 (2000), pp [2] J Elan Finding stuctue in tie, Cognitive Science, Vol 14 (1990), pp [3] Y Koubaa Recusive identification of induction oto paaetes, Siulation Modeling Pactice and heoy, Vol 12 (2004), pp [4] CH Fang, SK in and SJ Wang On-line paaete estiato of an induction oto at standstill, Contol Engineeing Pactice, Vol 13 (2005), pp [5] YC in, C Fu and CY sai Non-linea sensoless indiect adaptive speed contol of induction oto with unknown oto esistance and load, Intenational Jounal of Adaptive Contol and Signal Pocessing Int J Adapt Contol Signal Pocess 2000; 14: Conclusion In this pape we intoduced a new ethodology fo induction oto identification based on Elan neual netwok in all states and conditions whethe tansient o steady As induction otos have highly nonlinea dynaic behavious and the paaetes vay with tie and opeating conditions, so it is too difficult fo 5