About Stability of Mechatronic Systems Driven by Asynchronous Motors

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1 Monica Adela Enache Soin Enache Micea Dobiceanu About Stability of Mechatonic Sytem Diven by Aynchonou Moto MONICA ADEA ENACHE SORIN ENACHE MIRCEA DOBRICEANU Electomechanical Faculty Univeity of Caiova Decebal Steet Caiova 44 ROMANIA Abtact: - hi pape peent two method fo tability analyi of mechatonic ytem diven by aynchonou moto: an analytical method and a numeical one oiginal conceived by autho. he peentation i accompanied by imulation and expeimental eult leading to cedible concluion. Key-Wod: - tability mechatonic ytem aynchonou moto paamete imulation Matlab expeiment. Intoduction he tability poblem fo mechatonic ytem diven by aynchonou moto i widely appoached in liteatue [] [] [3] [6] [4] [5] [6] etc. hi pape develop only two method of analyi. he fit one an analytical method analyze the machine inductivitie influence on tability. he econd one an oiginal numeical method conceived by autho [9] analyze the effect of the eitance and inetia moment modification. Analytical method Futhe on we aim that by uing known epeentation of the tanfe locu and of the amplitude-phae chaacteitic to analyze the influence of the machine winding eitance on tability. In thi pupoe it i impoed at the beginning to etablih an adequate mathematical model of the ytem which i efeed to. Futhe on the induction moto i uppoed to be upplied by mean of a inuoidal voltage ouce having vaiable fequency. In ode to obtain the elation neceay to cay out the popoed tudy the following matix equation witten in accodance with [] will be ued: I d ( I q ( = I df ( I qf ( =. Id ( Iq (. + U d( ( Idf ( I ( qf whee the following notation have been ued: = - time contant of the tato winding; R = - time contant of the oto winding; R = winding; h - leakage coefficient of the machine I ( I ( h df = d + Id ( h I qf ( = I q ( + I q (. ( ISSN: Iue Volume 7 Januay 8

2 Monica Adela Enache Soin Enache Micea Dobiceanu he motion equation i added to the elation (: J p d = 3 ph ( iqid idiq m. (3 dt If the electical tanient poce i conideed to be much fate than the mechanical one (J i vey geat it eult that the mathematical model which will be ued futhe on i limited to the matix equation. hi one may be alo witten a: [ Y ( ] [ A] [ Y ( ] + [ B] [ U ( ] = (4 o equivalently: [ Y ( ] = ( [ I ] [ A] [ B] [ U ( ] (5 which i the input-output opeational equation fo the analyzed multi-vaiable ytem. he tanfe matix i obtained fom thi equation: [ H ( ] = ( [ I ] [ A] [ B] adj( = det( [ I ] [ A] [] I [ A] [ B] (6 whee I i the unit matix. he tanfe function denominato will have the fom: 3 4 n ( a + a + a + a3 + a 4 = (7 with a = ( a = (8 + a = a3 = + a 4 =. Futhe on the following appoximation will be ued: µ = +. (9 Fo a concete cae of an induction moto ( R =75 h = 498 R =55 = 59 H = 58 H H the following data ae obtained: = µ =. ( In ode to detemine the tanfe function pole fo the tudied ytem it denominato will be made equal to zeo: n ( = ( with n( given by the elation (7 and (8. he following pole have been obtained by olving thi equation: a If µ 34 = µ ± µ ( ± j( + ; 4 ( b If µ < 34 = µ ± j µ ( ± ( +. 4 (3 A one can obeve in the elation ( µ > µ ( iepective of the 4 machine paamete o the opeation point. So the eal pat of the tanfe function pole i alway negative. In concluion the tudied ytem i alway table. Since the inductance and ae invee popotional with µ thee one have a nontabilizing effect on the induction moto opeating at vaiable fequency. 3 Numeical method hi method detailed in [] ha a tating point the following elation witten in pe unit value: i d h = k (4 ISSN: Iue Volume 7 Januay 8

3 Monica Adela Enache Soin Enache Micea Dobiceanu d = + ( k k( i + + j + k + j + k ( + j (5 whee ( = k k = = x x. (6 At the ame time it mut be mentioned that the pe unit quantitie ued in the peviou equation have been noted with the quantitie depicted hee having the ignificance fom [9]. he equation (5 may alo be witten in the following fom: k = i h d (7 a anfe locu. o equivalently: k = G ( id with G ( =. (8 h Similaly the equation (6 become: i d = G( ( (9 whee + j G + ( = k + ( k + k + j + k ( + j ( he peviou elation lead to the equivalent cheme of the induction machine opeating at vaiable fequency. b Amplitude phae chaacteitic. Fig.. Machine block cheme in the mentioned ituation. c Pulation - amplitude chaacteitic. 4 Simulation A MAAB pogam fo the tability analyi ha been conceived by uing the peviou cheme. he epeentation fom figue 3 and 4 have been obtained by unning thi pogam fo the concete cae of a moto ated at kw. hee mut be alo mentioned the impotance of the intoduced method eulting fom the poibility to emphaize the machine paamete influence and epecially the inetia moment influence on tability when opeating at vaiable fequency fact that povide oiginality to thi method. d Phae - pulation chaacteitic. Fig.. Gaphic dependence coeponding to the cae R =75 (continuou line and R =5 (dotted line. ISSN: Iue Volume 7 Januay 8

Monica Adela Enache Soin Enache Micea Dobiceanu In ode to catch quantitatively thee intedependence the following table ha been filled. a anfe locu. able Pa.

Pe unit value Phae magin [degee] 75 988 7554 R 5 33 74 55 75 7554 45 593 537 4 34 7554 J h 3 43 4765 R hee eult help u to emphaize a few impotant concluion

ha alo a an effect the deceae of the machine tability and conveely; - the inetia moment inceae contibute to the tability inceae.

5 Expeimental cicuit In ode to confim the peviou concluion a eie of expeimental tet have been pefomed; a few of them ae detailed futhe on.

4 Monica Adela Enache Soin Enache Micea Dobiceanu In ode to catch quantitatively thee intedependence the following table ha been filled. a anfe locu. able Pa. Ab. value [ ] [H] [kgm ] Pe unit pa. Pe unit value Phae magin [degee] R J h R hee eult help u to emphaize a few impotant concluion egading the eitance influence on the tudied ytem tability: - the deceae of the tato winding eitance lead to the tability deceae; - the oto eitance deceae ha alo a an effect the deceae of the machine tability and conveely; - the inetia moment inceae contibute to the tability inceae. b Amplitude phae chaacteitic. 5 Expeimental cicuit In ode to confim the peviou concluion a eie of expeimental tet have been pefomed; a few of them ae detailed futhe on. hu the expeimental cicuit ha the tuctue depicted in the following figue []. c Pulation - amplitude chaacteitic. d Phae - pulation chaacteitic. Fig.3. Gaphic dependence coeponding to the cae R' =55 (continuou line and R' =45 (dotted line. Fig.4. Scheme of the expeimental cicuit. he notation have the following meaning: IM induction moto; VFSC voltage and fequency tatic convete; DAS data acquiition boad; ISSN: Iue Volume 7 Januay 8

Monica Adela Enache Soin Enache Micea Dobiceanu CSB command and ynchonization block; PB potection block; MPB magnetic powde beak; BCB bake command block; SA 6 connection block.

In ode to obtain the detemination in dynamic egime the expeimental cicuit depicted befoe ha been caied out having an acquiition boad DAS a a cental element.

5 Monica Adela Enache Soin Enache Micea Dobiceanu CSB command and ynchonization block; PB potection block; MPB magnetic powde beak; BCB bake command block; SA 6 connection block. A pictue of thi cicuit i depicted fo confomity. Fig.5. Pictue of expeimental cicuit. In ode to obtain the detemination in dynamic egime the expeimental cicuit depicted befoe ha been caied out having an acquiition boad DAS a a cental element. hi high peed analogical and digital inteface ha been aembled inide a compute. he acquiition and the adequate data poceing ae enued with the help of a pogam conceived in Matlab. he main chaacteitic of the boad ae peented in the following table. able Chaacteitic Numbe of analogical input Reolution of the analogical-numeical convete Input: unipola bipola Value 6 unipola input o 8 diffeential bit + V 3 ± V 4 Domain election By the pogam 5 Amplification 5 of the input domain 6 Channel DA ( bit 7 Digital line IO 3 bit 8 Maximum ampling khz fequency 9 Acquiition time 4 m he coepondence between the amplification of the input domain the input type and the maximum ate fo canning eveal channel o that to obtain the ame eult a in the cae when a ingle channel i canned i emphaized in the following table. able 3 Amp Unipola Bipola Fequency + V ± V khz + V ± V khz mv ± mv 7 khz 5 + mv ± mv 3 khz Data tanfe can be made in thee way: - by diect tanfe into the memoy without the intemediay mico-poceo DMA (Diect Memoy Acce; - by uboutine of inteuption; - by pogam. he command and ynchonization block CSB enue the data acquiition tat befoe the moto tating. he delay occuing between the two moment i then coected by oftwae. he module PI ha been ued fo adapting the meaued cuent to the value equied by the boad. It contain a cuent tanfome in whoe econday thee i connected a calibated eitance; the voltage dop occuing on thi eitance i of maximum + V. 6 Expeimental Reult he gaphic depicted in the following figue have been obtained with the help of the peviou cicuit fo the cae of an indiect voltage and fequency tatic convete. Fig.6. Gaphic dependence coeponding to the cae R =75 ( and R =5 (. ISSN: Iue Volume 7 Januay 8

Monica Adela Enache Soin Enache Micea Dobiceanu - the inetia moment value inceae lead to the inceae of the cuent tabilization time and to the tability deceae.

A one can obeve thee expeimental concluion confim the concluion obtained with the new numeical method fo analyi. Fig.7. Gaphic dependence coeponding to the cae R' =55 ( and R' =45 (. Fig.8.

6 Monica Adela Enache Soin Enache Micea Dobiceanu - the inetia moment value inceae lead to the inceae of the cuent tabilization time and to the tability deceae. Moeove when the invete with pe-etablihed commutation moment i ued it i alo noticed that the maximum value of the moto phae cuent ae modified. A one can obeve thee expeimental concluion confim the concluion obtained with the new numeical method fo analyi. Fig.7. Gaphic dependence coeponding to the cae R' =55 ( and R' =45 (. Fig.8. Gaphic dependence coeponding to the cae J=6 kg.m ( and J=4 kg.m (. A few inteeting concluion egading the induction moto paamete influence on the dynamic egime behaviou of the analyzed diving ytem can be emphaized with the help of the pogam detailed befoe: - the tato eitance deceae inceae vey little the duation of the cuent tanient poce and deceae the ytem tability epectively; - the oto eitance deceae caue the inceae of the tabilization time and the tability deceae epectively; - when the value of the tato inductance inceae the tanient poce duation inceae; - the oto inductance value inceae alo involve the inceae of the tanient poce duation; - the main inductance deceae detemine a fate tabilization of the poce (tability inceae; Refeence: [] R. Belman. D'Hondt Analyi of the Audible Noie of hee Phae Squielcage Induction Moto Supplied by Invete IEEE anaction on Induty Application Volume IA-3 Septembe-Octobe 997 pp [] A. Campeanu I. Vlad A. Ionecu S. Enache Etabliement of Electical Machine Optimum Contuctive Dimenion EECROMOION 3 Maakeh Maoc vol. p INSPEC (Mateial Identity Numbe F7-4- Inpec claification code B83a.c. machine Optimiation technique. [3] A. Campeanu A. Ionecu I. Vlad S. Enache Modelling and Simulation of Magnetic Satuation in Induction Moto Intenational Electic Machine and Dive Confeence IEMDC 7 CD veion AF-6 IEEE Catalog Numbe: 7EX597C ISBN: [4] A. Campeanu I. Vlad S. Enache Apect Regading Optimal Deign of High Powe Electical Machine BaMov he 5th Intenational Confeence on Optimization of Electic and Electonic Equipment OPIM ' INSPEC (Mateial Identity Numbe D5-- Inpec claification code B83 a.c. machine. [5] A. Campeanu M. Radulecu I. Vlad S. Enache Influence of Co-Satuation fo Modeling and Simulation of the Dynamic Pocee in the Induction Moto IEEE Region 8 EUROCON7 - he Intenational Confeence on Compute a a ool Waaw Poland 9- eptembie 7 IEEE Catalog Numbe: 7EX67C ISBN: X ibay of Conge: p. 83. [6] Y. P. Chiu F. Cheng C. ing Algebaic Method fo Optimizing EPQ Model with Rewok and Scap WSEAS RANSACIONS on SYSEMS Iue Volume 6 Novembe 7 pp [7] B. Delemontey B. Jacquot C. Iung B. De Fonel J. Bavad Stability Analyi and ISSN: Iue Volume 7 Januay 8

7 Monica Adela Enache Soin Enache Micea Dobiceanu Stabiliation of an Induction Moto Dive with Input Filte 6 th Euopean Confeence on Powe Electonic and Application Sevilla Spain 995. [8] S. Enache I. Vlad M.A. Enache Apect Regading Dynamic Regime of Induction Moto Contol by the Stato Flux Powe Engineeing Enegy and Dive 7 POWERENG 7 Setubal Potugal Intenational Volume Iue -4 Apilie 7 ISBN IEEE Xploe DOI:.9 POWERENG pp [9] S. Enache R. Pejbeanu A. Campeanu I. Vlad Apect Regading Simulation of the Satuated Induction Moto Contol by the Voltage Invete Commanded in Cuent IEEE Region 8 EUROCON7 - he Intenational Confeence on Compute a a ool Waaw Poland 9- eptembie 7 IEEE Catalog Numbe: 7EX67C ISBN: X ibay of Conge: p. 86. [] S. Enache A. Campeanu I. Vlad M.A. Enache A New Method fo Induction Moto Stability Analyi when Supplying at Vaiable Fequency Poceeding of the 7-th WSEAS Intenational Confeence on SYSEMS HEORY AND SCIENIFIC COMPUAION (ISASC 7 Vouliagmeny Athen Geece Augut ISSN: ISBN: pp. 7-. [] M.A. Enache S. Enache M. Dobiceanu Conideation Regading Detemination of the Induction Moto Paamete Intenational Electic Machine and Dive Confeence IEMDC 7 CD veion AF- 393 IEEE Catalog Numbe: 7EX597C ISBN: [] M.A. Enache M.A. S. Enache M. Dobiceanu Influence of Induction Moto Paamete on Stability in Cae of Opeation at Vaiable Fequency WSEAS Intenational Confeence on SYSEMS HEORY AND SCIENIFIC COMPUAION Vouliagmeny Athen Geece Augut pp [3] M. Hani O. ouhami R. Ibtiouen M. Fadel S. Caux Modelling and Paamete Identification of a Synchonou Machine by Standtill et WSEAS RANSACIONS on CIRCUIS and SYSEMS Iue 9 Volume 6 Septembe 7 pp [4] J.. in. G. Shiau On Stability and Pefomance of Induction Moto Speed Dive with Sliping Mode Cuent Contol Aian Jounal of Contol Vol. No. pp. -3. [5] W. iu H. ang W. Fang Analyi of Powe anfe Ability and Stability fo Voltage Souce Inductive Coupled Powe anfe Sytem WSEAS RANSACIONS on CIRCUIS and SYSEMS Iue 7 Volume 6 July 7 pp [6]. ipo Stability Analyi of a Rectifieinvete Induction Moto Dive IEEE anaction on Induty Application pp [7]. Qing D. Xuegong. Xiong Y. Gang A Dynamic Weighing Sytem Baed on Sytem Model WSEAS RANSACIONS on SYSEMS Iue 8 Volume 6 Augut 7 pp [8] H. Mokull Stabilization of an Induction Moto Dive with Reonant Input Filte th Euopean Confeence on Powe Electonic and Application Deden Gemany 5 p.. [9] N. Vinatou eoia itemelo Ed. Univeitaia Caiova 996. [] Matlab Refeence Guide he Math Wok Inc. Natick Maachuett. ISSN: Iue Volume 7 Januay 8

Original Method for Stability Analysis of Mechatronic Systems with Asynchronous Machines

Original Method for Stability Analysis of Mechatronic Systems with Asynchronous Machines Soin Enache, Auel Campeanu, Oiginal Method fo Stability Analyi of Mechatonic Sytem with Aynchonou Machine SORIN ENACHE, AUREL CAMPEANU, ION VLAD, MONICA ADELA ENACHE Electomechanical Faculty Univeity of