HIGH GRADE CONTROL OF LINEAR INDUCTION MOTOR DRIVES HAIDONG YU. Presented to the Faculty of the Graduate School of

Transcription

1 HIGH GRADE CONTROL OF LINEAR INDUCTION MOTOR DRIVES by HAIDONG YU Presened o he Faculy of he Graduae School of The Universiy of Texas a Arlingon in Parial Fulfillmen of he Requiremens for he Degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF TEXAS AT ARLINGTON December 2007

2 Copyrigh by HAIDONG YU 2007 All Righs Reserved

3 ACKNOWLEDGEMENTS I am sincerely graeful o my supervisor Dr. Babak Fahimi for his supervision and suppor. His guidance and encouragemen has been vial o my learning. I hank him for menoring me for compleion of his disseraion. I would like o hank Dr. Raymond R. Shouls, Dr. Wei-Jen Lee, Dr. Kai-Sing Yeung, and Dr. Soonorn Orainara for being in my supervising commiee. Their views and suggesions have been valuable for compleeness of he disseraion. I wish o hank all he members from he Power Elecronics and Conrolled Moion PECM Laboraory for he suppor in compleion of his disseraion. I also wan o hank Dr. Seven D. Pekarek and Mr. Dezheng Wu from Purdue Universiy for heir cooperaion wih PECM lab. Las bu no leas, my hanks are exended o my parens for heir inexhausible love and suppor o me. I also wan o express my appreciaion o Helen Huang for her encouragemen and suppor. November 14, 2007 iii

4 ABSTRACT HIGH GRADE CONTROL OF LINEAR INDUCTION MOTOR DRIVES Publicaion No. HAIDONG YU, PhD. The Universiy of Texas a Arlingon, 2007 Supervising Professor: Babak Fahimi Linear inducion machines LIM have been widely uilized in miliary, ransporaion, and aerospace due o he impressive advanages such as simple configuraion, easy mainenance, and high acceleraion/deceleraion. However, he exisence of railing eddy curren effecs and magneic asymmery effecs undermines he expeced funcionaliy of vecor conrol even hough LIM possesses similariies from is roary counerpar. As a resul, i has been a focal research area o eiher improve he performance of vecor conrol for LIM or develop a new high grade conrol sraegy. iv

5 Therefore, he in-deph exploraion of elecromagneic behavior of LIM has been a fundamenal sep for invesigaion of LIM. From boh finie elemen analysis FEA and experimen, i is verified ha he wo open ends in he primary of LIM resul in he magneic asymmery effecs. Furhermore, boh he railing eddy curren effecs and magneic asymmery effecs cause non-sinusoidal magneo-moive force MMF. This undermines he basic assumpion of vecor conrol ha he fundamenal MMF should be sinusoidal. Moreover, FEA is a good ool for numerical-based analysis of elecrical machines. However, he compuaional effor is exremely inensive. Therefore, he field reconsrucion mehod FRM for LIM is proposed in his disseraion. FRM significanly reduces he compuaional ime, bu supplies seady sae calculaion in good accuracy. This disseraion also proposes a maximum force/ampere conrol, which has impressive advanages such as simple implemenaion, easy conrollabiliy, and maximum energy conversion raio. The maximum force/ampere conrol is validaed by boh simulaion resuls and experimenal verificaion. The conribuion of his disseraion can be summarized as follows: 1. Sysemaic exploraion of elecromagneic behavior of LIM; 2. Developmen of field reconsrucion mehod for LIM; 3. Invenion and implemenaion of maximum force/ampere conrol. v

6 TABLE OF CONTENTS ACKNOWLEDGEMENTS... ABSTRACT... LIST OF ILLUSTRATIONS... iii iv ix Chaper 1. INTRODUCTION Background and Significance Moivaion and Technical Objecives Conribuions ELECTROMAGNETIC BEHAVIOR OF LINEAR INDUCTION MACHINES LIM Model in FEA Trailing Eddy Curren Effecs Magneic Asymmery Effecs Experimenal Verificaion of Magneic Asymmery Effecs Magneic Asymmery Effecs on Force Characerisics of LIM Magneic Asymmery Effecs on IFOC of LIM Invesigaion on Magneic Asymmery Effecs on IFOC of LIM from a Magneic Perspecive Airgap Lengh Effec vi

7 2.5 Secondary Elecric Conduciviy s Effec Back EMF Characerisics FIELD RECONSTRUCTION METHOD OF LINEAR INDUCTION MACHINES Background Basis Funcion Idenificaion Primary Basis Funcion Derivaion Secondary Basis Funcion Derivaion Field Reconsrucion Verificaion of Field Reconsrucion Sauraion Effecs INDIRECT FIELD ORIENTED CONTROL OF LINEAR INDUCTION MACHINES Fundamenals of IFOC Idenificaion of Secondary Time Consan Deerminaion of Parameers in dq Axis Closed Loop Speed Conrol Using IFOC Simulaion Sudy of IFOC Experimenal Verificaion of IFOC MAXIMUM FORCE PER AMPERE CONTROL OF LINEAR INDUCTION MACHINES Principles of Maximum Force per Ampere Conrol Simulaion Sudy of Maximum Force per Ampere Conrol Experimenal Verificaion of Maximum Force per Ampere Conrol vii

8 5.4 Comparison beween IFOC and Maximum Force per Ampere Conrol CONCLUSIONS AND FUTURE RESEARCH Appendix A. SPECIFICATIONS OF LIM B. LIM DRIVE SYSTEM REFERENCES BIOGRAPHICAL INFORMATION viii

9 LIST OF ILLUSTRATIONS Figure Page 1 Imaginary Process of Obaining Linear Elecric Machines Classificaion of Linear Elecric Machines Air Train From Wikipedia Nagahori Tsurumi-ryokuchi Line in Japan From Wikipedia Cross Secional View of LIM under Invesigaion Primary Winding Scheme Iniial 2D Mesh of LIM in FEA Trailing Eddy Curren in FEA Flux Densiy Disribuion when Phase a is Excied by a DC Curren Flux Densiy Disribuion when Phase b is Excied by a DC Curren Flux Densiy Disribuion when Phase c is Excied by a DC Curren Exciaion Circui of Direc Mehod Normal Flux Densiy in he Middle of Airgap when Phase a is Excied by a DC Curren Normal Flux Densiy in he Middle of Airgap when Phase b is Excied by a DC Curren Normal Flux Densiy in he Middle of Airgap when Phase c is Excied by a DC Curren Indirec Exciaion Mehod Normal Flux Densiy of Three Connecions in FEA ix

10 18 Normal Flux Densiy of Three Connecions from Experimenal Tesbed Prooype of LIM under Invesigaion Flux Linkage of Phase a under a Se of Three Phase Balanced Sinusoidal Curren Sources Exciaion Flux Linkage of Phase b under a Se of Three Phase Balanced Sinusoidal Curren Sources Exciaion Flux Linkage of Phase c under a Se of Three Phase Balanced Sinusoidal Curren Sources Exciaion Average Force Variaions wih Respec o Frequency a Linear Speed of 5 m/sec Block Diagram of IFOC Funcionaliy Average Thrus Variaion wih Respec o Iq when Id is Fixed a 1 A Average Normal Force Variaion wih Respec o Iq when Id is Fixed a 1 A Magneizaion Curve of Primary wih Respec o Iq Magneizaion Curve of Primary wih Respec o Id Magneizaion Curve of Secondary wih Respec o Iq Magneizaion Curve of Secondary wih Respec o Id Force Variaions wih Respec o Airgap Lengh under Mooring Condiion 1 m/sec Force Variaions wih Respec o Airgap Lengh under Elecromagneic Braking Condiion 1 m/sec Force Variaions wih Respec o Airgap Lengh under Mooring Condiion 10 m/sec Force Variaions wih Respec o Airgap Lengh under Generaing Condiion 10 m/sec Force Variaions wih Respec o Airgap Lengh under Mooring Condiion 15 m/sec x

11 36 Force Variaions wih Respec o Airgap Lengh under Generaing Condiion 15 m/sec Force Variaion wih Secondary Elecric Conduciviy a Linear Speed 1 m/sec Force Variaion wih Secondary Elecric Conduciviy a Linear Speed 15 m/sec Back EMF Ampliude Variaion wih Frequency a 1 m/sec Back EMF Ampliude Variaion wih Frequency a 5 m/sec Phase Shif beween Back EMF and Phase Curren a 1 m/sec Phase Shif beween Back EMF and Phase Curren a 5 m/sec Posiive Direcions of Normal and Tangenial Componens Tangenial Basis Funcions of Three Phases Normal Basis Funcions of Three Phases Two Sep Procedure of Basis Funcion Idenificaion Field Reconsrucion Procedure Tangenial Flux Densiy Normal Flux Densiy Normal Flux Densiy in he Middle of Airgap a One Paricular Posiion Using FRM Normal Flux Densiy in he Middle of Airgap a he Same Posiion wih Figure 50 from Experimen 0.05 T/Div Thrus Variaions of Three Mehods Normal Force Variaions of Three Mehods Tangenial Flux Densiy wih Sauraion Normal Flux Densiy wih Sauraion xi

12 56 Thrus Variaions of Three Mehods wih Sauraion Normal Force Variaions of Three Mehods wih Sauraion Measuremen of Secondary Time Consan Verical Axis: Volage, Horizonal Axis: Time Block Diagram of Closed Loop Speed Conrol wih IFOC Speed Response of IFOC in Simulaion Block Diagram of Hardware Se Up Speed Response of IFOC from Experimen No Load Phase Saring Curren of IFOC No Load Transiion of Operaion Mode of Phase Curren in IFOC No Load Phase Braking Curren of IFOC No Load Speed Response of IFOC from Experimen 22 lbs Load Phase Saring Curren of IFOC 22 lbs Load Transiion of Operaion Mode of Phase Curren in IFOC 22 lbs Load Phase Braking Curren of IFOC 22 lbs Load Average Thrus Variaion wih Exciaion Frequency a Differen Linear Speeds Average Normal Force Variaion wih Exciaion Frequency a Differen Linear Speeds Conrol Block Diagram for he Maximum Force/Ampere Conrol Speed Response of Maximum Force/Ampere Conrol Profile of Opimum Exciaion Frequency Simulaed Reference Phase Curren and Prediced Phase Curren Zoomed Phase Curren Profile xii

13 77 Thrus Ripple Percenage wih Respec o Frequency a Linear Speed 5 m/sec Normal Force Ripple Percenage wih Respec o Frequency a Linear Speed 5 m/sec Thrus Variaions wih Exciaion Frequency for Two Airgap Lenghs when Linear Speed is 10 m/sec Normal Force Variaions wih Exciaion Frequency for Two Airgap Lenghs when Linear Speed is 10 m/sec Thrus Variaions wih Exciaion Frequency for Two Secondary Elecric Conduciviy Values Normal Force Variaions wih Exciaion Frequency for Two Secondary Elecric Conduciviy Values Speed Response of Maximum Force/Ampere Conrol No Load Transiion Phase Curren from Saring o Seady Sae No Load Transiion Phase Curren from Seady Sae o Braking No Load Zoomed Seady Sae Phase Curren Using Maximum Force/Ampere Conrol No Load Speed Response of Maximum Force/Ampere Conrol 22 lbs Load Transiion Phase Curren from Saring o Seady Sae 22 lbs Load Transiion Phase Curren from Seady Sae o Braking 22 lbs Load Zoomed Seady Sae Phase Curren Using Maximum Force/Ampere Conrol 22 lbs Load Speed Response of Boh Mehods No Load Speed Response of Boh Mehods 22 lbs Load Speed Profile Subjec o a Sudden Change of Load 22 lbs Using IFOC Speed Profile Subjec o a Sudden Change of Load 22 lbs Using Maximum Force/Ampere Conrol xiii

14 CHAPTER 1 INTRODUCTION 1.1 Background and Significance The origin of linear elecric machines can be raced back abou one cenury ago. However, only afer 1960, due o he occurrence of he modern power elecronics echnique, linear elecric machines have araced a grea deal of ineres. Linear elecric machines can be concepually realized by cuing and unrolling heir counerpar, roary elecric machines. The process is illusraed by figure 1. Figure 1 Imaginary Process of Obaining Linear Elecric Machines From he aspec of elecrical exciaion, linear elecric machines include linear dc machines, linear synchronous machines, linear inducion machines, and linear sep moors. Wih respec o geomery, linear elecric machines have fla and ubular ypes. 1

15 The whole family of linear elecric machines is classified in figure 2. Single Sided Linear Fla Machine Linear Elecric Machines Geomery Double Sided Exciaion Tubular Linear Elecric Machine Linear DC Machine Linear Synchronous Machine Linear Inducion Machine Linear Sep Moor Elecrical Synchronous Permanen Synchronous Relucance Figure 2 Classificaion of Linear Elecric Machines As one caegory of linear elecric machines, linear inducion machines LIM have been uilized in a wide range of applicaions [1]-[6] such as miliary, ransporaion, and aero space o name a few due o he impressive advanages such as simple configuraion, easy mainenance, high propulsion, and no need for he ransformaion sysems from roary o ranslaional movemen. Figure 3 and 4 illusrae applicaions menioned above. This disseraion will invesigae single sided linear fla inducion machine. 2

16 Figure 3 Air Train From Wikipedia Figure 4 Nagahori Tsurumi-ryokuchi Line in Japan From Wikipedia Convenionally, he moveable par of LIM is called primary, and he saionary par is called secondary. Primary usually conains a hree phase winding in he uniform slos of he laminaed core. Secondary is made of an aluminum copper shee wih or wihou a solid back iron core. Therefore, when he primary is excied by a se of 3

17 balanced sinusoidal currens, here will be eddy curren inducing on he secondary aluminum shee. These wo elecromagneic sources will reac o produce elecromagneic forces. The angenial force is called hrus. The oher componen of force is called normal force. 1.2 Moivaion and Technical Objecives There are hree mos popular conrol sraegies for linear inducion moor drives. They are scalar conrol V/F [7] and [8], direc orque conrol DTC [9], and vecor conrol [10]-[12]. Scalar conrol is also called Vol/Herz conrol. I regulaes he raio of volage wih frequency a a consan value. Direc orque conrol uses errors beween he references of primary flux and he force wih heir esimaed values o deermine he opimal swiching configuraion of he hree phase inverer every sample ime. Vecor conrol includes direc field oriened conrol DFOC [11] and indirec field oriened conrol IFOC [13]. Vecor conrol measures or esimaes he locaion of roor flux axis, and uses he flux angle o decouple he saor currens ino quadraure and direc componens, i.e. I q and I d. I d is normally regulaed a is raed value, and I q is regulaed o deliver commanded force. Since his family of machines possesses similariies wih heir roary counerpars, vecor conrol scheme is he mos ofen used echnique for LIM, and has been considered as he bes conrol soluion for LIM. Some oher conrol sraegies [13]-[15] based on vecor conrol incorporae advanced conrol mehods o improve he performance of LIM. However, some elecromagneic behavior of LIM such as railing eddy curren effecs [16]-[19] and magneic asymmery effecs [20] and [21] can undermine he 4

18 expeced funcionaliy of vecor conrol. As a resul, one can no harves he high grade conrol performance from LIM using vecor conrol. Therefore, he moivaion of his disseraion is o develop and implemen a high grade conrol scheme for LIM o achieve simple implemenaion, fas response, and maximum energy conversion raio. Furhermore, he new invened conrol scheme, maximum force/ampere conrol, will be compared wih he convenional IFOC boh in simulaion sudy and experimenal es o illusrae is superior performance. Developmen and implemenaion of a high grade conrol sraegy for LIM has led o exploraion of he complee undersanding of elecromagneic behavior of LIM. In addiion, finie elemen analysis FEA [22]-[25] is a widely used ool for numericalbased analysis of elecrical machines. However, FEA requires inensive compuaional effor, which is no ime efficien. Therefore, a new efficien field calculaion echnique, field reconsrucion mehod FRM [26] and [27], is proposed o ease he invesigaion of LIM. 1.3 Conribuions The conribuions of his disseraion can be summarized as: 1. Sysemaic exploraion of elecromagneic behavior of LIM and discovery of shorcomings of vecor conrol mehod in opimal conrol of LIM; 2. Developmen of field reconsrucion mehod for LIM; 3. Invenion and implemenaion of maximum force/ampere conrol. 5

19 CHAPTER 2 ELECTROMAGNETIC BEHAVIOR OF LINEAR INDUCTION MACHINES In order o develop and implemen a high grade conrol scheme for linear inducion machine, in-deph knowledge of elecromagneic behavior is necessary. Finie elemen analysis FEA is used in his procedure. 2.1 LIM Model in FEA Figure 5 shows he cross secional view of he prooype in FEA based on he machine consrucion deails. Commercially available package MagNe from Infolyica is used for his invesigaion. The primary winding scheme is shown in figure 6. The ype of he winding is in Sar or Y connecion. Figure 5 Cross Secional View of LIM under Invesigaion 6

20 Figure 6 Primary Winding Scheme Figure 7 illusraes he iniial 2D mesh of LIM under invesigaion. The solver mehod in FEA is Newon-Raphson ieraion mehod. The maximum ieraion number is 20, and he polynomial order is 1. In order o guaranee he accuracy of FEA calculaions, he maximum lengh of riangle sides locaed around he airgap, aluminum shee surface, and primary eeh surface is abou 1 mm. Figure 7 Iniial 2D Mesh of LIM in FEA 7

21 2.2 Trailing Eddy Curren Effecs As shown in figure 8, when linear inducion machines move forward from lef o righ, here is always eddy curren ha is no in he overlapped region beween primary and secondary. This eddy curren is called railing eddy curren. Trailing eddy curren can cause non-sinusoidal and asymmeric magneo-moive force MMF. These effecs will undermine he proper funcionaliy of convenional vecor conrol of LIM. Figure 8 Trailing Eddy Curren in FEA 2.3 Magneic Asymmery Effecs Unlike roary inducion machine, LIM has wo open ends in primary. Due o differen relaive posiions of phases a, b, and c in primary, he conribuion of each phase o he MMF will be unequal. Figure 9, 10, and 11 illusrae he flux densiy disribuion when phases a, b, and c are excied by a dc curren respecively under lock up condiion direc mehod. The exciaion circui is shown in figure 12. One can noice ha he peak flux densiies in he primary in each case are T, T, and T in sequence. There is a significan difference in primary flux densiy beween phase b, and phases a and c. 8

22 Figure 9 Flux Densiy Disribuion when Phase a is Excied by a DC Curren Figure 10 Flux Densiy Disribuion when Phase b is Excied by a DC Curren Figure 11 Flux Densiy Disribuion when Phase c is Excied by a DC Curren 9

23 Ia Coil_phase_A T1 T2 SIN Coil_phase_B T1 T2 Coil_phase_C T1 T2 Figure 12 Exciaion Circui of Direc Mehod Figure 13, 14, and 15 display he normal flux densiy in he middle of airgap when phases a, b, and c are excied by a dc curren respecively. One can noice he waveform of phase a is he mirror image of he waveform of phase c. However, he waveform of phase b is anisymeric iself. This observaion verifies ha he srucure of wo open ends on he primary conribues o he magneic asymmery effecs of LIM. 10

24 Nomal Flux Densiy T Posiion mm Figure 13 Normal Flux Densiy in he Middle of Airgap when Phase a is Excied by a DC Curren Normal Flux Densiy T Posiion mm Figure 14 Normal Flux Densiy in he Middle of Airgap when Phase b is Excied by a DC Curren 11

25 Normal Flux Densiy T Posiion mm Figure 15 Normal Flux Densiy in he Middle of Airgap when Phase c is Excied by a DC Curren Experimenal Verificaion of Magneic Asymmery Effecs Since he winding connecion of primary is Y connecion wihou access o he neural poin, in order o implemen experimens, he circui shown in figure 16 indirec mehod has been used. In he indirec mehod, when one phase is excied by a dc curren, he oher wo phases are conneced in parallel o supply he reurn pah for he firs phase curren. As a resul, when phase a is excied and phase b and c are conneced in parallel, his condiion is defined as A-BC. Based on he above mehod, figure 17 shows he normal airgap flux densiy of hree connecions in FEA. 12

26 Ia Coil_phase_A T1 T2 SIN Coil_phase_B T1 T2 Coil_phase_C T1 T2 Figure 16 Indirec Exciaion Mehod A-BC B-CA C-AB 0.2 Flux Densiy kg Posiion cm Figure 17 Normal Flux Densiy of Three Connecions in FEA 13

27 A-BC B-CA C-AB 0.2 Flux Densiy kg Posiion cm Figure 18 Normal Flux Densiy of Three Connecions from Experimenal Tesbed Figure 19 Prooype of LIM under Invesigaion 14

28 Figure 18 shows normal flux densiy of hree connecions of he experimenal LIM esbed shown in figure 19. Figure 19 illusraes a single sided, hree phase, 4 pole linear inducion machine being invesigaed in his disseraion. In figure 19, he blue par in he middle of railway is primary, and beneah ha is he aluminum shee backed wih iron core. Deailed informaion is given in APPENDIX A. Comparing figure 18 wih figure 17, one can observe a close mach beween he wo figures. In addiion, i is shown ha he waveform of exciaion connecion A-BC is mirror image o ha of exciaion connecion C-AB. However, he waveform of exciaion caused by B-CA connecion is anisymeric iself. These observaions are similar wih he resuls from he direc mehod. Therefore, differen relaive posiions of a, b, and c phases in primary resul in he magneic asymmery effecs. From [28], for convenional roary inducion machines, he following equaion holds: MMF s = K cos ω φ 1 e s However, for LIM, due o he asymmery beween conribuions of he primary phases, he above equaion will no hold any more, even hough a se of hree phase, balanced, sinusoidal curren sources are supplied. Figures represen he flux linkage of each phase under hree phase balanced curren exciaion. One can noice phase a and c have almos same magniudes abou 0.27 Wb. However, phase b exhibis a flux linkage of magniude bigger han 0.3 Wb. The difference of he flux linkage values is beyond 10%. Therefore, he flux linkage is no equally disribued among hree phases. In fac, he resulan MMF will impac he force characerisic of he machine and will hinder 15

29 he applicaion of convenional indirec field oriened conrol of his family of machines Flux Linkage of Phase a Wb Time msec Figure 20 Flux Linkage of Phase a under a Se of Three Phase Balanced Sinusoidal Curren Sources Exciaion Flux Linkage of Phase b Wb Time msec Figure 21 Flux Linkage of Phase b under a Se of Three Phase Balanced Sinusoidal Curren Sources Exciaion 16

30 Flux Linkage of Phase c Wb Time msec Figure 22 Flux Linkage of Phase c under a Se of Three Phase Balanced Sinusoidal Curren Sources Exciaion Magneic Asymmery Effecs on Force Characerisics of LIM Figure 23 represens he variaions of average hrus and normal force wih respec o primary exciaion frequency, where he power supply is a se of hree phase, balanced curren sources wih an ampliude of 2 A. The linear speed is kep a 5 m/sec. As can be seen, in figure 23 he maximum hruss during mooring and generaing modes exhibi angible differences. In addiion, based on [20], from synchronous frequency o posiive infiniy, he linear inducion machine operaes as a moor; from 0 Hz o synchronous frequency, LIM works as a generaor; and from negaive infiniy o 0 Hz, LIM operaes under elecromagneic braking Sysem has elecrical and mechanical inpus a he same ime. 17

31 10 5 Thrus Force Normal Force 0-5 Force N Frequency Hz Figure 23 Average Force Variaions wih Respec o Frequency a Linear Speed of 5 m/sec Magneic Asymmery Effecs on IFOC of LIM Due o he exisence of railing eddy curren effecs and magneic asymmery effecs, he convenional indirec field oriened conrol may no supply is expeced funcionaliy as for roary inducion machines. Equaion 2 and 3 govern he conrol sraegy of indirec field oriened conrol. Figure 24 represens he block diagram of IFOC. P 1 iqs ωe = ωr τ i r ds where rms i i 2 qs 2 ds ω e is he exciaion frequency, P is No. of poles, I = + 3 ω r is he equivalen angular speed of primary ransformed from he corresponding linear speed v, 18 τ r is he

32 secondary ime consan, i qs and i ds are he commanded quadraure axis q axis curren and direc axis d axis curren respecively, and I rms is he RMS value of phase curren. Deailed discussion of indirec field oriened conrol will be conduced in chaper 4. Figure 24 Block Diagram of IFOC Funcionaliy Figure 25 and 26 show he force variaions wih respec o I q when I d is fixed a 1 A under boh mooring and generaing condiions using indirec field oriened conrol. I can be observed ha boh hrus and normal force have significan asymmery performance under mooring and generaing condiions when indirec field oriened conrol is uilized. In figure 25, a change in sign of I q represens swiching beween mooring and generaing modes of operaion. Negaive sign of figure 23 and 26 mean ha he normal force beween primary and secondary is aracive. 19

33 Thrus Force N Iq A Figure 25 Average Thrus Variaion wih Respec o Iq when Id is Fixed a 1 A Normal Force N Iq A Figure 26 Average Normal Force Variaion wih Respec o Iq when Id is Fixed a 1 A 20

34 2.3.4 Invesigaion of Magneic Asymmery Effecs on IFOC of LIM from a Magneic Perspecive Figure 27 illusraes he peak magniude of flux densiy in he primary wih respec o I q, when I d is fixed a 1 A. Figure 28 is he similar characerisic wih respec o I d, when I q is fixed a 1 A. From boh curves, one can noice ha here is a difference beween mooring and generaing condiions in figure 27. However, curves represening mooring and generaing condiions in figure 28 mach reasonably. Figure 29 illusraes he peak magniude of flux densiy in he back iron of he secondary wih respec o I q, when I d is fixed a 1 A. Figure 30 is he similar characerisic wih respec o I d, when I q is fixed a 1 A. Again, here is a difference beween mooring and generaing condiions in figure 29. Curves of boh mooring and generaing condiions in figure 30 mach well. The above observaions indicae ha he effec of I q is no symmeric beween mooring and generaing condiions. However, I d illusraes a symmeric influence during mooring and generaing condiions. These observaions require modificaion in he convenional indirec field oriened conrol scheme. 21

35 2 1.8 Primary Moor Generaor B T Iq A Figure 27 Magneizaion Curve of Primary wih Respec o Iq Primary Moor Generaor B T Id A Figure 28 Magneizaion Curve of Primary wih Respec o Id 22

36 Secondary Moor Generaor 1.2 B T Iq A Figure 29 Magneizaion Curve of Secondary wih Respec o Iq Secondary Moor Generaor 1.2 B T Id A Figure 30 Magneizaion Curve of Secondary wih Respec o Id 23

37 2.4 Airgap Lengh Effec The effec of airgap lengh on he force characerisics of LIM a low linear speeds has been explored in [1]. Since he force characerisics under high speeds are more imporan in propulsion applicaions, i is necessary o opologies he airgap lengh effecs for he full speed range. When linear speed is 1 m/sec low speed range, and exciaion frequency is Hz mooring, he airgap lengh is varied from 1.5 mm, o 2.5 mm, 3.5 mm, and 4.5 mm in sequence. Figure 31 displays he hrus and normal force variaions wih airgap lengh. The exciaion is a se of hree phase balanced curren sources wih ampliude of 2 A. When exciaion frequency changes o Hz elecromagneic braking, figure 32 represens he force variaions wih respec o airgap lengh. From figure 31 and 32, one can observe ha boh hrus and normal force monoonically decrease wih airgap lengh. This phenomenon maches wih [1]. Furhermore, linear speed is increased o 10 m/sec o represen he high speed range. Figure 33 and 34 represen he force variaions wih respec o airgap lengh under mooring Hz and generaing Hz condiions respecively. From figure 33, one can noice ha he hrus does no change monoonically any more. The hrus reaches he peak value when airgap lengh is 2.5 mm, and hen drops. When machine works under generaing condiion figure 34, hrus and normal force monoonically decrease wih airgap lengh. However, here is a disconinuiy in he normal force changing rend. When linear speed is 15 m/sec, he force characerisics wih respec o airgap lengh under mooring and generaing condiions are shown in figure 35 and 36 respecively. Figure 24

38 35 shows ha he hrus has a maximum value a 3.5 mm airgap lengh. Compared wih value of figure 33, here is a rend ha when linear speed increases he airgap lengh for he maximum hrus also increases. In figure 36, he normal force has he maximum value when airgap lengh is 2.5 mm. This change is differen from ha illusraed in figures 32 and Thrus Force Normal Force Forces N Airgap Lengh mm Figure 31 Force Variaions wih Respec o Airgap Lengh under Mooring Condiion 1 m/sec 25

39 15 14 Thrus Force Normal Force 13 Forces N Airgap Lengh mm Figure 32 Force Variaions wih Respec o Airgap Lengh under Elecromagneic Braking Condiion 1 m/sec 11 Thrus Force Normal Force 10 9 Forces N Airgap Lengh mm Figure 33 Force Variaions wih Respec o Airgap Lengh under Mooring Condiion 10 m/sec 26

40 18 17 Thrus Force Normal Force Forces N Airgap Lengh mm Figure 34 Force Variaions wih Respec o Airgap Lengh under Generaing Condiion 10 m/sec Thrus Force Normal Force 7 Forces N Airgap Lengh mm Figure 35 Force Variaions wih Respec o Airgap Lengh under Mooring Condiion 15 m/sec 27

41 15 14 Thrus Force Normal Force Force N Airgap Lengh mm Figure 36 Force Variaions wih Respec o Airgap Lengh under Generaing Condiion 15 m/sec 2.5 Secondary Elecric Conduciviy s Effec In mos applicaions, he resisance of LIM secondary aluminum plae is subjec o he ambien emperaure change and heaing effec caused by eddy curren. This effec is governed by he following equaion: r R r = n R n 4 R n is he nominal value of secondary resisance, he nominal emperaure, and r is he real emperaure. R r is he real value of resisance, n is The varying secondary resisance will also affec he secondary elecric conduciviy. I is necessary o invesigae how secondary elecric conduciviy affecs he force characerisics of LIM. Figure 37 and 38 represen he hrus and normal force 28

42 variaions wih respec o secondary elecric conduciviy a 1 m/sec and 15 m/sec respecively. One can noice he incremen of secondary elecric conduciviy causes significan drop of normal force. However, he variaion of elecric conduciviy does no affec hrus very much. These observaions mean ha he variaion of secondary elecric conduciviy can cause significan normal force ripples. 25 Thrus Force Normal Force 20 Force N Elecric Conduciviy Siemens/m x 10 7 Figure 37 Force Variaion wih Secondary Elecric Conduciviy a Linear Speed 1 m/sec 29

43 16 14 Thrus Force Normal Force 12 Force N Elecric Conduciviy Siemens/m x 10 7 Figure 38 Force Variaion wih Secondary Elecric Conduciviy a Linear Speed 15 m/sec 2.6 Back EMF Characerisics Figure 39 and 40 are he back EMF ampliude variaions wih respec o frequency when linear speed is 1 m/sec and 5 m/sec respecively. For LIM, he hrus can be relaed o he elecrical inpu by he following equaions: P elecrical F = 5 Vlinear P elecrical = E I cos φ + E I cos φ + E I cos φ 6 a a a b b b c c c where F is he hrus force, P elecrical is he oal elecrical power, V linear is he linear velociy of LIM, E n n=a, b, or c is he magniude of back EMF, I n is he magniude of phase curren, and φ n is he phase shif beween back EMF and phase curren. From figure 39 and 40, i can be observed ha when exciaion is a se of hree phase balanced 30

44 dc curren sources 0 Hz, he ampliude of back EMF is very close o 0. In addiion, when increase exciaion frequency o posiive or negaive infiniy, he ampliude of back EMF increases monoonically. This fac will cause a high sress on power elecronic componens when exciaion frequency is very high, which may resul in conrol failure of LIM drive. Based on he daa from figure 39 and 40, and equaion 5 and 6, one can plo he phase shif beween he back EMF and phase curren shown in figure 41 and 42. Figure 41 has hyperbolic waveforms in firs and second quadrans. Figure 42 has he minimum phase shif a Hz, and sauraes o 90 degrees in he posiive infiniy frequency Back EMF V Frequency Hz Figure 39 Back EMF Ampliude Variaion wih Frequency a 1 m/sec 31

45 Back EMF V Frequency Hz Figure 40 Back EMF Ampliude Variaion wih Frequency a 5 m/sec Phase Shif elecrical degree Frequency Hz Figure 41 Phase Shif beween Back EMF and Phase Curren a 1 m/sec 32

46 Phase Shif elecrical degree Frequency Hz Figure 42 Phase Shif beween Back EMF and Phase Curren a 5 m/sec 33

47 CHAPTER 3 FIELD RECONSTRUCTION METHOD OF LINEAR INDUCTION MACHINES In he las chaper, elecromagneic behavior of LIM has been invesigaed based on FEA, and verified by experimenal resuls. FEA is well known and widely used as a ool for numerical-based analysis of elecric machines. However, he compuaional effor required o complee a finie elemen evaluaion is significan. Therefore, a socalled field reconsrucion mehod FRM for LIM has been developed. FRM only requires few number of FEA evaluaions o reconsruc he fields in he middle of airgap for any se of given exciaion and posiions. Based on he knowledge of fields in he middle of airgap and Maxwell Sress Tensor MST mehod [29] and [30], one can predic he forces acing on he primary. 3.1 Background All force calculaions hroughou his chaper are based on MST mehod. Using MST, he angenial and normal force densiies in he middle of airgap can be expressed as follows: f x 1 = Bx By 7 µ o f y = By Bx 8 2 µ o 34

48 where B x and B y are he angenial and normal componens of he flux densiies in he middle of airgap of he machine and µ o is he permeabiliy of he air; f x and f y are he angenial and normal force densiies in he airgap. The posiive direcions of normal and angenial componens are defined in figure 43. Figure 43 Posiive Direcions of Normal and Tangenial Componens Therefore, he hrus and normal force can be expressed by F = z f dl 9 l x where z is he sack lengh of LIM, F = z f dl 10 n l F n is he normal force. y 35

49 The following assumpions have been made for he invesigaion of FRM. The flux densiy in he axial direcion is zero, which means no end effec is included. The machine is no sauraed, such ha he superposiion can be applicable. Hyseresis and eddy currens in he primary and secondary back iron are negleced. The operaing emperaure is assumed o be consan. In anoher word, he heaing effec o machine parameers can be negleced. Furhermore, he primary eeh are assumed o be rigid. 3.2 Basis Funcion Idenificaion Based on he assumpion of no sauraion, he normal and angenial componens of flux densiy in he middle of airgap can be expressed by he sum of primary and secondary quaniies. B = B + B 11 x xs xr B = B + B 12 y ys yr where and B xs and B ys and B xr are angenial flux densiies of primary and secondary respecively, B yr are normal flux densiies of primary and secondary respecively. These four quaniies are also defined as Basis Funcion Primary Basis Funcion Derivaion A he firs sep, a saic FEA evaluaion is used o derive he primary basis funcion of phase a. In he FEA program, primary is fixed in he middle of he secondary railway o eliminae he railway asymmery effec on he primary basis funcion. In anoher word, he lengh of secondary railway is assumed o be infiniy. In addiion, phase a curren i a is se wih 1 A dc curren, and phases b and c are open. The 36

50 normal and angenial flux densiies are calculaed and sored as basis funcions B xsa and B ysa respecively. In order o sore he basis funcions, he infinie railway of secondary is runcaed ino an effecive and finie lengh. Furhermore, he effecive airgap is discreized ino n equally disribued poins. Hence, B xsa and B ysa are represened as wo n by 1 vecors in compuer. Because of he magneic asymmery effecs of primary, in order o calculae he basis funcions of phases b and c, he same procedure for phase a has o be repeaed in phase b and c respecively. Figure 44 and 45 illusrae he basis funcions of normal and angenial flux densiies respecively Primary Basis Funcion Bxsa Bxsb Bxsc Tangenial Flux Densiy T Posiion mm Figure 44 Tangenial Basis Funcions of Three Phases 37

51 Primary Basis Funcion Bysa Bysb Bysc Normal Flux Densiy T Posiion mm Figure 45 Normal Basis Funcions of Three Phases Using hese basis funcions, he flux densiy conribued by primary wih arbirary hree phase currens can be expressed as follows: B B l = i B l + i B l i B l 13 xs a xsa b xsb + c l = i B l + i B l i B l 14 ys a ysa b ysb + where l is he posiion informaion on he effecive airgap Secondary Basis Funcion Derivaion c xsc ysc Unlike B xs and B ys, B xr and B yr are no only deermined by he insananeous primary curren, hey are also subjec o he change of he primary curren. In fac, B xr and B yr are generaed by secondary eddy curren, which resuls from primary curren and primary moion. However, in realiy, he elecromagneic forces are only deermined by he slip frequency ω slip, which can be expressed as 38

52 P = ω 15 ω slip ω e 2 r Therefore, ω slip is he combined resul of elecrical and mechanical sysems. In he procedure of FR for LIM, for a given exciaion frequency and linear speed, he elecrical angular frequency corresponding o he linear speed is subraced from he exciaion frequency, and he resul is he slip frequency. In order o idenify secondary basis funcions, he primary speed is se a v = 0. Using a ransien FEA evaluaion, an impulse curren is used as phase a curren inpu signal. The impulse inpu has a value of 1 A a 0, and 0 elsewhere. A sequence of normal and angenial flux densiies for 0 is hen recorded. Using previously esablished primary basis funcions, he flux densiies generaed by secondary eddy curren can be represened as follows B xra = B B 16 xim xsa B yra = B B 17 yim ysa where B xim and B yim are he recorded values of flux densiies due o he impulse curren inpu, and B xra and B yra are secondary basis funcions of phase a. Using he same procedure, secondary basis funcions of phase b and c can also be idenified. Furhermore, all secondary basis funcions are in he forma of marices. The rows of he marices represen he n poins along he effecive airgap; he columns of marices describe he impulse response of hese poins in he ime domain. Therefore, he normal and angenial flux densiies due o secondary eddy curren can be summarized as following wo equaions: 39

53 B B xr yr l, = i B l, + i B l, + i B l, 18 a xra b xrb l, = i B l, + i B l, + i B l, 19 a yra where denoes he operaion of convoluion. The wo sep procedure of basis funcion idenificaion is shown in figure 46. b yrb c c xrc yrc Sep 1 In = 1 A n = a, b, c Magneosaic FEA Soluion Primary Basis Funcion Derivaion Bxsa, Bxsb, Bxsc, Bysa, Bysb, Bysc Sep 2 X In = 1 A impulse curren n = a, b, c ν = 0 Transien FEA Soluion + - Secondary Basis Funcion Derivaion Bxra, Bxrb, Bxrc, Byra, Byrb, Byrc Figure 46 Two Sep Procedure of Basis Funcion Idenificaion 40

54 Field Reconsrucion Once all basis funcions have been idenified, he oal angenial and normal flux densiies x B and y B in he middle of airgap due o arbirary primary exciaion curren can be obained as:,,,, l B i l B i l B i l B i l B i l B i l B xrc c xrb b xra a xsc c xsb b xsa a x = 20,,,, l B i l B i l B i l B i l B i l B i l B yrc c yrb b yra a ysc c ysb b ysa a y = 21 Since he secondary basis funcions are in he discree ime domain, he operaion of convoluion in equaion 20 and 21 will be conduced in discree ime domain. = = = = k m m k xrc m c k m m k xrb m b k m m k xra m a xsc k c xsb k b xsa k a k x l B i l B i l B i l B i l B i l B i l B 1 1 1,,,, 22 = = = = k m m k yrc m c k m m k yrb m b k m m k yra m a ysc k c ysb k b ysa k a k y l B i l B i l B i l B i l B i l B i l B 1 1 1,,,, 23 Finally, using MST he force densiies and hen elecromagneic forces can be compued. The procedure is shown in figure 47. Figure 47 Field Reconsrucion Procedure

55 3.4 Verificaion of Field Reconsrucion To verify he effeciveness of he proposed FR mehod, he consan speed operaion is simulaed. Consan speed operaion is useful in evaluaion of LIM seady sae performance. In he following session, he comparison beween direc FEA, slip frequency FEA, and FRM will be invesigaed. The direc FEA is he FEA simulaion including he linear speed. Slip frequency FEA is he ransien FEA program ha uses he slip frequency in he exciaion insead of real frequency, and does no have linear moion. FRM is he simulaion conduced in Malab/Simulink ha uilizes he slip frequency exciaion mehod o reconsruc fields of he LIM. Since he experimenal es will be conduced a linear speed of 0.1 m/sec, he linear speed is also se o 0.1 m/sec in he consan speed operaion for comparison. The elecrical angular frequency corresponding o 0.1 m/sec is 1 Hz. Therefore when exciaion frequency is 51 Hz, he slip frequency will be 50 Hz. A = 0 sec, he commanded hree phase curren are acivaed. The flux densiies resuls from boh slip frequency FEA and FRM a = 0.1 sec are shown in figure 48 and 49 respecively. One can noice here is no visual difference beween slip frequency FEA and FRM. Figure 50 and 51 illusrae he normal flux densiy variaions a he same posiion from FRM and experimen esbed. The oupu of he flux meer o oscilloscope is volage signal. The ampliude of his volage signal is 1.06 V, which is corresponding o abou 0.05 T. One can noice he resuls from figure 50 and 51 mach well. 42

56 Slip Frequency FEA FRM 0.03 Tangenial Flux Densiy T Posiion mm Figure 48 Tangenial Flux Densiy 0.06 Slip Frequency FEA FRM 0.04 Normal Flux Densiy N Posiion mm Figure 49 Normal Flux Densiy 43

57 Normal Flux Densiy T Time msec Figure 50 Normal Flux Densiy in he Middle of Airgap a One Paricular Posiion Using FRM Figure 51 Normal Flux Densiy in he Middle of Airgap a he Same Posiion wih Figure 50 from Experimen 0.05 T/Div 44

58 Using MST, he hrus and normal force variaions wih ime are illusraed in figure 52 and 53 respecively. One can noice in seady sae here are small values of dc error beween hese hree mehods. The reason of he dc error beween direc FEA and slip frequency FEA is ha he slip frequency FEA has no moion; herefore, here is no railing eddy curren effec in he slip frequency FEA. The dc error beween slip frequency FEA and FRM is caused by runcaing he infinie railway ino a finie effecive railway wih airgap and using finie discree ime domain convoluion. In addiion, one can noice due o he exisence of he railing eddy currens, he hrus value from direc FEA is less han he value from FRM. In anoher word, railing eddy curren can degrade he force performance of LIM. 7 6 Direc FEA Slip Frequency FEA FRM 5 Thrus N Time msec Figure 52 Thrus Variaions of Three Mehods 45

59 6 5 Direc FEA Slip Frequency FEA FRM 4 3 Normal Force N Time msec Figure 53 Normal Force Variaions of Three Mehods 3.5 Sauraion Effecs No sauraion is one of he fundamenal assumpions of FRM. However, i is necessary o invesigae he robusness of FRM o sauraion effecs. The comparison in he las session is repeaed here. Excep he curren ampliude, all he oher parameers are he same. In FEA calculaion and FRM, he phase curren ampliude is changed o 25 A, such ha he maximum flux densiy in primary of LIM is abou 1.49 T. This means he machine has been sauraed. Figure 54 and 55 illusrae he flux densiies from boh slip frequency FEA and FRM a insan 0.1 sec. One can noice here is some local visual difference beween he resuls from slip frequency FEA and FRM due o he exisence of sauraion effec. However, mos par of he waveform maches well. 46

60 Wih Sauraion Slip Frequency FEA FRM Tangenial Flux Densiy T Posiion mm Figure 54 Tangenial Flux Densiy wih Sauraion Wih Sauraion Slip Frequency FEA FRM 0.2 Normal Flux Densiy T Posiion mm Figure 55 Normal Flux Densiy wih Sauraion Figure 56 and 57 represen he resulan force profiles subjec o he sauraion effecs. One can noice ha he seady sae dc errors beween he hree mehods 47

61 increase o 2.5%. FRM can sill generae accurae enough resuls even hough he sauraion is exising Wih Sauraion Direc FEA Slip Frequency FEA FRM Thrus N Time msec Figure 56 Thrus Variaions of Three Mehods wih Sauraion Wih Sauraion Direc FEA Slip Frequency FEA FRM 100 Normal Force N Time msec Figure 57 Normal Force Variaions of Three Mehods wih Sauraion 48

62 CHAPTER 4 INDIRECT FIELD ORIENTED CONTROL OF LINEAR INDUCTION MACHINES Direc field oriened conrol direcly measures he locaion of roor flux axis, and uses he flux angle o decouple he saor currens ino quadraure and direc componens, i.e. I q and I d. I q and I d are also called force and magneizing curren respecively. The concep of indirec field oriened conrol is similar o ha of direc field oriened conrol in which he posiion of roor flux in he airgap is esimaed. The conrol core governed by equaion 2 and 3 has been inroduced in he chaper 2. The following assumpions have been made for vecor field oriened curren conrol. The sysem is hree phase balanced or symmeric in space and ime. In addiion, he ranslaional magneo-moive force is sinusoidal. Furhermore, he machine is no sauraed. Tradiionally, for roary inducion moor drives vecor conrol can guaranee fas response because he decoupled I q and I d are dc componens and easy o be regulaed by PI conrollers. Since LIM inheren similariies wih heir roary counerpars, vecor conrol has been predominanly applied o LIM in he pas. However, vecor conrol does no deliver he maximum force per ampere performance. On he oher hand, due o he exisence of railing eddy curren effecs and magneic asymmery effecs, 49

63 he firs wo fundamenal assumpions on he sinusoidal magneo-moive field and lack of sauraion have been undermined. This in urn influences he expeced funcionaliy of vecor conrol. In he following sessions, deails of indirec field oriened conrol IFOC will be explored. 4.1 Fundamenals of IFOC Since IFOC does no need he wo quadraure flux sensors o measure he roor or saor flux, i is more ofen used. Figure 24 illusraes he block diagram of IFOC, which is based on equaion 2 and 3 from chaper 2. These wo equaions are recalled here: P 1 iqs ωe = ωr τ i r ds In he diagram, rms i i 2 qs 2 ds I = + 3 L M is he magneizing inducance, L rr is he secondary inducance, r r is he secondary resisance, secondary ime consan τ r in equaion 2 is defined as L rr / r r, θ e is he flux angle used o decouple hree phase saor curren abc axis ino dq axis and conver he quaniies in dq axis back o abc axis. Under normal condiion, i ds will be regulaed a is raed value, commanded i qs is generaed hrough he speed conrol loop. The hrus generaed by he LIM drive can be expressed by he following wo equaions: F = K i 24 F qs F = M v+ Dv + F l 25 50

64 where F is he hrus, K F is he force consan, M is he oal mass of LIM primary sysem, D is he viscous fricion coefficien, v is he acceleraion speed, v is he linear speed Idenificaion of Secondary Time Consan From equaion 2 i is observed ha implemenaion of IFOC requires he LIM s secondary ime consan τ r. The ime consan is deermined by applying a DC curren of 3A for a shor period of ime o esablish a dc flux across he airgap and measuring he volage across one of he excied phases and he hird phase. The measured volage when he source is removed appears due o he ransien ha develops in he secondary. On he removal of he source, he volage drops and hen rises o zero. The rising profile of he curve gives he ime consan of he secondary which is abou 40 msec. Figure 58 illusraes he experimenal resul of secondary ime consan deerminaion. 51

65 Figure 58 Measuremen of Secondary Time Consan Verical Axis: Volage, Horizonal Axis: Time Deerminaion of Parameers in dq Axis In order o harves he bes performance ha IFOC can supply, he accurae informaion of i ds are uilized in his procedure., i qs, and K F raed values needs o be idenified. Equaion 2 and 3 A sandsill and normal condiion, equaion 2 and 3 will be modified as equaion 26 and 27 as follows: r 1 iqs ωe = 26 τ i r r ds where i r qs, i r ds, and r rms r 2 r i i 2 I = + 27 qs r I rms are he raed values of dq axis and phase currens respecively. ds 52

66 According o he specificaion of LIM, he raed phase curren is 4 A, and raed hrus is 7 lbs N. In addiion, from FRM he maximum sandsill hrus occurs when exciaion frequency is Hz. This frequency is he raed frequency a sandsill. Based on his informaion, r i ds =0.643 A, i r qs =3.948 A. Furhermore, r i qs and 53 r i ds can be esimaed as following values: K F can be idenified as N/A using equaion Closed Loop Speed Conrol Using IFOC In his session, closed loop speed conrol based on IFOC will be conduced. This includes simulaion sudy and experimen verificaion Simulaion Sudy of IFOC In he closed loop speed conrol, i ds is regulaed a is raed value, i qs is regulaed such ha i can develop he desired hrus o rack he reference speed. Once i ds and i qs references are generaed, hey will be ransformed back o abc axis o produce hree phase curren references. Furhermore, phase curren is conrolled using hyseresis conrol. Figure 59 illusraes he speed conrol loop of IFOC in Malab/Simulink. I mainly comprises of PI conroller, sauraion block, and LIM plan. The bandwidh of PI conroller should be much less han ha of curren conroller due o he fac ha he mechanical sysem ime consan is much larger. Therefore, i qs reference can be used in he diagram insead of he real i qs such ha equaion 24 can be modified as: = K Fiqs F 28

67 The block sauraion is used o preven he i qs exceeding is normal value. The oal mass M of he LIM primary sysem is 17 Kg, and he viscous fricion coefficien D is 0.05 N*sec/m. Figure 59 Block Diagram of Closed Loop Speed Conrol wih IFOC Based on figure 59, he characerisic equaion of he speed conrol loop is formulaed as follows: k s + a * K F * = 0 29 s 17s k is he proporion coefficien, a is he inegraion coefficien, and 1 /17s is he plan of he LIM. The bandwidh of he PI conroller is seleced a 20 Hz, and he damping raio is 0.9. Based on hese parameers, k and a can be compued as and 62.8 respecively. However, because of he non-lineariy of he sauraion block, k =80, and a =10 can give bes simulaion resuls by rial & error selecion. Figure 60 represens he speed response from he simulaion. Reference speed seps up o 0.1 m/sec a insan 0.2 sec. The reason ha linear speed reference chooses 0.1 m/sec is ha he lengh of he LIM secondary railway is limied. One can noice ha here is an overshoo abou 20% in he speed response, and speed reaches seady sae in abou 0.4 sec. 54

68 Speed m/sec Reference Speed Prediced Speed Time sec Figure 60 Speed Response of IFOC in Simulaion Experimenal Verificaion of IFOC In order o verify he funcionaliy of designed speed conroller for LIM using IFOC, experimenal resuls will be shown in his secion. Figure 61 illusraes he block diagram of hardware se up. The DC Power Supply will supply a solid 30 V dc bus for he sysem; Proecion Diode is used o preven he dc power supply absorbing curren; dc link capacior is a power buffer for regeneraive braking. The conrol saion collecs he hree phase curren informaion and linear speed value, and generaes a sequence of swiching signals for he corresponding IGBT swiches based on IFOC and curren hyseresis conrol. The hyseresis band for he curren conroller is 0.06 A. Deailed configuraion of hardware seup is shown in APPENDIX B. 55

69 Figure 61 Block Diagram of Hardware Se Up Figure 62 illusraes he speed response of a recangular speed reference a no load condiion. A insan 0 sec, speed reference seps up o 0.1 m/sec, and seps down o 0 a insan sec. One can noice ha i akes abou 1.5 sec for he speed o reach is reference value when saring, and 1 sec when braking. This is because when saring he hrus overcomes he fricion force; however, when braking hrus and fricion force will sum ogeher o decelerae he sysem. In addiion, for he iniial saring period 0.5 sec, he speed does no change much, ha is because he period is uilized for LIM o overcome he saic fricion force. Figure represen he phase curren during saring, mode ransiion, and braking under no load condiion. One can observe ha when LIM is saring or braking, phase curren mainains ampliude of 4 A o generae he maximum hrus o drive he sysem. Figure 64 illusraes ha in seady sae when linear speed reaches is reference value, he commanded force curren i * qs varnishes, as a 56

70 resul, he ampliude of phase curren decreases. Thereafer, he operaion mode swiches No Load Measured Speed Reference Speed 0.1 Speed m/sec Time sec Figure 62 Speed Response of IFOC from Experimen No Load Figure 63 Phase Saring Curren of IFOC No Load 57

71 Figure 64 Transiion of Operaion Mode of Phase Curren in IFOC No Load Figure 65 Phase Braking Curren of IFOC No Load 58

72 Figure 66 illusraes he speed response of a recangular speed reference when a 22 lbs mass is pu on op of he primary o increase he fricion force and ime consan of he mechanical sysem. One can noice ha compared wih no load condiion boh slopes of saring and braking are reduced, because he oal mass of primary is increased. From figure 62 and 66, one can observe ha in seady sae here is a dc error beween he reference speed and measured speed. This is mainly because of he railing eddy curren effecs and magneic asymmery effecs. In addiion, he performance of he speed conroller is resriced by he order of he speed conroller. Figure illusrae he phase curren during saring, mode ransiion, and braking when LIM is loaded by he 22 lbs mass. I can be noiced ha he profiles of phase curren when he machine is loaded are very similar o hose under no load condiion. In addiion, here is cerain amoun of noise in he curren waveform. This is mainly because he exciaion frequency no only depends on linear speeds, bu also relies on he i qs. However, i qs is also a funcion of linear speed. Therefore, he resulan exciaion frequency will suffer from wo sources of noise. 59

73 Heavy Load Measured Speed Reference Speed 0.1 Speed m/sec Time sec Figure 66 Speed Response of IFOC from Experimen 22 lbs Load Figure 67 Phase Saring Curren of IFOC 22 lbs Load 60

74 Figure 68 Transiion of Operaion Mode of Phase Curren in IFOC 22 lbs Load Figure 69 Phase Braking Curren of IFOC 22 lbs Load 61

75 CHAPTER 5 MAXIMUM FORCE PER AMPERE CONTROL OF LINEAR INDUCTION MACHINES Since he railing eddy curren effecs and magneic asymmery effecs have prevened IFOC of LIM harvesing is high grade performance, a simple, easy o implemen, and fas response conrol sraegy so called maximum force/ampere conrol is proposed and implemened in his chaper. 5.1 Principles of Maximum Force per Ampere Conrol Figure 70 and 71 illusrae he average hrus and normal force variaions wih respec o primary frequency a differen linear speeds. One can noice ha a any linear speed, here is always one pair of exciaion frequencies ha can produce he maximum driving force or braking force for he LIM sysem. These frequencies are characerized as opimum frequencies. If he graviy force and is by-produc, fricion force, are also aken ino accoun, one can summarize he following expression: F ξ M g + F = M a 30 fricion n where F is he hrus force, F n is he normal force, ξ fricion is he fricion coefficien beween LIM and supporing frame, g is he graviy consan, M is oal mass of he LIM sysem, and a is he acceleraion speed of he whole sysem. Using FRM, one can always find he pair of opimum frequencies for each linear speed. For example, 62

76 when linear speed is 5 m/sec, he opimum frequency of mooring is Hz, and opimum frequency of generaing is 25.9 Hz. Based on he knowledge of he opimum frequencies for he discree linear speeds and inerpolaion mehod, lookup ables beween linear speed and opimum frequency under mooring and generaing condiions can be se up. Furhermore, he opimum frequency is fed ino he power converer o produce a se of hree phase, balanced, curren sources of opimum frequencies using hyseresis conrol. As a resul, a any linear speed maximum force/ampere can be guaraneed. Finally, linear speed is regulaed wih he usage of hyseresis conrol. The complee funcionaliy of he maximum force/ampere conrol is shown in figure 72. As shown in figure 72, hyseresis comparaor in he block diagram deermines wheher he machine should work as a moor or as a generaor. This informaion will be given o he block called Frequency Selecor. Two lookup ables sore he opimum frequencies a discree linear speeds. One of he oupus from he lookup ables will be seleced based on he operaion mode. The following wo expressions can explain he funcion of Frequency Selecor in deails: f _ ou = f _ in mooring, if Speed _ ref Speed _ ou > Hyseresis band 31 f _ ou = f _ in generaing, if Speed _ ref Speed _ ou < Hyseresis band 32 where f _ is he oupu of he frequency selecor, f in mooring and ou _ f in generaing are he oupus of he wo lookup ables, Speed _ ref is he reference _ linear speed, and Speed _ ou is he measured linear speed. 63

77 m/sec 10 m/sec 15 m/sec 0 Thrus Force N Frequency Hz Figure 70 Average Thrus Variaion wih Exciaion Frequency a Differen Linear Speeds m/sec 10 m/sec 15 m/sec 0-5 Normal Force N Frequency Hz Figure 71 Average Normal Force Variaion wih Exciaion Frequency a Differen Linear Speeds 64

78 Figure 72 Conrol Block Diagram for he Maximum Force/Ampere Conrol 5.2 Simulaion Sudy of Maximum Force per Ampere Conrol Figure 73 represens he speed response of a recangular reference speed. A insan 0.2 sec, speed reference seps up o 0.1 m/sec, and seps down o zero a insan 0.8 sec. The hyseresis band of he speed regulaor is 0.01 m/sec. I is noable ha under acceleraing condiion, he fricion force resiss moion; however, under deceleraing condiion, he fricion force helps he braking. Therefore, figure 73 has larger braking slope han he one of saring. This is very similar o he phenomenon of figure 62 and 66. Figure 74 is he simulaed opimum exciaion frequency profile. I can be observed ha depending on he mode of operaion, frequency swiches beween mooring posiive frequency and generaing negaive frequency condiions. 65

79 Speed m/sec Reference Speed Prediced Speed Time sec Figure 73 Speed Response of Maximum Force/Ampere Conrol Frequency Hz Time sec Figure 74 Profile of Opimum Exciaion Frequency Figure 75 illusraes he reference phase curren and he prediced phase curren using hyseresis conrol. Figure 76 is he zoomed version of figure

80 8 6 Reference curren Prediced Curren 4 Phase Curren A Time sec Figure 75 Simulaed Reference Phase Curren and Prediced Phase Curren 6 Reference curren Prediced Curren 4 Phase Curren A Time sec Figure 76 Zoomed Phase Curren Profile Figure 77 and 78 represen he hrus and normal force ripples wih respec o frequency a linear speed of 5 m/sec. One can noice here is one peak in figure 77. The 67

81 reason is ha when linear speed approaches synchronous speed, he hrus approaches zero. As a resul, even a small value of ripple in he force will cause an exremely large hrus ripple percenage. However, here are wo peaks in figure 78. The reason of he peak in he negaive frequency is ha when frequency approaches negaive infiniy or posiive infiniy, normal force changes o repulsion force from aracion force [20]. When normal force is zero, he normal force ripple percenage will be infiniy. The second peak happens when hrus force ripple percenage has a minimum value. When linear speed is 5 m/sec, he opimum frequency of mooring is Hz, and opimum frequency of generaing is 25.9 Hz. Boh of hese wo frequencies will generae relaively small force ripples a his linear speed. This means ha he maximum force/ampere conrol has good immuniy wih respec o force noise Thrus Force Ripple Percenage % Frequency Hz Figure 77 Thrus Ripple Percenage wih Respec o Frequency a Linear Speed 5 m/sec 68

82 30 25 Normal Force Ripple Percenage % Frequency Hz Figure 78 Normal Force Ripple Percenage wih Respec o Frequency a Linear Speed 5 m/sec In he session 2.4 and 2.5, he impac of airgap lengh and secondary elecric conduciviy effec has already been explored. I is necessary o invesigae wheher he maximum force/ampere conrol can olerae he airgap lengh and secondary elecric conduciviy variaions. Figures 79 and 80 represen he hrus and normal force variaions wih respec o exciaion frequency when airgap is se a 2.5 mm and 4.5 mm respecively linear velociy is 10 m/sec. I can be observed ha when airgap lengh discrepancy is 80% o he raed value 2.5 mm, he pair of opimum frequencies a 10 m/sec linear speed do no change. This observaion validaes ha he proposed conrol has good immuniy o airgap lengh variaion. Due o he exisence of heaing effec of secondary reacion plae, he elecric conduciviy of aluminium plae will change. For insance, 20% discrepancy of he 69

83 elecric conduciviy will resul in he real elecric conduciviy being Siemens/m 79% of Aluminum elecric conduciviy. Figures 81 and 82 illusrae he force variaions wih respec o exciaion frequency when secondary elecric conduciviy is Siemens/m 100% of Aluminum elecric conduciviy and Siemens/m respecively. One can noice ha he pair of opimum frequencies for mooring and generaing almos remains he same. Therefore, he proposed maximum force/ampere conrol is verified o olerae he secondary heaing effec well mm 4.5 mm 5 Thrus Force N Frequency Hz Figure 79 Thrus Variaions wih Exciaion Frequency for Two Airgap Lenghs when Linear Speed is 10 m/sec 70

84 mm 4.5 mm 5 0 Normal Force N Frequency Hz Figure 80 Normal Force Variaions wih Exciaion Frequency for Two Airgap Lenghs when Linear Speed is 10 m/sec 10 79% Al 100% Al 5 Thrus N Frequency Hz Figure 81 Thrus Variaions wih Exciaion Frequency for Two Secondary Elecric Conduciviy Values 71

85 % Al 100% Al 0 Normal Force N Frequency Hz Figure 82 Normal Force Variaions wih Exciaion Frequency for Two Secondary Elecric Conduciviy Values 5.3 Experimenal Verificaion of Maximum Force per Ampere Conrol Figure 83 illusraes he speed response under no load condiion using maximum force/ampere conrol. One can noice ha when speed reference seps up o 0.1 m/sec a 0 sec, he speed response is racking he reference immediaely. In addiion, he maximum force/ampere conrol has excellen speed regulaion in seady sae. Furhermore, he braking slope is larger han ha of saring. Figure illusrae he ransiion of phase curren from saring o seady sae, from seady sae o braking, and during seady sae. Figure 86 verifies ha during seady sae, depending on he operaion mode, exciaion frequency swiches. In addiion, i has very similar forma wih he simulaed waveform. Furhermore, he curren waveform has less noise han he curren waveform from IFOC, because he 72

86 exciaion frequency in maximum force/ampere conrol only depends on linear speed once No Load Measured Speed Reference Speed 0.1 Speed m/sec Time sec Figure 83 Speed Response of Maximum Force/Ampere Conrol No Load Figure 84 Transiion Phase Curren from Saring o Seady Sae No Load 73

87 Figure 85 Transiion Phase Curren from Seady Sae o Braking No Load Figure 86 Zoomed Seady Sae Phase Curren Using Maximum Force/Ampere Conrol No Load 74

88 Figure 87 represens he speed response when he primary is loaded wih 22 lbs mass. Again, he seady sae speed is sill regulaed well wih small ripples. Figure display he ransiion of phase curren from saring o seady sae, from seady sae o braking, and during seady sae wih 22 lbs load Heavy Load Measured Speed Reference Speed 0.1 Speed m/sec Time sec Figure 87 Speed Response of Maximum Force/Ampere Conrol 22 lbs Load 75

89 Figure 88 Transiion Phase Curren from Saring o Seady Sae 22 lbs Load Figure 89 Transiion Phase Curren from Seady Sae o Braking 22 lbs Load 76

90 Figure 90 Zoomed Seady Sae Phase Curren Using Maximum Force/Ampere Conrol 22 lbs Load 5.4 Comparison beween IFOC and Maximum Force per Ampere Conrol As can be seen, he speed response of boh mehods is ploed ogeher in figure 91 and 92. I can be seen ha maximum force/ampere conrol has faser response and beer regulaion on he linear speed. In addiion, he curren waveforms from maximum force/ampere conrol are much cleaner han hose from IFOC. This will resul in a smaller value of THD oal harmonic disorion. Furhermore, i is necessary o invesigae he sabiliy and robusness of he wo mehods. Figure 93 and 94 illusrae he linear speed reacion when he 22 lbs mass is suddenly pu on he moving primary in he seady sae. In figure 93, a he insan abou 0.1 sec, he load is pu on he primary, here is a big dip in he speed profile. This is 77

91 because he design of he PI conroller for IFOC is based on he no load LIM plan 17 Kg. The sudden change of load will change he plan immediaely. In figure 94, a he insan abou 0.3 sec, he mass is pu on he primary, however, he linear speed is no affeced by his disurbance much. The reason is ha a any insan he maximum force/ampere conrol always generaes he maximum force per ampere based on he curren linear speed value No Load Maximum Force/Ampere Conrol IFOC Reference Speed m/sec Time sec Figure 91 Speed Response of Boh Mehods No Load 78

92 0.14 Heavy Load Maximum Force/Ampere Conrol IFOC Reference Speed m/sec Time sec Figure 92 Speed Response of Boh Mehods 22 lbs Load 0.12 Disurbance Speed m/sec Time sec Figure 93 Speed Profile Subjec o a Sudden Change of Load 22 lbs Using IFOC 79

93 0.12 Disurbance Speed m/sec Time sec Figure 94 Speed Profile Subjec o a Sudden Change of Load 22 lbs Using Maximum Force/Ampere Conrol 80

94 CHAPTER 6 CONCLUSIONS AND FUTURTE RESEARCH Linear inducion machine LIM offers advanages such as easy mainenance, simple configuraion, and high propulsive performance. Therefore, for he pas few decades linear inducion machines have been widely used in ransporaion, aerospace, and miliary. As a resul, looking for a high grade conrol sraegy has been a focal area. Vecor conrol has been a preferred mehod of conrol in LIM because LIM possesses similariies from is roary counerpar. However, some elecromagneic characerisics such as railing eddy curren effecs and magneic asymmery effecs have been proven o undermine he proper funcionaliy of vecor conrol for LIM. In addiion, he invesigaion on airgap lengh effec, secondary elecric conduciviy effec, and back EMF characerisics has led o developmen of he in-deph knowledge of LIM elecromagneic behavior which resuls in furher differences in he way hese machines should be conrolled. To address he need for an effecive conrol, a new analysis mehod known as field reconsrucion mehod FRM has been verified and applied in LIM. I is more compuaionally efficien han he radiional ool, i.e. finie elemen analysis. In he meanime, FRM also guaranees excellen compuaional accuracy. Thereafer, a new conrol scheme, maximum force/ampere conrol, is proposed in his disseraion. Maximum force/ampere conrol is simple, easy o implemen, and fas 81

95 echnique. Boh he simulaion resuls and experimenal es have validaed he effeciveness of maximum force/ampere conrol. On he basis of elecromagneic behavior, field reconsrucion mehod, and maximum force per ampere conrol in he linear inducion machines, he fuure research arge should be focused on how o use FRM o deec fauls in LIM and how o adop a self healing mechanism ha can seamlessly recover he drive in he even of a failure in one of he phases of he machine. Furhermore, advanced magneic design approaches can benefi from he fas response of FRM. Finally, i will be desirable o combine he LIM wih he magneically leviaed sysem MagLev o achieve ulra fas fricionless ransporaion, and opimize he design of LIM in he conex of his applicaion. 82

96 APPENDIX A SPECIFICATIONS OF LIM 83

97 No. Parameer Descripion Type Power supply Winding Configuraion Linear Inducion Machine 240V, 3 phase AC wye Poles 4 Slos per pole per phase 1 Air Gap mm Primary Dimensions in x, y, and z Direcions mm 250 x 72 x 100 Reacion Plae 08. Dimensions in x, y, and z Direcions mm Back iron Dimensions in 09. x, y, and z Direcions mm 10. Maerial of Primary Laminaion 1524 x 3 x x 6 x 100 M Maerial of Reacion Plae Aluminum: 3.8e7 Siemens/meer 12. Maerial of Back Iron CR10: Cold rolled 1010 seel 84

98 APPENDIX B LIM DRIVE SYSTEM 85

99 Conrol Saion and DC Power Supply Three Phase IGBT Inverer Inerface and Proecion Circui of Linear Posiion Encoder Conrol Board and ADC Circui 86