Modeling and Simulation of Shanghai MAGLEV Train Transrapid with Random Track Irregularities

Transcription

1 Modelng and Smulaon o Shangha MAGLEV ran ranrapd wh Random rack Irregulare ro. Shu Guangwe M.Sc. ro. Dr.-Ing. Renhold Menger ro. Shen Gang h.d. Shangha Inue o echnology, Shangha,.R. Chna Nuremberg Unvery o Appled Scence, Nuremberg, Germany ongj Unvery, Shangha,.R. Chna Abrac he MAGLEV ranrapd a knd o new ype hgh peed ran n he world whch levaed and guded over he rack ung elecro magnec orce. Becaue he elecro magne are unable, hey have o be conrolled. Snce he worldwde r commercal ue o uch a hgh peed ran baed on German echnology runnng ucceully n Shangha udong Arpor,.R.Chna. In h paper modelng o he hgh peed MAGLEV ran ranrapd dcued, whch condered he whole mechancal yem o one vehcle wh opmed upenon parameer and all conrolled elecro magne par n vercal and laeral drecon. he dynamcal mulaon code generaed wh MALAB/SIMILINK. For he degn o he conrol yem, he opmal Lnear Quadrac Conrol or mnmum conrol energy ued or each ngle elecro magne. he mulaon reul are preened wh he gven vercal and laeral random rack rregulare. he reearch work wa carred ou ogeher wh ro. Shen Gang, h.d. durng he me ro. Dr. Menger wa vng proeor n Shangha 6 and ro. Shu Guangwe, M.Sc. wa vng proeor n Nuremberg 7. ISSN Sonderdruck Schrenrehe der Georg-Smon-Ohm-Fachhochchule Nürnberg Nr. 39, Jul 7

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3 Schrenrehe Georg-Smon-Ohm-Fachhochchule Nürnberg See 3. Inroducon In order o mprove he rde qualy o he Shangha MAGLEV ran, an nvegaon ha been carred ou on he poble opmaon o pave upenon and alernave conrol raege wh he ad o compuer mulaon. Hence a degnaed mulaon model creaed o acheve reaonable balance beween accuracy, ecency and co eecvene. here are many compuer model creaed or deren purpoe [,3,6,8,], generally whch can be claed no he ollowng caegore: model or degn magnec levaon conrol [,,3,5], model or upenon opmaon [4], model or rack-ran neracon [3,5,6,]. Dependng on varou requremen he cale o he model vary n dely rom a ngle magnec block [,3,7] o he whole ran yem [6,8]. Regardng he ool o compuer oware, here are commercal oware package uch a SIMACK, ADAMS,ec. [9,,], and alo el generaed code [3,5,6,7,8,]. he prncple dea behnd modelng n h paper o develop a whole vehcle model wh dealed upenon elemen and praccal conroller wh a reaonable decrpon o he rack rregulare, whou couplng o he gudeway.. Mechancal Syem Model he ran con o ve econ, each econ con o a car body and runnng gear whch connec he levaon and gudance magne. he runnng gear alo called Magnec Wheel. wo adjacen Magnec Wheel are conneced o orm a o-called levaon boge. here are our uch levaon boge under a car body. he levaon boge are degned o enable ranmon o vercal orce o uppor he car body and o ranm laeral orce o gude he ran, ranmon o longudnal orce provde or brakng and racon orce. Conequenly a very mporan componen n he vehcle or boh aey and comor. Car body Zc Q C Levaon boge Ar prng Levaon Frame Zb8 Zb7 Zb6 Zb5 Zb4 Zb3 Zb Zb Z7 Z6 Z5 Z4 Z3 Z Z Q 7 Q 6 Q 5 Q 4 Q 3 Q Q Laeral mounng ne Levaon magne Gudance magne enor Eddy curren brakng magne Bump op Laeral equvalen ne Yb8 Yb7 Yb6 Yb5 Yc Yb4 Yb3 Yb Yb y b8 y b5 y C y y y b7 b6 b4 y b3 y b y b Fg. : Sde vew o he model here are many upenon elemen whn he levaon boge, or example, wo ar prng, an-roll bar and rubber elemen, prmary meal-rubber elemen whch connec he levaon magne, laeral bump op meal-rubber elemen, meal-rubber elemen whch connec he brakng magne, ec.. he car body conneced vercally by 6 wng-rod ha provde laeral lexbly. here are wo rubber ack a one end o he Modelng and Smulaon o Shangha MAGLEV ran ranrapd wh Random rack Irregulare

4 Schrenrehe Georg-Smon-Ohm-Fachhochchule Nürnberg See 4 wng-rod o gve lexbly n he axal drecon. he longudnal orce are ranmed by 4 racon rod o he our rame eparaely. hee upenon elemen olae mo durbance rom he gudng rack, boh vercally and laerally. A vehcle model creaed conderng 5 degree o reedom or he car body and 4 degree o reedom or each magnec levaon rame and degree o reedom or each magne par. here are egh levaon rame, 4 levaon magne, gudance magne and eddy curren brake module or boh de. oally here are 93 degree o reedom condered n he mechancal model a how n Fgure and. Fg. : Cro econ o he model Wh he aumpon o a rgd car body, ve degree or he car body are condered ncludng vercal, laeral, yaw, pch and roaon movemen. here are our levaon boge beneah he car body, each con o wo relavely rgd rame, called levaon rame. wo levaon rame are conneced by a longudnal rucure wh relave lexbly and lgh ma. So he levaon boge can be reaed a wo rgd par levaon rame connecng va hear ne n he vercal and laeral drecon ogeher wh a roaonal angular ne. Each levaon rame condered wh our degree or vercal, laeral, pch and roaon movemen repecvely. Each levaon magne upended rom wo adjacen levaon rame wh relave lexbly vercally and longudnally. Hence each levaon magne condered a havng wo degree or vercal and pch movemen repecvely. he gudance magne are alo mlar o levaon magne, whch are conneced o he de o adjacen levaon rame wh relave laeral lexbly. he gudance magne are condered a wo degree alo,.e. degree or laeral and yaw movemen repecvely. Secondary upenon beween car body and levaon rame are provded hrough a combnaon o ar prng, rubber ack, wng-rod and roaon arm ec. a hown n Fgure. he roaon arm and wngrod are relavely lgh n wegh. Hence no neceary o conder her neral eec. Whole rucure can be mpled wh hree ne,.e. laeral ne Ky, roll ne Kr and vercal ne K. hee hree parameer are dened a he uncon o ne o ar prng, an-roll ne and everal geomerc dmenon a ollow: W K y L ; L K K a L ; L L3 K r L L3 K a K L L Modelng and Smulaon o Shangha MAGLEV ran ranrapd wh Random rack Irregulare

5 Schrenrehe Georg-Smon-Ohm-Fachhochchule Nürnberg See 5 Where W he upended wegh o on each rame. Oher parameer are hown n Fgure. rmary upenon are mple n h cae. here only vercal ne o he levaon magne and laeral ne o he gudance magne. For he praccal applcaon, wo magne con a par o vercal magne levaon block wh wo gap and acceleraon enor or each magne. he lnear quadrac conrol can be ued or mnmum conrol energy wh lneared coecen a he workng pon [,3]. he conroller can be reaed or ndvdual or modal conrol. 3. Conrol Syem Modelng Wh he aumpon o a ngle levaed ma a hown n Fgure 3, he conroller are degned or boh levaon and gudance. here m he levaed ma ncludng levaon rame and magne, he dynamc magne orce, he rack durbance and he magne devaon. S he nomnal magne gap, he mall devaon rom he nomnal gap, L L e L he whole nducance, wh he eecve nducance L e and he conan ray nducance L. R he reance, I he nomnal curren and u he mall devaon rom he nomnal magne volage R I. Fg. 3: Model o a ngle ma vehcle or vercal moon he lnear equaon o he ngle ma magnec levaon yem can be derved wh LAGRANGE Funcon a hown n [,3,4,5]: η I η I L L m S m S m m R I η u L S L where η L L, η L I, S Conderng he dynamc magne orce η L I S, hen 3 Subung eq. no eq.3 and akng noe o, here Modelng and Smulaon o Shangha MAGLEV ran ranrapd wh Random rack Irregulare

6 Schrenrehe Georg-Smon-Ohm-Fachhochchule Nürnberg See 6 u η η 4 where R L he me conan. In order o accord wh he vehcle coordnae yem n Fgure and Fgure he ranormaon made a below: ; Selecng magne devaon, vercal velocy and dynamc magne orce a he ae varable, ha,he ollowng ae equaon obaned [ x ] u m η η η / 5.e. E B Ax x v u Wh magne gap devaon, vercal velocy and vercal acceleraon a he meauremen he ollowng oupu equaon obaned n pracce compued by an oberver [5,]: m 6.e. D C x y v o opme he yem he quadrac lo creron J [ mn d u R u Q Cx C x ] 7 ued. here and are he weghng marce wh Q R [ ] 33 dag q q q Q. hen he conroller eedback marx K obaned a B R K 8 where can be olved rom he marx RICCAI-equaon - QC C B BR A A 9 hen he opmal eedback conrol law y u K he weghng n eq.7 ued or he conrol yem degn or mnmum conrol energy are [ ] dag Q, R. Modelng and Smulaon o Shangha MAGLEV ran ranrapd wh Random rack Irregulare

7 Schrenrehe Georg-Smon-Ohm-Fachhochchule Nürnberg See 7 he above ngle ma conrol model can be appled o each magne o he mulaed MAGLEV vehcle wh he opmed parameer or ndvdual and modal conrol raege alernavely a hown n Fgure 4. he equaon and he degn mehod o gudance conrol yem are mlar. rack Gap Magne par Gap Conroller Force Force Conroller a Indvdual conrol o he magne par rack Gap Gap Magne par Conroller ch GapGap Gap-Gap Vercal Conroller Force X Force b Modal conrol o he magne par Fg. 4: Alernave conrol raege 4. Smulaon Code and Man Reul he SIMULINK dagram hown n he Fgure 5. I con o everal ubyem block. he mo op block o he car body. Below ha here are 8 block or econdary upenon. hen ollowng are 4 levaon boge rame block, 6 gudance block and one brake magne block, 7 levaon magne block and relevan conroller block. he npu o he yem are gven by rack laeral rregulary block and rack vercal rregulary block on he le de n he dagram. A an example, or he cae a n Fgure 4, he conroller block dagram or he rgh de levaon magne hown n he Fgure 6. Where Z repreen he vercal movemen o magne, and repreen he pch roaon movemen o he magne, d repreen he hal pace beween le and rgh magne, l repreen η / he dance beween ron pon and he rear pon o he meauremen, G repreen, aa repreen η, he elemen o he K n eq. are K, K and K3. he npu o he block are rack rregulare and ae o magne o rgh de. he oupu rom he block are he magnec orce acng on he ron and rear pon o he magne. 4. rack rregulare Aumng a hghly rgd and heavy ma rack, he neracon beween vehcle and he rack can be mpled by ju conderng r order bendng wh even load drbuon. he rack rregulary con o random urace rregulare and perodc deormaon. I mporan o meaure he eld rack rregulare or he MAGLEV yem o clary he derence beween he MAGLEV rack and ralway rack. I ha been ndcaed ha here are derence n deren requency Modelng and Smulaon o Shangha MAGLEV ran ranrapd wh Random rack Irregulare

8 Schrenrehe Georg-Smon-Ohm-Fachhochchule Nürnberg See 8 Fg.5: SIMULINK dagram o he vehcle mulaon model Modelng and Smulaon o Shangha MAGLEV ran ranrapd wh Random rack Irregulare

9 Schrenrehe Georg-Smon-Ohm-Fachhochchule Nürnberg See 9 band [6], generally rend o he SD curve o he rregulare are mlar. A he momen here no ucen daa colleced, o a pece o meaured ralway rack rregulare wh a reducon o over 4 n magnude ha been ued n h paper. he peak perodcal deormaon o he gudng rack aumed o be mm n he orm o ne wave. he deormaon o gudng rack wh 4 m n each lengh hown a he op o Fgure 7 or he r m. he ollowng curve are vercal and laeral random rregulare o he cenre lne o he rack, and he la he rack cro-level rregulary. Fg.6: SIMULINK dagram o he block wh he conroller Fg.7: Space hory o rack rregulare Modelng and Smulaon o Shangha MAGLEV ran ranrapd wh Random rack Irregulare

10 Schrenrehe Georg-Smon-Ohm-Fachhochchule Nürnberg See 4. Man Smulaon Reul Opmaon o he upenon parameer ha been made by he calculaon o repone o he vehcle o he above rack npu. Wh he opmed upenon parameer, a ypcal acceleraon o car body are lluraed n Fgure 8, and he gap durbance beween magne and rack are lluraed n Fgure 9. he me doman reul or ndvdual conrol and modal conrol are approxmaely mlar. Fg.8: Laeral and vercal acceleraon o a car body Fg.9: Laeral and vercal gap durbance o magne Modelng and Smulaon o Shangha MAGLEV ran ranrapd wh Random rack Irregulare

11 Schrenrehe Georg-Smon-Ohm-Fachhochchule Nürnberg See 5. Concluon For he purpoe o nvegaon o deren conrol raege and rde perormance o vehcle or boh vercal and laeral drecon a praccal MAGLEV vehcle model creaed. he conrol yem degn wa carred ou wh a mple ngle ma model ung Lnear Quadrac Conrol. Employng MALAB/SIMULINK, a compuer mulaon model wh 93 DOF o mechancal yem and 5 ae or elero magne orce ha been creaed o enure hgh calculaon ecency. Reaonable reul are obaned or opmaon o upenon parameer and dynamc perormance o he MAGLEV vehcle wh opmal conroller or mnmed energy conumpon. Reerence [] E. Goen, B.O. Lange: Magnec Supenon Conrol Syem or he MBB Hgh Speed ran, Auomaca, Vol. 975, pp [] D.A. Lmber, H.H. Rchardon, D.N. Wormely: Conrolled Dynamc Characerc o Ferromagnec Vehcle Supenon rovdng Smulaneou L and Gudance, Journal. Sy. Mea. Conrol, ran, ASME, 979, 9, pp.7~. [3] X.J. Zheng, J.J. Wu, Y.H. Zhou: Numercal Analy on Dynamc Conrol o Fve-Degree-o-Freedom Maglev Vehcle Movng on Flexble Gudeway, Journal o Sound and Vbraon, 35, Augu, pp [4] H. Coey, J. Solnky, J. Colon, J. Woodbury: Dynamc perormance o he SRI Maglev vehcle, IEEE ranacon on Magnec, Vol., 3, 974, pp [5] R. Menger: Conrol Syem or Flexble Maglev Vehcle Rdng over Flexble Gudeway, IUAM Sympoum on he Dynamc o Vehcle on Road and Ralway rack, Amerdam, Neherland, 975, pp.53~554. [6] C F. Zhao, W.M. Zha: Maglev Vehcle/Gudeway Vercal Random Repone and Rde Qualy, Vehcle Syem Dynamc, 383,, pp.85-. [7] Y.D. Xe, W.S. Chang: Modellng and Smulaon o Elecromagnec Supenon Vehcle SyemEMS n Vercal Drecon, Journal o he Chna Ralway Socey, 84, 996, pp [8] C.F. Zhao, W.M. Zha, Q.C. Wang: Smulaon Analy o he Dynamc Repone o Low-peed Maglev Vehcle Curve Negoaon, Chna Ralway Scence, 63, 5, pp [9] H. Ohak, R. W. Early, E. Suuk: Numercal Smulaon o he Vehcle Dynamc o he Superconducng Maglev Syem, he 6 h Inernaonal Conerence on Magnecally Levaed Syem and Lnear Drve, Ro de Janero, pp [] Y.Q. Deng, S.H. Luo: Sably Reearch and Smulaon o a Sngle Magnec Syem, Elecrc Locomove Ma ran Vehcle, 85, 5. [] H.J. Hong, J. L, S.J. L: Knemac Smulaon o Maglev ran Baed on Vrual rooype, Elecrc Drve or Locomove, 5, pp [] R. Menger: Beraege ur Regelung ener Magnechwebahn au elachem Fahrweg. Dr.-Ing. Deraon, U Muenchen 977. [3] R. Menger: Ermlung der Bewegungglechungen ene elecromechanchen Syem mel LAGRANGE-Funkon. Schrenrehe Hel 3, Georg-Smon-Ohm Fachhochchule Nuernberg 999 S. -5. [4] SHU Guangwe, CHEN Wegong, R. Menger: he Reearch on he Model o a Magnec Levaon Syem [J].Elecrc Machne and Conrol, 5: pp [5] R. Menger, Shu Guangwe, Cu Zwe: Smulaon o MAGLEV Syem wh MALAB/Smulnk. roceedng o Aan Smulaon Conerence / he 5h Inernaonal Conerence on Syem Smulaon and Scenc Compuer, Bejng:Inernaonal Academc ublher /Bejng World ublhng Corporaon,,pp Modelng and Smulaon o Shangha MAGLEV ran ranrapd wh Random rack Irregulare