DESIGN OF A RAILWAY CARRIAGE, DRIVEN BY A LINEAR MOTOR WITH ACTIVE SUSPENSION/TILT MODULE

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1 ubmsson to te 9 t IFAC ymposum on Control n Transportaton ystems 000, June.13-15, 000, Braunscweg, Germany DEIGN OF A AIWAY CAIAGE, DIVEN BY A INEA MOTO WITH ACTIVE UPENION/TIT MODUE Markus Henke, Xaobo u-henke, Joacm ückel, Horst Grotstollen, Karl-Peter Jäker New alway ystem Paderborn, Unversty of Paderborn Polweg 55, D Paderborn (Germany) Tel.: , Fax: E_Mal: {enke, lu}@nbp.un-paderborn.de Abstract : Ts paper presents te desgn of a ralway carrage wose drve s realzed by a lnear motor. An ntegrated suspenson/tlt module makes possble ncreased rde comfort and cornerng speed n comparson to exstng systems. Copyrgt 000 IFAC Keywords: near motors, Actve vecle suspenson, Modellng, mulaton, Controldesgn, always 1. INTODUCTION In te past years, tecnologcal progress n ralway tecnology as brougt about a large network of ralways tat does not need extenson. It s sutable bot for te fast transport of passengers and for tat of eavy fregt. Te prncple of te force-closed drve va contact of weel and ral as not canged muc, yet tere are stll some drawbacks to t: on te one and, togeter wt velocty, frcton wll ncrease, and so wll energy consumpton and te wear of te components; on te oter and, te force closure wll decrease n te case of wet or cy rals and durng cornerng. Te suspenson n conventonal trans, realzed by means of relatvely ard sprngs and dampers, s very uncomfortable for te passenger. In contrast, a system drven by a lnear motor wll offer te advantage of a frctonless drve of te respectve vecle. Many of tese systems requre a new lne of ter own, especally f te lnear drve s combned wt magnetc levtaton, as s te case wt te German g-velocty system Transrapd (Hennng, 1995) or te Japan-based HT (Jayawant, 1981). Te envronment wll be extensvely affected; fnancal and poltcal problems wll serously endanger future realzaton.. APPOACH TO A OUTION Te researc team New alway ystem Paderborn as desgned a ralborne, lnear-motor-drven ralway carrage tat combnes te advantages of te two systems. Te drve s effected by means of a travellng magnetc feld, contact-free va te lnear drve and not va te contact between weel and ral. Te motor can be ntegrated nto te exstng ralway system and te nfrastructure of te latter can tus be used. lateral drecton tlt Y α X A1 longtudnal drecton γ D ptc A drve/brake module yaw vertcal drecton suspenson/ tlt module B1 C B support/ gudance module Fg. 1 Te fully automated modular ralway system

2 Decouplng te drve from te weels allows an optmal desgn of an actve suspenson/tlt module, because te boge can be mounted easly and unsprung masses wll be reduced. Tus rde comfort can be mproved; te actve tltng devce allows ger cornerng veloctes. Wen te exstng ralway weel-ral-system s used, te functons "supportng" and "gudng" can be realzed wtout furter energy expendture. Te ralway carrage conssts of tree modules (ückel et al. 1999): Drve and brake module: Wt a lnear drve, t s possble to start up and brake a carrage wear-free. Tus exstng ralway lnes can be used for te concurrent operaton of conventonal and novel systems. Actve suspenson and tlt module: Actve suspenson brngs about comfortable suspenson of te coac body, reduces senstvty to unevennesses n te track bed, and te same actuator system allows to realze te tltng module n order to ncrease cornerng speed. upport- and gudance module: Use of te exstng ralway weel-ral-tecnology. Tese tree modules, coupled wt te passve prmary suspenson, make up a fully automated undercarrage tat allows te suttle to operate flexbly, wtout a drver, and for te transport bot of passengers and of fregts. Te modular structure of te undercarrage allows for an ndependent desgn and testng of te drve and te suspenson/tlt modules ystematcs 3. THE DIVE YTEM Te lnear motor n te man conssts of te followng electro-mecancal components: - te prmary (stator), nstalled between te rals, - te secondary, mounted on te undercarrage. In te stator, a magnetc travellng feld s generated tat exerts a force on te electrcally excted secondary n te carrage (Fg. ). Prmary and secondary are nterlnked only magnetcally by te ar gap, wt te latter, wc s ndspensable for te proper functonng, beng ensured by te trackng of te carrage. A comfortable control of te longtudnal dynamcs can be easly obtaned because te power s drectly transmtted to te secondary wtout power losses due to te transmsson. Fg - Trust buld-up n te lnear motor In many an applcaton of te lnear-motor tecnology, te exctaton feld s generated n te secondary and te trust s controlled by means of te stator current accordng to reference values set by superordnated control loops concernng velocty and longtudnal dynamcs. Only one secondary per stator segment can ten be operated because te stator current as control varable would affect all coaces. In order to make te carrage moton more flexble, a relatve moton between dfferent coaces on te same stator as to be made possble. Ts puts g demands on te actuators as well as on te control and nformatonprocessng unts (Fg. 3). A syncronous long-stator lnear motor s not able to produce te desred relatve moton; terefore te secondary n te coac wll be equpped wt a treepase wndng. Tus te exctaton flux can be vared relatve to te poston of te coac and an asyncronous operaton comes wtn reac. Fg 3 - Overall structure of te drve system Te actual trust control s effected on board and te motor s double-fed,.e., prmary and secondary can algn ter magnetc fluxes at any tme ( Kel, 1999; Henke, 1999). In order to avod constant power supply to te entre track, te latter s dvded nto segments tat are suppled wt voltage by dfferent power-supply unts (substatons). Tey ndex te power supply to te next poston n dependence of tat of te coac. As a result, te energy consumpton of te drve s optmzed because te track s suppled wt power only n te respectve segment were tere s a coac on te stator. 3.. Modellng of te Drve ystem To analyze te beavour of te lnear motor ts matematcal model s drawn up and te overall beavour of te drve s analyzed n te smulaton. Coordnate ystem Te currents n te secondares are gong to be controlled accordng to a unform coordnate system common to all coaces; tus te nteractons between te suttles can be traced clearly. Te prmary and te secondares sare te same electrcal poston of te stator current as te statorflux lnkage depends also on te respectve current of te secondary.

3 Te coordnate system employed s tus orented accordng to te stator current. Te model of te secondary n te coac s bult up orented to te stator current and te stator-current orentaton makes up te d-axs of te coordnate system (Fg. 4) wt = 0. q - Fg. 4 - tator-current-orented coordnate system Electrcal ubsystem Te equatons of te electrcal subsystem of te double-fed lnear motor rely on tose of te asyncronous lnear motor. In te followng, all varables are related to te secondary are ndexed, all stator varables,. As regards motor parameters, tere are:, σ : mutual and leakage nductances, : resstance of secondary and prmary ψ, ψ : flux lnkages ω K ω : angular velocty of te stator feld : angular velocty of te secondary σ, ρ : leakage and resstance coeffcents Te complex equatons relatng to te voltage of te prmary and secondary are dsplayed n (1) and (): d σ = u u + + jω + jω K + jω jω K d σ = u u + + jω jω K - (1) () Te equatons are transformed nto te statorcurrentorented coordnate system. Transformaton yelds te real part of te equaton (1) as follows: σ d d = u d d u d + d ω (3) q Te magnary part s dq σ = u q q + ω K u d q + ω K d q = 0 ω d (4) Tus te angular frequency of te stator current results n d 1 ω K = ( uq uq + q ω d + ωk ). (5) d Equatons (3) and (4) represent te dynamcs of te statorcurrent. To determne te electrcal states n te secondary, we now ave to derve te equatons of te secondary voltage; tey yeld te secondary currents: dd σ σ d q = u = u d d ωk q q + ωk q d u d + + ω u K q q ω K d + ω d d Te force equaton of te motor s te followng: p (6) (7) 3 π Fm = d. (8) q τ Te power s tus proportonal to te stator current d and to te secondary component q. Fg. 5 dsplays te block dagram of te motor. Here, fve varables ave to be controlled: Te velocty of te coac, te components of te rotor current, te stator-current frequency, and te ampltude of te stator current ( d ). ua ub u c ua ub u c a,b,c d,q a,b,c d,q ε K ε K ud ud uq uq / / / 1 1 / / 1 σ / / σ σ d d d d d q q ωk ω ωk q ωk ωk ω ω ω q d q q -3/ / Fg. 5 - Model of te double-fed lnear motor Te electrcal actuator of te lnear motor s a converter generatng te voltage values tat te control requres. On board, a converter supples power to te on-board batteres and te exctaton wndngs. Mecancal ubsystem Te coac s modelled as a one-mass system. Ts yelds te smple mecancal equaton for te coac moton: π/τ P ωk d π/τ P FM d / ωk F / 1/m v uq uq

4 & (9) mx = F m F Te load F affectng te secondary of te motor s a combnaton of: - wnd resstances, gradents, frcton - load forces resultng from te energy transmsson to te coac - longtudnal vbratons of te coac For ts purpose, magnetc-feld sensors on board te coac are used to determne te poston n relaton to te stator feld. Te use of g-performance sgnal processng allows to estmate te poston on te bass of measured current and voltage values for trust control. Fg. 6 dsplays n detal te overall structure of te coac control: ψ 3.3. Drve Control We ave already stated tat te system beavour forces to decouple te stator-feld control from te control of te coac. ψ ε Control of te tator Feld Contrary to conventonal lnear drve systems, te stator ere bulds a unt wose current as to be controlled as to constant frequency and ampltude durng operaton. Dsturbances ere are te voltages nduced by te movng secondares. Control of te ongtudnal Dynamcs of te Vecle Every coac controls ts own longtudnal dynamcs va te electrcal poston of te exctaton flux and uses te stator flux common to all coaces. Here, te control takes nto account te swtcng between te stator segments. As te stator current s fxed at a constant value, te only remanng actuatng varable of te trust control s te q-component q of te secondary current, cf. equ. (8). Control of te Energy Te current component d and te slp s (te latter can be regulated only to a certan degree) do not affect te buld-up of trust, yet tey ave nfluence on te energy flux n te ar gap. Te actuatng varable u d serves to regulate te current d so as to brng about te desred energetcal beavour. Te reference value of d can be set so as to mnmze te secondary losses. Furtermore, to feed te secondary, energy as to be provded on board by batteres wose carge nfluences te reference values for te energy control. Fg. 6 - tatorcurrent-orented control structure e ar gap between te prmary and te secondary as to be assessed because a cange would mmedately affect trust and brakng forces (Geras, 1995). Alteratons n te ar gap affect te buld-up of force and voltage as alteratons n te gan, so te trust controller wll ave to be adapted accordngly mulaton For te control sown above, a smulaton model as been made up (Henke, 1999). Te smulaton s based on parameters of a lnear drve, wc s used to propell a 1:5 scaled prototype of te ralway vecle. Fg. 7 dsplays te smulaton results. ε 3.4. Global Control tructure For te control of te carrage, tere are tus tree remanng varables to be controlled: te complex components of te secondary current and, superordnated, te velocty v of te carrage. Te actual values of d and q are drectly determned from te measured prmary and secondary currents n a flux model. Precse knowledge of te poston of te coac s vtal to ts control. Te poston as to be detected wt very g precson and g dynamcs. Fg. 7 - mulaton result At te tme t = 0.1 s, a step n te reference value of te velocty s gven. At t =1 s an alteraton of te ar gap affects te coac.

5 Ts alteraton results n an ncrease of te secondary current as te requred trust as to be generated wt a reduced man nductvty. Te forceequaton (8) sows, tat a decrease n can only be compensated by a ger q-current n te secondary, because d remans constant. Te secondary fluxcomponent ψ also decreases, so tat d ψ as q to be ncreased va q to mantan te desred fluxdensty n te argap between prmary and secondary. Future work wll concentrate on te verfcaton of te results on te drve testbed. 4. THE ACTIVE UPENION/TIT MODUE Wle four actuators on te sde lft and tlt te coac body, te oter two actuators n te mddle provde for lateral moton, wt ptcng beng prevented by actuators on te sde, and longtudnal and yawng movements beng precluded by lemnscate lnks (Otto, 1999). secondary suspenson (arsprng) prmary uspenson (passv) coac body ydraulc actuator upper plate under plate valves ydraulc supply 4.1. Demands on te uspenson/tlt Module Te passve system wt sprng and damper operates n a frequency range (of up to about 00 Hz) tat s unpleasant for te passenger because te force proportonal to te velocty brngs about g damper forces n te upper frequency range. As regards te coac-body suspenson, a bandw of about 1 Hz s acceptable for te passenger s well-beng. It can be reaced by means of an actve suspenson wose am t s to produce te desred dampng resp. sprng caracterstcs n te respectve frequency range. Anoter demand on te ralway carrage s for t to corner track curves at g speed wt constant rde comfort and safety. For ts an actve tlt module s employed. 4.. Concept of te uspenson/tlt Module In contrast to conventonal suspenson systems, te concept presented s concerned wt elmnatng all passve dampers n te secondary suspenson and on connectng te coac body to te undercarrage only va te arsprngs (ückel, et al., 1999). Wle te arsprng solates te vbratons n te upper frequency range, te desred dampng n te lower frequency range s obtaned by an actve nterventon. Tus transmsson of te dsturbances stemmng from unevennesses n te track algnment to te coac body s nearng zero. Te result s a more tan satsfactory rde comfort bot n te vertcal and orzontal drectons. Te nformaton requred to dsplace te arsprng base s measured by approprate sensors and processed n a erarccally structured multvarable control (Fg. 8). Te actve tltng of te coac body can be realzed wt te same actuator system troug a feedforward of te cornerng acceleraton. Te core of te actuator system conssts of te mecancal components upper and under plate (boge) resp. te arsprngs, te actuators, te sensors, and te nformaton processng (Fg. 8). Fg. 8 cematc dagram of te suspenson/tlt module Every suspenson/tlt module as to ensure tree drectons of moton: vertcal, lateral, and tltng motons. Te suttle (consstng of two modules) allows all controlled rotatonal and translatonal motons n lateral and vertcal drectons. Te translatonal moton n longtudnal drecton (trust) s controlled by means of te lnear drve Modellng and Analyss of te ystem Beavour In order to analyze te beavour of a dynamcal system and ten to desgn a multvarable control, we at frst draw up te pyscal and te matematcal substtute model accordng to functon prncples n vew of te demands. Te model as to represent te knematc, te statcal and te dynamc beavour of te system n vew. Followng approprate smplfcatons a 3-D model (Krcner, 1999) s made up for te analyss of te suspenson/tlt module (Fg. 9): drve drecton secondary suspenson arsprngs ydr. actuators prmary suspenson A AC B C D BC A1 B1 BC IC BC XCylnder BC BC coac body upper plates under plates (boge) upper edge of track Fg. 9-3-D model of te suspenson/tlt module

6 Modellng process s fully supported by te software envronment CAMe (Computer-Aded Mecatroncs aboratory) developed at te MaP. CAMe permts consstent treatment of te mecatronc system n te computer from te objectorented, nteractve buld-up of te modularerarccal system n a topologcal/pyscal model descrpton, automatc dervaton of te correspondng matematcal equatons to an automatc generaton of C code to a ardware-n-te-loop smulaton n real tme (Han, 1999). Ts requres systematc analyses of te entre system. Knematcs of te ystem Te knematc beavour of te system s determned from te degrees of freedom and te geometry of te suspenson/tlt module, accordng to sutable coordnate systems. Fg. 9 dsplays te IC (Inerta Coordnate ystem) on te upper surface of te rals, te BC (Body Coordnate ystem) n every rgd body, te AC (Attacmentpont Coordnate ystems) n te couplng ponts between elements and te coordnates of every cylnder pston x Cylnder. By means of coordnate transformatons te knematcs and te nverse knematcs of te entre system are computed and later embedded nto te global control structure. Dynamcs of te ystem Te dynamcs of te entre system results from te dynamcal propertes of te mecancal supportng structures, actuators, sensors and dgtal sgnal processng. - Mecancal upportng tructure Te coac body as well as te upper and te under plate of te suspenson/tlt module are modelled as rgd bodes wt sx degrees of freedom eac. Correspondng equatons of moton are generated symbolcally by means of te agrange formalsms n CAMe. Te complex operatonal mode of te arsprng requres muc computng (Krettek, et al., 199). Terefore te smplfed substtute model wt PDT1 beavour s employed for eac degree of freedom. - Actuator Dynamcs As actuators for te control motons, we use ydraulc dfferental cylnders wc ave a seres connecton to a servo valve (Fg. 10). Here, te electrcal voltage of valve s te nput value and te cylnder force te output value of te entre transfer beavour. Troug te dsplacement of te valve slder, te servo valve converts te electrcal sgnal nto an ol flow. Ts dynamcs s modelled by a system of nd order (Panter, 1984) and descrbes te dependence of te poston of te valve slder on te nput voltage. Fg Hydraulc nterconnectons n te actuator Te actuatng force of te cylnder s te product of te pston area multpled by te pressure dfference between te two cylnder cambers resultng from te nflowng and outflowng ol. Ts dynamcal process s modelled n a dfferental equaton of 1st order wc descrbes te dependence of te pressure cange of te two cylnder cambers on te alteraton of volume flows, on te compressblty of te pressure medum, and on losses due to leakage. - Dynamcs of te ensor ystem and of te Dgtal gnal Processng Wen a dgtal controller s realzed te sample tme and te processng tme requred for computng te control algortm can be descrbed by means of te dead-tme beavour. Ts effect s mplemented nto te model troug a Padé approxmaton. Te sensors narrow te bandw of te system. In te modellng, a PT low-pass s used n order to emulate te sensor dynamcs. - Overall Dynamcs Accordng to tese analyss above te dynamcs of te entre module s modelled n te CAMe envronment wt te models of every subsystem beng topologcally lnked to sutable nterfaces n te computer. Wt regard to te knematcs te supportng structure s extended by actuators, sensors, and dgtal effects to buld up te overall dynamcs of system. Control Concept and tructure Te multvarable controller s erarccally structured nto two controller groups: global ones operatng at te centre and local ones operatng decentrally. Fg.11 dsplays ts erarccally structured multvarable control of te suspenson/tlt module. Te superordnated global conssts manly of tree blocks. Te vertcal and lateral dsplacements as well as te tlt angles of te coac body are derved from te measured cylnder postons and ar-sprng postons n te block Decouplng tat s based on te system knematcs. From ts te desred sprng and damper forces are generated n te block tunng forces. Wt regardng to acceleraton te forces brng about te reference values for te subordnated control loops n te Couplng block.

7 As local controls, tere are te cascade control structures wt tree loops tat can brng te dynamcs of te ndvdual actuator under control quckly enoug. Te nner control loop s made up of te poston control of te gate valve. Te velocty of te cylnders s realzed va te mddle control loop and te outer control loop s made up of te poston control of te cylnder. Te parameters of ts erarccally organzed control structure s optmzed n te CAMe envronment by means of a vector qualty crteron. measured dsplacements Y arsp_measure Z arsp_neasure Z arsp_mearsure X Z_measure_A1-A X Z_measure_B1 X Z_measure_B X Z_measure_CD X _velocty X Z_soll_A1-A X Z_soll_B1 X Z_soll_B X Z_soll_C-D X _leteral decouplng K F F lft_t F lateral_t M tlt_t local control structure okale egelung Aktor A1-A actuator A1-A local control structure actuator B1 local control structure actuator B local control structure actuator C-D X _A1-A X Z_A1-A X _B1 X Z_B1 X _B X Z_B X _C-D X Z_C-D ft ateral Y W Tlt X Z_soll tunng forces poston control of cylnder + + DT- Y W Z Element W DT- Z W Element α W α DT- W Element nonln. compensaton F ub F quer M nege + couplng overall control structure velocty control of cylnder DT-element X Z_soll_A1-A X Z_soll_B1 X Z_soll_B X Z_soll_C-D local control structure poston control of gate valve Fg.11 - Herarccal control structure reference postons for local controllers sensor sensor system model mulaton and Dsplay of esults Te controlled entre system was expermented n te computer. In order to sow te potental for mprovng te actve control, te passve system was analyzed n te same operatng condtons. A step exctaton produced by te track s employed. Fg. 1 dsplays te coac-body moton of te actve and te passve system n vertcal drecton. Te step responses of te nonlnear smulaton of lateral and vertcal drectons sow smlar curves. Te smulaton result sows te system beavour of te actve system to boast a consderably ger dampng tan tat of te passve system. x s x z couc acceleraton [m/s²] passve (arsprngs, dampers) actve (arsprngs, wtout dampers) 5 Frequent [Hz] Fg.13 pectra of te coac-body acceleratons 4.4. Testbed of te uspenson/tlt Module Fg. 14 llustrates te wole testbed concept of te suspenson/tlt module. It makes up a alf-suttle wt a suspenson/tlt module on a scale of 1 : 5. Te coac body as tree degrees of freedem, n vertcal and lateral drectons as well as tlt, respectvely. Te exctaton cylnders n te test nfrastructure emulate te vbratons resultng from te prmary part of te undercarrage and from unevennesses n te track bed, as well as from lateral dsturbances of te coac body. Te testbed rests on sx arsprngs so as to decouple te system from te vbratons comng from ts envronment. On ts lab testbed te desgned erarccal control structures and te entre confguraton of te system can be measured, analyzed and valdated under realtme condtons 50 vertcal dsplement [m] -1,830-1,835-1,840-1,845 passve (arsprngs, dampers) actve (arsprngs, wtout dampers) -1,850 0,0 1,0,0 3,0 tme [s] Fg. 1 tep response of te coac-body moton As a measure of te acceleratons te passenger s subject to, te ampltude spectra of te coac-body acceleraton were determned. Te area ntegrated from ampltude spectrum of te actve suspenson s consderably smaller tan tat of te passve system (Fg. 13). Tus te actve suspenson system brngs about a rde comfort tat s many tmes better tan tat of te passve system. Fg Testbed concept

8 Fg. 15 dsplays te partal realzaton of testbed. Te postons of cylnder and gate valve as well as te dsplacements of te ar sprng are measured; te measured sgnal are ten transmtted by A/D converters to a DP were te control algortms are processed and te sgnals transmtted to te actuatng valves va D/A converters. sensor cylnder for coac body exctaton from transverse acceleraton arsprng cylnders for exctaton from track unevennesses cylnder valve suspenson/tlt module test envronment Fg. 15 ealzaton of testbed 5. UMMAY Te paper presented te desgn of a tecncally gly complex ralway carrage wt te drve and te suspenson/tlt modules beng examned n more detal. Te drve by means of a lnear motor allows a very precse control of te longtudnal dynamcs because te motor can act on te undercarrage drectly wtout a gear. Te actve suspenson allows to solate vbratons of te coac body, resultng from unevennesses of te tracks tat mgt mpar te passenger's well-beng. Te result s an ncrease n rde comfort. Te tlt module s realzed wt te same actuator system. As regards te drve and te suspenson/tlt modules, we presented te desgn from modellng to smulaton tll realzaton. Te ralway carrage, combnng te lnear wear-free drve wt an actve suspenson/tlt module, as been desgned on several testbeds and s currently beng optmzed. teme unter Verwendung von Merkörpersystemformalsmen. Dss., MaP, Unversty of Paderborn, 1999 (to be publsed, n German). Henke M., Grotstollen H.: egelung enes angstator- nearmotors für en spurgefürtes Banfarzeug, P/IPC Drves 1999, Nürnberg, Hennng U., Kamp P., and Hocletner J.: angstator- yncronmotorantreb des TANAPID, Elektrsce Banen, July 1995 (n German). Jayawant B.V.: Electromagnetc evtaton and uspenson Tecnques, Edward Arnold, Kel J.: Modellbldung und mulaton enes geregelten, doppeltgespesten Asyncron - nearmotors. Internal report, Inst. for Power Electroncs and Electrcal Drves, Unversty of Paderborn (n German), Krcner A.: Modellbldung und Analyse ener aktven Wagenkastenfederung für en neues Zugmodul, Internal report, MaP, Unversty of Paderborn, Aug (n German). Krettek O., Grjnert J.: De uftfeder, re Berecnung und dynamscen Egenscaften,.Federungs- und Dämpfungssysteme, Aacen: Veweg-Verlag, 199 (n German). ückel J., Grotstollen H., Jäker K.-P., Henke M. and u X.: Mecatronc Desgn of a Modular alway Carrage, 1999 IEEE/ AME Internatonal Conference on Advanced Intellgent Mecatroncs, Atlanta, GA, UA, ept. 19-3, Otto.: Entwurf enes Esenbanfarwerks mt aktver Feder-/ Negetecnk und nearmotorantreb, Internal report, MaP, Unversty of Paderborn, Feb (n German). Panter M.: Identfkaton pyskalscer ystemparameter mecansc-ydraulscer Mergrößensysteme. Fortscr.-Ber. VDI-Z, ee 8, Nr. 76, VDI-Verlag, Düsseldorf, 1984 (n German). 6. EFEENCE Geras J.F.: near Inducton Drves, Oxford: Oxford cence Publcatons Han M.: OMD - En Objektmodell für den Mecatronkentwurf. Anwendung n der objektorenterten Modellbldung mecatronscer ys-