SYSML-MOTIVE: SYSML BASED SPACECRAFT POWER MANAGEMENT FUNCTION MODELING, TESTING, INTEGRATION, VERIFICATION AND EXECUTION

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1 SYSML-MOTIVE: SYSML BASE SPACECRAFT POWER MANAGEMENT FUNCTION MOELING, TESTING, INTEGRATION, VERIFICATION AN EXECUTION S. Chhaniyara (1), C. Saaj (1), P. Ginst (2), V. Coipau (2) (1) Surry Spac Cntr, Univrsity of Surry, Guildford, UK GU1 7XH (2) Airbus fnc and Spac, Ls Muraux, Franc ABSTRACT Modl basd Systms Enginring (MBSE) is an immrging approach, which advocats a diagrammatical, vrifiabl and tstabl approach that nabls communications amongst various domain xprts, systm of systms, hardwar and softwar. This papr prsnts an MBSE approach to modl th Powr Managmnt Function (PMF) of a spaccraft systm in ordr to trad-off diffrnt stratgis for optimizing powr distribution of th vhicl. Figur 1 -orbitr multi-mission concpt [1] Th rsults prsntd in this papr ar basd on th outcoms of th SysML-MOTIVE 1 projct for a ris rmoval mission scnario. This papr will prsnt dvlopmnt of th PMF sub-systm architctural and bhavioural modl to prform trad-off study btwn various ky battry and solar cll tchnologis. Th MBSE mthodology prsntd hr will b usful for valuating th suitability of SysML basd Systm Enginring approachs for futur complx spac missions. 1 INTROUCTION Modrn day spaccraft Powr Managmnt Function (PMF) is an xampl of a complx scalabl systm involving systm of systms and intr-connctions of volving sub-systms. Th powr budgt for a spaccraft systm plays a crucial rol in phas-0/a mission analysis du to vr incrasing powr rquirmnts covring payloads (PL), robotic lmnts, Elctric propulsion, attitud and orbit control subsystm (AOCS) tc. Th problms associatd with dsigning th afor-mntiond sub-systms can b a non-trivial on. Hnc, a typical phas-0/a study of a spaccraft PMF involvs translating all customr and systm rquirmnts into dtaild functional analysis, trad-off analysis, and concrt systm architctural modl i.., with th viw to carry out a dtaild mission analysis of th systm. To addrss this problm, currnt stat of th art mploys th Modl-Basd Systm Enginring (MBSE) approach as a mans to allviat this problm. Oftn, most MBSE approachs advocats a diagrammatical, vrifiabl and tstabl approach that nabls communications amongst various domain xprts, systm of systms, hardwar and softwar. This study has dvlopd an MBSE approach to modl th PMF of a spaccraft systm in ordr to trad diffrnt stratgis for optimizing powr distribution of th vhicl. This study has modlld a top-lvl powr subsystm with focus on trad-off analysis of solar cll and battry tchnologis for satllit srvicing and ris rmoval mission scnarios lik in [1] and Fig.1. 2 SysML-SEP: SySML BASE SYSTEMS ENGINEERING PROCESS FRAMEWORK Across product dvlopmnt lifcycl, on crucial ara whr thr has bn a srious lack of a commonly accptabl languag support is th concptual stag, during which th functional architctur (and somtims th physical architctur) is dcidd upon. It is wll undrstood that this lack of support during product concptualisation will mak it xtrmly difficult to fficintly trac th ralisation of rquirmnts in th product. In addition to this, lack of a formal rprsntation for concpts hamprs th ability to mak important dcisions at th lvl of systms in th product i.. during fasibility studis. Byond that, th lack of a clar vision of th product architctur amongst th various systm stakholdrs hindrs tam undrstanding and communication. Thus, this in turn incrass th risk of intgration issus. This papr prsnts on of such SysML-SEP approachs as shown in Fig.2, for supporting phas 0/A of a robotic spaccraft dvlopmnts. 1 SysML-MOTIVE study is sponsord by AIRBUS fnc and Spac, Ls Muraux, Franc

2 SysML-SEP Framwork (Phas 0/A) Projct Contxt Modular SysML-SEP Profil Gnration OORS Moduls (ECSS-E10 Compliant) Modl Systm Contxt SysML Modlling Rquirmnt Managmnt trmin Rquirmnts Modl basd Tsting & Vrification Top Lvl Uscas Analysis Top Lvl Contxt iagram (Block iagram) Top Lvl Rquirmnt iagram (Block iagram) Top Lvl Scnarios (Activity/Squnc or a Stat Machin diagram) Rquirmnt Elicitation and Tracing (Systm) riv Systm Intrfacs (Intrnal Block iagram) Top Lvl Paramtric Modlling (Paramtric iagram) Trad-off analysis (Paramtric iagram) Modl basd Tsting Formal Vrification n-lvl Uscas Analysis Systm Contxt iagram (Intrnal Block iagram) Rquirmnt licitation and tracing (Sub Systms) n-lvl Scnarios (Sub Systm - Activity/Squnc or a Stat Machin diagram) Modl basd Tsting N-lvl Sub-Systm Intrfacs (Intrnal Block iagram) N-Lvl Paramtric Modlling (Paramtric iagram) Rquirmnt licitation and tracing (N-Lvl Systms) Formal Vrification Trad-off analysis (Intrnal Block iagram) Rquirmnt Vrification Full Systm Tsting & Vrification Figur 2 SysML-SEP framwork Arguably, it is ths and othr non-trivial challngs ncountrd during th concptual phas of product and systm dvlopmnt lifcycl that th Systm Modlling Languag (SysML) and Modl Basd Systm Enginring (MBSE) approachs ar dsignd to mitigat. Th proposd approach is a cas of spcial itrativly incrmntal systm nginring procsss, which nabls systms nginr to dvlop functional and physical systms through a tird modl dvlopmnt. This approach is dsignd in such a way that it is modular and scalabl so that it could b applid for th Phas B and following stags of any typical spac missions. This approach is a rsult of lsson larnd and bst practics that volvd from prvious projcts [2] [3] [4] [5] [6]. Thr ar thr principl activitis as part of th SysML-SEP approach: SysML modls, rquirmnt managmnt and modl basd tsting, validation & vrification that runs in paralll as shown in th Fig.2. A first stp in th SysML-SEP framwork is to stup and gnrat a modular packag structur by importing custom profil dvlopd for this projct. Thr ar thr rasons for having such modular packag structur. Th first rason is du to th fact that SysML is a smi-formal languag and would rquir dfining strict modling guidlins as dscribd by [3] and [4]. Scondly to support co-dvlopmnt by multipl tams at a sam tim and finally to aid itrativ and tird approach of product dvlopmnt. Mor dtaild information about th SysML-SEP modular packag structur and lifcycl is illustratd in [3] [3]. Th following sctions will illustrat th rmaining stps of th SysML-SEP framwork using a spaccraft PMF sub-systm modlling as part of th SysML- MOTIVE projct. 3 SysML-MOTIVE: SYSTEMS ENGINEERING OF SPACECRAFT PMF USING SysML-SEP Th orbital rang of th spaccraft considrd in this study is much widr than a classical LEO mission. Hnc, this put xtra mphasis for highr adaptability of all subsystms and spcially on PMF sub-systm. This is achivd by architctural, bhavioural and paramtric modling of th spaccraft PMF using SysML-SEP. 3.1 Stockholdr rquirmnts and modlling systm contxt Th top-lvl rquirmnt foldr within th SysML-SEP packag structur contains all th rquirmnts (stockholdr rquirmnts) which will driv th analysis

3 and systm functional modlling. Rquirmnts ar structurd basd on ECSS-E-ST-10-06C which is a part of th ECSS standard for tchnical rquirmnts and spcification. Ths top lvl stakholdr rquirmnts usually importd from th rquirmnt managmnt softwar, lik OORS in this SysML-MOTIVE projct. Typically, OORS maintains projct documnts, usr documnts, and documntation of changs. Systm spcification, rquirmnt analysis and modling ar prformd within Rational Rhapsody. IBM Rhapsody Gatway is bing usd to import and sync ths stakholdr rquirmnts to th SysML modl within a top-lvl rquirmnt packag as mntiond in [3] and Fig.3, 4. Th Rhapsody Gatway imparts th bnfits of a samlss bi-dirctional information xchang intrfac with 3rd party rquirmnts and authoring tools to xtnd a complt tracability solution, which allows dvloprs to xamin th upstram and downstram impact of rquirmnts changs, in ral tim, at any lvl of itrations. Th nxt stp in this procss is to crat rquirmnt viws showing important tracability links btwn rquirmnts using a top-lvl rquirmnt diagrams. In paralll to th rquirmnt diagram and managmnt procss at th top-lvl, anothr important stp is to idntify and crat a systm contxt diagram. This is basd on th SysML block dfinition diagram (B) and th intrnal block dfinition diagrams (IB). Th top-lvl contxt diagrams hlp in idntifying systm boundaris and actors outsid of th boundaris that could intract with th systm undr dvlopmnt (SU). This diagram provids a highst-lvl viw of a systm. Th purpos of th systm contxt diagram ralisd through a B is to dscrib th systm hirarchy and systm/componnt classifications. On of such B systm contxt diagram is shown in th Fig 5. Th aim of th systm contxt diagram ralisd using th IB is to spcify th intrfac (mssags) to xtrnal systms in th form of itm flows. Ths itm flows and mssags usually ar abstract at this lvl of functional analysis. Th ida is to map ths abstract flows and mssags to concrt mssag typs during th nxt lvl of analysis. 3.2 Top lvl uscas analysis and PMF contxt diagram Us cas diagrams dfin th various scnarios that a systm can hav. Th us cass giv th basic ida of how th systm would act undr diffrnt conditions and which stakholdrs ar rsponsibl for a particular us cas. Us cas analysis forms basis of systm dsign and systm bhaviour. For ach us cas it is important to idntify prim actor, triggr, prconditions, nominal scnario scnarios and any contingncy scnarios if xist. It is rcognizd that th first lvl us cas is a driving for systm functional brakdown and also for dvlopmnt of packag structur. Th rsulting first itration of th contxt diagram of th SysML-MOTIVE PMF sub-systm basd on th us cas analysis is shown in Fig.5(b). It shows th PMF sub-systm and associatd functional brakdown in th form of SysML blocks. Each block rprsnts th basic unit of structur in SysML. Figur 3 OORS rquirmnt databas snapshot1 Figur 4 Managmnt viw - Rhapsody Gatway 3.3 Top lvl systm scnarios Top-lvl systm scnarios ar usd to rprsnt two main bhavioural aspcts of th SU, on to show oprational mods and scondly systm scnarios. Th systm may hav a numbr of oprational mods prcivd by stakholdrs that can b modlld using a stat machin diagram as shown in Fig.6 (a). Th activity and squnc diagrams ar usd to analyss th xpctd usag of th systm basd on idntifid prcondition, post condition, scnario stps during th us cas analysis. Each us cass usually rsults in at last 5/6 top lvl scnarios at th first lvl of itration of such complx systm. 3.4 Idntification of systm intrfacs ata modlling and idntification of intrfacs ar also important part of rquirmnt analysis. Top lvl intrfacs (.g. mssags to/from th systm) should b consistnt with th data modl for ach of th subsystms (.g. dcomposition of mssags).

4 Figur 5 (a) Systm contxt diagram (b) Top lvl contxt diagram (1 st itration basd on th USE Cas Analysis) Figur 6 (a) Oprational mods (b) Intrnal block dfinition diagram of th PMF sub-systm Th rquirmnt analysis starts with an idntification of systms contxt and spcification of th intrfacs. This idntifid abstract mssags and intrfacs usually ar btwn actors and SU. Whras th contxt diagram for th SU and bhaviour analysis hlps in dtrmining abstract intrfacs btwn functional dcomposition of SU. Th intrfacs btwn parts of PMF subsystm ar shown on IB. Ports can b dfind on a block or part to spcify intrfacs on th blocks. Whilst th port provids a structural fatur, it also nabls th connction to th block to b spcifid in mor complx ways such as spcifying th intrfac (.g. providd and rquird oprations) and th associatd bhaviour within th port. This is achivd by giving th port a typ and grouping similar typ of mssags. 3.5 Top lvl paramtric modling Undrstanding and analysing of rquirmnts associatd with orbital paramtrs, powr rquirmnt for subsystms and data on past missions hlp dvlop a comprssiv modl of systm constraints. Mass, volum and cost ar ky paramtrs that driv th spaccraft systm nginring as wll. bris rmoval is a complx mission. In ordr for this mission to b succssfully stabilizing th spac nvironmnt from ris and prov to b a financially viabl, spaccraft nds to rmov at last fiv larg ris pr yar. This has dirct implication on PMF sub-systm architctur and bhavioural dsign. Th spaccraft altitud is dirctly proportional to orbit priod and clips tim. This dos put xtra dmand on th battry discharg and th charg cycl and availabl avrag orbit powr. Basd on litratur, th powr systm mass as a prcntag of th satllit dry mass can rang from 25% in LEO satllits to 45% in GEO satllits. Powr and nrgy and mass budgts for th mission hav bn itrativly updatd basd on paramtric analysis. Ths incrmntal changs to th powr, nrgy and mass constraints hav bn incorporatd in th SysML modl using paramtric diagrams. Paramtric diagrams show

5 mathmatical rlationships (such as prformanc constraints) among th pics of th systm bing dsignd. Th Paramtric Constraint Evaluator solvs quations for sts of attribut valus, taking into account th constraints that ar dfind. In this sction, on of such xampl for clips constraint on spaccraft is prsntd hr Orbital paramtrs and clips constraints LEO orbits ar usually circular orbits at km altitud (>200 km to avoid larg drag and <1000km to avoid van Alln blts radiation). Orbit priod for such orbit is roughly btwn 90 to 100mins. Th main orbit paramtr rlvant for PMF is inclination to th quatorial plan, which govrns possibl clips priods. This is xplaind hr and capturd in th SysML modl through a paramtric diagram as shown in Fig 7. T = Eclips priod f =Eclips fraction T = Orbit priod h = Altitud of satllit o R = Radius of Earth = Angl btwn th sun and orbit plan = G* M = x 10 5 G = gravitational km 3 /s 2 constant M = Mass of th mor massiv body (arth) a = orbit s smi-major axis 2 T 1 1 h 2Rh fe cos Unit: dimnsion lss To ( R h)cos Sinc th maximum clips fraction is rquird for this study, th angl β, is assumd to b qual to zro h 2Rh ( fe ) max cos ( R h) Man motion = 3 = 3 r 3 a a r To 2 = 2 = S -1 T P*( f ) max E max 3 km 3 S -2 * Km -3 = S -2 4 BATTERY SUB-SYSTEM AN TRAE-OFF STUIES Slction of th optimum battry for spac applications rsults in a saf, ffctiv, fficint, and conomical powr storag capability. Th optimum battry also nhancs launch oprations, minimizs impacts to rsourcs, supports contingncy oprations, and mts dmand loads. For th application undr considration, a typical battry systm dsign should considr ths rquirmnts battry capacity, dpth of discharg (O), stat of charg (SOC), man and nd of charg cll voltag, r-chargability, numbrs of clls and thir configurations, wight, spcific nrgy and transmission fficincy. Figur 7 Constraints posd by clips is capturd in this paramtric diagram Figur 8 Plot of bta angl, satllit altitud h and clips fraction F Ths paramtrs hav bn capturd as attributs in th battry SysML block. Th Fig 9 shows thr diffrnt battry tchnologis in form of Battr1, Battry2 and Battr3 connctd to th Battry block BL_UC07_01_Battry using th gnralisation rlationship. Th gnralisation rlationship indicats that on of th two rlatd blocks is considrd to b a spcialisd form of th othr and suprblock is considrd as gnralisation of sub-block. Typically, larg spaccraft runs on 50V-120V bus, which dos rquir numbrs of clls ithr in sris and paralll arrangmnts. With so many clls in sris, th possibility of on failing is ral. On opn cll would brak th circuit and a shortd on would lowr th ovrall voltag. Cll matching has always bn a challng. Figur 9 Contxt diagram of a battry sub-systm

6 4.1 Battry modling and Trad-off Studis Battry sizing can b on of th mor complx and important calculations in S/C systm dsign. It is important to stimat accurat battry bank siz, if th battry bank is ovrsizd, it could pos challng to kp it fully chargd; if battry bank is sizd too small, it won't b abl to run your intndd loads for as long as it is bing plannd. Trad-off analysis and rsults for two diffrnt battry tchnologis ar prsntd in th Tabl 1. Th mathmatical modl is prsntd blow and capturd using paramtric diagrams Fig. 9. Watt Hours of lctricity usag pr orbit and clips rquirmnts Estimatd dpth of discharg limit Thy hav to show a limitd dgradation during tim du to cosmic radiations and ultraviolt, and thy hav to rsist to th mchanical solicitations mainly linar acclrations and vibrations during launch and orbital manouvrs bcaus of ths constraints th clls for spac ar smallr than thos for trrstrial applications. n cll V V V d dd 1 n cll - Numbr of battry clls V - Minimum battry discharg voltag (bus voltag) V - Bypass diod voltag ovr th faild cll dd V d - End of charg cll voltag P* T Cr A hr ( O)* N * n* V C r PT W hr ( O)* N * n C r - Total S/C battry capacity P - Avrag clips load (watts) T - Eclips duration (hr) O - pth of discharg (0 o 1) N - Numbr of battris (nd at last two if want som partial rdundancy) n - Transmission fficincy btwn battry and load (typical valu is 0.9) m batt Cr * V N ( W * hr) SpE kg m batt - Mass of battris SpE - Spcific nrgy 5 SOLAR ARRAY SUB-SYSTEM AN TRAE- OFF STUIES Solar clls for spac applications hav to b highly fficint, capabl to stand thousands of thrmal cycls in orbit whr th tmpratur, according to th mission profil may vary from -150 C to mor than 120 C. Figur 10 Paramtric diagram for th battry capacity assssmnt Tabl 1 Prformanc trad-off study btwn two typs of battris Variabls Units/T Battry 1 Battry2 BattryCapacity yp Ah O doubl transefficincy doubl 0 0 ncll (numbrs of doubl clls) T S V V 4 3 dd V V V V 4 2 d pclosrveclips W _PMF N doubl 1 1 Mass of Battry kg spcific_nrgy WhPr Estimatd mass of Kg kg Mass Battry of a cll kg In th past silicon was th most usd solar cll matrial and th rachabl bulk fficincy was not highr than 14%. Th advnt of GaAs basd solar clls in th last dcad of th 20th cntury took th fficincy up to 19%, and nowadays tripl and multi junction solar clls show mor than 30%. Tripl junction GaAs solar clls ar populating mor and mor solar gnrators worldwid, whil manufacturrs ar activly working on four to six junction clls as a way forward always incrasing convrsion fficincy.

7 Th starting point for th solar array sizing is th corrct idntification of th powr dmand throughout th whol mission of th spaccraft. Such powr dmand may chang during th satllit liftim ithr bcaus of diffrnt oprational mods forsn during th mission or, mor simply, bcaus of dgradation of th lctrical prformancs of th lctrical loads. u to solar clipss, and possibl pointing rror along th orbit, an analysis of th nrgy dmand is rcalculatd. In cas of insufficint illumination, th on-board battry will supply th lctrical powr. Ths diffrnt powr dmand is modlld through various nominal and nonnominal scnarios. Comparativ prformanc mtrics (of Spcific powr (W/kg), powr dnsity (W/m2), spcific mass (kg/m2), and spcific cost ($/W).) can hlp study and compar diffrnt solar cll and array tchnologis for th mission scnarios. Th ultimat purpos of this trad-off study is to maximiz prformanc, whil minimizing cost. 5.1 Solar array sizing Th solar array sizing is don for th spaccraft at nd of mission lif (EOL) powr rquirmnt using standard solar array sizing procdurs and by considring all th s. Th solar array siz computd by using following Eqs. (1.5) (1.12). AM - Solar cll assmbly and SCA - Solar cll mismatch loss assmbly ara - Calibration loss - UV C fb - Solar array fabrication loss - Solar array flight loss fi H - Harnss and diod loss - Solar intnsity i MO - Micromtorits/orbital ris loss OP - Solar array oprational loss R - Solar cll dgradation UV dgradation V - Solar cll offst voltag P cll RA - Random loss cll - Solar cll powr Pf - Packing PSA - Solar array powr T SA - Tmpratur of th clls in orbit t SA - Tst Tmpratur of th cll P Eol - Solar SA array powr at EOL P Eol - Solar cll powr at EOL tc - Thrmal cycling loss fi = uv MO RA tc (1) T = (T SA-t SA) (2) i 6 (3) ( a) = (4) op i T v fb = AM c H (5) P Bol = I SCA (6) cll Sun SA Psa Eol = Pcll Eol Ncll (7) (PsaEol SCA) SA_Siz = (8) (Pcll Eol P f ) Th trad-off analysis rsults for two diffrnt scnarios and for thr diffrnt solar array tchnologis ar prsntd in th Tabl 2.3. Th solar array powr rang chosn is up to 31 KW. Along with ths two scnarios for SA sizing, th analysis is also don for mass and costs constraints for solar array trad-offs. Figur 11 Paramtric diagram of th solar array sizing Tabl 2 Prformanc trad-off study btwn two typs of Solar Array tchnologis cas 1 (SA1 Thin film CIGS, SA2 GaInP2/GaAs/G MJ, SA3 Multijunction rfractiv concntrator) T - Tmpratur dgradation Pcll Bol - Solar cll powr at BOL

8 Tabl 3 Prformanc trad-off study btwn two typs of Solar Array tchnologis- cas 2 (SA1 Thin film CIGS, SA2 GaInP2/GaAs/G MJ, SA3 Multijunction rfractiv concntrator) 5.2 Modl basd tsting and rquirmnt licitation Modl basd tsts ar addd in ordr to nsur that th modl indd corrctly capturs th rquirmnts. Bhaviour scnarios dvlopd during us cas analysis phas ar usd as tmplt for dfinition of tst cass. IBM Rhapsody MT covrag mtrics (rquirmnts covrag and modl covrag) guarants th compltnss of th modl basd tst suit. Automatic cod gnration is usd to gnrat an implmntation from th modl. Back-to-back tsting btwn modl and cod constitut th ky lmnt for cod vrification. Cod covrag mtrics ar usd in ordr to nsur compltnss of th tst suit with rgard to th prdfind cod covrag critria. This MT workflow provids opportunity to tst systm undr tst arly in lif-cycl of product dvlopmnt. Th nd of analysis phas will rsult in drivd rquirmnts for th sub-systms. Ths drivd rquirmnts will thn b starting point for th nxt phas of itration. 6 CONCLUSION AN FUTURE WORK SysML basd SE can dlivr th functional spcifications, paramtric studis, bhavioural undrstanding, and structur dfinitions of any complx systms and systms of systm. Using modling and simulation mthods, systms nginrs can trac th stakholdr rquirmnts and prototyp th systm wll in advanc. Ths stratgis togthr can nhanc communication and improv systm quality of any complx projct. It prmits rus of systm spcifications and modl lmnts. This all confirms that SysML modling is a prfct and valid approach in spac nginring. Using it in pr-implmntation phas, will idntify any problms arly in th projct and hnc will sav tim and mony. This projct has primarily shown following ky capabilitis: 1. In this projct, a SysML modl of satllit srvicing scnario for th Powr managmnt function sub-systm was succssfully dvlopd. Paramtric studis taking into account powr consumption profil coming from mission analysis. 2. Trad-off studis providing comparison btwn diffrnt architctur and diffrnt tchnologis. 3. Tst cass for nominal / non-nominal situation in ordr to assss robustnss of th slctd solution. 4. Idntification and licitation of main rquirmnts of th powr subsystm lmnts (solar panls, battris, and propulsion driv units) was idntifid. 7 Rfrncs [1]. ALARY, Astrium s viws on OOS & AR Activ bris Rmoval Confrnc, Europan On- Orbit Satllit Srvicing and, Brussls, Blgium, Octobr 30, [2] S. Chhaniyara, C. Saaj, M. Althoff-Kotzias, I. Ahrns and B. Madigr, SysML basd systm nginring: A cas study for spac robotic systms, 62nd Intrnational Astronautical Congrss., Cap Town, [3] S. Chhaniyara, C. Saaj, M. Althoff-Kotzias, I. Ahrns and B. Madigr, MOEL BASE SYSTEM ENGINEERING FOR SPACE ROBOTICS SYSTEMS, in ESA/ESTEC, [4] E. Hiron and P. Miramont, Procss basd on SysML for nw launchrs sytm and softwar dvlopmnts, in ata systm in Arospac: ASIA 2010, Budapst, Hungary, [5]. I. Obr Iulian, A nw vrsion of th profil and th tools, in UML & AAL- 15th IEEE ICECCS, [6]. I. Obr Iulian, Unambiguous UML compsit structurs : th OMEGA2 Exprinc, in Intrnational confrnc on currnt trnds in thory and practic of computr scinc, LNCS, [7] H. Hoffmann and A. Tllogic, SysML-basd systms nginring using a modl-drivn dvlopmnt approach, 2006.