NEAR REAL-TIME AUTONOMOUS HEALTH MONITORING OF ACTUATORS: FAULT DETECTION AND RECONFIGURATION

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1 NEAR REAL-TME AUTONOMOUS HEALTH MONTORNG OF ACTUATORS: FAULT DETECTON AND RECONFGURATON Sanjay Jayaram UCF/Aximric nc Rogr W. Johnson UCF Guru Prasad Aximric nc Absrac This papr is concrnd wih h Nar Ral-im Auonomous Halh Monioring of auonomous sallis and auonomous unmannd ground vhicls. Th dynamics of such unmannd sysms is uncrain du o facors such as high non-linariy considraion of highr modal frquncis high dimnsionaliy mulipl inpus and oupus opraional consrains as wll as unxpcd failurs of snsors and/or acuaors. Hnc a sysmaic framwor of dvloping a high fidliy dynamic modl of h srucural sysm nds o b undrsood. Th faul dcion mchanism ha will b an ingrad par of an auonomous halh monioring sysm compriss h dcion of abnormaliis in h snsors and/or acuaors and corrcing hs dcd fauls if possibl. Applying h robus conrol law and h robus masurs ha ar capabl of dcing and rcovring/rplacing h acuaors rcifis h acuaor fauls. Th faul olran concp applid o h snsors will b in h form of an Exndd Kalman Filr EKF. Th EKF is going o wigh h informaion coming from mulipl snsors rdundan snsors usd o masur h sam informaion and auomaically idnify h fauly snsors and wigh h bs sima from h rmaining snsors. Spcifically his papr addrsss h difficulis currnly ncounrd by h auonomous vhicls. Th insrion of his uniqu concp nhancs h inllignc of h vhicl rducs h cos incrass h safy and rliabiliy o improv h global prformanc of h ovrall sysm. nroducion Prsn and fuur spac missions will us flxibl lighwigh muli-body srucural spac sysms. Such sysms ar xpcd o hav significan flxibiliy in h srucural mmbrs. Th flxibl muli-body sysms ar lily o b highly non-linar wih im varying srucural paramrs wih a gra xn of inaccuracis and uncrainis in h mahmaical modl. Furhrmor i calls for h ulima pursui of a highr dgr of auonomous opraion possibly in ral-im. Hnc o m h dmanding prformancs ha hav o b achivd highly sophisicad conrollrs li a Non-linar Robus Conrol nds o b dsignd. Sinc spac srucurs nd o b oprad for a long duraion of im wihou frqun lcommunicaion from h ground saion a Ral-im Modl-Basd Auonomous Halh Monioring approach will b a promising and viabl ool for h prsn and fuur spac missions. Ral-im Auonomous Halh Monioring is incrasingly bcoming a popular and accpd mhod for drmining and monioring h ovrall halh of h srucur. Th analysis usd hr for halh monioring is o dc any abnormaliis in h sysm

2 Auonomous Rconfiguraion paramrs by dvloping a high fidliy dynamic modl of h nominal sysm and comparing h masurmns an from snsors from h acual sysm. Th sing consiss of drmining sysm paramrs i.. naural frquncis damping and siffnss consans mod shaps c. of h flxibl srucural sysm from is rspons o a nown xciaion. Pracically h ind of xrnal disurbanc or xciaion in spac nvironmns ar highly unprdicabl hnc robus mhods ar proposd o compnsa for hs uncrainis. This papr concrns h accomplishmn of nar ral-im auonomous halh monioring of a flxibl lighwigh srucur using a high fidliy dynamic modl-basd simulaion and dvloping a faul olran robus conrol mchanism for is conrol. Tchnical Objcivs This papr dvlops an ingrad conrol framwor ha nabls auonomy monioring diagnosis and faul-rcovry and slf-haling xcuion a wo lvls of conrol. Spcifically h proposd nw conrol schm addrsss h chnical difficulis currnly ncounrd in h dsigns of auonomous managmn sysms. Procsss and componns in h sysm mus b conrolld coninuously and hir halh has o b moniord in h prsnc of dynamic variaions. Typically conrol and monioring ar don convnionally using sandard off-h-shlf conrol/snsor moduls. Th problms arising in monioring dynamic sas nds o b rsolvd. Whil advancd conrols such as nonlinar robus conrol adapiv conrol c. ar idal candidas in h dsign of an auonomous sysm opraing in an unnown and changing nvironmn spac-bound compurs a his im hav vry limid compuaional powr in analyzing all daa in ral-im and synhsizing all conrol signals. To ovrcom h abov wo major obsacls a proposd inllign conrol framwor is discussd ha can achiv h chnical objcivs of Robusnss Faul Tolranc Auonomy and slf-rconfiguraion and nllignc. Hnc h proposd inllign conrol sysm will rduc h cos nhanc rliabiliy and incras safy so ha fuur spac sysms and vhicls can opra in an uncrain nvironmn. Sysm Dscripion Th bloc diagram of h sysm considrd in his papr is shown in Figur. Th sysm consiss of a s of acuaors ha driv h plan bing considrd. Th sysm and acuaor oupu ar moniord. Th masurd signals of snsors will pass hrough a Kalman filr or Exndd Kalman Filr [5 6]. Th filrd signals will hn b sn o h convnional conrol bloc for ral-im xcuion afr passing hrough faul dcion modul and a robus conrol modul. n h faul dcion modul h halh of h acuaors ar moniord using robus masurs so ha faul idnificaion can b don in h prsnc of significan uncrainis. Manim h sam modul also moniors prformanc of h sysm. Whn sysm prformanc is lss han dsird h diagnosic algorihm will invo h nonlinar robus conrol ha is capabl of guaraning prformanc. Whn a faul is dcd h nonlinar simaion is acivad so ha conrol acion can b synhsizd afr xcluding h fdbac from h fauly acuaor. Corrciv Conrol Command Corrciv Conrol

3 Figur : Sysm Bloc Diagram Kalman Filr Basd Snsor Faul Dcion Ral-im halh monioring of a dynamic sysm dpnds on accura idnificaion of h sysm paramrs from h on-board snsors and acuaors. n h cas of a salli ha is flying in h Low Earh Orbi LEO h numbr of good passs ha h salli will hav ovr h ground saion is vry fw around hr o four passs in a day and ach good pass abov h ground saion would las for lss han igh minus horizon o horizon. Hnc for ach and vry good pass h daa collcd from various insrumns on-board h salli is ransmid o h ground saion and various compuaions nds o b don in ral-im fas and accuraly. For his rason paralll procssing Exndd Kalman filr is h bs candida o compu h bs sima of h sysm paramrs. Exndd Kalman Filr To dvlop h saisical rcursiv algorihm for h Exndd Kalman Filr h gnral form of h dynamic quaions of moion dvlopd in h prvious chapr will b usd. niially h gnralizd scond ordr diffrnial quaions ar convrd o firs ordr diffrnial quaions using h sa spac analysis. Th Exndd Kalman filr is an xnsion of Kalman filr from linar sysm o h mor gnral cas dscribd by h nonlinar sochasic diffrnial quaion

4 w f = &... = = v h Z = P H K P = h Z K = f = = h H f F = = Th vcor f is a nonlinar funcion of h sa and w is zro man gaussian nois having spcral dnsiy marix Q. Th nonlinar masurmn has h form Whr h dpnds upon boh h indx and h sa a ach sampling im and v is a whi random squnc of zro man gaussian random variabls wih associad covarianc marics R. This consius a class of simaion problms for nonlinar sysms having coninuous dynamics and discr-im masurmns. Hr w oo h sam assumpion and noaion as sandard Kalman filr. Th drivaion procdur of EKF is as sam as Kalman Filr xcp o now ha in ordr o g h mhods of compuing h man and covarianc marix which don dpnd upon nowing P w nd o xpand f in a Taylor sris abou h nown vcor if w slc o xpand f abou h currn sima hn w can g h EKF formula as follows: Masurmn upda phas Tim upda phas projc ahad And h dfiniions Th abov quaions ar h EKF formula for nonlinar coninuous sysm wih discr im masurmn. Snsor Faul Dcion and solaion ] [ = T T R H P H H P K = T d Q F P P F P

5 Th chniqu dvlopd for isolaing fauly snsor masurmn is o us a ban of Kalman filrs or Exndd Kalman filrs. Th criical paramrs of h sysm ar snsd by on-board snsors criical paramrs li Roll Pich and Yaw angls and angular ras. Each s of snsors and rdundan snsors monioring h sam paramrs is assignd o a diffrn Kalman filr s Figur for procssing h daa. Each Kalman filr will compu h bs sima of h sas and compus h covarianc valus. Th covarianc valus ar h indicaion of h sandard dviaion of ach snsor masuring h sa covarianc is invrsly proporional o h sandard dviaion. Th highr h covarianc valus h lowr h sandard dviaion of h snsor hnc mor wigh is givn o h informaion collcd by ha snsor. By his mhod w can always g h bs sima of h sa variabl or criical paramr of h sysm. During h wighing procss h Kalman filr auomaically rjcs h informaion from h snsors wih h highr sandard dviaion hus isolaing h fauly snsor masurmn conribuion during h compuaion of h bs sima of h sa. Th idnificaion of fauly snsors is accomplishd by analyzing h profil of h covarianc valus compud by h Kalman filr procss. Th covarianc valus ar invrsly proporional o h sandard dviaion of h snsor h smallr sandard dviaion; hrfor mor wigh is givn o ha snsor. Th snsor wih h las covarianc valu will hav h largs sandard dviaion. is o b undrsood ha w ar obsrving h rnd of h covarianc valus bfor maing h conclusion ha h snsor is fauly. A Modl-basd Simulaion procdur discussd lar will b usd o dmonsra his concp. MODEL ESTMATE x m z KALMAN ETENDED FLTER ESTMATE x COVARANCE P DFF xˆ z KALMAN ETENDED FLTER ESTMATE x COVARANCE P DFF xˆ z KALMAN ETENDED FLTER ESTMATE x3 COVARANCE P3 DFF x ˆ 3 z KALMAN ETENDED FLTER ESTMATE xn COVARANCE Pn MEASUREMENT VECTOR BEST ESTMATE = x i THAT GVES MNMUM xˆ i FOR i = o n DFF x n ˆ Figur : Modl-basd Snsor Faul Dcion and solaion

6 To dc and isola h fauly snsor w nd o dfin h dynamic hrshold for snsor paramr valus. Th Man Squar Error Thrshold dvlopd hr dpnds on h rror bwn h Kalman filr simad valu and h modl valu. This rror is squard and muliplid by h sandard dviaion of h snsor. Th sandard dviaion dfind hr is dynamic maning i dpnds on h spcific covarianc valu of a paricular snsor. Th covarianc valu is h wighing facor of h snsor. Highr h wighing valu mor lily h conribuion from ha snsor will b owards h compuaion of h bs sima. Th invrs of h covarianc valu will b h sandard dviaion of h snsor. Th iniial hrshold is dfind for ach snsor is dfind as: MSET = xi sima x modl Pi Whr MSET Man Squar Error Thrshold Pi- invrs of h covarianc valu which will b h iniial sandard dviaion of h snsor s s o b qual o. rad for angular snsors and. rad/sc for angular ra snsor x sima x modl Simulaion Rsuls Th dmonsraion of h abov mhodology for isolaing and idnifying h fauly snsors prformd vry wll during h simulaion. Fauly masurmns wr innionally inducd ino h snsor daa o invsiga h prformanc of h Kalman filr. Th rsuls showd ha h fauly snsors wr idnifid and h fauly masurmns from hos snsors wr rjcd during h compuaion of h bs sima. Th fauly snsors idnifid during h simulaion can ihr b rplacd or prmannly isolad. Figurs shows h simulaion rsuls which was prformd for hr rdundan snsors masuring h roll pich and yaw angls. Each snsor consisd of h simulad masurmns o which random nois was addd wih a nown man and sandard dviaion. Thos filrd masurmn from h snsors ha xcdd h hrshold limi was auomaically isolad and hos filrd masurmn ha had h las sandard dviaion was usd o compu h bs sima.

7 .5. Snsor Snsor Snsor Figur : Snsor Masurmns from hr rdundan snsors masuring roll angl. Snsor givs h bs sima..5. Snsor Snsor Snsor Figur : Snsor Masurmns from hr rdundan snsors masuring pich angl. Snsor givs h bs sima

8 .3.5. Snsor Snsor Snsor Figur 3: Snsor Masurmns from hr rdundan snsors masuring yaw angl. Snsor givs h bs sima Modl-basd Acuaor Faul Dcion Th problm of dvising a faul-olran robus conrol for h acuaors is discussd hr. Various possibl failur scnarios of h acuaors and/or h dynamic paramr sysm sa variabls ar considrd and robus faul olran masurs ar dvlopd o idnify sabiliy-vulnrabl failurs. Basd on h valuaion of h robus masurs h faul-olran robus conrol will swich islf o h rdundan acuaor and rconfigur h fauly acuaor or in h cas of dynamic paramr failur a conrol masur is slcd undr h spcific fauly condiions. Th proposd schm guarans no only h dsird prformanc undr normal opraions bu also robus sabiliy and bs achivabl prformanc whn hr is dcd failur. Faul diagnosis and faul olran or rconfiguraion conrol has bn primarily sudid for linar and/or paramrizabl sysms. Th proposd robus faul-dcion masurs and h robus conrol sragy is drivd using h Lyapunov dirc mhod. Th proposd robus masurs ar o dc hos fauls ha hindr h sysm prformanc and /or ponially d-sabiliz h sysm. Problm Formulaion Th high fidliy modl of h non-linar sysm wih h modl of h acuaor dynamics is incorporad ino h simulaion. Mahmaically h non-linar dynamics ar givn by h following diffrnial quaions:

9 x& = fx Bx[ f xv x z] and z& = gz gz v z u whr x is h sa of h sysm and z is h sa of h acuaor and u is h conrol o b dsignd and v dnos h vcor of unnowns/uncrainis fx gz and Bx ar nown pars of h sysm dynamics and fxv x and gzv z ar uncrainis in h sysm dynamics and acuaor dynamics rspcivly. Du o h prsnc of unnowns/uncrainis a succssful conrol mus b robus. For h purpos of dsigning a faul olran conrol ponial failurs of h acuaors ar considrd. To his nd w ar going o masur h oupu of h acuaor and dc any failurs in h acuaors. f any failur is dcd h robus conrol should shif o h rdundan acuaor and rcovr h faild acuaor if possibl. Faul Dcion Th non-linar subsysm considrd in his papr can b mahmaically givn by h following diffrnial quaions: x & = f x B x z and z& = g z u Faul diagnosis and faul olran conrol hav bn sudid primarily on linar sysms bu in h non-linar sysms h faul olran conrol is much mor complicad and h prsnc of uncrainis in h sysms mas h diagnosis mor difficul. To ovrcom hs difficulis w driv h robus faul-dcion masurs o dsign robus conrol sragis using h Lyapunov dirc mhod. Whn an acuaor failur is dcd a Kalman Filr is usd o compu h bs sima of h sa. Th Kalman Filr in ssnc is monioring h rdundan snsors and saisically sing h opimal gain basd on h wighd avrag of h covarianc marix. Robus Masurs for dnifying Acuaor Failur Th approach is o dvlop a sabiliy/prformanc-basd masur by which a fauly condiion will b diagnosd if i causs sabiliy problm or prformanc dgradaion. Spcifically h following criria will b usd: L m z m < L c and V m xˆ < V c Whr L. and V. ar h Lyapunov funcions. Th L c and V c ar dfind by h diffrnial quaions: L& c = γ 6 oγ 5 Lc β [ b c β β r u ] β c b c β V& c = γ 3 oγ Vc β β β β ' [ b cr z ] c b c β

10 Simulaion Exampl To illusra h faul olranc robus conrol h following dynamics of h salli along wih h acuaor dynamics a ra gyro is considrd: θ& = { [ 3ω sin θ ]} 6θ θ ; θ& x z =.θ y & φ = { [ 4ω x ψ& = { [ ω y z y z sin φ ]} 6φ φ z sin ψ ]} 6ψ ψ z x ω ω ψ φ ; ; ψ& & φ =.5φ =.ψ n h cass w hav considrd h oupu of h fauly acuaor jumps from is currn valu o is maximum valu and says hr indicaing h wors yp of faul for sabiliy. Th uncrain dynamics ar chosn o b fxv x =.4sinθ.3sinθ gzv z =.45θ.cosθ c r sinπ. Lyapunov funcions ar Vθ =.5[θ φ ψ ] and Lθ =.5[θ φ ψ ]. Th dsign paramrs ha ar xracd ar b = b = c =.6 c r =. c r = c = c = =.5 β=.5 =5 = ε z =.5. Th robus conrollr paramrs ar ε r =.8 ε =.5 a =.4 l =4 r = τ= n h simulaions prformd hr is an acuaor failur and dpnding upon h squnc of h failur h proposd robus conrol law is nrgizd. Thrsholds can b placd on uncrainis o auomaically dc whhr acuaor failurs hav bn dcd and/or corrcd which in urn mas i possibl for h faul olran conrol o rsor is opraion and nsur sysm prformanc. Figur 6 shows h acual sas of h sysm and also of h acuaor and h simad sas of h sysm as wll as h acuaor. Figur 7 is anohr plo ha shows h faul dcd in h acuaor a.5 sc and h rcovry mad a.55 scond. Finally Figur 8 shows h robus conrol acing a.5 scond as soon as h acuaor fails and rcovrs i a.55 scond. During ha brif priod of.5 scond h robus conrol shifs o acuaor from acuaor so ha h ovrall sysm is sill sabl. n his simulaion all h acuaors roll pich and yaw ar dsignd o fail a h sam im. Th robus faul olran conrollr is applid o all h acuaors a h sam im and h rconfiguraion o h rdundan acuaors occurs a.55 sconds on all h hr axs. Simulaion rsuls for only on axis is shown hr.

11 . Th sa and simad x-solidx-sim-dashdz-doz-sim-dashd do im sc Fig 6: Sa Esimas xˆ and Z Pich Axis 5 Th acuaor signal x-solidz-dashd im sc Fig. 7: Faul dcd in acuaor a.5 sc rconfigurd o acuaor a.55 sc Pich Axis

12 3 Th Conrol Th l im sc Fig 8: Faul olran robus conrol applid a.5 sc Pich Axis Conclusions W hav sudid h applicaion of faul olran robus conrol in non-linar sysms wih uncrainis. W may xprinc acuaor failurs in such sysms and h proposd robus conrol is mad faul olran by ingraing robus conrols ha ar dsignd undr fauly condiions and hav usd robus algorihms capabl of dcing fauls. Also h robus conrol has h capabiliy o swich h acuaor from h fauly on o h rdundan acuaor using hs robus masurs robus conrol sragis and faul olran conrol; his conrol framwor is hrfor dfind and synhsizd using h Lyapunov s dirc mhod. Th faul olran concp is applid o h snsors by using a Kalman Filr. Th Kalman filr wighs h informaion coming from mulipl snsors and auomaically wighs ou fauly snsors and compus h bs sima from h rmaining snsors. Rfrncs. Sanjay Jayaram Ral Tim Halh Monioring And Conrol Sysm Mhodology For Flxibl Spac Srucurs Ph.D. Dissraion UCF April 4.. Z.Qu Robus Conrol of Nonlinar Uncrain Sysms John Wily & Sons nrscinc Division H. Khalil "Nonlinar Sysms" Prnic Hall nd d R. A. Frman and P.V. Kooovic"Robus Nonlinar Conrol Dsign: Sa Spac and Lyapunov Tchniqus" Birhausr Boson 996.

13 5. B.C.Williams ``Modl-basd auonomous sysms in h nw millnnium" Procdings of APS R. Johnson S. Jayaram S.Li C.Ham " "Ral-Tim Aiud And Orbi Conrol Of A Small LEO Salli Wih Paralll-Procssing Approach n a Ground Saion" 4h Annual AAA/USU Confrnc on Small Sallis Uah. 7. R. Johnson S. Jayaram S. Li " Disribud Procssing Kalman Filr for Auomad Vhicl Paramr Esimaion - A Cas Sudy" ASTED - ASM Jul BANFF Canada. 8 Z. Qu "Robus conrol of nonlinar uncrain sysms undr gnralizd maching condiions" Auomaica vol.9 pp Z. Qu "Global sabilizaion of nonlinar sysms wih a class of unmachd uncrainis" Sysms and Conrol Lr vol.8 pp Z. Qu "Robus Conrol of Nonlinar Uncrain Sysms Wily nrscinc Z. Qu Curis M. hlfld Yufang Jin Apiwa Sangdjing " Faul-Tolran Robus Conrol of Non-linar Uncrain Sysms Agains Snsor Failurs" EEE Confrnc on Dcision and Conrol Orlando FL.. Rogr W. Johnson Zhi Hua Qu Sanjay Jayaram Yufang Jin Auonomous Spaccraf Vhicl Halh Monioring and Conrol Sysm Basd on Ral-Tim Modl- Basd Simulaion ASTED - nllign Sysms and Conrol Confrnc Florida pp