A Shunt Connected DC-Motor Feedback Linearization Technique with On-Line Parameters Estimation

Transcription

1 A Shut Coecte DC-Motor Feebac Learzato Techque wth O-Le Paraeters Estato M.S.IBBINI Al Huso Uversty Collee Al Balqa Apple Uversty P.O.Box 5, Al Huso-Jora Abstract The es o syste cotrollers s usually accoplshe base o oal operat cotos. I partcular, syste paraeters aopte or cotroller es are those o oal values a are assue to be costat or all practcal purposes. However, the oal values o syste paraeters ht vary a have eret values ue to a, coputer trucato, a evroetal chaes such as teperature. I ths auscrpt, eebac learzato techque s use to es state cotrollers or wely use DCaches such as, seres, shut a separately excte otors. A o-le paraeter estato techque s corporate the cotroller es to elate the eect o paraeter chaes o the perorace o the ese systes. Sulatos are use to eostrate the eectveess o the o-le paraeter estato techque whe paraeter varatos are to be cosere.. Itroucto Feebac learzato has ae ore atteto the last two ecaes [,, ]. I act, the techque cossts o a state a put coorate trasorato ollowe by a state eebac to elate the olearty. DC aches are heretly olear especally whe arature reacto a saturato eects are cosere. Those aches are ote ealt wth us lear techques ater learz ther oels the vcty o ther operat cotos. However, those aches are show to be eebac learzable a eret authors eostrate the ececy o ths ew techque a ts superorty over exst covetoal oes [, ]. Whle eebac learzato cotrollers see to be very ecet, ther pleetato ees a perect owlee o the oel, orer to perectly elate ther oleartes. I act, ths perect owlee requres the exact values o syste paraeters, whch s ot ote possble. Syste paraeters are, eeral, subjecte to varatos ue to copoet a, coputer trucatos, a chaes evroetal cotos such as teperature []. Ths proble ca be allevate us a recetly propose uzzy loc cotrollers [5]. Ths auscrpt attepts to o-le estate syste paraeters that are cosere uow but costat or very slowly te vary. O-le estato techque s propose a the eebac cotroller s costatly e by the upate values o the paraeters allow a perect cacellato o the oleartes.. Shut Coecte DC-Motor Moel DC shut otors have a olear atheatcal oel eve whe saturato a arature reacto eects are electe. A two esoal yacal olear oel, wth the arature voltae a the loa torque cosere as puts, was propose [] a s aopte ths auscrpt or es a sulato = + V () ω = ω + ω + 5 V + 6Tl () where = R / L, = /( R ), a J = F / J, = / L, 5 = / J, s the el curret, ω s the aular velocty, a are the el a arature R R a resstaces, respectvely. s the el uctace, s the coupl coecet, F s the rcto coecet, J s the rotor L

2 a loa erta costat, V s the put DC voltae, a T s echacal loa torque. l. Feebac Learzato Feebac learzato techque s use to trasor the olear syste eretal equatos to a cotrol caocal or, whch s the ollowe by a learz eebac. The eebac learzato cotos are state a a bre escrpto s ve below. More o the eebac learzato techque ca be ou [,,]. Le ervatve, whch s ee as vector ervatve wth respect to aother vector, o R wth respect to R s ve by: [, ] = a = x x () wth a x x are the Jacobea o a, respectvely. Let s ee a = [, a ] epeet whch s equvalet to the cotrollablty coto lear systes.. The Le bracet o ay two vectors o the set U = [, a,..., a ] s the [,,..., () set U tsel, ths seco coto s ow as volutvty o the set U. I the case o a ult-put olear syste, s substtute by: a G = ] (7) U = u, u,..., u ] (8) [ The two etoe cotos rea the sae except that s substtute by G the two above cotos ra[,..,, a,.., a,... a ].., a U = [,..., = ], a I these two cotos are vere, the oe ca a trasorato such that T ( x ) = [ T ( x ).. T T ( x)] =,..., a s volutve, a T [ z z.. z ] = Z (9) wth < T, >= T + =,,..., () a a T a o < T, > = (5) < < T, >, also h s a scalar el a s a vector Z = T =. el, the the Le ervatve o h wth respect to s.. h h < h, >= (6) x x The two ecessary a sucet cotos or state eebac learzato are:. All vectors o the vector el [, a,..., a ] are learly Maro et al.[] propose a experetally coveret estator o the rotor resstace o a three phase ucto otor. A slar estator s evelope the ollow, to estate the arature a el resstaces o the DC shut otor. Those paraeters are chose, because o ther heret teecy to chae ue to varato o ther teperature. The estato proceure stas by bul a > () Whch s alreay a olear cotroller caocal or. The cotrol put appears oly the last equato a s use to reove the olearty. Oce the olearty s reove, the result syste ca tha be ealt wth us ay lear techque.. O-Le Estato o Syste Paraeters,.

3 observer oel or arature a el resstace estato that ca be wrtte as: = + V + ( ) + v ω = 5 V + 6Tl V = + ω + ω + [ γ () η + ] + [ + ωω] γ () where, ω, a are the estate o, ω, a, respectvely. s a arbtrary postve costat a be ese latter o. The error sals are: v s a atoal sal to () So, to uaratee the stablty o the observer syste, the ollow aaptato laws are ee: = γ [ η ] () = () V = + ω + ω (5) Sce = /( Ra J ) a = F / J are ω = ω ω (5) always eatve ro practcal pot o vew, = (6) Eq.(5) s eatve ete. γ ω ω = () a hece, = The, the error yacs are: = = v (7) (8) ω = ω (9) To copesate the elay trouce by curret easureets, the ollow lter has bee ese as: ξ = v () wth η = ξ a s assue to be a postve uber. Let v = η, the Eq.(8) ca be wrtte as = η () De the ollow Lyapuov ucto as: V = ( + ω + + ), where γ γ γ a γ are postve ubers. The te ervatve o the Lyapuov ucto s: As a result, Eqs.(6), (7), (5), (6) a (7) are the yacs o the arature a el resstace estators o the DC-shut otor. V. State Feebac Learzato wth O-Le Estator The cotrollablty a volutvty cotos, Eqs. () a (), o the propose atheatcal oels are vere [], a cosequetely, a T state trasorato Z = [ T ( x) T x)] ca be ou. z. z z z U = + ψ ( z) β ( ) (6) where ψ (z) represets a ucto cota the olearty whch s e by the estate states a values o the syste. Hece, by choos the olear cotrol law ( V re ψ ( z)) U = (7) β ( z) oe copletely reoves the olearty, a the olear cotroller ca the be wrtte as: (

4 V U = α re [ + + ] α (8) where, a are uctos o the, states a paraeters o the syste. α a α are es paraeters to be ajuste by pos o the result lear syste to acheve a certa perorace, such as eevalue asset. Apply the above techque to the DC shut otor, oe obtas = ω +. (9) 5 5 = 5 = 5 ( + 5 ) ω ω ω () () The olear cotroller s ese such that the close loop eevalues are place at ( + ) ω = ( ω + 5 ( )) + () 5. Nuercal Results a Dscussos VI. Paraeter Estator I the ollow, the uercal values o the DC seres a shut coecte otors are those o practcal systes aopte ro [,6]. I a rst set o sulato, the estator was sulate or a tal chae the el a arature resstaces o about 5% hher tha ther oal values, a the results show F. eostrate the perect coverece o the el a arature resstaces estato towar ther oal values. For sulato purposes, was chose to be, γ a γ were chose to be 5 a.5, respectvely. VI. Close Loop Resposes wth a wthout Estators whe the Syste s Subjecte to Paraeter Varatos a, respectvely. Moreover, t s esre to eostrate the eectveess o the paraeter estato techque propose ths auscrpt a hece, to evaluate the overall perorace wth o-le paraeter estato. I a rst set o sulatos, a % crease both arature a el resstaces s assue the case o shut coecte DC otor, a both the actual output (wth the sturbe resstace values) a that o the ucopesate syste (wthout o-le estato) are plotte a show F.. It shoul be ote that the evatos the esre spee a el curret are ue to the act that the estator s o a hece, the eebac cotroller paraeter values are ot upate. However, whe the o-le value estator output s e to the cotroller, the rotor spee a that o the el curret coveres towar the esre values. F. eostrates the eectveess o the o-le paraeter estato propose earler ths auscrpt. 6. Coclusos Most Feebac techques es s base o oal values o syste paraeters. Whle those paraeters are assue costats or all practcal purposes, ther values ht ot be exactly ow. I partcular, DC aches paraeters ht have values eret tha those use the cotroller es process. Ao those paraeters are arature a el resstaces, rcto coecet, oet o erta a ay others. Dereces ca, ay cases, be relate to copoet a, coputer trucato, a heat sspato. The perorace o ese eebac cotrollers ht heretly be aecte by those uesre varatos syste paraeters. The eect o paraeter chaes a the propose paraeters estato alorth that ca allevate ths proble are scusse a aalyze. A o-le paraeter estator output ca be use to upate the paraeters values the cotroller yacs a hece, results better perorace. Feebac learzato, a techque s base o exact owlee o paraeters values orer to perectly elate the uesre oleartes, s use to eostrate the superor perorace o the o-le upate eebac cotrollers over curretly propose oes.

5 Appex Nuercal Paraeters: The uercal values or the shut coecte DC otors use ths auscrpt, or sulato purposes, are aopte ro []. Those uercal values are cte below or reereces: R = Ω, L = H, R =.6 Ω, =.9888 N. / Ap. Volt, J = K., F =, V = Volt, T = 9.5 N.. Reereces: ) M.S.Ibb a W.S.Zaara, Feebac Learzato o DC Motors, Electrcal Maches a Power Systes, Vol., No., 996. ) Phlp D. Olver, Feebac Learzato o DC Motors, IEEE l a Tras. O Iustral Electrocs, Vol.8, No.6, Deceber, pp.98-5, 99. ) Staslaw H. Za a Carl A. Maccarley, State-Feebac Cotrol o Nolear Systes, It. J. Cotrol, Vol., No.5, pp.97-5, 986. ) Rccaro Maro, Sere Peresaa, a Patrzo Toe, Expoetally Coveret Rotor Resstace Estato or Iucto Motor, IEEE Tras. O Iustral Electrocs, Vol., No.5, pp.58-55, October ) M.S.Ibb a O.S.Jaar, Sel-Tu Fuzzy Loc Cotroller or a Seres DC Motor, EuroEps -Power a Eery Systes, Crete, Greece. 6) Krause, Aalyss o Electrcal Machery, McGraw-Hll, h o a t ο e st c e a s t re e F l 8 6 h o a t ο e st c e a s t re re a tu A r (a) (b) Fure Shut otor el a arature resstaces estato a) Fel resstace estato wth tal value 5% above ts oal value b) Arature resstace estato wth tal value 5% above ts oal value Fel.7 o a t e c) Cur. S.6 E s t ret / a (A (R t p).5. oec e 8. S pee r 6. C. R oto c to. F r Fure Devato o the el curret a otor aula velocty ue to Paraeters evatos a) Fel curret evato, ro oal, whe the o-le estato s o 5

6 b) Motor aular velocty evato, ro oal, whe the o-le estato s o p) t(a C ure e F l (a) e c) S / a (R S pee r R oto (b) Fure Feebac learzato wth o-le estato a) The el curret coverece towar the esre oe whe the o-le estator s o b)rotor aular velocty coveres towar the esre oe whe the o-le estator s o. 6