X SIMPOZIJUM Energetska elektronika 10 th SYMPOSIUM on Power Electronics. Novi Sad, Yugoslavia,
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1 X SIMPOZIJUM Energetka elektronika 1 th SYMPOSIUM on Power Electronic Novi Sad, Yugolavia, Ee'99 ESTIMACIJA BRZINE I IDENTIFIKACIJA OTPORNOSTI STATORA ASINHRONOG MOTORA BEZ DAVAČA BRZINE Veran Vaić, Slobodan Vukoavić*, Miodrag Zubić Fakultet tehničkih nauka, Novi Sad, Jugolavija *Elektrotehnički fakultet, Beograd, Jugolavija Sadržaj: U radu je prikazana etimacija brzine primenom MRAS obervera u pogonu bez davača na vratilu ainhronog motora uz predlog paralelne etimacije otpornoti tatora u realnom vremenu (on-line). Da bi e brzina rotora etimirala a zadovoljavajućom tačnošću i uz odgovarajući kvalitet potrebno je itovremeno (paralelno) a etimacijom brzine rotora etimirati i otpornot tatora, kako bi e otvarila korekcija vrednoti R u MRAS oberveru. U predloženom paralelnom MRAS oberveru referentni i podeivi model u izmenljivi. Za etimaciju R ova dva modela menjaju voje uloge u odnou na uloge koje imaju pri etimacije brzine. Sveobuhvatne računarke imulacije pokazuju efikanot predloženog paralelnog MRAS obervera za etimacije brzine rotora. Ključne reči: MRAS oberver/etimacija/otpornot tatora/brzina rotora SPEED ESTIMATION AND STATOR RESISTENCE IDENTIFICATION OF INDUCTION MOTOR WITHOUT SPEED SENSOR Abtract: Thi paper propoe a novel model reference adaptive ytem (MRAS) for peed controlled enorle induction motor, with integral the adaptation mechanim for the on-line tuning of the tator reitance (R ). In an intent to accurately etimate the ω at low peed, under the full load condition without deterioration the drive performance, the R i alo etimated, parallel with the ω etimation to compenate for the R fluctuation value ued in the MRAS oberver. The reference model and adjutable model are interchangeable for parallel ω and R etimation. Extenive computer imulation and experiment prove the effectivene of the propoed olution. Key Word: MRAS oberver/etimation/stator reitance/rotor peed 1. UVOD Ainhroni motor e maovno koriti u indutrijkim aplikacijama. Upotreba enzora brzine na vratilu motora manjuje pouzdanot a u pogonima za vrlo velike brzine potoji problem da e davač brzine montira. Više različitih metoda koriti e za realizaciju pogona bez davača na vratilu ainhronog motora. Većina ovih metoda za etimaciju brzine ima problema a tačnošću etimirane brzine i kvalitetom odziva brzine 33
2 i momenta pri malim brzinama uled termički izazvane razdešenoti otpornoti tatora u modelu obervera i u motoru. Ovi problemi e mogu upešno izbeći itovremenom etimacijom brzine i otpornoti namota tatora. Shauder, u pionirkom radu [1] o primeni MRAS obervera brzine u elektromotornim pogonima, je dao jedan predlog off-line etimacije R. Međutim, znatno je intereantnija on-line etimacija R i brzine rotora kao što e predlaže u [2,3]. U [3] brzina rotora je etimirana potpunim oberverom i paralelno a ovom etimacijom, etimiraju e R ili R r [4]. Razlika između tvarne truje tatora i etimirane truje zajedno a etimiranim flukom rotora luži za pokretanje odgovarajućeg adaptivnog mehanizma. Kubuta za itovremenu etimaciju brzine rotora i rotorke vremenke kontante koriti tet ignal injektiran u referentnu truju po d- oi. U [2] ita kriterijumka funkcija, neoetljva na varijacije induktivnoti raipanja, koriti e u adaptivnim mehanizmima za brzinu i za R pri čemu ova dva adaptivna mehanizma niu itovremena. Pri ovako zamišljenom načinu etimacije R i brzine, tokom etimacije R pogon otaje bez etimacije brzine koriteći vrednot koja je etimirana pre početka etimacije R. U ovom radu e predlaže nov paralelni MRAS oberver, koji poeduje dva modela (referentni i podeivi) i dva adaptivna mehanizma za itovremenu etimaciju brzine i R. Uloge referentnog i podeivog modela u izmenljive. Tokom etimacije brzine jedan etimator fluka rotora e koriti kao referentni model a drugi kao podeivi dok e pri etimaciji R uloge etimatora promene. Predloženi oberver omogućuje upešnu etimaciju i pri malim brzinama. On-line etimacija R a paralelnim MRAS oberverom ne iključuje etimaciju brzine rotora. Predloženi adaptivni mehanizam e može jednotavno implementirati u pogonu a vektorki upravljanim ainhronim motorom bez davača brzine. Računarke imulacije pokazuju efikanot paralelnog MRAS obervera. 2. ADAPTIVNI MEHANIZMI ZA PARAENU ESTIMACIJU BRZINE ROTORA I OTPORNOSTI NAMOTA STATORA MRAS oberveri brzine e razlikuje po veličini koja je izabrana za izlaznu veličinu referentnog odnono podeivog modela. Najčešće e korite MRAS oberveri koji za kriterijumku funkciju korite flukeve rotora ili indukovanu elektromotornu ilu. U radu je korišćen MRAS oberver, a flukom rotora kao izlaznom veličinom, koji je ujedno najjednotavniji za dizajn i implementaciju. Tačnot etimirane brzine, ovim MRAS oberverom, je ulovljena a tačnošću kojom e poznaju parametri motora pre vega R. Informacije o naponu i truji uz matematički model ainhronog motora u neophodni za etimaciju brzine i R primenom MRAS obervera. Napon tatora e uobičajeno ne meri već rekontruiše na onovu upravljačkih PWM ignala prekidača invertora uz zanemarenje mrtvog vremena. Većina predloženih rešenja a MRAS oberverom koriti R kao kontantan parametar motora. Međutim, teškoće nataju pri malim brzinama kada omki pad napona na R predtavlja dominantan udeo napona tatora što e upešno prevazilazi uvođenjem adaptivnog mehanizma za etimaciju R. Adaptivni mehanizmi koji e korite za paralelnu etimaciju brzine rotora i R upotavljeni u primenom teorije hipertabilnoti Popova. MRAS oberver brzine e realizuje u tacionarnom koordinatnom itemu (α,β) a potrebni etimatori rotorkog fluka u opiani a ledećim pace vector jednačinama. Referentni model ili naponki etimator rotorkog fluka (U - I ): 331
3 gde u: [ u ( R σ p) i ] 2 pψ! r! m = + ; σ = 1 rv m r. (1) Podeivi model ili trujni etimator rotorkog fluka (I - ω): p! m ψ ω! ψ! T i 1 = j. r Tr (2) Adaptivni mehanizam: K ω! Iω = K pω + eω ; eω = ψ! ψ! = ψ! p rv αψ! βrv ψ! βψ! αrv. (3) - K pω i K Iω PI parametri adaptivnog mehanizma za etimaciju brzine; - V, I u indeku označavaju rotorki fluk etimiran naponkim odnono trujnim etimatorom; - označava etimiranu veličinu. Razlika flukeva referentnog i podeivog modela koriti e u adaptivnom mehanizmu da bi e obezbedila konvergencija etimirane brzine!ω ka tvarnoj vrednoti. Da bi e obezbedila tačna etimacija brzine i pri malim brzinama, otpornot tatora je etimirana itovremeno a etimacijom brzine pomoću novog adaptivnog mehanizma kao što je prikazano na l.1.. Sl. 1. Paralelni MRAS oberver brzine i otpornoti tatora 332
4 Jednačine ainhronog motora uz izbor flukeva rotora kao promenljivih tanja r pψ [ ( σ p) rv m m = u R + i ]; pψ ω ψ m T i 1 = j. (4,5) r Tr Pretpotavlja e da u ve induktivnoti u modelu MRAS obervera (1)-(2) jednake a induktivnotima u motoru (4)-(5). Pomatra e iključivo razdešenot otpornoti tatora u motoru i u modelu MRAS obervera. Adaptivni mehanizmi na l. 1. određeni u na onovu teorije hipertabilnoti Popova. Kada e razmatra razdešenot R, jednačina tanja greške naponkog etimatora (voltage etimator tate error equation) e dobija oduzimanjem jednačine (4) od (1): r pε V = ( R R! ) i ; εv = ψ ψ! = εα εβ rv rv V + j V. (6) m Slično e dobija jednačina tanja greške trujnog etimatora kada e (5) oduzme od (2). 1 pε = jω ε + j( ω ω! ) ψ! ; ε ψ ψ ε ε I T I r I =! = αi + j βi. (7) Jednačine (6) i (7), mogu e prikazati u znatno praktičnijoj matričnoj notaciji: 1 ε ω αi T εαi r ε βi ε 1 βi p ω εαv = Tr εαv W = A ε W. (8) ε βv εβv gde je ε T = [ ε I ε I ε V ε V] = [ ε T I εv T ] α β α β, a W je nelinearni blok definian kao: 1 ψ! α ω J W = 1 ψ! ω β = I Ψ r 1 α i M R i M R (9) r 1 iβ ω = ω ω! ; R = R R! T ; Ψ = [ ψ! α ψ! β ] ; T 1 i = [ i α i β ] ; J = 1 ; I = 1 1. Sitem a l. 1. je hipertabilan ako je forward path tranfer matrix iz (8) triktno pozitivno realna a ulaz i izlaz nelinearnog bloka W zadovoljavaju kriterijum Popova (1) [1]: S = ε T Wdt γ ε εt r Ψ ε I V T M. (1,11) Uz (11) integral Popova (1) je:, ; ( ) ( ) T r ( ) ( ) S dt dt M R dt T S I V T r = = + = + M S 2 ε W ω ε J Ψ ε i 1 2 γ (12) " $$ $ # $$$$ % " $$ # $$ % S1 S2 333
5 Tačnot tvrđenja iz (12) može e proveriti uz primenu nejednakoti (13) i (14) i adaptivnih mehanizama (15) i (16) za paralelnu etimaciju brzine rotora i R, repektivno. S T 1 ( ) dt I 1 2 = ω ε J Ψ γ ; S R( ) dt V T 2 = ε i γ 2 2 ; (13,14) KIω ω! = K ω + ( ) T p I ε J Ψ ; p!r ( ) K KIR = + ε pr V T i. (15,16) p gde u K pω, K Iω, K pr, K PI parametri za adaptivni mehanizam etimacije IR brzine odnono R. Brzina rotora i R e mogu paralelno etimirati pomoću (15) i (16) pri bilo kojoj brzini rotora, jer vaki algoritam uključuje amo merene veličine. Adaptivni mehanizam za brzinu (15) je identičan kao kod MRAS obervera kod koga e etimira amo brzina rotora. 3. REZUTATI SIMUACIJA Napravljen je Simulink model kojim e realizuje imulacija vremenkog odziva pogona a indirektnim vektorkim upravljanjem ainhronim motorom koji ne poeduje davač brzine na vratilu. Etimacija brzine rotora i otpornoti tatora realizovana je paralelnim MRAS oberverom. Rezultati imulacija u prikazani za Severov motor ZK- 8 Na l prikazani u rezultati računarkih imulacija. Uticaj razdešenoti R na tačnot etimirane brzine pri različitim momentima opterećenja prikazan je na l. 2. Sa povećanjem referentne brzine greška etimirane brzine e manjuje. ω [rad/] R m = 1,25R R m = R R m =,8R m m [Nm] Sl. 2. Etimirana brzina pri razdešenom otporu tatora ω [rad/]!ω ω ω * t [] Sl. 3. Brzine u pogonu a predloženim paralelnim MRAS oberverom Na l prikazani u rezultati imulacija vremenkog odziva pogona. Otpornot tatorkog namotaja je za 25 % veća od vrednoti koja je u MRAS oberveru Rm = 1, 25R. Etimacija otpornoti tatora započinje u 1,5 ; motor je neopterećen do t =2. Opterećenje motora je uledilo u t = 2, 3 i 4 a 1 Nm, 3 Nm i 5 Nm, 334
6 repektivno. Adaptivni mehanizam za etimaciju R je dota efikaan kao što e vidi a l R [Ω] R!R t [] ψ [Wb] ψ r * ψ D ψ Q t [] Sl. 4. Etimirana otpornot tatora Sl. 5. Flukevi rotora kada e primeni paralelna etimacija brzine i otpornoti tatora 4. ZAKJUČAK U ovom radu je predložen nov paralelni MRAS oberver, koji poeduje dva modela (referentni i podeivi) i dva adaptivna mehanizma za itovremenu etimaciju brzine i R. Uloge referentnog i podeivog modela u izmenljive. Primenom teorije hipertabilnoti Popova upotavljeni u adaptivni mehanizmi za etimaciju ω i R. Etimacija R proširuje primenu MRAS obervera brzine i u oblat malih brzina. 5. ITERATURA [1] C. Schauder, Adaptive peed identification for vector control of induction motor without rotational tranducer, Conf. Rec. IEEE Ind. Appl. Soc. Ann. Meet., 1989, pp [2]. Zhen,. Xu, Senorle field orientation control of induction machine baed on a mutual MRAS cheme, IEEE Tran. on Indutry Application, Vol. 45, No.5, October 1998, pp [3] G. Yang, T. H. Chin, Adaptive peed identification cheme for a vector - controlled peed enorle inverter - induction motor drive, IEEE Tran. on Indutry Application, Vol. 29, No.4, July/Aug.1993, pp [4] H. Kubota, K. Matue, Speed enorle field-oriented control of induction motor with rotor reitance adaption, IEEE Tran. on Indutry Application, Vol. 3, No. 5, Sep/Oct. 1994, pp
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