A Novel Discrete-Time Predictive Current Control for PMSM

Transcription

1 A Novel Dicete-Time Peictive Cuent Contol fo SM Jung-Won Sun, Jin-Woo Lee, Jin-Ho Suh, Young-Jin Lee, an Kwon-Soon Lee Depatment of Electical Engineeing, Dong-A Univeity 840, Haan-ong, Saha-gu, Buan, , Koea Dept. of Electical Intument an Contol, Koea Aviation Polytechnic College 438 Egeum-ong, Sachon City, Kyungnam, , Koea Diviion of Electical, Electonic, an Compute Eng., Dong-A Univeity 840, Haan-ong, Saha-gu, Buan, , Koea Abtact: In thi pape, we popoe a new icete-time peictive cuent contolle fo a SM(Pemanent Magnet Synchonou Moto). The main objective of the cuent contolle ae to enue that the meaue tato cuent tact the comman value accuately an to hoten the tanient inteval a much a poible, in oe to obtain high-pefomance of ac ive ytem. The conventional peictive cuent contolle i ha to implement in full igital cuent contolle ince a finite calculation time caue a elay between the cuent ening time an the time that it take to apply the voltage to moto. A new contol tategy in thi pape i een the cheme that get the fat aaptation of tanient cuent change, the fat tanient epone tacking. Moeove, the valiity of the popoe metho i emontate by numeical imulation an the imulation eult will peent the impovement of peictive contolle an accuacy of the cuent contolle. Keywo: SM, Peictive Cuent Contol, SPWM, Full igital Sytem 1. INTRODUCTION The main objective of the cuent contolle ae to enue that the meaue tato cuent tack the euie value accuately an to hoten the tanient inteval a much a poible. Until the peent, vaiou cuent contolle ae popoe. Like the following thoe, geneally, we claify into the fou main type of cuent contol cheme [1][]. (1) Hyteei Contol: The hyteei cuent contol metho ha avantage uch a a fat tanient epone an imple cicuit in implementation. But it how high an non-contant witching feuency in the invete. By the eult, it geneate the hamonic an euce the length of cicuit. () Ramp Compaion Contol: The Ramp Compaion Cuent Contol metho ha the avantage of limiting the maximum invete witching feuency an poucing well-efine hamonic. Even though the contolle ha optimize gain, thee ae magnitue an phae elay eo in teay tate ince the contol metho ha low pa filte chaacteitic. (3) Synchonou Fame Popotional Intege Contol: In aition to the oto ynchonou fame PI contol, enation of the back EMF an co-coupling tem give fat tanient epone an zeo teay-tate eo iepective of opeating conition. (4) Peictive Contol: In the peictive contol cheme, the witching utie of the invete witche ae etemine by calculating the euie voltage focing the moto phae cuent to follow coeponing efeence. If the moto an invete paamete ae well known, the peictive contolle how the fat tanient epone an no teay tate eo. But If we o not know thoe, the peictive cuent contolle i not implemente well. With the evelopment of micopoceo technology, mot cuent contol cheme can be implemente in full igital ytem. The pupoe of thi pape i to peent a new peictive cuent contol cheme bae on a icetize moel of the SM. In both tanient an teay tate, the popoe contolle pefom bette than the conventional peictive contolle oe in a full igital contol ytem. In the implementation of the contolle, the effect of oto poition iffeence, voltage limitation ae icue an enate. The imulation eult ae alo peente to pove the feaibility an effectivene of the popoe peictive cuent contolle uing a pototype. Kw SM evo ive ytem.. SYSTEM DESCRIPTION.1 Pemanent Magnet Synchonou Moto The euivalent cicuit of SM how in Fig. 1. (a) -axi cicuit (b) -axi cicuit

2 Fig. 1 The euivalent cicuit of SM In the Fig. 1, the moto loe (coppe, coe, an mechanical), magnet atuation, ai gap pace hamonic an hamonic onent of voltage an cuent ae neglecte in oe to implify the analyi. In oe to imulate, the voltage euation of SM in the ynchonou efeence can be expee a follow: The onent of the full igital evo ive ytem i peente a Fig.. The ytem i conite of the thee pat. The fit i Spee contolle. The econ i cuent contolle. The thi i invete. = R i + pλ ω λ (1) = R i + pλ λ () with ω = n λ e = p w ( L + L m λ = ( L + L + ϕ m whee i, i : - axi cuent ;, : - axi voltage ; φ : : flux linkage ue to pemanent magnet pe phae ; R : eitance of pimay ; : m, Lm L elf-inuctance of pimay ; L : - axi onent of magnetizing inuctance ; ρ : /t ; ω e : electical angula velocity ; τ : pole pitch ; ν : velocity ; If the voltage euation i aange, the euation can be expee a follow [4]. Fig. 1 Full Sytem of the ive fo SM.3 Space ecto PWM The voltage pace vecto coeponing to eight witching tate of the invete ae hown in Fig.. The ection of the voltage pace vecto i ivie into ix ection. An the magnitue of each voltage vecto that coepon to ix active tate i /3 c, an thee vecto fom a hexagon. An the voltage vecto u 0 an u 7 that coepon to feewheeling tate ae zeo voltage vecto. The Relation between voltage pace vecto an voltage comman in -axe i hown in Fig. 3. The c i the c link voltage, an the i the magnitue of the pace. The of voltage comman i calculate fom the,, an θ e. Ri + L i Li we t Ri + L i + L we + φ t = (3) = (4) Fom the above voltage euation, the icete-moel voltage euation of a Synchonou Moto i ecibe a follow. = R i L + T + L ω i +φ ( i i ω ) e e L = Ri + ( i i ) T Li ω e whee T : ampling time ; Thi euation i the icete-moel voltage euation of conventional peictive cuent contolle. Sytem of the moto ive (5) (6) Fig. Switching oltage vecto of the thee-phae invete In oe to pefom the S-PWM(Space ecto Pule With Moulation), we nee the following euence. Hee, we will icu the Ι Section. In the fit time, we mut elect whee the comman voltage i exite. If the comman voltage i putte in the Ι ection, it i that atify a following o if it on t atify the following, comman voltage i in the othe ection. An it mut fin a atifactoy ection, immeiately. β > 0 an 3 α β > 0 (7)

3 Next time, the eciion of witching time i a follow: 3T 3 1 T1 = ( α β ) (8) c 3T T = ( β ) (9) c T3 = T ( T1+ T ) (10) An, the witching function of the Ι ection i ecibe a Table 1. The ymmetical witching function ha vaiou avantage. Epecially, in the invete, the cheme of PWM i impotant element of SM, becaue the cheme affect the invete eeply. aiou PWM cheme have been popoe. But the SP-PWM i known a a goo cheme fo a epone of tanient cuent contolle. Thi ha avantage of much cope of linea contol, the itubance of low hamonic, an the epone of api tanient. Section Switching Function Section Ι Table 1 The witching function of ection Ι On moe Off moe T 0 T T 1 T 0 T 1 T T a T b T c Timing Seuence of the cuent Contol Fig. how the timing euence of the cuent contolle. The kth inteupt ignal geneate by the PWM geneato tat the contol poce, a hown in Fig. (a). Synchonize with thi inteupt ignal, the AD convete ample the euie value uch a phae cuent, c link voltage, an oto poition to calculate the output voltage at the ame time The gay ection how in Fig. (b) epeent the uation of the calculation time fo the cuent contol. The output value of the cuent contolle i uploae into the PWM geneato uing the ignal, a hown in Fig. (c). Duing the (k+1)th peio of the cuent contol poce, the phae voltage calculate in the peviou peio ae applie to the moto though the invete, a hown in Fig. (). The eultant phae cuent ae ene, uing the (k+)th inteupt ignal, a hown in Fig. (e). Fom the tating time of the cuent contol to the ening time of the eultant phae cuent, thee ae not one, but two ampling peio elay. Fig. 3 Timing Seuence of cuent contolle.5 The Conventional Peictive Cuent Contolle In a conventional peictive cuent contolle, the contol voltage which pouce the euie tato cuent can be calculate uing (3) an (4) a = R i + w L i + L i + w λ i T (10) i i = Ri + L (11) T w L i whee i an i ae the efeence cuent value at the th ampling time. The conventional peictive cuent contolle i a kin of high gain contolle if the oto pee an the back EMF tem ae known an enate popely. Fig. 4 how the imulation eult fo the cuent ynamic of the conventional peictive cuent contol implemente in the full igital ytem. The cuent comman i change at the peak of the phae cuent when the oto pee i about 1500 pm. Since one moe peio i neee fo the contol calculation in the ytem than i expecte, a lage ovehoot an ocillation have been obeve when the cuent comman in the -axi i change fom -1 A to 1 A. Fig. 4 wave of conventional Peictive Cuent Contol.6 Popoe Peictive Cuent Contolle.6.1 The Popoe Cuent Contolle

4 Thi pape popoe the novel peictive cuent contol in oe to olve that the conventional peictive cuent contol metho geneate the ovehoot an ocillation. If we ajut the euation (10) an (11) of the voltage euation of the conventional peictive cuent contol fo SM, the ajute voltage euation can be expee a Whee, = Ai + Bi Lω i (1) + λω = Ai + Bi L ω i (13) A = R L / T, B = L / T Duing the (k+1)th peio, a hown in Fig. (), the SM wa opeate by the contol voltage (k+1) which i calculate uing the (th peio. = Ai + Bi + Lω i + λ = Ai + BI L ω i ( k + ) ω ( k + ) (14) (15) Fo the egulation of the cuent, i ( k + ) an ( k + ) can be coniee a the eie cuent. An, in the euation (14) an (15), tem, which i fom thi tem to lat tem, i value which geneate by eal SM. theefoe, uing the (k+1)th peio, the contol output voltage, which i applie in the SM, can be expee a. = Ai + L ω i = Ai L ω i + Bi + λ + Bi ( k + ) i ω ( k + ) (16) (17) Hee, i ( k + ) an ( k + ) i the efeence cuent an voltage of the ampling moment. Fom euation (16) an (17), the metho, which can olve the i ( k +1), an i ( k + ), w ( k +1 fom 4. to Compenation of the iffeence pee an poition The Compenation of the iffeence pee an poition i a half of iffeence between kthy an (k+1)th of the pee an poition. The iffeence of the pee an poition i vey mall becaue a the vey mall time of the ampling time. An, the enate value i optimal value by imulation Theefo, the enation of the iffeence pee an poition can be expee a 4.3 The value of the i The moment, which come out fom the pee contolle, i fat a one tep than the moment which i geneate fom SM Theefoe, an ( k ame. Hee, ( k the -axi voltage etimate in the kth. w θ Table. Compenation of the iffeence pee an poition Kth -( k-1)th <0 Kth (k-1)th > 0 w w θ θ w w θ θ The value of the an ( k ) can be expee a euation (18) an (19), fom the voltage euation of SM ( k 1) = Ai + Bi (18) + L ω i + λ ω = Ai + Bi (19) + L ω i + λ ω If we ubtact the euation (18) fom euation (19), we can know the iffeence voltage value of the moment of kth 1) = A{ i i } { i i } ( k (0) + B We can conie a = 0 in oe to know i which make the iffeence voltage a 'o' in euation (0), If we ajut thi, thi can be expee a. { i i } i A i ( k 1) + = + (1) B We can olve the i a the coue of the i. { i i } i A i ( k 1) + = + () B Hee, i an i the cuent value of (k+1)th moment i 4.4 The value of the i ( k + ) The value of the i an can obtain uing the incement matix C. The incement matix C i expee a euation (3) co( ω( T ) C = in( ω( T ) i in( ω( T ) co( ω( T ) (3) Hee, we mut apply the w ( k +1) becaue of obtaining the efeence cuent of (k+1)th moment If we aange uing thi, the efeence cuent i of the (k+1)th moment can be expee a

5 i = co(( ω + in(( ω + co(( ω i = in(( ω i i i i (4) (5) the -axi efeence cuent change fom 30A to -30A at the moment of 0.3 econ. When the efeence pee change 1000pm at 0ec, an -1500pm at 0.ec, 1500pm at 0.4ec, -1000pm at 0.6ec, 1000pm at 0.8ec, Fig. 6 i the meaue pee tack the efeence pee 4.5 oltage limitation Afte the voltage comman i calculate in (16) an (17), thee i a uetion a to whethe the magnitue of the coeponing voltage pace vecto i beyon the actual voltage limitation o not. If thi magnitue i geate than the maximum available invete output voltage, the contol voltage houl be ajute. Othewie the coect voltage comman fo the next peio cannot be obtaine ince the applie voltage i iffeent fom the calculate one. The ajute voltage can be obtaine fom the comman voltage a (a) v v c = v (6) 3 c = v (7) 3 Hee, = + Table 3. Rating an Paamete of the SM (b) ITem alue Rate Powe. Kw Rate Spee 000pm R Ω mh L Pole pai 4 5. Simulation The pefomance of the popoe cuent cheme ha been analyze by imulation uing the actual paamete of.kw SM ive with the aumption a follow: no atuation in flux linkage, inuoial EMF', an contant pee uing a ampling peio. The iual C++ language pogam i ue in the imulation. The c link voltage, which i aume to be ieal, eual 0. The ating an paamete value of the SM ae lite in the Table 3. In the imulation, the invete witche ae coniee a ieal, I.e., zeo conuction voltage op an zeo commutation time. The ampling peio i 150 µ. The ynamic pefomance of the popoe cuent contolle ha been tuie by conieing the whole ytem. In the Fig. 5(a), the -axi efeence cuent i i '0' an the -axi efeence cuent change fom 3A to -3A at the moment of 0.3 econ. In the Fig. 5(b), the -axi efeence cuent i i '0' an the -axi efeence cuent change fom -3A to 3A at the moment of 0.3 econ. An, in Fig 5(c) an Fig. 5(), (c) () Fig. 5 Cuent epone of the popoe cuent contol 1: -axi cuent comman, : -axi cuent epone 3: a-phae cuent comman, 4: a-phae cuent epone

6 (a) on Powe Electonic, ol. 11, No., pp , [4] C. E. Mille, et. al., Moelling A Pemanent Magnet Linea Synchonou Moto fo Contol Pupoe, IEEE Afica 00, pp , 00. [5] Young Soo Seo an Young Jin Kim, ecto Contol of Inucto Moto fo etimating Back-EMF of Hypetable MRAS, Jounal of Reeach Intitute of Inutial Technology, ol. 0. pp , 001. [6] In-Hwan Oh, Gun-Woo Moon, Sung-kwun Kim, A Novel Peictive Cuent Contol Inuction Moto Uing Reonant DC Link Invete, IEEE, pp , [7] Li Zhen an Longya Xu, Senole Fiel Oientation Contol of Inuction Machine Bae on a Mutual MRAS Scheme, IEEE Tan. on Inutial Electonic, ol. 45, No. 5, Octobe [8] Seung-Gi Jeong an Myung-Ho Woo, DSP-Bae Active Powe Filte with Peictive Cuent Contol, IEEE Tan. on Inutial Electonic, ol. 44, No. 3, June (b) Fig. 6 epone of the whole ytem with fat pee chang 1: pee comman, : pee epone, 3: a-phae cuent comman, 4: a-phae cuent epone 6. Concluion Thi pape peent a novel peictive cuent contol metho fo a SM that conie the finite calculation elay of contol evice. the conventional peictive cuent contolle i ha to implement in the full igital cuent contolle ince a finite calculation time caue a elay between the cuent ening time an the time it take to apply the voltage to the moto. By moifying a conventional peictive cuent contolle that conie the calculation elay, thee i a lage impovement in the cuent contol pefomance in the both tanient an teay tate. ACKNOELEDGEMENT Thi wok wa uppote by the National Reeach Laboatoy Pogam of the Koean Minity of cience & Technology (MOST). REFERENCES [1] H. T. Moon, H. S. Kim, an M. J. Youn, A Dicete-Time Peictive Cuent Contol fo SM, IEEE Tan. on Powe Electonic, ol. 18, No. 1, pp , 003. [] M. A. Rahman, Analyi of Cuent Contolle fo oltage-souce Invete, IEEE Tan. on Inutial Electonic, ol. 44, No. 4, pp , [3] O. Kuke, Dicete-Time Cuent Contol of oltage-fe Thee-Phae PWM Invete, IEEE Tan.