Research Article FPGA Realization of Sensorless PMSM Speed Controller Based on Extended Kalman Filter

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1 Mathematical Problem in Engineering Volume 213, Article ID , 13 age htt://dx.doi.org/1.1155/213/ Reearch Article FPGA Realization of Senorle PMSM Seed Controller Baed on Extended Kalman Filter Ying-Shieh Kung, 1 Nguyen Vu Quynh, 2 Nguyen Trung Hieu, 1 and Jin-Mu Lin 1 1 Deartment of Electrical Engineering, Southern Taiwan Univerity of Science and Technology, 1 Nan-Tai Street, Yong-Kang Ditrict, Tainan City 71, Taiwan 2 Deartment of Electrical Engineering, Lac Hong Univerity, 1 Huynh Van Nghe Street, Buu Long Ditrict, BienHoaCity84,DongNaiProvince,Vietnam Correondence hould be addreed to Ying-Shieh Kung; kung@mail.tut.edu.tw Received 9 Setember 213; Acceted 22 October 213 Academic Editor: Teen-Hang Meen Coyright 213 Ying-Shieh Kung et al. Thi i an oen acce article ditributed under the Creative Common Attribution Licene, which ermit unretricted ue, ditribution, and reroduction in any medium, rovided the original work i roerly cited. Baed on extended Kalman filter (EKF), the deign and FPGA imlementation of a enorle control intellectual roerty (IP) for ermanent magnet ynchronou motor (PMSM) drive are reented in thi aer. Firtly, the mathematical model for PMSM i derived and the vector control i built u. Secondly, the rotor flux angle (FA) and rotor eed which are etimated by uing EKF are decribed. Thee etimated value are feedbacked to the current loo for vector control and to the eed loo for eed control. Thirdly, the very-high-eed IC hardware decrition language (VHDL) i adoted to decribe the behavior of the enorle eed control IP which include the circuit of ace vector ule width modulation (SVPWM), coordinate tranformation, EKF, and PI controller. Finally, to evaluate the effectivene and correctne of the rooed of ytem, a coimulation work erformed by Simulink and ModelSim i firtly conducted. Then, an exerimental ytem by FPGA chi and motor driving board i et u to further validate the erformance of the rooed EKF-baed enorle eed control IP. 1. Introduction PMSM ha been increaingly ued in many automation control field a actuator, due to it advantage of uerior ower denity, high-erformance motion control with fat eed, and better accuracy. However, conventional motor control need a eed enor or an otical encoder to meaure the rotor eed and feedback it to the controller for enuring the reciion eed control. Such enor reent omediadvantageuchadrivecot,machineize,reliability, and noie immunity. In recent year, a enorle control without oition and eed enor for PMSM drive become a oular reearch toic in the literature 1 7. Thoe enorle control trategie have liding mode oberver (SMO), extended Kalman filter (EKF), reduced-order EKF, and o forth. The EKF i baically a full-order tochatic oberver for the recurive otimum tate etimation of a nonlinear dynamic ytem in real time by uing ignal that are in noiy environment 7. Comaring with SMO, EKF can directly etimatetheangulareedandithahighconvergencerate which can give a more raid eed reone 5. However, EKF require heavy online44matrix comuting; therefore, the comlex comutation become a challenge for a fixedoint roceor ytem. In realization, a fixed-oint roceor uing digital ignal roceor (DSP) and field rogrammable gate array (FPGA) both can rovide a good olution in thi iue. Particularly, FPGA with rogrammable hardwired feature, fat comutation ability, horter deign cycle, embedding roceor, low ower conumtion, and higher denity i better for the imlementation of the digital ytem 8, 9thanDSP. Recently, a coimulation work by Electronic Deign Automation (EDA) Simulator Link ha been gradually alied to verify the effectivene of the Verilog and VHDL code in the motor drive ytem The EDA Simulator Link 13 rovide a coimulation interface between MATLAB or Simulink and HDimulator-ModelSim 14. Uing it you

2 2 Mathematical Problem in Engineering can verify a VHDL, Verilog, or mixed-language imlementation againt your Simulink model or MATLAB algorithm 13. Therefore, EDA Simulator Link let you ue MATLAB code and Simulink model a a tet bench that generate timulu for an HDimulation and analyze the imulation reone 13. In thiaer, a coimulationby EDASimulator Link i alied to enorle eed control for PMSM drive. The PMSM, inverter, and eed command are erformed in Simulink and the EKF algorithm; current vector controller and eed PI controller decribed by VHDL code are executed in ModelSim. After ucceful verification in imulation, an FPGA-baed exerimental ytem i etablihed with configuration a in Figure 1 for realizing the rooed IP code again, and exeriment reult will validate the effectivene of the enorle eed control ytem of PMSM drive. 2. Sytem Decrition of PMSM Drive and Senorle Seed Control The enorle eed control block diagram for PMSM drive i hown in Figure 1.ThemodelingofPMSM,theEKF-baed rotor flux angle (FA) and rotor eed etimation, and the PI controller are introduced a follow Mathematical Model of PMSM. The mathematical model of a PMSM i decribed, in two-axi d-q ynchronou rotating reference frame, a follow: di d dt = r L d i d ω e L q L d i q 1 L d V d, di q dt = ω L d e i L d r λ f i q L q ω e 1 V q L q L q, q where V d, V q are the d and q axe voltage; i d, i q, are the d and q axe current, r i the hae winding reitance; L d, L q are the d and q axe inductance; ω e i the rotating eed of magnet flux; and λ f i the ermanent magnet flux linkage. The current loo control of PMSM drive in Figure 1 i baedonavectorcontrolaroach.thati,ifthei d i forced to, the PMSM will be decouled, and controlling a PMSM i like controlling a DC motor. After decouling, the motor torque i roortional to i q : (1) T e = 3N P 4 λ fi q Δ = Kt i q. (2) Conidering the mechanical load, the overall dynamic equation of PMSM drive ytem i obtained by J m d dt ω r B m ω r =T e T L, (3) where T e i the motor torque, N P i ole air, K t i torque contant, J m i the inertial value, B m i daming ratio, T L i the external torque, and ω r i rotor eed Extended Kalman Filter (EKF). Foramotortochatic nonlinear equation, it can be written in the following form: x (t) =fx (t) Bu(t) σ(t), (4) y (t) =hx (t) μ(t), (5) where x(t), u(t), and y(t) are ytem tate, ytem inut, and ytem outut, reectively. The σ(t) and μ(t) rereent ytem noie and meaurement noie which are zero-mean white Gauian ditribution with covariance Q(t) and R(t), reectively. Once a nominal olution to a motor nonlinear equation can be found in (4)-(5), the linearized erturbation equation i δx (t) =F(x (t)) δx (t) Bδu(t) σ(t), (6) δy (t) =H(x (t)) δxμ(t), (7) where the Jacobian and outut matrice are defined a follow: F (x (t)) = f, H (x (t)) = h x x=x(t) x x=x(t) After dicretization with amling time T c,(6)become x(t n )=Φ(t n,t n 1,x(t n 1 )) x (t n 1 ). (8) t n Φ(t n,t n 1,x(t n 1 )) Bdτ u (t n 1 )(t n 1 ), t n 1 where Φ(t n,t n 1,x(t n 1 )) i an exonential matrix and it comutation can be imlified by Further, (9) Φ(t n,t n 1,x(t n 1 )) I FT c. (1) t n Φ (t n,t n 1,x(t n 1 )) Bdτ BT c. (11) t n 1 Therefore, the dicrete model of (6)-(7) become x (n) =(IFT c )x(n 1) BT c u(n 1) (n 1), (12) y (n) =H x(n) ξ(n 1), (13) where t n =nt c and t n 1 =(n 1)T c. TheEKFianotimaletimatorwhichearchethe cot function J = m n=1 E{ x2 (n)} at the leat quare ene. The x(n) i defined by x(n) = x(n) x(n), which i the difference of etimation of tate x(n) and ytem tate x(n). The EKF algorithm i decribed by the following twote recurive equation.

3 Mathematical Problem in Engineering 3 Ac ource Nio II roceor CPU On-chi ROM On-chi RAM Avalon bu UART PIO Timer SPI SDRAM controller Seed command generation ω r ω r Seed controller PI i d = i q in θ e, co θ e Current controller PI PI q d i q i d Park 1 d, q α, β d, q α, β Park α β i α i β Modify clark 1 α, β a, b, c α, β a, b, c Clark ref1 ref2 ref3 i a i b i c FPGA SVPWM A/D interface Rectifier PWM 1 PWM 2 PWM 3 PWM 4 PWM 5 PWM 6 A/D A/D i u LPF i w LPF C L Inverter in /co of flux angle θe ω r Rotor flux and rotor eed etimation baed on EKF α β i α i β PMSM Load Figure 1: Architecture of FPGA-baed enorle PMSM drive ytem. Ste 1 (rediction te). From (4) and uing a imle rectangular integration, or from (12) x n n 1 = x n 1 (f x n 1 B u n 1 )T c (14) x n n 1 =Φ n 1 x n 1 BT c u n 1. (15) The covariance i udated by P n n 1 =Φ n 1 P n 1 Φ T n 1 Q d. (16) Ste 2 (innovation te). Conider x n = x n n 1 K n (y n H x n n 1 ), (17) P n =P n n 1 K n HP n n 1. (18) The Kalman gain i calculated by K n =P n n 1 H T HP n n 1 H T R 1. (19) Figure 2 how the rocedure of EKF with two te above, after meaurement udate, it will be changed to time udate Deign of the Senorle PMSM Baed on EKF. The circuit equation of PMSM on the d-q rotating coordinate in (1)ireformulated a V d = r V q ω e ω e i d, (2) r iq ω e λ f where Δ =Ld =L q. Tranforming (2), the circuit equation of PMSM on the α β fixed coordinate can be derived by the following equation: V α V β = r r i α iβ ω e λ f in θ e co θ e, (21) where V α V β T i voltage on fixed coordinate; i α i β T i current on fixed coordinate; θ e iangularoitionatmagnet flux; and i differential oerator. If we chooe the x(t) = i α,i β,ω e,θ e T a the tate variable of the PMSM mathematical model, then (21) can be exanded to the following formulation: d dt r i α ω eλ f in θ L e = r i β ω eλ f co θ L e ω e 1 1 V α =fb Δ V α, V β V β i α i β ω e θ e i α = 1 i β 1 i α i β ω e θ e (22) Δ =h, (23)

4 4 Mathematical Problem in Engineering Time udate (rediction) Calculate temorary tate variable x n n 1 = x n 1 (f x n 1 B u n 1 )T c or x n n 1 =Φ n 1 x n 1 BT c u n 1 Calculate temorary covariance matrix P n n 1 =Φ n 1 P n 1 Φ T n 1 Q d Meaurement udate (innovation) Calculate Kalman gain K n =P n n 1 H T HP n n 1 H T R 1 Udate tate variable and covariance matrix x n = x n n 1 K n (y n H x n n 1 ) P n =P n n 1 K n HP n n 1 Initial P n n 1,Q d,r Figure 2: Demontration of the EKF oeration. where x(t) = i α i β ω e θ e T, y(t) = i α i β,andu(t) = V α V β T.From(8)and(22), the Jacobian and outut matrice can be obtained: F (x (t)) = f x x=x(t) r = r λ f in θ e λ f co θ e 1 ω e λ f co θ L e ω e λ f in θ L e, (24) H (x (t)) = h = 1 x x=x(t) 1. (25) tate value of x(n) = i α (n), i β (n), ω e (n), θ e (n) T i etimated at each amling eriod; then the rotor eed can be derived by ω r (n) = ω e (n). (27) N P Finally, a ummary for the etimation of rotor FA and rotoreedbaedonekfireentedafollow. Ste 1. Set the initial value of Q d, R, P,andn=1. Ste 2. Meaure the value of i α (n), i β (n), V α (n), andv β (n) from PMSM ytem. Ste 3. Etimate the temorary tate variable from (14). In addition, refer to (22), and the calar form of the rediction equation can be exreed a follow: Further,ubtituting (24)into(1), the exonential matrix i hown a follow: Φ(t n,t n 1,x(t n 1 )) IFT c 1 r T c = 1 r T c Δ = G φ 13 φ 14 G φ 23 φ T c 1 λ f T c in θ e ω e λ f T c λ ft c co θ e ω e λ f T c 1 T c 1 co θ e in θ e (26) A the reult, the EKF algorithm in (14) (19) can be carried outtoetimatethetatevalue.theinitialvalueof Q d, R,and P need to be choen. Through the recurive calculation, the i α (n n 1) = (1 T c r ) i α (n 1) ω e (n 1) T c λ f in ( θ e (n 1)) T cv α (n 1), r i β (n n 1) = (1 T ) i L β (n 1) ω e (n 1) T λ f co ( θ e (n 1)) T cv β (n 1), ω e (nn 1) = ω e (n 1), θ e (nn 1) = θ e (n 1) ω e (n 1) T c. Ste 4. Calculate the Φ n 1 from (26). (28)

5 Mathematical Problem in Engineering 5 FPGA-baed enorle eed control IP A22 Nio II embedded roceor IP A D31 CPU UART D Sram be3 Sram be2 Sram be1 Sram be Sram oe Sram we Sram c Avalon bu On-chi ROM On-chi RAM Avalon bu PIO Timer SPI ω r 15.. Alication IP Clk Clk-te Frequency divider CK ADIN11 Clk Clk-te ω r 15.. ω r 15.. Clk Clk-te Seed controller (PI controller) Rotor flux and rotor eed etimation baed on EKF Clk Clk-te i q 11.. θ e 11.. α 11.. β 11.. i α 11.. i β 11.. Current controller and coordinate tranformation (CCCT) Clk i a 11.. i b 11.. i c 11.. Clk Clk-te rx 11.. ry 11.. rz 11.. ADC interface SVPWM generation ADIN BDIN11 BDIN CHA CHB RCA RCB STSA STSB PWM 1 PWM 2 PWM 3 PWM 4 PWM 5 PWM 6 Figure 3: Internal architecture of a enorle eed control IP in FPGA. Ste 5. Obtain the temorary covariance matrix P n n 1 from (16). Becaue matrix P n n 1 i ymmetric matrix by ij = ji, itcanbechoenbythefollowingform: P n n 1 = (29) Hence, from (16), individual element of P n n 1 could be udated a follow: 11 G Gφ Gφ φ 14 φ φ φ q 11, 12 G 2 12 Gφ Gφ φ 23 (G 13 φ φ ) φ 24 (G 14 φ φ ), 13 G 13 φ φ 14 34, 14 (G 13 φ φ )T c (G 14 φ φ ), 22 2G (φ φ )G 2 22 φ φ φ 23 φ q 22, 23 G 23 φ φ 24 34, 24 (G 23 φ φ )T c G 24 φ φ 23 34, q 33, 34 T c 33 34, T 2 c 33 2T c 34 q 44. (3) Ste 6. Calculate the Kalman gain from (19). Uing (25) and (29), the formulation i further imlified a follow. Firtly, HP n n 1 H T R 1 = R 11 R 22 = R 1 11, R (31)

6 6 Mathematical Problem in Engineering λ f T c θ e (n 1) in in( θ e (n 1)) 1 Tc r î α (n 1) T c L α (n 1) î α (n n 1) φ 13 Q 11 Q 22 Q 33 Q 44 T c ω e (n 1)λ f T c ω e (n 1)λ f T c L β (n 1) φ 24 in( θ e (n 1)) ω e (n 1) î β (n n 1) ω e (n 1)λ f T c ω θ e e (n 1) (n n 1) λ f T c î β (n 1) L θ θ e (n 1) e (n 1) co( θ e (n 1)) T c co( θ e (n 1)) co r 1 T c λ f T c φ 14 φ 23 Obtain the temorary covariance matrix P n 1 P n n Calculate Jacobian matrix and redict tate variable î α (n n 1) î β (n n 1) î α (n) K i α (n) 11 k ĩα(n) 21 Udate P ĩ α (n) n ĩ α (n) k î α (n n 1) P n n 1 matrix P 12 n k 22 and ĩ α (n) calculate ĩ β (n) ĩ α (n) ω e (n n 1) ĩ β (n) matrix K n K n k 41 i β (n) ĩβ(n) k 31 ω e (n) k R 42 î β (n n 1) 11 R 22 k 32 ω r (n) SR2 ĩ β (n) Prediction of temorary covariance matrix P n î β (n) θ e (n n 1) ĩ β (n) θ e (n) Calculation of error Udate P n and calculate K n Udate etimated tate Figure 4: State diagram of FSM for decribing the EKF-baed algorithm. where R rereent the uncertaintie of meaurement variable which are very difficult to know. Hence, R i often choen a unity matrix for imlifying the tak but doe not affect the outcome (31). Since P 12 = P 21,(31) canberewritteninthe following form: HP n n 1 H T R = (32) To normalize the inut value and to revent the numerical overflow condition which occurred during comutation, (32) i normalized and thoe value are all divided by 4. Therefore, (32)become 22 1 HP n n 1 H T R 1 = 1 M Δ = t 11 t 12 t 21 t 22, (33) where M=( )/4.Then,from(19), the Kalman gain can be calculated by K n Δ = = k 11 k 21 k 31 k k 12 k 22 k 32 k t t 21 = 21 t t t t t t 21 t 11 t 12 t 21 t t t t t t t t t 22 (34)

7 Mathematical Problem in Engineering 7 φ φ SL1 SL1 G q 11 φ 14 SL1 φ 14 G 2 φ φ φ G 2 33 t 33 q G t φ 24 t12 t 14 φ t φ14 φ G 2 φ T c φ 23 G 34 φ φ 24 t G q t 22 φ φ SL1 φ 23 SL1 t φ 13 G 13 G φ φ 14 φ 23 t 13 t φ φ T c 44 φ t t T c t t φ t q T 44 c t G t t t 24 t t t t t T c P n 1 Product Q Sum SL1 Q n n 1 Predicted etimate covariance Shift left 1 bit P n n 1 Figure 5: State diagram of FSM for rediction of covariance matrix P n n 1.

8 8 Mathematical Problem in Engineering SR2 r2 X X M SR2 r2 A/B 12 t M 11 SR2 r2 A/B.25 M SR2 r2 A/B M t 22 t 12 SR2 r2 A/B X k 11 k 12 k 21 Shift right 2 bit Divide Product Sum t k 11 X t 11 X k t 11 X k X 21 t 11 k t X 12 X 12 t t 12 X t 12 X t 12 X t 12 X k 32 k 12 k t X 13 t 12 X 12 k 22 t 22 X X t t X 23 t 22 X 22 k 22 k 31 k 32 Matrix K n P n n 1 22 K n (a) t 33 t k 12 k k k t k k k t k k k Product Sum t t 23 k H 11 k k31 k 12 P 13 n n 1 k P n 23 t k k K k 22 n Udate covariance 22 matrix P n 44 k k42 t t 34 t 11 t 12 t 13 t 14 t 22 t 23 t 24 t 33 t (b) Figure 6: State diagram of FSM for (a) the calculation of matrix K n and (b) the udate of covariance matrix P n. Ste 7. Tune the reent tate variable from (17), and it calar form i hown a follow: i α (n) = i α (nn 1) k 11 i α (n) k 12 i β (n), i β (n) = i β (nn 1) k 21 i α (n) k 22 i β (n), ω e (n) = ω e (nn 1) k 31 i α (n) k 32 i β (n), θ e (n) = θ e (n n 1) k 41 i α (n) k 42 i β (n), (35) where k ij i the element in Kalman gain K n i α (n) = i α (n) i α (n n 1) and i β (n) = i β (n) i β (n n 1).

9 Mathematical Problem in Engineering 9 Seed command Convert ModelSim. (work-1) cmd Current command Rotor eed Seed loo PI controller Convert Contant1 i q current command ModelSim. cmd i q (work-2) cmd i d Flux angle Phae a current PMW1 PMW2 PMW3 PMW4 PMW5 PMW6 i d out i q out Convert ln1conn1 ln2conn2 ln3conn3 ln4conn4 ln5conn5 ln6conn6 IGBT-baed inverter Seed command Rotor eed and Kalman eed DC voltage ource.1 Contant2 Tm A N m B S C Permanent magnet ynchronou machine -K- Gain1 Torque Rotor eed wm (rad/) Electromagnetic torque T e (N m) Rotor angle thetam (rad) S-function Stator current i d (A) Flux angle Stator current i q (A) tranformation Stator current i a (A) Stator current i b (A) Stator current i c (A) Motor d/q current V α out Phae b current V β out I α out Phae c current I β out CCCT and SVPWM α β i α i β ModelSim. Flux angle (work-3) wr i d/q Real and etimated flux angle Convert Data tye converion 1 d-axi current Stator current Full-order EKF Convert -K- Data tye converion 1 Saturation Gain6 Convert -K- Data tye converion 11 Saturation1 Gain7 Convert -K- Data tye converion 12 Saturation2 Gain8 Figure 7: The Simulink/ModelSim coimulation architecture for enorle eed control of PMSM drive. Ste 8. Udate the reent covariance matrix P n from (18), where K n HP n n 1 canbedirectlyobtainedafollow: k k k k k k k k k k k k k k k k K n HP n n 1 =. (36) k k k k k k k k k k k k k k k k Ste 9. Calculate the rotor eed from (27); then et n=n 1 and go back to Ste Deign of Senorle Seed Controller IP Figure 3 illutrate the internal architecture of the rooed FPGA imlementation of a enorle eed control IP for PMSM drive ytem. The internal circuit comrie a Nio II embedded roceor IP and an alication IP. The Nio II roceor i deicted to generate the eed command, collect the reone data, and communicate with external device. All rogram in Nio II roceor are coded in the C language. The alication IP include mainly a circuit of an EKF-baed rotor FA and rotor eed etimation, a eed PI controller, a circuit for current controller and coordinate tranformation (CCCT), a SVPWM circuit, and an ADC interface circuit. The amling frequencie of the eed control loo and current control loo are deigned with 2 khz and 16 khz, reectively. The frequency divider generate 5 Mhz (Clk) and 12.5 Mhz (Clk-te) clock to uly all circuit in Figure 3. The internal circuit of CCCT erform the function of two PI controller, table look-u for in/co function, and the coordinate tranformation for Clark, Park, invere Park, and modified invere Clarke. The detailed circuit deign of CCCT, eed PI controller, ADC interface, and SVPWM generation in Figure 3 refer to 8. Herein, only the digital hardware circuit deign of the EKF-baed rotor FA and rotor eed etimation i decribed. To reduce the FPGA reource uage, a finite-tate machine (FSM) i emloyed to model the EKF-baed algorithm whoe deign rocedure and mathematical formulation are reented in the reviou ection. The deign reult i hown in Figure 4 which ue one adder, one multilier, one divider, two in/co looku table, hifter, regiter, and o forth and maniulate 131 te machine to carry out the overall comutation. The data tye adot 16-bit length with Q15 format and 2 comlement oeration. The multilier, adder, and divider aly Altera LPM (Library Parameterized Module) tandard. In Figure 4, the te 12 execute the calculation of Jacobian matrix and redict temorary tate variable; erform the comutation of temorary covariance matrix; te 69 7 are for tate error calculation; te udate of

10 1 Mathematical Problem in Engineering Seed (rm) Seed command Etimated rotor eed Actual rotor eed (a) Flux angle (FA) (deg) Current (A) 5 4 Actual rotor FA Etimated rotor FA by EKF (c) id i q (b) Figure 8: PMSM running at low eed (2 rm) and invere eed (±2 rm) condition. (a) Seed te reone, (b) current reone, and (c) actual rotor FA and etimated rotor FA. Seed (rm) Etimated Seed rotor eed command 1 2 Actual rotor eed (a) Current (A) i q i d (b) Flux angle (FA) (deg) Etimated rotor FA by EKF (c) Actual rotor FA Figure 9: PMSM running at wide-range high eed (2 rm) and invere eed (±1 rm) condition. (a) Seed te reone, (b) current reone, AND (c) actual rotor FA and etimated rotor FA. the reent covariance matrix P n andcalculatethekalman gain K n ; decribe the reent tate tuning a well a executing the comutation of rotor FA and rotor eed. According to (3), the comutation of temorary covariance matrix P n n 1 in Figure 4 i decribed in Figure 5. Further, according to (18), (33)-(34), and (36), the udate of the reent covariance matrix P n andcalculationthekalmangain K n in Figure 4 are illutrated in Figure 6. The oeration of each te in Figure 4 i 8 n (12.5 MHz) in FPGA; therefore a total of 131 te need only 1.48 μ oeration time. The FPGA (Altera) reource uage of EKF-baed rotor FA and rotor eed etimation in Figure 4 i 4,158 LE (logic element) and 2,89 RAM bit. Additionally, the FPGA reource uage of the circuit of CCCT, eed PI controller, ADC interface, and SVPWM in Figure 3 are 864 LE and 24,576 RAM, 2,43 LE and RAM bit, 136 LE and RAM bit, and 1,221 LE and RAM bit, reectively. 4. Simulink/ModelSim Coimulation and It Simulation Reult The Simulink/ModelSim coimulation architecture for enorle PMSM eed control ytem i hown in Figure 7. The SimPowerSytem-Blocket in the Simulink execute the PMSM and the IGBT-baed inverter. The EDA imulator link for ModelSim execute the coimulation uing VHDL code

11 Mathematical Problem in Engineering 11 Rectifier L Inverter T A T B T C Ac ource C U, V, W T A T B T C Load Iolated and driving circuit PMSM PWM1 PWM6 LP filter circuit External memory CPU On-chi ROM On-chi RAM Avalon bu UART PIO Timer SPI SDRAM controller Digital circuit of eed PI controller, EKF-baed rotor FA and eed etimation, and current vector controller for PMSM ADC ADC i a i b Embedded roceor IP Alication IP (Nio II roceor) FPGA-baed enorle eed control IP (a) (b) Figure 1: Exerimental ytem (a) with block diagram and (b) in real ytem. running in ModelSim rogram. It execute the function of the enorle eed controller by three work. The work-1 to work-3 of ModelSim in Figure 7, reectively, erform the function of eed loo PI controller, the function of current controller and coordinate tranformation (CCCT) and SVPWM, and the function of EKF-baed rotor FA and rotor eed etimation. The amling frequency in current control loo and EKF-baed etimation algorithm i deigned with 16 khz, but in eed control loo i 2 khz. The clock of 5 MHz and 12.5 MHz will uly all work of ModelSim. The FPGA (Altera) reource uage of work-1 to work-3 are 2,43 LE and RAM bit, 2,85 LE and 24,576 RAM bit, and 4,158 LE and 2,89 RAM bit, reectively. In imulation, the deigned PMSM arameter ued in Figure 7 are a follow: ole air are 4, tator hae reitance i 1.3 Ω, tator inductance i 6.3 mh, inertia i J =.18 kg m 2, and friction factor i F =.13 N m. PI gain in eed control loo are deigned with K =.2442 and Ki =.458. To evaluate the rooed controller erformance, PMSM running at low eed (2 rm) and invere eed (from 2 rm to 2 rm or vice vera) condition i firtly conidered, and it imulation reult regarding a the eed te reone, the current reone a well atheactualrotorfluxangle(fa)andtheetimatedrotor flux angle are hown in Figure 8. It how that the motor eedgiveagooddynamicreoneerformancewitha

12 12 Mathematical Problem in Engineering Seed (rm) Seed command Rotor eed Flux angle (deg) 4 Actual rotor FA Etimated rotor FA (a) (b) Figure 11: (a) Ste eed reone of actual rotor eed and etimated rotor eed and (b) actual rotor FA and etimated rotor FA. Seed (rm) Seed command Actual rotor eed Etimated rotor eed (a) Current (A) i q.5.5 i d (b) Figure 12: (a) Ste eed reone of actual rotor eed and etimated rotor eed and (b) current reone. little overhoot and 25 m riing time. It alo how that the etimated rotor eed can track actual rotor eed well. Figure 8(b) how a ucceful vector control becaue i d i controlled to zero. Figure 8(c) how that the etimated rotor FA can fat track the actual rotor FA even in the invere eed command condition. Further, another imulation cae while the PMSM running at wide-range high eed (from rm 1 rm 2 rm 1 rm 1 m 2 rm) and invere eed (from 1 rm to 1 rm) condition i teted, and it imulation reult are hown in Figure 9. It reent that not only at eed tracking but alo at rotor FA tracking, the etimated value adoted by EKF method can give a good follow to the real rotor value. However, excet in the initial condition, the actual rotor eed give a fat te reone by 18 m riing time, near mm teady-tate value, and maximum 17.5% overhoot. 5. Exerimental Sytem and Reult After confirming the correctne of the rooed EKF-baed enorle control IP by imulation, the VHDL code are directly alied to the exerimental FPGA-baed enorle PMSM drive ytem. The block diagram and real exerimental ytem are deicted in Figure 1. Themaindevice include a PMSM, a DE2 board with Altera CycloneII FPGA, a motor driver, and a ower ulier. The arameter of the PMSM are r =.63 Ω, L = 2.77 mh,and4oleair.the inut voltage, continuou current, rating torque, rating eed, and continuou ower of the PMSM are 22 V, 12 A, 2.3 N- m, 3 rm, and 75 W, reectively. The Altera CycloneII EP2C35 chi adoted in the deign oee 33,216 LE, maximum 475 available I/O in, 483,84 RAM, and 35 embedded multilier. The chi can be embedded with a Nio II multicore roceor that i equied with everal 32-bit CPU, flexibility of core ize, 1 to 16 Mbyte of flah memory in the available memory chi, 1 Mbyte SRAM, 16 M byte SDRAM, and 4 Gbyte memory outide of the chi. In imlementation, excet the VHDL code of CCCT, EKF, and PI controller, the VHDL code of ADC interface circuit hould be added and integrated and then downloaded into FPGA. The PI gain of eed control loo in exeriment are deigned with K =.512 and Ki =.21. In the exerimental cae, PMSM running at low eed (2 rm) and invere eed (from 2 rm to 2 rm or vice vera) condition are firtly conidered, and it exeriment reult regarding the eed te reone a well a the actual rotor FA and the etimated rotor FA are hown in Figure 11. Figure 11(a) howthatthemotoreedgivea good dynamic reone erformance with a little ocillation and overhoot and it ha 15 m riing time. Figure 11(b) how that the etimated FA can fat track the actual rotor FA even in the invere eed command condition. Further, another exerimental cae while the PMSM running at medium eed (from rm 3 rm 6 rm 9 rm 6 rm 9 rm) condition i evaluated, and it exeriment reult are hown in Figure 12.The Figure 12(a) reent a fat eed tracking with 15 m riing time and no occurrence of overhoot condition. Figure 12(b) how a ucceful vector control due to the i d being controlled to zero. Therefore, from the imulation reult in Figure 8 and 9 and the exerimental reult in Figure 11 and 12, itidemontratedthattheekfbaed etimation algorithm ued in enorle PMSM drive and the behavior decrition by uing VHDL are effective and correct.

13 Mathematical Problem in Engineering Concluion Thi tudy ha reented a enorle PMSM drive baed on EKF and uccefully demontrated it erformance through coimulation by uing Simulink/ModelSim and imlementation by uing FPGA. In realization aect, the VHDL i ued to decribe the behavior of EKF algorithm, and FSM i ued to reduce the FPGA reource uage; therefore, it only need 4,158 LE and 2,89 RAM bit. In comutational ower aect, the oeration time to comlete the comutation of EKF algorithm i only 1.48 μ, which i le than the 62.5 μ (16 KHz) amling time in current control loo. In imulated and exerimental reult, it how that the ue of EKF in enorle PMSM drive can accurately etimate the rotor FA and rotor eed, and it can give a good te reone erformance in cae of low eed control, invere eed control, and high eed control a well. Acknowledgment Thi work wa uorted by the National Science Council of China under Grant no. NSC E L. Idkhajine and E. Monmaon, Deign methodology for comlex FPGA-baed controller alication to an EKF enorle AC drive, in Proceeding of the 19th International Conference on Electrical Machine (ICEM 1),.1 6,Setember H.-H.Chou,Y.-S.Kung,N.VuQuynh,andS.Cheng, Otimized FPGA deign, verification and imlementation of a neuro-fuzzy controller for PMSM drive, Mathematic and Comuter in Simulation,vol.9,.28 44, Y. S. Kung and T. H. Nguyen, Simulink/Modelim Co-imulation of EKF-baed Senorle PMSM drive, in Proceeding of IEEE International on Power Electronic and Drive Sytem (PEDS 13), , Y.Li,J.Huo,X.Li,J.Wen,Y.Wang,andB.Shan, Anoen-loo in microteing driver baed on FPGA and the co-imulation of modelim and imulink, in Proceeding of the International Conference on Comuter, Mechatronic, Control and Electronic Engineering (CMCE 1), , Augut The Mathwork, Matlab/Simulink Uer Guide, Alication Program Interface Guide, Modeltech, ModelSim Reference Manual, 24. Reference 1 V. C. Ilioudi and N. I. Margari, PMSM enorle eed etimation baed on liding mode oberver, in Proceeding of the 39th IEEE Annual Power Electronic Secialit Conference (PESC 8), ,June28. 2 S. Chi, Z. Zhang, and L. Xu, Sliding-mode enorle control of direct-drive PM ynchronou motor for wahing machine alication, IEEE Tranaction on Indutry Alication, vol. 45, no. 2, , V. Delli Colli, R. di Stefano, and F. Marignetti, A ytem-onchi enorle control for a ermanent-magnet ynchronou motor, IEEE Tranaction on Indutrial Electronic, vol. 57, no. 11, , S. Bolognani, R. Oboe, and M. Zigliotto, Senorle full-digital mm drive with ekf etimation of eed and rotor oition, IEEE Tranaction on Indutrial Electronic, vol.46,no.1, , M.C.Huang,A.J.Moe,andF.Anayi, Thecomarionof enorle etimation technique for PMSM between extended Kalman filter and flux-linkage oberver, in Proceeding of the 21t Annual IEEE Alied Power Electronic Conference and Exoition (APEC 6), , March W. Wang, M. Zhang, and Q. Wu, Alication of reduced-order extended kalman filter in ermanent magnet ynchronou motor enorle regulating ytem, in Proceeding of the International Conference on Digital Manufacturing and Automation (ICDMA 1), , December J.-S. Jang, B.-G. Park, T.-S. Kim, D. M. Lee, and D.-S. Hyun, Parallel reduced-order extended Kalman Filter for PMSM enorle drive, in Proceeding of the 34th Annual Conference of the IEEE Indutrial Electronic Society (IECON 8), , November Y.-S. Kung and M.-H. Tai, FPGA-baed eed control IC for PMSM drive with adative fuzzy control, IEEE Tranaction on Power Electronic,vol.22,no.6, ,27.

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