永磁同步馬達位置控制之FPGA晶片研製

全文

(1)

(2) FPGA

(3) Design and Implementation of a FPGA Position Control Chip for a Permanent Magnet Synchronous Motor. .

(4) FPGA

(5) Design and Implementation of a FPGA Position Control Chip for a Permanent Magnet Synchronous Motor. :

(6) . Student Advisor. . A Thesis Submitted to Department of Electrical and Control Engineering National Chiao Tung University in partial Fulfillment of the Requirements for the Degree of Master in Electrical and Control Engineering June 2005 Hsinchu, Taiwan, Republic of China. !"#$%&'(). Tsun-Yao Fan Dr. Shir-Kuan Lin.

(7) FPGA

(8) !"#$%& '(#) * +,-./012345 (FPGA) 6789:;<=>?236 7 Nios @ABCDEF FPGA 67!;+GHIJKLMNO?PQ R>?2367!;+STUVWXGHYZ[\]^_àBb. cdefghiejklm noe^pqO PI Brstuvwx R Nios @AB!;+ C WXGHhy PI Be?P P Be+_z{ |}~] SECS QR> ~ Q GHj0; +>]Q RG]P;~ Nios 8IJKLMN] ; =E¡¢£¤@Aeb @Ae¥¦§st]¨©q;ª« ¬IJKLMN?P];®¯G>°]Zd±²³ >]n<;x´µ¶·]-t¸HQK¹;Rº» ¼E½ ¥;¾¿ RS232 ÀÁÂ+ SECS ªÃz{|};+GHÄ» Å]stQ. i.

(9) Design and Implementation of a FPGA Position Control Chip for a Permanent Magnet Synchronous Motor. Student : Tsun-Yao Fan. Advisor : Dr. Shir-Kuan Lin. Department of Electrical and Control Engineering National Chiao Tung University. ABSTRACT In this thesis, a FPGA (Field Programmable Gate Array)-based Chip design is taken to implement a position control chip conceptual core for permanent magnet synchronous motor (PMSM) drive, and the control chip integrate digital logic IC and Nios processer in single FPGA chip. The function of the digital logic IC includes current and encoder feedback processing, coordination transformation, sinusoidal pulse width modulation (SPWM), current-loop proportional-integration (PI) controller, and so on. And the function of Nios processer includes speed-loop proportional-integration (PI) controller, position-loop proportional controller, and SECS communicating protocol. All the numerical system are normalized with Q-format concept to increase the precision during the operation. As for the experimental setup and related system collocation, it is construct from the Nios developement kit of the core concept for controlling a PMSM, and peripheral circuit boards for motor drive, signal feedback, and interface expand function. Besides, it demonstrates the effectiveness of the proposed FPGA-based control system for the performance improvement for PMSM drive can be achieved by adjustment of the control parameter and measurement and analysis of experimental data. It also develop a user interface in PC-base by SECS protocol through RS232 connecter to communicate with FPGA chip, and fulfill the function of remote control and monitor.. ii.

(10) ÆÇ;ÈÉÊËÌÈ]ÍÎ

(11) ;R ÏÐÑ']Ò !;ÍÎÓ¼ÈÔÕ]Ö×QØ¨;ÍÎRÙ ÏÚÛ]ÜÝ Þeßà]áEâãÈäËå-[]æçQèé;êëËÌìíI. e îï ðñíò®A;RóôO!ªõÈö÷ øù;úËÌû ?øùüýþ* ÿj;+_þÈ ½]QËÌí÷ e +_ì

(12) eÌ eðì? RÈ ¿!þÈè]ÿ;ËÌÈ]K ee!e; !eæ"e#$e%&'(ÈRG)E *+,- ./_ ;R01]23!E*4e¬;åÈR Ï ÐÑ'´56ÕQ 78;ÈÊËÌÈ]9½;:;RÐ<¹=>=?]Ó@ÈAÛB C;åÈtDE«¬ ]FGQRØH+*I ]JKLÓÈ]9½ è:BeõMÈÎ_N;êë]ËÌO;Q.

(13) . i. . ii. . i. . iv. . viii.

(14) 1.1 1.2 1.3 1.4. 1. ¤P] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . QRHS . . . . . . . . . . . . . . . . . . . . . . . . . . . [TV . . . . . . . . . . . . . . . . . . . . . . . . . . . * U . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2.1. IJKLMN>u. . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 VWXYVWÑZfgO=]hiB[ . . . . . . . . . . i. 1 2 3 4. 5 5 8.

(15) P\. ii. VWÑZKL]hfgO=]hiB[ . . . . . . . . . . 2.1.3 MN^_v]>u. . . . . . . . . . . . . . . . . . . . . 2.1.4 MNhÎJ`]>u. . . . . . . . . . . . . . . . . . . 2.1.5 a³>þb]u. . . . . . . . . . . . . . . . . . . . . ÎJKLMNOYZ[\ . . . . . . . . . . . . . . . . . . 2.2.1 ^cde¥ . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 YZ[\ . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2.1.2. 2.2. ! "#$%&'()*+, 3.1. 3.2 3.3 3.4. 3.5. 3.6 3.7 3.8. fT gh¥i . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 67 fT -Quartus II . . . . . . . . . . . . . . . . . . . . 3.1.2 Nios @AB fT -SOPC Builder . . . . . . . . . . . . . . 3.1.3 ½¥ fT -LabVIEW . . . . . . . . . . . . . . . . . . >_ Q hi . . . . . . . . . . . . . . . . . . . . . . . . . . . 67st<TUj . . . . . . . . . . . . . . . . . . . . . . . . . . . b k@A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 ^b @Aq . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 àBb laq . . . . . . . . . . . . . . . . . . . . . . . fghi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 jmkn>o¸ . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 VWXYVWÑZfghi . . . . . . . . . . . . . . . . . 3.5.3 VWÑZKL]hfghi . . . . . . . . . . . . . . . . . jklm no . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ^ PI B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nios @ABst01 . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10 11 14 17 19 19 20. 22 22 22 25 27 28 30 32 32 34 37 37 40 43 45 47 49.

(16) P\. iii 3.8.1 3.8.2. y PI B?P P B . . . . . . . . . . . . . . . . RS232 z{|} . . . . . . . . . . . . . . . . . . . . . . .. - $%./012 4.1 4.2 4.3 4.4 4.5. ^b k@Ap . . . . . . . . . . . . . . . . . . . . . . . . . àBb k@Ap . . . . . . . . . . . . . . . . . . . . . . . . fghip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . jklm nop . . . . . . . . . . . . . . . . . . . . . . . . . . . ^ PI Bp . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3 &'456780(9:;<. 49 51. 55 56 58 61 66 68. 71. 5.1. GSTU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 71. 5.2. ALTERA Stratix FPGA Development Board . . . . . . . . . . . . . . .. 73. 5.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 75. £¤qq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 b qq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Nios ¦§qq . . . . . . . . . . . . . . . . . . . . . . . . . . GJK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1. 5.4. = 9. 76 77 78 79. 84.

(17) 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8. MNfghirÖj ( VWXYfghiVWÑZfg ) . . . . MNfghirÖj ( VWÑZfghiKL]hfg ) . . . . IJKLMNr-qu.rÖj . . . . . . . . . . . . . . . . . ±sâ^MNaqrÖj . . . . . . . . . . . . . . . . . . . . KL]hfgt]MNu.uj . . . . . . . . . . . . . . . vw^BOMNuj . . . . . . . . . . . . . . . . . . «xlyOMN d Zuj . . . . . . . . . . . . . . . . . . . . «xlyOMN q Zuj . . . . . . . . . . . . . . . . . . . .. fT] ^j . . . . . . . . . . . . . . . . . . . 3.2 Quartus II fT] ¥j . . . . . . . . . . . . . . . . . . . 3.3 SignalTap II ~ghj . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 SOPC Builder–Nios @AB ¥j . . . . . . . . . . . . . . . . . 3.5 LabVIEW fT] ¥j . . . . . . . . . . . . . . . . . . . . . . 3.6 Q14 >z . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 IJKLMN?P67 Uj . . . . . . . . . . . . . . . 3.8 ^b k@A^j . . . . . . . . . . . . . . . . . . . . . . . . 3.9 ^b k@A67st01j . . . . . . . . . . . . . . . . . . 3.10 {àBJj . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11 {àB}|}MN~ehykj . . . . . . . . . . . . . . 3.1. Quartus II. iv. 6 6 12 17 18 20 21 21 23 24 25 26 27 29 30 32 33 34 35.

(18) jP\ 3.12 àBb laq67st01j . . . . . . . . . . . . . . . . . 3.13 àBb klBst01j . . . . . . . . . . . . . . . . . . 3.14 T!]jkn>¸j . . . . . . . . . . . . . . . . . 3.15 Tuj . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.16 jmkn>o¸67stu01j . . . . . . . . . . . . . . . 3.17 VWXYfghVWÑZfg]67st01j . . . . . . . . . 3.18 VWÑZfghVWXYfg]67st01j . . . . . . . . . 3.19 ±¹Y ]Tj . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.20 jklm no]¤Ã Aj . . . . . . . . . . . . . . . . . . . . . 3.21 jklm no]67st01j . . . . . . . . . . . . . . . . . . 3.22 v- @A]Dt PWM k¸rj . . . . . . . . 3.23 ^ PI Buj . . . . . . . . . . . . . . . . . . . . . . . . . . 3.24 ?PB_yB^j . . . . . . . . . . . . . . . . . 3.25 |}z{j . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.26 SECS p^j . . . . . . . . . . . . . . . . . . . . . . 3.27 SECS »p ( ) _»p ( ) ^j . . . . . . 3.28 Quartus II fT! FPGA 67>©Uj . . . . . . . . . . . . 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8. ^b k@Astpuj . . . . . . . . . . . . . . . . . . ^b k@Astpuj . . . . . . . . . . . . . . . . . . àBb k@Astpuj . . . . . . . . . . . . . . . . . MNjh~dstpuj . . . . . . . . . . . . . . . . . . MNh~dstpuj . . . . . . . . . . . . . . . . . . MNjhhydstpuj . . . . . . . . . . . . . . . . . . MNhhydstpuj . . . . . . . . . . . . . . . . . . jmkn>o¸stpuj . . . . . . . . . . . . . . . . . . . .. v 36 36 38 39 39 41 42 44 45 46 46 48 50 51 53 53 54 56 57 58 59 59 60 60 61.

(19) jP\ 4.9 jmkn>o¸stpuj . . . . . . . . . . . . . . . . . . . . 4.10 jmkn>o¸stp}|lj . . . . . . . . . . . . . . . . . 4.11 fghistpuj . . . . . . . . . . . . . . . . . . . . . . . . 4.12 fghistpuj 1 . . . . . . . . . . . . . . . . . . . . . . . 4.13 fghistpuj 2 . . . . . . . . . . . . . . . . . . . . . . . 4.14 jklm nostpuj . . . . . . . . . . . . . . . . . . . . 4.15 jklm nostpuj . . . . . . . . . . . . . . . . . . . . 4.16 jklm nostpuj . . . . . . . . . . . . . . . . . 4.17 ~bj . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.18 ^Bstpuj . . . . . . . . . . . . . . . . . . . . . . 4.19 ^Bstpuj ( E©± ) . . . . . . . . . . . . . . . 4.20 ^Bstpuj ( ©± ) . . . . . . . . . . . . . . . 4.21 ^Bstpuj ( X©± ) . . . . . . . . . . . . . . . GSTUj . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 FPGA q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 FPGA qqUj . . . . . . . . . . . . . . . . . . . . . . . . 5.4 ¨©qqO=]ÀÁ . . . . . . . . . . . . . . . . . . . . . . 5.5 ¨©qq=k]ÀÁ_^¤Y . . . . . . . . . . . . . . . . . 5.6 £¤qq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 W(KEtK¹]q . . . . . . . . . . . . 5.8 b qq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9 Nios ¦§qq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.10 ¸½¥ïj . . . . . . . . . . . . . . . . . . . . . . . . 5.11 ?PuE~bj (10 − 170 ) . . . . . . . . . . . . . . . 5.12 ?PuE~bj (100 − 270 ) . . . . . . . . . . . . . . .. 5.1. ◦. ◦. ◦. ◦. vi 62 63 63 64 65 66 67 67 68 68 69 70 70 71 74 74 75 75 76 77 77 78 79 81 81.

(20) jP\ 5.13 ?PuE~bj (100 − 300 ) . . . . . . . . . . . . . . . 5.14 ?Pu~bj (10 − 170 e150 − 250 e180 − 350 ) 5.15 0rpm ¡hy]ybj . . . . . . . . . . . . . . . . . . 5.16 ¡hy¢8 0rpm ]ybj . . . . . . . . . . . . . . . . . . . ◦. ◦. ◦. ◦. ◦. ◦. ◦. ◦. vii 81 82 83 83.

(21) 3.1 3.2 3.3 4.1 4.2 4.3 4.4 4.5 4.6 5.1. MN>g£þ¤¸ . . . . . . . . . . . . . . . . . . . . K Q /¸r]ç¥¸ . . . . . . . . . . . . . . . . . . . . . SECS ¦az¸ . . . . . . . . . . . . . . . . . . . . . . ^b k@ApuvO§?zï¸ . . . . . . . . . . . àBb k@ApuvO§?zï¸ . . . . . . . . . jmkn>o¸puvO§?zï¸ . . . . . . . . . . . . fghipuvO§?zï¸ . . . . . . . . . . . . . . . . . jkmlnoO§?zï¸ . . . . . . . . . . . . . . . . . . . . ^BO§?zï¸ . . . . . . . . . . . . . . . . . . . . . Stratix. 670 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. viii. 28 29 52 57 58 62 64 66 69 73.

(22) 1.1. . MNR¨©¼ªÕ';U«®]Ô¬¬;® YZ[\_âÁh¯[\r;°ãH±MNb~ë×][ \;¿²³ö´]AeDSP @ABð>?67 ]µ*e¶·s ¸¹]}ñ|º;°åMN67R»e¼b½<= Nº]¾¿Q RMNÀÊ]b~,=t;1y]b+_ö´]A Áo]êëÂÊ;Ð¹Ã~¹m_Ä ]Å@AB/+ÆrA ÇÈ]GH;ÉèÊ5]Ë÷ÌÍ7ÎµÏ¹=]Ð;ö xÑÄ¸b]ywxÒÓb~ÔTq (Application Specific Integrated Circuit, ASIC) ÕÖ×ÈGHØÙ]A;É67>©23ÚûÛÜ eÝ÷;ÞÍ@Ay1]ßà;8¼N»]MN;Î ÕãE~EF DSP @ABávEFÒÓb~ÔTqªâYã ;ä+ åæç;ÕÖN¼b1è»]JK;É ¬*éêØ; úÌëìªÕ¹=ªÃÑí¥=]<=;î+MN£¤67Ðïð¬¬ ]ñ/ª;òóÍ-]Ã<=_1y]ðºñ#+¢ô¬*;ãê ëÂÊ]EõQ Rön<=67 (System on chip, SOC) ]MN¨©!;ALTERA 1.

(23) 1 ÷ ø 2 ùú] Nios ãN¬ØEPg]è!Eï[;û]Òà8/+ >EF Nios @ABC FPGA 67!;CDEF67ü |K¹ÞÍÅ@ ABö÷ØÙt,;+_ÒÓb~ÔTq1yt,]<=.67 ª;xòóE~ØEÒàªN»]MNcd;ã* 7Ê]P ]Q 1.2.

(24). ý'ªþTñ#?]}ÿ º;åÅ@AB (Microprocessor, P) ð>?k@AB (Digital Signal Processor, DSP) ] v¬¬ÕÏ ;RMN¨©] «|HÓMN~]>?k@A B;R N¬x>?]h;ØÉ¼¶·q¹È² ¹=Í+_È Ñ] à;e¼>?¥]<=QÉR Ê

(25) ]_]ØÙYþ8; ÐCµÏ¸e@Ay+_ Ê5]@A;DSP @AB« [ í]0Ê

(26) Q ²³PþT/Ù]?¬;MN]åY<=6 7ö;+ÒÓb~ÔTq8H±MN67]Âà;è67>© 23ÚÝ÷]è@Ay;x/01¬8MNUÏ ]67 t«x =ûïMN]À

(27) ;RZñt]¬* Ì·~Å@AB DSP @AB v;þC ^MN ]67ï¶;ASIC 67ÞÍÔ]ßQ RMN]b~ãa;ÛB½;÷¤9 !;MN?]À

(28) ª »;Ï+R?P!"#ÊÍ6]b +_¶];êØö´]AÁµ$E%ë~] PI &pq B;¯Cö´B]JØÙ;D'~ ASIC 67ÈGHØÙ ]A;Ì(vZ]67Ô;RMN)wö´ A¹;°Ì~EF DSP @ABªGHö´]B;78< MN¬¼+ ASIC 67@AyÀ

(29) 1]^m no} |;+ DSP @ABGHØÙ]öÁCy_?P]*67U.

(30) 1 ÷ ø 3 Q Í+C*67U]À

(31) ;û9ùú}|]67 ,ÐYð;+ ALTERA Ð9+>?67*9]ùúú}|¼:;]ê b-;èEã.EF ARM @AB] IP;+. í/w U!; 0Ëïl1-ãR|]>? IC 67!/+Û÷01|EF Nios @A B;!òKE% DSP @ABEÏ;2¼9*>@AO¨;ú/+ÀJ 34]Te ¹Be5|}¥_E%}|}w5;ú6ª!?]ñ ;Ðï-7]ßà!ãÏ01]@ABÞÍÔ]7½; í/+ Û÷ÀÊ]@AB¹;~]©±/+82;å@AB] ã 7= í]À

(32) ;+9ì IC ]:=Q* üã+ ALTERA }| ] Nios 8 _p];+=<= ;^;_N1 y _p]¬-Q 1.3. . ¯C«<] ASIC 67 67<=«¬ÀÊÔ]¹=;>7 8p?@;< AB] <¿!"#ÂºðC;8¼¹=DE] 9ì;* ~/ÂØ01p1y] ALTERA Nios Development Kits( +teF Nios );è!¡¢¼EF ALTERA Stratix EP1S10 ],-b /2345 (Field Programmable Gate Array, FPGA) 67;û /R FPGA 67>©01|EF Nios @AB;~+$G| DSP @AB] st;E~!/01] FPGA 67e}w}|~e34}w}| H;ò LEDeIJeK<LrBr;Ã8£¤q_[\GH] gh;RST~EFÎJKLMNÃ8r¥; £¤ qqeb qq_ Nios ¦§qqª«¬< MN; PC »MÀÂ;M8No ¡+_Lrhyð~k]¥QR ] fT;* ~ Altera ùú] Quartus II _ Nios SDK Shell fT±O ªFG_`PSTUVWX (VHDL) C WXC FPGA _ Nios @AB!;á =¨©]£¤_¥q;Ãst]p;+DE67GH|ÞÍb 1y]ÎJKLMN?P67Q.

(33) 1 ÷ ø 1.4. . 4. * UQ±8(÷QE÷8ø;ï¼* ¤P]e QR_HS;+_ [TV;78RV¼* ]Uw ÷8IJKLMN>uYZ[\;}|IJKLMN]> u.U;¥iYZ[\b~CÎJKLMN]]u._ ujwX÷8IJKLMN?P67O01 ;*÷ r fT]¥eï67þbû u]stUw &÷867stpu;E~ fTu|lj;ªpûst u]j½wS÷8STUGOJK±²;Ê¥i~] ALTERA TeMN£¤qeb @Aq+_ Nios ¦§q;RØ Gt;Á67]GJKUMEïw(÷8J;Vþ* ]67]U+_-KME WJ;01Xª/] YQ.

(34) !"#$%&' ( 2.1. . ^MNYèJ]K/±8ËbMN (induction motor)eIJKLM N (synchronous motor) +_JZMN (reluctance motor) X¶;* ~] ãEF&[IJKLMN;è]h AeVòt\}wXY]h]Ó IJKLMN¹;^¿^Â]^Ëb|]hJ,;J,Ì^)h^ ]IJ`;+¤h^ðC]hQ IJKLMNRMb ¹;òK~MN^_v>u.!]³ >ªÃ;\³>O=ÌâYy=;[Ü ;åRÌ ÍØÙ×ÈGH]JK;Ï+* R}IJKLMN>u.]¿ !;)w¼YZA];< MN]>u.URòj 2.1_ j 2.2Ïr]Ñ fghi;þCIJKLMN]J_]h¹M¤Þ> u.]}±²;¡¢¼MN^_vO>u.eMNhÎJÒ> u.e+_a³>þb]u.Q. 5.

(35) 2 ÷ IJKLMN>uYZA. 2.1: (

(36)

(37) ). 2.2: (

(38) ). 6.

(39) 2 ÷ IJKLMN>uYZA 7 fgZz a-b-c fgVWXYfgQ aebec Z±O8 aebec Y^_vO[ÂYQ α-β fg VWZfgQ α ZY a Y^_v][YYE_Q β ZY8¨Ç α ZY 90 ]`ZQ d-q fg KL]hfgQ d ZYIaJ` N [b|]J,ÂKYQ q ZY8¨Ç d Y 90 ]`ZQ MN³>z T MNh¯Q T c/,¯Q ω h^2~yQ − → f MN^YZo>;/+w]YZe^YZeJdY Zr³>Q θ 2~?e;8^~?e φ ðh^~?e φ Of;+ (2.1) ¸rOQ e. L. e. e. s. θe = φs − φr. r. (2.1). è [/¯hÎaJ`2~yMÔ±xå;ò (2.2)Q θe =. Z. ωe (t)dt + θe (0). (2.2).

(40) 2 ÷ IJKLMN>uYZA 2.1.1. 8. >?!@>?ABCD(EFGHIJ. ³gj 2.1;hEàCVWXYfg!/¸r8 −→f s. 4π 2π − → fs = fa + fb ej 3 + fb ej 3. (2.3). è! f ef ef ±O8ûàCXYfg! aebec Z];xhEàCV WÑZfg!/¸r8 −f→ a. b. c. αβ. −→ fαβ = fα + jfβ. (2.4). è! f ef ±O8ûàCÑZfg! αeβ Z];J= (2.3) ð (2.4);/åVWXYVWÑZfg=Íòt]hiB[ α. β. −→ fαβ = fα + jfβ 4. 2. = k(fa + fb ej 3 π + fc ej 3 π ). (2.5). ÁèG©ð`©±i·¶[>;/G¬t5Ñ 4π 2π 1 1 − → fα = kRe{ fs } = kRe{fa + fb ej 3 + fb ej 3 } = k(fa + fb + fc ) 2 2. √ √ 4π 3 3 − → j 2π j fb − fc ) fβ = kIm{ fs } = kIm{fa + fb e 3 + fb e 3 } = k( 2 2. (2.6). (2.7). áÁ]YZð^YZw −→f !;/å 1 1 vα = k(va + vb + vc ), 2 2 1 1 iα = k(ia + ib + vc ), 2 2. √ √ 3 3 vβ = k( vb − vc ) 2 2 √. √ 3 3 iβ = k( ib − ic ) 2 2. (2.8). (2.9). è!;k 8VWXYfgVWÑZfg=]hi[>QèRXYÝj !;XY^ÍòtB[ ia + ib + ic = 0. (2.10).

(41) 2 ÷ IJKLMN>uYZA 9 ¯ (2.8) (2.10);VWÑZfgt]xk¹s¸ (Instantaneous Power)P /¸ròt αβ. Pαβ = vα iα + vβ iβ 1 = k 2 {va ia + vb ib + vc ic − [va (ib + ic ) + vb (ia + ic ) + vc (ia + ib )]} 2 3 = k 2 { (va ia + vb ib + vc ic )} 2 3 2 k Ps (2.11) = 2. è! P = v i + v i + v i 8VWXYfgt]xk¹s¸Q* Cfg hiù}]¿!µ k 8 ;+å< ù]¶8eDQ E~X~n>]~B[±|G©`©;\/+5|VWXYlVW ÑZfghi]¯4¸ròt s. a a. b b. c c. 2 3. . . . cos( 2π ) 3. . . cos(− 2π ) 3. cos0 f   α      fβ  = k  sin0 sin( 2π ) sin(− 2π ) 3 3    1 1 1 f0 2 2 2. f  a      fb    fc. (2.12). è! f 8mYÊ±Z (Zero-Sequence Component);èXY±ZO=] B[òt 0. 1 f0 = k{ (fa + fb + fc )} 2. (2.13). mYÊ±ZRMNXYÝj_v¹;è8mQRÐ eno t;áÁX~n>$i|>;/Á (2.12) eòt  . fα. . . 1 = 2 3 0 fβ. 1 2 √ 3 2. −. 1 2 √. 3 2. . . fa. . . 2     3  =  fb    0 fc. 1 3. 1 3. √1 3. − √13. . . fa. .      fb    fc. (2.14). Yªg;VWÑZfghVWXYfg]¸r/¸ròt . . . 1 0 f  a     1 √3   fb  =  2 2    √ 1 fc − 23 2. .    f  α    fβ. (2.15).

(42) 2 ÷ IJKLMN>uYZA 2.1.2. 10. >?ABKGCD(EFGHIJ. òj Ïr;VWÑZfg α Z]hÑZfg d ZO=]p~8 θ ; ¡ e −→f = f + jf \ÑfgO=]B[ò (2.16) ð (2.17) Ï r 2.2 −→ fαβ = fα + jfβ. e. r. d. q. − → −→ −jθe fr = fαβ e. (2.16). −→ − → fαβ = fr ejθe. (2.17). ð¬¯4];\ÑfgO=]hiB[/G8 . fd. . fα.  . fq. fβ. . . =. −sinθe cosθe. . . cosθe −sinθe. =. cosθe. sinθe. sinθe. cosθe. . fα. . fd.  . fβ. fq.  .  . (2.18). (2.19).

(43) 2 ÷ IJKLMN>uYZA 2.1.3. 11. LMNOFP. ³gj 2.3ÏrOIJKLMNr-qu.rÖj;RMN^XY _v8Ýj]ent;XY}wqã@CXYÝj]rÞ;^ ]]:=YZ/¸r8 (2.20) 2. 2. vs = va + vb ej 3 π + vc e−j 3 π. t. (2.20). (2.20) !]Y]RXYfg!]^_v2/¸rò va = rs ia +. dλa dt. (2.21). vb = rs ib +. dλb dt. (2.22). va = rs ic +. dλc dt. (2.23). d Λs dt. (2.24). +¯4/¸r8 Vs = Rs Is +. è!. . . . r 0 0 v  s  a     Vs =  vb  Rs =  0 rs 0    0 0 rs vc   λ 0 0   a   Λs =  0 λb 0    0 0 λc. ;. . ;.    . . . i  a    Is =  ib    ic.

(44) 2 ÷ IJKLMN>uYZA. 2.3: è! v MN^ a Y_vOY] v MN^ b Y_vOY] v MN^ c Y_vOY] i MN^ a Y_vOY^ i MN^ b Y_vOY^ i MN^ c Y_vOY^ r MN^_vOZ λ ¿ a YOJd> λ ¿ b YOJd> λ ¿ c YOJd> L ^_vDY]ÛËZ L ^_vDY]sËZ a. b. c. a b. c. s. a b. c. ss. ls. 12.

(45) 2 ÷ IJKLMN>uYZA 13 MN^R aebec Y]Jd λ eλ eλ ;DY*tÛËZ+_DY è:ÑY^hÔ=âYËb]ZÍB;±O¸rt a. b. c. λa = Lsasa ia + Lsasb ib + Lsasc ic + λf 2π 4π = Lss ia + Lss ib cos( ) + Lss ic cos( ) + Lls ia + λf cosθe 3 3 1 1 = (Lls + Lss )ia − Lss ib − Lss ic + λf cosθe 2 2 λb = Lsbsb ib + Lsasb ia + Lsbsc ic + λf cos(θe −. (2.25). 2π ) 3. 2π 4π 2π ) + Lss ia cos( ) + Lls ib + λf cos(θe − ) 3 3 3 1 2π 1 ) = − Lss ia + (Lls + Lss )ib − Lss ic + λf cos(θe − 2 2 3. = Lss ib + Lss ic cos(. λc = Lscsc ic + Lsasc ia + Lsbsc ib + λf cos(θe +. (2.26). 2π ) 3. 2π 4π 2π ) + Lss ib cos( ) + Lls ic + λf cos(θe + ) 3 3 3 1 1 2π = − Lss ia − Lss ib + (Lls + Lss )ic + λf cos(θe + ) 2 2 3 = Lss ic + Lss ia cos(. (2.27). è! λ 8hÎJ`RûY^_v]WJdQ +¯4¸ròt      f. L + Lss − 21 Lss λ − 12 Lss  ls  a      λb  =  − 21 Lss Lls + Lss − 12 Lss    λc − 21 Lss − 12 Lss Lls + Lss   λf cosθe     +  λf cos(θe − 2π  ) 3   2π λf cos(θe + 3 ). i  a      ib    ic. (2.28). ¯C^XYÝj]n;Á (2.10) w/Áe8      L + 3L λ 0 0  ls 2 ss  a      λb  =  0 0 Lls + 23 Lss    λc 0 0 Lls + 23 Lss   λf cosθe     +  λf cos(θe − 2π  ) 3   2π λf cos(θe + 3 ). i  a      ib    ic (2.29).

(46) 2 ÷ IJKLMN>uYZA 7ÁJde8òt]¯4e. 14. Λs = Ls Is + Λf. (2.30). u= (2.24) ð (2.30);\IJKLMNRVWXYfg]^] +¯4/¸ròt d Λs dt d = Rs Is + (Ls Is + Λf ) dt. Vs = Rs Is +. è!. .   Ls =  . 2.1.4. Lls +. 3 L 2 ss. 0. 0. Lls +. 0. 0. . 0 3 L 2 ss. ;. 0 Lls + 23 Lss.    . (2.31) (2.32). . λf cosθe   Λf =  λf cos(θe − 2π ) 3  λf cos(θe + 2π ) 3.     . GMQFP. òÏV;8¼82³>=]y=Ã~;+CMNh¤;R }hÎJ`>u.¹;)w¼fghi];Á^]VWXYf gh8h^]KL]hfg;¯ (2.16) w (2.5) /å − → fr = fd + jfq = e−jθe (fα + jfβ ) 4π. 2π. = k(e−jθe fa + ej( 3 −θe ) fb + ej( 3 −θe ) fc ). (2.33). ¯/}|VWXYfghKL]hfg]B[òt . . . cos( 2π 3. cos( 4π 3. cosθe f − θe ) − θe )  d  2     fq  =  −sinθe sin( 2π − θe ) sin( 4π − θe ) 3 3  3  1 1 1 f0 2 2 2. G8¯4e]\8. fr0 = Krs fs. . . f  a      fb    fc. (2.34). (2.35).

(47) 2 ÷ IJKLMN>uYZA è!. . fd. ;. fa. .         fr0 =  fq  fs =  fb      fc f0  cosθe cos( 2π − θe ) cos( 4π − θe ) 3 3   Krs = 32  −sinθe sin( 2π − θe ) sin( 4π − θe ) 3 3  1 2. Krs. . . O¯4òtÏr  cosθe. 15. 1 2. 1 2. −sinθe. 1.     . .     2π (Krs )−1 =  cos( 2π − θe ) sin( 3 − θe ) 1  3   4π 4π cos( 3 − θe ) sin( 3 − θe ) 1. Á (2.35) M¯4;/åKL]hfghVWXYfg]B[ òt fs = Krs −1 fr0. (2.36). å¼VWXYfghKL]hfg]B[ (2.36) 8;ÁO$wMN VWXY] (2.31) ]]e^Jdv!;/åKL]hZt h^]] Vs = (Krs )−1 Vr0 = Rs (Krs )−1 Ir0 +. d [(Krs )−1 Λr0 ] dt. (2.37). ÁrÑ4K + K ;ÁÑY ]Å±Ywð8ÑvYv;\ (2.37) /<A8 r s. d [(Krs )−1 Λr0 ] dt r −1 dΛr0 d(K s) Λr0 + = Rs Ir0 + Krs dt dt. Vr0 = Rs Ir0 + Krs. (2.38). KA;Áhi (2.36) $wJdù (2.30) !;/å Λs = (Krs )−1 Λr0 = Ls [(Krs )−1 Ir0 ] + Λf. (2.39).

(48) 2 ÷ IJKLMN>uYZA áÁrÑ4K + K ;ð<A/åt. 16. r s. Λr0 = Ls Ir0 + Krs Λs  L + 3L 0 0  ls 2 ss  =  0 0 Lls + 23 Lss  0 0 Lls + 32 Lss. ¡L. ;Á. . vd. .      vq    v0. id. . . 1. .           iq  +  0  λf     0 i0. (2.40). $w (2.38);ð<A/å. = Lls + 32 Lss (2.40)     0 id rs 0 0         =  0 rs 0   iq  +  ωe     0 i0 0 0 rs    dLs i 0 0  dt  d      s +  0 dL 0   iq  dt    s i 0 0 dL 0 dt  s r + dL −ωe Ls 0 dt  s  s =  ωe Ls rs + dL 0 dt  s 0 0 rs + dL dt s. . −ωe 0 0 0. .  . Ls. 0.     0   0   0 0. . Ls 0. 0. . id. . . 1. 0 i   d         iq  +  ωe  λf     0 i0. (2.41). êØ;¯ (2.41) /<AåIJKLMNRKL]hfgO ^]òt  . vd vq. . . =. rs + sLs. −ωe Ls. ωe Ls. rs + sLs.  . id iq. . . +. 0 ωe λf. .           0   iq  +  0  λf       0 i0 Ls. . . .  . (2.42). Á]+^Å±¸r;ðev/<A¬MNKL]h deq Z]^Å± did 1 rs = − id + ωe iq + vd dt Ls Ls. (2.43). 1 1 diq rs = − iq − ωe id + vq − ωe λf dt Ls Ls Ls. (2.44).

(49) 2 ÷ IJKLMN>uYZA 2.1.5. 17. RSTUVFP. ÊÁMNa³>)wU!;ÆÇÊ}|MN]a¤Þ ;á =MNh¯Áu.]o>w8J,^ (d Z^ ) h¯^ (q Z^ );öx}|^[]YZu.Q¯CYZ A][±sâ^MN[¶x;°ãä¯DZ^] ÎªNMNh¯];öxþhy_~M;+±sâ^M NaqrÖj 2.4ªM8u.}]ðCQ. 2.4: !" è! T c/,¯ T MNh¯ J h¤yZ B Zz[> ω hâ~y ¯j 2.4;á =MNa~y2~yO=]hiù L e. m. m. m. ωm =. 2 ωe P. (2.45).

(50) 2 ÷ IJKLMN>uYZA /ÁMN]a¤Þ¸ròt Te − TL = Jm. ωm 2 dωe + Bm ωm = (Jm + Bm ωe ) dt P dt. 18. (2.46). è! PMN[> xMNh¯/¯MN}w}|tZ{|}| 3 Te ωm = (vd id + vq iq ) 2. (2.47). Á (2.43) _ (2.44) w (2.47) !;!/+åMNh¯;L rh¯ q Z^=8Â½]B[ 3 Te = P λf iq = KT iq 4. è!. (2.48). h¯ë> }lØ;J= (2.43)e (2.44)e (2.46) _ (2.48);!/+åI JKLMN®¯YZA}8;hiKL]hfgt]MNu .uj;òj 2.5ÏrQ KT. 2.5: #$%&'(.

(51) 2 ÷ IJKLMN>uYZA 2.2 2.2.1. !"#$%&'(. 19. WXYZ[\. MN;R½¶}öL]¿!;~³ÔÂÊ]~;E~Â^ /+ñËbJ,]Ò½;áv]h] ;åÈ;/+ÇÈ]Á thi8at;b~R!û +ñ|,èG~]BÞQE% MNY}wq]K/±8Ñ¶â^MN^MNQ¯Câ^ MN=eD;MNhyËb¤¬j·;xMNh¯^¬ j·; ÊMN];!/+^;öxhy_h ¯;Ï+â^MNÍyeD_?6]Ò½;ÐãRMNO ;â^MN ñ/b~]Ê êQ¿â^MNêÍ à;¯CèhZ]<^^R]hÁ¹;ÌÍHxñ ë;2¼ÌÍÔ]H;"#]¨;úåâ^MN[R È],=!~;Ð¼èb~]ç¥Q ^MNJÍ;Ï+Íâ^MNÀ_~,=Ð ];xJ¶e¬*¶ô;ý'ªR/!;^MNR ûï,=!«µ$¼â^MNQÉRy_?-t;¯C^MN ]¤ÞÅ±ãE êÂ½ey=]YZëÅ±;èh¯XY ^YB;R>Ê |Bã×È]õQ|]^MN [òNo}wqÄ¸;[Áh¯^hi¬j·]B[;Ï+^M NRòâ^MN%×ÈQý'ª;R^cd[\]ö; E~fghi]B[;ÁMNX Yf 120 Y]XYfghiÑ âY]â~fg;+¢ô!]o>>Z;öx}åh¯ Ô=Hj·]B[;å^MNRhy_~]å+ÇÈ GH;ý$E~Ø|][\ÍâÁh¯[\ (Direct torque control) +_YZ[\rQ âÁh¯Êã^J8;Ædh¯ ¡h¯O =]@fyýCm;U ÀZd^]_^k+d|^ J_MNh¯;¾¿o¸|Yþb]]YZ;®¿oÄB}|k.

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(60) ] Nios @AB;Pw !Q SOPC Builder Âòj 3.4Ïr;4¼!8/+01l Nios @A B!]¹st_;ò@AB?¹>U]ÃÃeRAM _ ROM ] ×ZÎeTimer !?¹=]eUART Ä¸ðK?¹coeEthernet ste Progammable I/O Pin ]r;°/+Y¤ í]À

(61) ªM7=¼ SOPC Builder.

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(63) 3 ÷ IJKLMN?P67O01 3.1.3. 27. bR\c+,_5 -LabVIEW. R½¥]FG;ã~ National Instruments ùú] LabVIEW fT;LabVIEW ã8 Laboratory Virtual Instrument Engineering Workbench ]e F;ê8ÇÍ`B]st;/Á`ðBeÃD;>ejL rÈ¨âÁCº¼;+$GGTÅB]st;R/ ëÉÊª |=ùúñ#Ë]Å½¥Q è ¥òj 3.5ÏrQfT>¼ªÕj¸_ðB;/ Control bar !Ì£|ª;Æ í/+ÔÇÈ]+j]¥ÕÏ] `¥Q4¼8 Pq¼ (Panel);ÏÍÉÊ]ð Be³>;o>}we Íj}|¥°ãRØ¼=|`] q;®¿ í`Î8¬û]½¥©±w4¼8 uj¼ (Diagram);Ï ¹°ÌÍYþb]}w}|5Cuj !;xû!]FG©±üRØ¼«¬QRuj!/+Mj ]FG; ÊÌ£ Function bar !]ûïuÃkÀÁ] ¤Ã;ü/|ÉÊ];x/+Áë~]Î±-uv¬Ü ]stu;Cè:!Ì£b~;ú/(v]/½Q. 3.5: LabVIEW 34$5689.

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(65) 3 ÷ IJKLMN?P67O01 29 E%R FPGA >?67!Ã>@A¹;?¹> t¸N<>©±; ú ÐC<>=];\)wj0]8;Î>]¬¼Â à;Ð¹!"#)w Q ªÃ8>hi]¥;* Ï~]z{.Þ 8 Q14 ;/¯j 3.6g| Q14 Ï$¸]Öá;!òKR 14 ?¹_ 15 ?¹=âwE Î>à;Î>àO]?¹>+]ã¸ä(;Î>à O8]?¹>+±OE]ã¸äà;+Øª¸rÎ>þèÃ> Q. 3.6: Q14 HCDIJ >]7?¹ (most-significant-bit, MSB) ¼8Ík> (sign bit);+ Q14 ªg;/+¸r]7j> (0x7FFF) 8 1.99993896;x7Îc> (0x8000) 8 -2.0; Q15 ·¶;/¸r7j>8 0.99996948;7Îc>8 -1.0; (v Q ÕÖ/+(v»;Éé¢ô¼/¸r]>ç¥;¸ 3.28 ï Q Ï¸H]ç¥Q*G]6701ã+ Q14 8;Êã è/¸r]>ç¥å¿ ±1;¸rGæ]ßAç¥/å¿g£;å 67]¼~ç¥ 87½;xèlCê>xçèÛÕQ @ 3.2: K Q HL@ $MND@ %(ö Q15 %ö Q14 %ö Q0 %ö 7FFF. 0.99996948. 1.99993896. 32767. 3FFF. 0.49996948. 0.99993896. 16383. 1FFF. 0.24996948. 0.49993896. 8191. E000. -0.25000000. -0.50000000. -8192. C000. -0.50000000. -1.00000000. -16384. 8000. -1.00000000. -2.00000000. -32768.

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(67) 3 ÷ IJKLMN?P67O01 31 R67!ûstuk=]B[/gj 3.7RVòtKL] hZt]] v _ v ÌöwKL]hfghVWÑZfg]stu v!;hi¬8VWÑZ]] v _ v ;áöwVWÑZfghV WXYfg]stuv!;hi¬8VWXY]] v ev _ v ;x ØXYkl]Ìöwjklm nostuv!;ÁXYkh8( ] PWM k;+Ã8MN£¤]}|k;Ø PWM kÌ®¯¨©]o ÄBhi8MN]XY»]\ÃMN]XY}w;+£MNh¤QK ¹;¨©q]^ËdBÌÁè!ÑY^k¾¿¶·h>?67Áè b|l67!;¾¿ A/D b @AstuvÁb ]^kDE]é µê ¬XY^b k i ei _ i ;ØkÌ®¿VWXYfghV WÑZfg]stuv;ÁXY^b kh8VWÑZ]^b k i _ i ;á®¿VWÑZfghKL]hfg]stuv;hi8KL] hfg]^b k i _ i ;+±OöwJ,^B (d Z^ B ) +_h¯^B (q Z^B ) !ªö÷^];}| ]+ö÷MN]Q RMNh¤]K¹;MN]àB?]ñ| aebez XYb k;öwàBb @Astuv!;+}|MN]hy ω e2~ θ +_a~ θ ;è!2~Ìb jmkn>o¸stuv!;Y °\¹]2~o|jkn> sinθ emkn> cosθ +_cjkn> −sinθ +.ÓVWÑZKL]h=fghi~;xMNhy_a~ \ã±Ob Nios @AB!]hyBstuv+_~Bstu v; =¨ PC »®¯stuv}w]hy ¡ ω _~ ¡ θ ªö÷MN]y_?P;+«¬< MN?P67]s tQ d. q. α. β. a. a. α. b. b. c. β. d. q. e. e. m. e. e. e. e. m. ∗. ∗. c.

(68) 3 ÷ IJKLMN?P67O01 3.4. ;<=>?@. 32. IJKLMN]YZ¾C&pq[;/+±8X ª«]&p q^pqeypq+_?PpqQR&pq][\ t;"#ÍcdBÁb ]kcd|ª;|b67!Ã&pq;è !^pq~^ËdBÁY^]Î_YËb|jc]; ®¯¨©q!] A/D hiqÁ]hi8 A/D IC /µ]ç¥; ]¶·kë A/D IC h8>?k8;áëb67>]^b @A qMXY^kê ]¤Ã;è@A^_k]Noòj 3.8Ïrw xypq_?PpqÏÀ]b kÊãY°MN]{` aB (Encoder) ñ] AeBeZ XYk;|67> ¬hy_~ k;áb B!My_?P]&pqQ. 3.8: UVWX>? 7 3.4.1. dXef` dg. R^pq!;"#.b XY^k;®¯fghi8KL ]h d-q Zfgt]^k;áöw^B!M&pqQb ] ^kÏ®¿]^òj 3.8Ïr;Y^®¿^ËdB8;ÌÁjc 5 ìí]^Â½]h8jc 4 îÒ]];®¿qh8jc 5 îÒ] ]Ã8E]b k}|;¯C*GÏ~] A/D IC ¶·}wïþ ï8 2 îÒ;x¨©q] A/D IC ·¶»?8 1.65 îÒ;Ï+b.

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(73) 3 ÷ IJKLMN?P67O01 35 {àBb| AeBeZ XYk®¿ 8;/+}|MN~h y;è A/¯j 3.11!]koªlþ\MN]h¹;¤úûø ?]¾{ÿ?{ËdB+ñ| AeB Ñ Y?f 90 ]k;»dØÑ YkO=Y?]¨Ç 8/?|MN]jh;0Á AeB Yk ±OMetÅ±;ÁkM;ü/å&ãÄkQ ◦. 3.11: ]^_+abcdefghWX \å¿¼MNjh_&ãÄk;MN~!/+òt x åÏ\»d&ãÄkml¹;!?MN]jh;\MN?8j h¹;~øB!Y >;O\MN?8h¹;~øB!Y t >;òØü¹]g >&ãÄkmlü/ >|MN]Yþ~; xùþ~?\ã¾¿ Z Yk]»d«¬;Ï\MNh«E;Z YkÌñE ml;\E»dØml¹;!Á~øBöGwE ;òØEªMNÏhE;~øB!ÌÍEéùþ?]¤Ã;+ ~ >?@]Ô@f=¬MN~]d?@Q xMNhy]d\ãE~3 >&ãÄml>P]ªN ¬;òj 3.11tÏr;R T ]µÏ¹=!; >&ãÄk]ml>8 N ;Y¤Ø/+ |MNhy ω ;ùòt s. s. r. ωr =. 2π · Ns (rad/s) 4Np · Ts. (3.1). è! N 8àBøl²;ú!ãMNhEÏtñ]l>Q p.

(74) 3 ÷ IJKLMN?P67O01 36 àBb laq67st01òj 3.12Ïr;AeBeZ XYkÇ ±O®¿>?lB;®l@A8] phaephb kÇ®¿&ãÄk@ A;éµè_tk/å&ãÄk pls;?ñ|jh g dir;78á®¿yd_?P >q;@A¬MNhy dif pu _~ angle k;+Ã8àBb laq]}|kQ. 3.12: ^_+UV/_QRYZ[\ ¯C >BþCÙ] Y\ Ë;R AeB Yb köw&ã Älaq;ÌÇ®¿>?lBM@A;èqUòj 3.13Ïr;¯ X D .jBÃ8øB;E~ RS jBM23@A;~+2k o]4Ù+_¢ÞÙ;+b j] AeBeZ Yb kQÃ~X D .jBªM@A]P]8;ÇÍ¡]¹ºkzª«¬l]¤ Ã+_l@A¹=Ûa=¬]¹ºQ. 3.13: ^_+UVWXij+YZ[\.

(75) 3 ÷ IJKLMN?P67O01 3.5. 37. AB34. 8¼GHYZA;fghiÓ¼ÔÂÊ]?;R67 GH ¡¢¼VWXYfghVWÑZfg (clark uv )eVWÑZfghVW XYfg (clark inv uv )eVWÑZfghKL]hfg (park uv )eKL ]hfghVWÑZfg (park inv uv )e+_fghiÌ~]jmkn >o¸ (sincos table uverom uv )Q 3.5.1. klmno. RVWÑZKL]hfghi¹;Y v!Ì|HMN]h2~ θ ]jmkn>;è! θ /²³MN]]hx¯àBb laq x å;Ø¹á¾¿jmkn>o¸ü/å sinθ ecosθ _ −sinθ v;+«¬ VWÑZKL]hfghi]qQ *GÏ~]MN[>8&[;$¸MNhE¹/å 720 ] 2~o;xàB]l²8 2000 m

(76) ;®¿àBb lauv !]&ãÄlaq8;/å 8000 m

(77) ]l²;/å2~ 0 l 360 ]oÌ®¿ 4000 m

(78) Q>R2~ 360 ]oç¥! 2000 ]jkn>z{;$¸&ãÄm

(79) !;ÏÑ m

(80) !ÌÍEYþb]jk n>/®¯o¸´å;¯Ø/¿ÏÑ jkn>=]2~l²8 360 /2000 = 0.18 Q Rjkn>¸]GH;ÇE~ Matlab | 2000 16bit ]j kn>¸;CTC± *.mif(Memory Initialization File) !;TC ±]>×òj 3.14Ïr;O8E~ Quartus II fT!] Megafunction EF T (ROM);ÁûTC±)wè!ü«¬jkn>¸;è ñ|]ujòj 3.15ÏrQè!}w5 clock 8Eo¸k;\j 8o¸stu!ÌY¤}w]?8|Yþb]Ã}|;x 11bit ] address }w?k=¼ 2000 z{Z]Î;16bit ]jkn>} |k q ú=¼< 67jck 2’ æ>] 16 ?¹>]0Q e. e. e. e. e. ◦. ◦. ◦. ◦. ◦. ◦.

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(82) 3 ÷ IJKLMN?P67O01 . 39. 3.15: klmn4'( Rjmkn>o¸ (sincos table) stu!;Ájkn>¸+¹ (Component) ]MÁ§þb;ü/«¬jkn>o¸stw¯ Cmkn>jkn>Y?f 90 ;/¾¿Á~?e];}| 82~ 90 ]mk~;á$wjkn>¸ü/

(83) |û2~]mkn >;GHòt>}w]2~ θ ÎC 270 ;\ ÊÁ2~v 90 ojkn>¸ü/å θ ]mkn>;>2~C 270 ;\Á 2~à8 270 ;áÁèojkn>¸ü/å|mkn>wxck ]jkn>/âÁÁoå]jkn>M 2’ æ>ü/´å;j 3.16Ï rü8jmkn>o¸]67st01jQ ◦. ◦. e. ◦. ◦. e. ◦. 3.16: rustCDv@QRYZ'([\. ◦.

(84) 3 ÷ IJKLMN?P67O01 . 40. >?!@>?ABCDGH. 3.5.2. XY^b k®¿¶·h>?@A8;tELÊM]!ã¾¿fg hiÁVWXYfg]^h8VWÑZ]fg;Á^$w (2.14) !/åVWXYhVWÑZ]fghi¸r  . iα iβ. . . =. 2 3. 1 3. 1 3. 0. √1 3. − √13. . . ia. .      ib    ic. (3.2). è!;ê8XY^Ýj]no;è/Á (3.2) eòt  . iα iβ. . . =. 1. 0. 0. 0. √1 3. − √13. . . . i  a     ib     ic. (3.3). ¯ (3.3) /¿;Ê«¬VWXYhVWÑZ]fghi; Ì~ë > 1e _ − ]Y vQ 0E;}|]"#®¯fghiÁVWÑZfg]h8 VWXYfg];/+Æjkm nostuñ|ðBõi k;ä+£¤MNQÁ]w (2.15) !/åVWÑZhVWXY]f ghi¸r √1 3. √1 3. . . . 1 0 v  a     1 √3   vb  =  2 2    √ 3 1 vc − 2 2. .    v  α    vβ. (3.4). ¯ (3.4) /¿;Ê«¬VWÑZhVWXY]fghi; Ì~ ë> 1e e e_ − ]Y vQ ¯ (3.3) _ (3.4) /g|;RVWXYVWÑZ=]fghi Ì Íë>vY ]¤Ã;Ï+RGHØfghi][;!/+E~± v?eáYv]¤Ã;ªµ$PE [B;Ø[/+ð [BR FPGA 67!Ó~Ý¶Ô];+µ67Ô]~¬*Q 1 2. √ 3 2. √ 3 2.

(85) 3 ÷ IJKLMN?P67O01 41 ~±v?eáYv][O;ÊÇþÀY ]ë>vMj0_± l]¤Ã;j0]¤ÃãE~E 16 ?¹eQ14 ]>ªýx|ûë >;áÁûY°Yþb]?¹MÍ-?¹±l¸r]¤Ã;òØ!/ +E~±v?eáYv][ªGH +ûë>]>¸rQ +VWXYhVWÑZfghiùª;ë> ]j0_±l@ Aòt √1 3. 1 normalization √ = 0.57735 =⇒ 0010010011110011(16bit, Q14f ormat) 3 1 1 1 1 1 1 1 1 = + + + + + + + 2 16 128 256 512 1024 8192 16384. (3.5). ¯ (3.5) /g|; /+ýx8¯ _ <>éÏv¬]>; òØEª;R67>©GH; + Ð ë>!/+~±veáYv ]@AªGH;< VWXYfghVWÑZfg]67st01j/ òj 3.17Ïr √1 3. 1 2. 1 2. √1 3. 3.17:

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(87) $QRYZ[\.

(88) 3 ÷ IJKLMN?P67O01 42 x+VWÑZhVWXY]fghiùª;ë> _ ]j0 _±l@Aòt 1 2. √. 3 2. 1 normalization = 0.5 =⇒ 0010000000000000(16bit, Q14f ormat) 2 1 = 2. (3.6). √. 3 normalization = 0.866025 =⇒ 0011011101101100(16bit, Q14f ormat) 2 1 1 1 1 1 1 1 1 1 = + + + + + + + + 2 4 16 32 64 256 512 2048 4096. (3.7). KÏ];RVWÑZhVWXY]fghi!;ÏÀY ]ë>v _ ú/+®¯j0_±l]¤Ã¬8+ _ <>éÏv¬]>; R67]GHKÏ+±veáYv]@AªGH;< VWÑZf ghVWXYfg]67st01j/òj 3.18Ïr √ 3 2. 1 2. 1 2. 1 2. 3.18:

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