uk j Shft-Senorle Speed Control of the Permnent Mgnet Synchronou Motor under Periodiclly Time-Vrying od ƒf NSC 87--E-009-07 86 8 87 7 knping @cc.nctu.edu.tw o uk j ¼v kƒ Utkin ¼ j uk j ¼ j j¼ uk j j ukj¼ ƒ u ƒ k q k w k ƒ (encoder g (reolver (tchometer šg ä¼ å gk jw ¼ j g jk k kˆn kˆjkm vš 0 90 80 70 š km (ck emf š [~] um j kˆ m n k m v n v z g g n¼ Jone & ng [4] ow, ee & Chng [] uenerger [6] ƒ ¼ ƒk ¼ (loclly tle Cho, ong, Oh, & Youn [7] Wlcott & Zk [8] ¼ ky i, i ¼ u, Zhu, i, & Go [9] Utkin [0] ¼ k ¼ [] [] Utkin Wlcott & Zk ¼ ¼ [] y [] uk ¼ k m
i, i ¼ Chen & Chin [] k m k ¼ ¼ k j uk uky di R = i in ( v ( dt di R = i co ( v ( dt d = ( dt d = i in( i co( dt B τ (4 i i mv v m τ n B k R m K u ( ~ (4 ƒ (Prk trnformtion [4] k n exp( J i = exp( J i ( v = exp( J v (6 i = i i i = [ i i ] T [ ] T v [ ] T = v v [ ] T 0 v = vd vq J = 0 ( (6 (~(4 di d R = id Niq vd (7 dt d q diq R = iq Nid vq (8 dt d = (9 dt d B = iq τ (0 dt k p k τ = τ 0 ( τ 0 n τ& = 0 ( τ = τ0 A in( t φ ( τ& = Aco( t φ (4 & τ = A in( t φ = ( τ τ0 ( τ 0 A φ τ = τ τ = τ& ( ~ ( τ& 0 0 0 0 τ0 τ& = 0 0 τ (6 τ& 0 τ [][] Utkin ¼ (Sliding mode oerver uk ¼ k kn nk mz¼ nk ¼ d S = i ˆ i (7 S = i ˆ i (8 uk ¼ & R i in( gn( i = v K S (9 & R i co( gn( i = v K S (0 & = ( & = in( co( τ i N i N B
G K gn( S G gn( S ( & τ = G K gn( S G K gn( S 4 ( î î ˆ ˆ τˆ n( ~ (4 ( (9 ~ ( ˆ ˆ ƒš u kn R S& = S ˆ co( ˆ e in( ˆ e K gn( S (4 R S& = S ˆ in( ˆ e co( ˆ e - K gn( S ( = e (6 = S in( iˆ co( ˆ e S co( ˆ iˆ in( ˆ e B e eτ G gn( S G gn( S (7 eτ = G gn( S G4 gn( S (8 e = ˆ e = e τ = τ τ K co( N e in( N e, K > mx, (9 in( N e co( N e rn S & S &S S m gn( = N e N e eq co( in( K gn( S = in( N e N e eq co( [ K S ] [ ] (0 ( G = M (in( N N co( ( G = M (in( N N 4 co( ( (0~((6~(8 0 0 co( i N in( in( i N B G e = co( co( G N G e τ e e τ G in( N M M 0 (4 λ λ λ τ (4 ¼ } M ( ( λ λ λτ = G = G ( λλ λλ τ λλ τ λλ λ τ N co( N in( N i N co( in( N co( N i N in( B ( λ λ λτ K N (6 uk j ¼(9 ~ ( j¼ ˆ 0 4 τ & = G gn( S G gn( S (7 τ ˆ & = τˆ G gn( S G6 gn( S (8 τ ˆ & ˆ = (ˆ τ0 τˆ G7 gn( S G8 gn( S (9 ¼ } ( ( G (in( ˆ co( ˆ = M (40 G = M (in( ˆ co( Nˆ (4 6 G (in( 7 = M ˆ co( ˆ (4 G (in( ˆ co( ˆ 8 = M (4 ºƒ n
0 0 0 0 co( i N in( in( i N B G & co( co( e G N G 0 0 e e τ 0 = & in( e G eτ 0 τ e τ τ eτ M M 0 0 0 M M 0 0 M M ( τ 0 τ 0 (44 e τ 0 = τ0 τ0 e τ = τ τ e τ = τ τ λ λ λ λ 4 λ (44 ¼ } M M M G G P M = M = P P Q ( ( M = ( Q ( 0 G = G P co( ˆ in( ˆ (4 (46 τ τ (47 ˆ in( ˆ ˆ co( ˆ K N = λi P = λλ i j i= i=, j=, i j P4 = λλλλ i j k l i=, j=, k=, l=, i j k l ˆ Q P ˆ iˆ co( N iˆ in( N P B ˆ ˆ P = λλλ i j k i=, j=, k=, i j k P = λλλλλ 4 (48 P Q = P NP N P 4 N ( ( N ( τ0 τ P Q = P P Q N ( ( me uk¼ k. kz R =. ( Ω = 64. 0 ( kg m N = 4 K = 79. 0 ( V/rd = 97. 0 ( B = 806. 0 ( Nm/rd k ( { #7CB0-SE6F [] j (two-loop controller mj ~ λ p = z λ = 0 z λ c = 00 z 000rpm u Utkin ¼ ¼ [] u¼ k j τ = 0. 0.* in( t Nm (49 ¼ ku¼ ~ k j¼ n j j j {#7CB0- SE6F k ( UT-90 (m g~ f 86 me v¼ j mj PI kz 4 kzj ~ 0 z 00 z k k j ¼ ƒ y i¼ ~ j¼ y jn u¼j kj k j Utkin ¼ 4
j¼ j k n n j j ¼ j z j ¼ ¼ ¼ ¼ ¼ * 000 Velocity Controller i * d = 0 i q * Current Controller i d i q v d v q 0.4.0ec. Spce Vector V, τ ¼ - to d-q Utkin Sliding Mode Oerver PWM ignl Genertion i i iu, iv, i PMSM / Time(. Wu, R. nd G.-R. Slemon, A Permnent Mgnet Motor Drive without Shft Senor, Conference Record-IAS Annul Meeting, pp.~8, 990.. oque, M.-A. nd M.-A. Rhmn, Speed nd Poition Senorle Permnent Mgnet Synchronou Motor Drive, Cndin Conference on Electricl nd Computer Engineering, v., pp.689~69, 994.. Xing, Y.-Q. nd S.-A. Nr, Etimtion of Rotor Poition nd Speed of Synchronou Reluctnce Motor for Servodrive, IEE Proc.-Electr. Power Appl., Vol.4, No., My 99. 4. Jone,.-A. nd J.-. ng, A Stte Oerver for the Permnent-Mgnet Synchronou Motor, IEEE Trn. on Indutril Electronic, Vol.6, No., pp.74~8, 989.. ow, T.-S., T.-. ee, nd K.-T. Chng, A Nonliner Speed Oerver for Permnent-Mgnet Synchronou Motor, IEEE Trn. on Indutril Electronic, Vol.40, No., pp.07~6, 99. 6. uenerger, D.-G., An Introduction to Oererver, IEEE Trn. Auto. Control, Vol.AC- 6, No.6, pp.94~60, 97. 7. Cho, K.-Y., S.-S. ong, D.-. Oh nd M.-J. Youn, Speed Control of Permnent Mgnet Synchronou Motor Uing Bouundry yer Stte Oerver, Electronic etter, 6th, Vol.6, No., pp.08~08, 990. 8. Wlcott, B.-. nd S.-. Zk, Oervtion of Dynmicl Sytem in The Preence of Bounded Nonlineritie/Uncertintie, Proceeding of th
Conference on Deciion nd Control, Athen, Greece, pp.96~966, 986. 9. u, J., D. Zhu, Y. i nd J. Go, Appliction of Sliding Oerver to Senorle Permnent Mgnet Synchronou Motor Drive Sytem, PSEC Record- IEEE Annul Power Electronic Specilit Conference, v., pp.~6, 994. 0. Utkin, V.-I., Sliding Mode in Control nd Optimiztion, Springer-Verlg, New York, pp.07~0, 99.., m, u, 994.., uk, u, 996.. Chen, J.-J. nd K.-P. Chin, The Complete Oervility of Speed Senorle PMSM Control Sytem, umitted for puliction, 998. 4. Fitzgerld, Kingley C., Jr nd S. Umn D., Electric Mchinery, McGrw-ill, 990. 6