T k Current Reference Generator i k i qk Decoupling Control Cz Cz 1 Tu Vc Tu Vc T k T SVM qk θek θek SPMSM INV i uk uw i wk θ ek q k k T k Current Ref
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1 SPMSM Final-State Control for SPMSM Base on Voltage imit Circle with Transient Term -Examination of Feeforwar Input for Improving Torque Response- Takayuki Miyajima, Hiroshi Fujimoto (The University of Tokyo) Masami Fujitsuna (DENSO CORPORATION) Abstract SPMSMs (Surface Permanent Magnet Synchronous Motors) are employe for many inustrial applications SPMSM rive systems shoul achieve quick torque response an we operating range For quick response, authors propose final-state control base on voltage limit circle with transient term Final-state control rives an initial state to a final state with feeforwar input uring finite time The propose metho achieve quick torque control in fiel-weakening region but inverse response of torque was cause In this paper, a new feeforwar input which improves torque response is propose Simulations an experiments are performe to compare two types of feeforwar input In aition, in orer to analyze torque response uner voltage limit, the voltage limit circle of SPMSM with transient term is propose PWM (SPMSM, voltage limit circle, PWM hol moel, final-state control, linear matrix inequality ) 1 (Surface Permanent Magnent Synchronous Motor: SPMSM) (Electric Power Steering: EPS) EPS SPMSM, q IPMSM (1) () (3) (4) (FB) (5) (6) (FF) (7) (8) (9) SPMSM (MI) (1) FF (FSC ) q FSC SPMSM q SPMSM q SPMSM q y = x = T, u = v v q T (1), (), (3) } T ẋ(t)=a c (ω e )x(t)b c {u(t) ω ek e (1) y(t)=c cx(t) () R 1 ω Ac(ω e e) B c := ω e R 1 (3) C c I v, q :, q R: : ω e :, q :, q K e : T (4) T = K mt (4) K mt := P K e, P : (1) PWM (11) 1 ω e K e
2 T k Current Reference Generator i k i qk Decoupling Control Cz Cz 1 Tu Vc Tu Vc T k T SVM qk θek θek SPMSM INV i uk uw i wk θ ek q k k T k Current Reference Generator i k C 1z T ffk T ffk ˆxk P nz T u V c I C z T k ek ik H PWM (SVM) θ ek θ ek θ ek q uw SPMSM INV S (Tu) PWM (5), (6) T = T T q T ( T, q :, q ON ) V c : xk 1 = A s (ω e )xk B s (ω e ) T k T B s (ω e ) ω e K e (5) yk = C sxk (6) A s (ω e ) := e A c(ω e )T u, B s (ω e ) := e A c(ω e ) Tu Bc V c, ( ) B s (ω e ) := A 1 c (ω e ) e Ac(ωe)Tu I B c, C s := C c PWM FF (1) FB C(s) (7), (8) (9) PI C(s) T u Tustin Cz v v q > V max(v max: ) Cz v ref k=v ref k ω e k k (7) vq ref k=v qref k ω e k( k K e ) (8) C(s)= s R, τ = 1T u (9) τs T, q i, i q (8) (Space Vector Moulation: SVM) θ e (= 5ω e T u ) (13) (1) T T k k = T k T max if T k > T max T k otherwise (1) T max : q ON T k: 3 FF C 1 z, 3 FF C 1 z FB C z FF (5) (11) T ff k = B 1 s (ω e)a s(ω e)ˆxkb 1 s (ω e)x k 1 T ω e K e (11) B 1 s (ω e )B s (ω e ) i k 3 FSC Input Generator Inverse system B 1 s (ωe)as(ωe)ˆxk B 1 s (ωe)i k B 1 s (ωe)bs(ωe) ωeket C 1 z T ffk FF ˆxk := î k î qk T (1) FF FSC FF FF FF 1 FB C z C z FB Cz (8) MI MI FF (5) SPMSM PWM k =, 1,, N 1 (1) ω e = const ω e MI Y = ΣU (1) Y := xn A N s x Σ U EMF (13) Σ := A N 1 s B s A N s B s B s (14) Σ := A N 1 s B s A N s B s B s (15) T 1 U := T T T T 1 T T N (16) U EMF := ω e K e 1 1 T (17) (1) U (18) J = E T QE, Q > (18)
3 E := e1 T e T en T T (19) ek := i xk = i i q T xk () T A := A s A s A N s (1) B s A s B s B s B := () A N 1 s B s A N B s B s B s A s B s B s B := (3) A N 1 s B s A N s B s B s I := (i ) T (i ) T (i ) T T (4) E (5) E = I Ax BU B U EMF (5) Σ ΣΣ =, ΣΣ = I Σ R N (N ), Σ R N (6) Ũ U := Σ Σ Ũ (6) (6) (1) Y = I Ũ q R (N ) 1 T Ũ = Y q (7) (18) (5), (6), (7) (8) J = R(q) S(q) T QS(q) (8) Z := I Ax BΣ Y B U EMF (9) R(q) := Z T QZ Z T QS(q) (3) S(q) := BΣ q (31) γ J < γ MI (3) (9) γ R(q) S(q) T > (3) S(q) Q 1 MI SPMSM (33) T T k T k T max (k =, 1,, N 1)(33) 1 i (i 1) 1 g(i) R N (i := k 1) g(i) N MI (33) (34) I U(q) T g(i) T g(i)u(q) T max (34) 1 SPMSM Inuctance 18 mh Resistance R 157 Ω Pairs of poles P 4 Back EMF constant K e 746 mv/(ra/s) (3), (34) γ q SPMSM PWM x xn N FSC U 3 1 q q 1 1 (i 1) 1 f(i) R 1 N f(i) (k 1)T u q k 1 (35) k 1 = f(i) (Ax BU B U EMF ) (35) q (36) f(i) (Ax BU B U EMF ) (36) (3), (34), (36) γ q SPMSM PWM x xn N q FSC U FSC 4 SPMSM 1 T u=1 ms, V c =36 V 1 rpm 4 V V max = 3 c 3 T, T max = 3 u 3 V a = 95V max q ON T a, q ON ( )δ (37) T a = T T q, δ = tan 1 T (37) T q 4(c), 4(g), 4(k) T max ( ) FB FB
4 (a) (Conventional) (e) (Propose 1) (i) (Propose ) (b) (Conventional) (f) (Propose 1) (j) (Propose ) Amplitue of input ms Amplitue of input ms Amplitue of input ms (c) T a (Conventional) (g) T a (Propose 1) (k) T a (Propose ) 4 (Propose 1: N = 4, Propsoe : N = 49) 1, Q = I FSC N 1 N = 4 N = 49 1 q q q 1 1 q 5 (9 ms) rpm V c = 8 V V cn 36 V θ = 9ω et u 5 1, FSC FSC FF Angle of Input ra Angle of Input ra Angle of Input ra () δ (Conventional) (h) δ (Propose 1) (l) δ (Propose ) N FF FF q 1 q q q (1) SPMSM q (v vq Vmax) (38) ( Vmax ) ( C ) ( C q ) (38) C = R ω e (39) C q = ω e R ωeke iq (4) C, C q, q, q, q,
5 iq iq iq iq (j) iq (Propose ) (i) (Propose ) 図 () δ (Conventional) (h) δ (Propose 1) (l) δ (Propose ) (k) Ta (Propose ) 実験結果 (Propose 1: N = 4, Propsoe : N = 49) i q C i q i < i Cq i i q > 図 6 過渡項を考慮した電圧制限円 (ωe 力行) 6 電 圧 制 限 下 に お け る SPMSM の 電 流 応 答 ωe 力行を考えると C, Cq となる よっ て 図 6 に示すように過渡項を考慮した電圧制限円の中心は q 座標の第四象限上に存在する ここで ωe, iq の 動作点において所望する応答は i かつ i q という 第二象限の領域である しかしながら 電圧制限円の中心は 第四象限上にあるために所望の第二象限は狭く 高速な応答 は期待できない また i q が最大となる点は第一象限上にあ り i となってしまう 以上より 第二象限上の領域を広げる操作が必要となる そこで 式 (39), (4) を, iq で偏微分すると 式 (41), (4) を得る C R =, ( ) C = ωe, iq 4 (g) Ta (Propose 1) (f) iq (Propose 1) (e) (Propose 1) iq (c) Ta (Conventional) (b) iq (Conventional) (a) (Conventional) 1 Amplitue of input ms 3 iq Phase of input ra 5 75 Phase of input ra 1 Phase of input ra Amplitue of input ms Amplitue of input ms Cq = ωe (41) ( ) Cq R = (4) iq これより 電圧制限円の中心は i < によって第一象限の 方向に推移し i q > によって第四象限の方向に推移する 図 7 高速駆動における過渡項を考慮した 電圧制限円中心の推移 (ωe 力行) となるた 特に弱め界磁制御が必要な高速域では ωe R め 図 7 のように C の変化は i q Cq の変化は i が支配的 となる つまり i q > によって第二象限上の領域がさらに減少す るため 過渡応答の始めに q 軸電流変化量を大きく取るのは 好ましくない 一方 i < によって q 軸切片が増加する ため 予め負の 軸電流を優先的に流すことで q 軸電流変 化量を改善できる また 負の 軸電流を過剰にすることで i > とできるため 第一象限上の点も選択することができ る 第一象限は i q の最大点が存在するため 高速な q 軸電 流応答が実現できる さらに q 軸電流の逆応答を許容でき れば 第三象限上の点を選択することで i を負に大きくで きる 以上の動作を行うことで高速な応答を実現できる シミュレーションにおける過渡項を考慮した電圧制限円中 心の推移をプロットしたものを図 8 に示す 従来法では 円 の中心が第一象限へ推移していたのが 徐々に 軸方向に推 移しており 第二象限上の領域を減らしている これにより
6 1 1 1 /t A/ms 1 Center of Circle /t A/ms 1 Center of Circle /t A/ms 1 Center of Circle i /t A/ms i /t A/ms /t A/ms (a) Conventional 8 (b) Propose 1 ( ) (c) Propose q 1 q q q q q 1 q q PWM 7 (8) FSC q FSC q 1, q FSC PI 1 B-H Bae an S-K Sul: A Novel Dynamic Overmoulation Strategy for Fast Torque Control of High-Saliency- Ratio AC Motor, IEEE Trans In Appl, Vol41, No4, pp , 5 S eruomsak, S Doki, an S Okuma: Voltage imiter Calculation Metho for Fast Torque Response of IPMSM in Overmoulation Range, The 35th Annual Conference of the IEEE Inustrial Electronics Society, pp , 9 3 K Kono, K Matsuoka, Y Nakazawa, an H Shimizu: Torque fee-back control for salient pole permanent magnet synchronous motor at weakening flux control range, IEEJ Trans IA, Vol119, No1, pp , 1999 (in Japanese) 4 T-S Kwon, G-Y Choi, M-S Kwak, an S-K Sul : Novel Flux-Weakening Control of an IPMSM for Quasi- Six-Step Operation, IEEE Trans In Appl, Vol44, NO6, pp17 173, 8 5 H Nakai, H Ohtani, E Satoh, an Y Inaguma: Development an Testing of the Torque Control for the Permanent-Magnet Synchronous Motor, IEEE Trans In Electron, Vol5, No3, pp8 86, 5 6 W Hatsuse, Y Notohara, K Ohi, K Tobari, K Tamura, C Unoko, an Y Iwaji: A Stable Fiel-Weakening Control Using Voltage Phase Operations in the High- Power Region, The 1 International Power Electronics Conference, pp599 64, 1 7 T Totani an H Nishimura: Final-State Control Using Compensation Input, Trans of the SICE, Vol3, No3, pp53 6, T Miyajima, H Fujimoto, an M Fujitsuna: Proposal of Flux-Weakening Control for SPMSM Base on Final State Control Consering Voltage imit, IEE of Japan Technical Meeting Recor, IEE Japan, SPC-11-8, pp19 4, 11 (in Japanese) 9 M Hirata, T Hasegawa, an K Nonami: Seek Control of Har Disk Drives Base on Final-State Control Tracking Account of the Frequency Compensates an the Magnitue of Control Input, The 7th International Workshop on Avance Motion Control, pp4 46, 1 S Boy, E Ghaoui, E Feron, an V Balakrishnan: inear Matrix Inequalities in System an Control Theory, Society for Inustrial an Applie Mathematics, K P Gokhale, A Kawamura, an R G Hoft: Deat beat microprocessor control of PWM inverter for sinusoal output waveform synthesis, IEEE Trans In Appl, Vol3, No3, pp91 91, K Sakata an H Fujimoto: Perfect Tracking Control of Servo Motor Base on Precise Moel with PWM Hol an Current oop, The Forth Power Conversion Conference, pp , 7 13 J Kuo, T Noguchi, M Kawakami, an K Sano: Mathematical Moel Errors an Their Compensations of IPM Motor Control System, IEE of Japan Technical Meeting Recor, IEE Japan, SPC-8-5, pp5 31, 8 (in Japanese)
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(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x
![(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x](/thumbs/104/162595168.jpg "(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x")
Compton Scattering Beaming exp [i k x ωt] k λ k π/λ ω πν k ω/c k x ωt ω k α c, k k x ωt η αβ k α x β diag + ++ x β ct, x O O x O O v k α k α β, γ k γ k βk, k γ k + βk k γ k k, k γ k + βk 3 k k 4 k 3 k
ＷＴ3000 プレシジョンパワーアナライザ ユーザーズマニュアル
WT3000 IM 760301-01 8th Edition: February 2014 (YMI) All Rights Reserved, Copyright 2004 Yokogawa Electric Corporation All Rights Reserved, Copyright 2013 Yokogawa Meters & Instruments Corporation YOKOGAWA
2005 1
2005 1 1 1 2 2 2.1....................................... 2 2.2................................... 5 2.3 VSWR................................. 6 2.4 VSWR 2............................ 7 2.5.......................................