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1、單一的神經(jīng)網(wǎng)絡(luò)PI控制高可靠性直線電機(jī)磁浮摘要:本文論述了一種可以改善系統(tǒng)可靠性的新型線性鼠籠電機(jī)(linear induction motor, LIM)從LIM的標(biāo)準(zhǔn)電路方程考慮動(dòng)力學(xué)終端效應(yīng),當(dāng)制 動(dòng)特性同時(shí)作為影響力時(shí),可以建立包含有大的補(bǔ)償終端效應(yīng)的等效電路 模型。等效電路模型可以用作LIM的二次磁場(chǎng)定向控制。同時(shí)討論了單 神經(jīng)網(wǎng)路PI單元作為L(zhǎng)IM的輔助驅(qū)動(dòng)效果,驅(qū)動(dòng)控制的數(shù)學(xué)模型的有效 性通過(guò)模擬實(shí)驗(yàn)被證實(shí)。關(guān)鍵字:線性鼠籠電機(jī)(LIM),磁場(chǎng)定向控制,終端效應(yīng)-12- 刖言線性鼠籠電機(jī)是在低速磁浮系統(tǒng)中作為耐熱系統(tǒng),來(lái)驅(qū)動(dòng)車輛。LIM 之所以有終端效應(yīng)取決于它獨(dú)特的裝置。由動(dòng)力

2、學(xué)終端效應(yīng)產(chǎn)生的渦流動(dòng) 力導(dǎo)致了線性電機(jī)的額外損失,從而減少了推動(dòng)力。當(dāng)矢量控制策略應(yīng)用 于LIM時(shí),就必須考慮終端效應(yīng)的影響,并且建立更精確的數(shù)學(xué)模型來(lái) 完善控制系統(tǒng)的整體性能。在本文中,討論了在考慮終端效應(yīng)很大時(shí)LIM的電路方程,推導(dǎo)出 了 LIM的計(jì)算模型。智能控制方法被用來(lái)解決人力所難以操作的問(wèn)題。 而單神經(jīng)PI控制單元之所以能被用于LIM的輔助驅(qū)動(dòng)是由于它簡(jiǎn)單的構(gòu) 造。模擬實(shí)驗(yàn)已經(jīng)證實(shí)了這些模型在改善整體性能上的有效性和可靠性??紤]了終端效應(yīng)的LIM的電路方程在一個(gè)長(zhǎng)的二級(jí)類型的LIM中,和一級(jí)不同的是在二級(jí)類型中連續(xù) 更換了新材料,這種新材料傾向于抵制滲透通量的突然增加,且只允許空

3、 間間隙中滲透密度的逐漸積聚。在二級(jí)板塊的進(jìn)口端和出口端,因?yàn)榇磐?量的突然轉(zhuǎn)變,會(huì)產(chǎn)生渦流,這種感應(yīng)電流可以避免氣隙磁場(chǎng)的突然改變??紤]到動(dòng)力學(xué)終端效應(yīng),線性電機(jī)的有效長(zhǎng)度假設(shè)為1,二級(jí)參數(shù)轉(zhuǎn) 化為一級(jí)參數(shù),在二級(jí)核心的進(jìn)口端,渦流迅速增加,增加速率可以由下 式計(jì)算:T1=、/ Rr式中:Lr1由二級(jí)轉(zhuǎn)化為一級(jí)的滲漏電感系數(shù);Rr 由二級(jí)轉(zhuǎn)化為一級(jí)的等效電阻。因?yàn)門1 = Lr1 / Rr的值很小,故可以忽略。二級(jí)渦流可以迅速的達(dá)到一級(jí) 勵(lì)磁電流,而一級(jí)電流的渦流階段則相反。二級(jí)渦流的時(shí)間常數(shù)的減少可 以用下式描述:T2 =(Lm+ Lr1)/ Rr=Lr / Rr式中:LrLIM的電感系數(shù)

4、。在二級(jí)出口板上,渦流迅速增加至Im,然后隨著時(shí)間常數(shù)L的變化而降 低。瞬態(tài)過(guò)程見(jiàn)圖1.給予以上分析,終端效應(yīng)可以添加到等效電路中。圖1圖1: (a)氣隙磁動(dòng)力;(b)二級(jí)板磁動(dòng)力一級(jí)和二級(jí)之間的相對(duì)速度決定了氣隙磁場(chǎng)的分布。假設(shè)v是一級(jí)速度,在T2時(shí)間,一級(jí)的移動(dòng)長(zhǎng)度為vT2。一級(jí)通過(guò)二級(jí)的點(diǎn)的時(shí)間為:T = 1/v ,v則標(biāo)準(zhǔn)電機(jī)長(zhǎng)度為:在這里Q是一量剛的常數(shù),代表了在標(biāo)準(zhǔn)時(shí)間)/度下的電機(jī)長(zhǎng)度,二級(jí)渦流的平均值為:I2 eam jQ e - xdx = I2 eaQ 0皿 Q等效勵(lì)磁電流為:1 疽 Im - 12 ea /_-心 I /這里Imea是考慮了動(dòng)力學(xué)終端效應(yīng)的等效勵(lì)磁電流。消

5、磁效應(yīng)可以反應(yīng) 修正的勵(lì)磁電流,所以總的勵(lì)磁電流為:L -e-Q)/Q在進(jìn)口端二級(jí)渦流的虛擬值為:I =.:上件e - 2 xdx = I :12er,Q 0m 2Q進(jìn)口端的渦流損失:Pent廣 1 Mt1 Pent廣 1 Mt1 e -2Q2Q(7)出口端的渦流損失:p _ L I21 - e-Q )exit2TV(8)二級(jí)過(guò)程中總的渦流損失:1 - e-Q =12 Rm r 2Qeddy entry exit=I2R l - e-Q )/Q渦流損失可以定義為勵(lì)磁回路中的串聯(lián)電阻R (-e-Q)Q)。設(shè) f(Q)= ( - e-q )Q。圖2所示為考慮了終端效應(yīng)的T型等效電路。圖2圖2: L

6、IM的等效電路圖考慮了終端效應(yīng)的LIM模型在二級(jí)渦流的定向矢量控制中,同步參照系和二級(jí)渦流是一致的,在 q軸線上無(wú)分量。中rd=W2, Wrq=?;谝陨戏治觯琇IM模型的描述如下:u = R i + R f(Q) + i )+ 四* -v Vsd s sd rsd rd d 兀 1 sq、dv-u = R i +sp + v vsp s sp dt 兀 1 sd0 = R i + R f Q)( + i )+ Lr rd rsd rd dt0 = R i + G1 -v 2,日v d = G L f Q) + L G f Q)(15)(16)(17)(18)(15)(16)(17)(18)(

7、19)V = L i + L i sq S sq m rqv d = L (1 f Q) +(L L f Q & d0 = L i + L im sqr rq 3兀(.)F = V i-Vi 7e2sd sq sq sdG - f (Q )vIrd sq匕 f (Q) i i r1 i iL 1sq sd在式(19)中的第二部分,是終端效應(yīng)產(chǎn)生的動(dòng)力學(xué)動(dòng)力。單神經(jīng)網(wǎng)絡(luò)PI單元減少LIM模型中輔助驅(qū)動(dòng)系統(tǒng)的參數(shù)偏差很重要。智能控制方法被 用來(lái)解決人力所難以操作的問(wèn)題。而單神經(jīng)PI控制單元之所以能被用于 LIM的輔助驅(qū)動(dòng)是由于它簡(jiǎn)單的構(gòu)造。由于LIM中的氣隙很寬,而導(dǎo)致 的滲漏磁力流很大,所以很難

8、有一個(gè)精確的LIM模型。在LIM的輔助控 制中引入人工神經(jīng)網(wǎng)絡(luò)是很有用的。其中單神經(jīng)控制更為實(shí)用。單神經(jīng)網(wǎng) 絡(luò)的結(jié)構(gòu)圖見(jiàn)圖3。單神經(jīng)網(wǎng)絡(luò)的輸出為:氣(k )= r (k )-y (k )=e(k ),(20)七()=e()e -1)= Ae(k),(20)x (k)= e(k)- 2e(k 一1)+ e(k 一 2)圖3單神經(jīng)控制的圖3單神經(jīng)控制的PI單元其中Xj(k)(i=1、2、3),代表了常規(guī)PID調(diào)節(jié)器的整體單元、比例單元和 微分單元??刂破鞯妮敵鰹? TOC o 1-5 h z u(k)= u(k -1)+ K Xrn (k)x (k)/泛偵 |(21)L i=1 i L其中Iu (

9、 ) u maX u max最大限額,相當(dāng)于線性電機(jī)的最大拉力,權(quán)重因子為:M +1)=.()+門 r),(22)其中 r (k)= e(k(k)x (k)。ii圖4所示的是二級(jí)渦流定向控制模型的電路圖,有一個(gè)LIM、一個(gè)帶 有單神經(jīng)控制PI單元的速度反饋控制回路、一個(gè)PWM變壓器和一個(gè)矢 量控制器組成。圖4:帶有單神經(jīng)控制PI單元的二級(jí)定向控制模型注:圖4:帶有單神經(jīng)控制PI單元的二級(jí)定向控制模型注:ASR一速度調(diào)節(jié)器;ATR 一回路調(diào)節(jié)器;AWR一流量調(diào)節(jié)閥;SFB一速度反饋單元。結(jié)果和討論基于以上對(duì)數(shù)學(xué)模型和控制計(jì)算的分析,有人做了一個(gè)LIM的模擬實(shí) 驗(yàn),對(duì)單神經(jīng)PI調(diào)節(jié)和普通PI調(diào)節(jié)做

10、了對(duì)比。在輔助系統(tǒng)中所使用的 LIM型號(hào)是三相的,Y端連接兩極、2.5kW、50Hz、380V。LIM的參數(shù)是: Rs=4.097 Q, Rr=8.8 Q, Ls=0.1002H, Lm=0.0771H,Lr=0.08H, t =0.063m。圖5中所示是前面討論的LIM模型的模擬實(shí)驗(yàn)的結(jié)果。圖5:模擬實(shí)驗(yàn)結(jié)果。(a)速度;(b)電流id; (c)電流iq圖6所示為普通PI單元和單神經(jīng)網(wǎng)絡(luò)PI單元的速度追蹤實(shí)驗(yàn)結(jié)果的 比較。在模擬實(shí)驗(yàn)中可以看出,單神經(jīng)網(wǎng)絡(luò)PI調(diào)節(jié)的反應(yīng)速度很快,并 且穩(wěn)態(tài)誤差較小。,在階躍反應(yīng)中,速度波動(dòng)較小。本文討論了判斷LIM終端效應(yīng)的一種電路方程,此方程適用于終端效 應(yīng)

11、比較大時(shí)的條件。矢量控制的模型已經(jīng)提出,單神經(jīng)網(wǎng)絡(luò)PI單元已經(jīng) 被用于LIM的輔助驅(qū)動(dòng)。模擬實(shí)驗(yàn)的結(jié)論表明,終端效應(yīng)可以通過(guò)此過(guò)程 得到彌補(bǔ),并且控制系統(tǒng)的性能有所改善。單神經(jīng)網(wǎng)絡(luò)PI單元適用于控 制計(jì)算的設(shè)計(jì)。圖6:階段反應(yīng)的速度曲線參考文獻(xiàn)Boldea, I., Nasar, S.A., 1999. Linear electric actuators and generators. IEEE Trans. on Energy Conversion, 14(3):712-717.doi:10.1109/60.790940Duncan, J., Eng, C., 1983. Linear in

12、duction motor-equivalent-circuit model. Proc. IEE, 130(1):51-57.Sung, J., Nam, K., 1999. A New Approach to Vector Control for a Linear Induction Motor Considering End Effects. Conference Record of the IEEE IAS Annual Meeting1942284-2289.Takahashi, I., Ide, Y., 1993. Decoupling control of thrust and

13、attractive force of a LIM using a space vector control inventor. IEEE Trans. Ind. Appl., 29(1):161-167.doi:10.1109/28.195902Wu, X.M., 2003. Maglev Vehicle. Shanghai Science and Technology Press, Shanghai (in Chinese).Ye, Y.Y., 2000. Linear Motor and Its Control. Machine Press,Beijing (in Chinese).Si

14、ngle neuron network PI control of high reliabilitylinear induction motor for MaglevFANG You-tong, FAN Cheng-zhiAbstract: The paper deals with a new model of linear induction motor (LIM) to improve the reliability of the system. Based on the normal equation circuit of LIM considering the dynamic end

15、effect, an equivalent circuit model with compensation of large end effect is constructed when the end effect force at synchronism is of braking character. The equivalent circuit model is used for secondary-flux oriented control of LIM. Single neuron network PI unit for LIM servo-drive is also discus

16、sed. The effectiveness of mathematical model for drive control is verified by simulations.Key words: Linear induction motor (LIM), Field-oriented control, End effectINTRODUCTIONThe linear inductance motor (LIM) is used in such low-speed Maglev system as HSST system to drive vehicles (Wu, 2003). LIM

17、has the end effect owing to its unique configuration. The eddy current produced by the dynamic end effect causes additional loss of linear motor which reduces thrust (Duncan and Eng, 1983; Boldea and Nasar, 1999). When the vector control strategy is applied to LIM, the influence of the end effect mu

18、st be considered and an exact mathematical model should be constituted to improve the whole performance of the control system.In this paper, the equation circuit of LIM considering large end effect is discussed, and the calculation model of LIM is deduced. The intelligent control method is adopted t

19、o solve the problem of robustness. The single neuron control PI unit is adopted for LIM servo-drive because of its simple configuration. The simulation has validated the obvious effects of those methods on improving the whole performance, including reliability.EQUATION CIRCUIT OF LIM CONSIDERING END

20、 EFFECTIn a long secondary type LIM, as the primary moves, the secondary is continuously replaced by new material. This new part material tends to resist a sudden increase in flux penetration and only allows a gradual buildup of the flux density in air gap. Eddy current in the entry or exit end of s

21、econdary plate will be produced because of a sudden change of magnetic flux. This inductive current will prevent the change of air gap magnetic field (Sung and Nam, 1999).Considering the dynam ic end effect, the effective length of linear motor primary is supposed as l, and the secondary parameter i

22、s converted into the primarys. At the entry end of secondary core, the eddy current increases promptly, and the increasing rate can be decided by T1=Lr1/Rr (Lr1 is the secondary leaking inductance converted into the primarys, Rr is the secondary equivalent resistance converted into theprimarys).Beca

23、use T1=Lr1/Rr is very small and can be neglected, the secondary eddy current can reach the primary exciting current Im rapidly, while the phase of eddy current is contrary with primary current. The time constant of secondary eddy current decrease can be described as T2=(Lm+Lr1)/Rr=Lr/Rr (Lm is the m

24、utual inductance of LIM). At the exit of secondary plate, the eddy current increases to Im promptly, and then decreases with the time constant T1. The transientprocess is shown in Fig.1. Based on the above analysis, the end effect can be added into the equivalent circuit.Fig.l (n) Air g叩 Fig.l (n) A

25、ir g叩 inBnHie如旺;(b) Secondarypl* inagnetk motn e forctThe relative velocity between the primary and secondary decides the distribution of magnetic flux along air gap. Suppose v is the primary velocity, in T2 time the primary moves a length of vT2. The time of the primary passing a point on the secon

26、dary isTv=l/v.(1)Then normalize the motor lengthQ=l/(vT2)=vTv/(vT2)=Tv/T2=lRr/(Lm+Lr1)v,(2)where Q is a dimensionless parameter representing the motor length on the normalized time scale. The average value of secondary eddy current is effect. The demagnetizing effect can be reflected by amending the

27、 exciting current, so the total exciting current is:I2eaImjQeI2eaImjQe-xdx = I 上堂Q 0 QEquivalent exciting current isma m2 eam-e-Q )/Q(4)where Imeais the equivalent exciting current considering the dynamic end(5)The virtual value of the secondary eddy current at entry is(6)r 12 M 】 r 1 。*(6)I= y m J

28、Q e 2xdx = I 2-The eddy current loss at entry end is1 e 2QLry = 2/廣Q(8)The eddy current loss at exit end is p _ L 12( - e Q )_ 12 R ( e q ) exit2Tm r 2Q(8)The total loss of the secondary isP = P + P = 12 R ( e - q ) Q eddy entry exit m rThe eddy current loss can be described as a series resistance (

29、Rr(1-e-Q)/Q) in exciting circuit.Suppose f(Q)=(1-e-Q)/Q, the T-type equivalent circuit considered the end effect is shown in Fig.2.MODEL OF LIM CONSIDERING END EFFECTIn the secondary-flux oriented vector control, the synchronous reference frame is aligned to the secondary-flux. There is no component

30、 along the q axis, Wrd=w2, wrq=0. Based on above analysis, the LIM model is described as follows:一兄Fig. 2 Lquivaknt circuit for LIMusd=Rsisd+ usd=Rsisd+ Rf(Q)( + i )+ 竺-Tvvsd rd d 1 sq(10)usp=R*dVt+ d sp + v v (11)0 = 0 = R i + R f(Q)(+ i )+ dv-dr rd rsd rd dt(12)0 = R i +匕。1 -v2,0 = R i +匕。1 -v2,日=

31、(L - L f (Q) + L G - f (Q)(13)Vsd(14)Vsq=L i + L iS sq m rq(15)Vrd=L G - f(Q) d +(L-L(Q、(16)0 = L i0 = L i + L im sqrrq3(.)F=Vi-Vi7e2tsd sq sq sd(17)(18)G - f G - f (Q )VIrd sq(19)The second term in Eq.(19) acts as dynamic brake force caused by end effect.SINGLE NEURON NETWORK PI UNITIt is very impo

32、rtant to reduce the parameter deviation of LIM model for servo-drive system. The intelligent control method has been adopted to solve the problem of robustness. The single neuron control PI unit is adopted for speed control because of its simple configuration (Ye, 2000).Since the leaking magnetic fl

33、ux in LIM is quite large for its wide air gap, it is difficult to have an accurate model of LIM. It is useful to introduce the artificial neural networks into the LIM servo-control, where the single neuron control is more practical. The configuration of single neuron is shown in Fig.3. The input of

34、single neuron isFig.3 Siugle ue-uion connol PI unit氣(k)= r(k)-y(k)=e(k),x (k)= e()_ e( -1)= Ae(k),(20)x3(k)= e(k)- 2e(k -1)+ e(k - 2)where xi(k) (i=1, 2, 3) stand for integral unit, proportional unit and differential unit of normal PID adjustor.The output of controller isu(k)= u(k -1)+ K rn (k)x (k)

35、/ |(21)L i=1 i ii=wwhere U(k)l 恩max, Umax is the maximum of limitation, equal to themaximum given pull of linear motor. The weight factor is(22)(k +1)=(k)+門 r (k),(22)where r (k)=e(k)U(k貝(k)。iiFig.4 shows the block diagram of secondary-flux oriented control model, which consists of a LIM (Takahashi

36、and Ide, 1993), a speed feedback control loop with single neuron control PI unit, a PWM voltage source translator, and vector control translation components.fif.-l- Secandan-flui oriented coulral model with -mAVRpeeP Fig.4 shows the block diagram of secondary-flux oriented control model, which consi

37、sts of a LIM (Takahashi and Ide, 1993), a speed feedback control loop with single neuron control PI unit, a PWM voltage source translator, and vector control translation components.fif.-l- Secandan-flui oriented coulral model with -mAVRpeeP 性翻ator; ATR: Torue regulator;A i/R: Flux regulator; SFB: Sp

38、eed feedback unitRESULTS AND CONCLUSIONSBased on the above analysis of mathematics model and control arithmetic, a simulation for LIM is performed. Comparison between single neuron PI adjustment and normal PI adjustment has been performed. The LIM used in the serve system is three-phase Y-connected

39、two-pole 2.5 kW 50 Hz 380 V type. The parameters of LIM are: Rs=4.097 Q, Rr=8.8 Q, Ls=0.1002 H, Lm=0.0771 H, Lr=0.08 H, =0.063 m.Fig.5 presents simulation result by LIM model discussed above.the speedsingneuronstment istheesponse oi the speedsingneuronstment istheesponse oi unentsteady-state error is smaller.For step response, the speed fluctuation is small.Fig.6 shows the comparison of speed tracking with normal PI unit and(c)single neuron network PI unit. From the simulation, it can be concluded thatIn this paper, an equat

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