基于 MATLAB6的磁化曲線擬合

基于MATLAB6.5的磁化曲線擬合一、問題的提出。在進(jìn)行感應(yīng)電機(jī)磁路計(jì)算時(shí)，需要根據(jù)定轉(zhuǎn)子齒部和軛部磁通密度確定相應(yīng)的磁場強(qiáng)度。數(shù)據(jù)手冊中磁通密度和磁場強(qiáng)度是以數(shù)據(jù)表的形式給出的。因此，在確定磁場強(qiáng)度時(shí)就有必要進(jìn)行查詢。采用直接查表然后進(jìn)行帶入運(yùn)算在進(jìn)行手算程序時(shí)對(duì)精度要求不是很高的情況下尚可滿足要求。但是在進(jìn)行計(jì)算機(jī)電機(jī)程序設(shè)計(jì)時(shí)，通過查詢數(shù)表操作來完成運(yùn)算時(shí)卻顯得很不方便。最關(guān)鍵的是直接查詢數(shù)表有相當(dāng)大的局限性。對(duì)與哪些沒有落在數(shù)表內(nèi)點(diǎn)上的數(shù)據(jù)，往往要進(jìn)行局部線性化的近似處理，這就給程序設(shè)計(jì)帶來了一定的麻煩。因此，是否可以通過找到一個(gè)與一系列離散數(shù)據(jù)高度擬合的連續(xù)曲線來通過代入任意一個(gè)磁通密度值確定磁場強(qiáng)度？二、問題分析。本問題中涉及到的鐵磁物質(zhì)型號(hào)為D23，在《電機(jī)設(shè)計(jì)?機(jī)械工業(yè)出版社》一書附錄5中對(duì)應(yīng)有磁通密度和磁場強(qiáng)度數(shù)據(jù)150組。將這150組數(shù)據(jù)描點(diǎn)后必有一條曲線與這150組數(shù)據(jù)高度擬合。考慮到傅里葉級(jí)數(shù)定義任何周期函數(shù)都可以用正弦函數(shù)和余弦函數(shù)構(gòu)成的無窮級(jí)數(shù)來表示，若對(duì)一個(gè)非周期函數(shù)進(jìn)行周期延拓后便可適用于傅里葉級(jí)數(shù)分解。由此，可以假設(shè)任取一個(gè)經(jīng)周期延拓的非周期函數(shù)曲線上的一段，可以表示成正弦函數(shù)和余弦函數(shù)級(jí)數(shù)的和的形式。因此，借助于MATLAB6.5,可以選用三角函數(shù)sinx,cosx,sin2x,cos2x,?sin(mx),cos(mx)為基底函數(shù)，進(jìn)行最小二乘法擬合。MATLAB6.5中命令x=lsqcurvefit(fun,x0,xdata,ydata)

[x,resnorm]=lsqcurvefit(fun,x0,xdata,ydata)的功能是根據(jù)給定的數(shù)據(jù)(xdata,ydata),按函數(shù)文件fun給定的函數(shù)，以x0為初值作最小二乘擬合，返回函數(shù)fun中的系數(shù)向量x和殘差的平方和范數(shù)resnorm。根據(jù)以上分析，函數(shù)文件fun中的函數(shù)可定義為f=A1sinx+A2cosx+A3sin2x+A4cos2x+A5sin3x+A6cos3x+?三、問題解決。根據(jù)以上分析，編寫m文件，對(duì)磁化曲線進(jìn)行擬合，源程序如下所示。源程序段1：定義擬合函數(shù)文件，保存名為hanshu.mfunctionf=hanshu(a,B)f=a(1);fori=1:1:30f=f+a(2*i+1)*cos(B.*(i))+a(2*i)*sin(B.*(i));end源程序段2：磁化曲線擬合函數(shù)，保存名為magnetization_curve_fit.m%%%%%%%%%%%%%%%%%%%%%%%%%%%%中小型三相感應(yīng)電動(dòng)機(jī)電磁計(jì)算程序%%%%%%%%%電機(jī)設(shè)計(jì)作業(yè)——磁路計(jì)算;%%%%%%姓名：孫鵬學(xué)號(hào)：08044017班級(jí)：08044017;%%%%已知數(shù)據(jù)：輸出功率PN=13KW,電壓U1=380V(A-△接法)，相數(shù)m1=3，頻率f=50Hz，極數(shù)2p=6，同步轉(zhuǎn)速n1=1000r/min,效率n=0.875,功率因數(shù)cos?=0.83;clcclearB=0.40:0.01:1.89;H=[1.38,1.40,1.42,1.44,1.46,1.48,1.50,1.52,1.54,1.56,...1.58,1.60,1.62,1.64,1.66,1.69,1.71,1.74,1.76,1.78,...1.81,1.84,1.86,1.89,1.91,1.94,1.97,2.00,2.03,2.06,...2.10,2.13,2.16,2.20,2.24,2.28,2.30,2.36,2.40,2.45,...2.50,2.55,2.60,2.65,2.70,2.76,2.81,2.87,2.93,2.99,...3.06,3.13,3.19,3.26,3.33,3.41,3.49,3.57,3.65,3.74,...3.92,4.01,4.11,4.22,4.33,4.44,4.56,4.67,4.80,...5.07,5.21,5.36,5.52,5.68,5.84,6.00,6.16,6.33,...6.52,6.72,6.94,7.16,7.38,7.62,7.86,8.10,8.36,8.62,...8.90,9.20,9.50,9.80,10.1,10.5,10.9,11.3,11.7,12.1,...12.6,13.1,13.6,14.2,14.8,15.5,16.3,17.1,18.1,19.1,...20.1,21.2,22.4,23.7,25.0,26.7,28.5,30.4,32.6,35.1,...37.8,40.7,43.7,46.8,50.0,53.4,56.8,60.4,64.0,67.8,...72.0,76.4,80.8,85.4,90.2,95.0,100,105,110,116,...122,128,134,140,146,152,158,165,172,180];a0=zeros(1,61);[a,resnorm]=lsqcurvefit(@hanshu,a0,B,H)y1=a(1);fori=1:1:30y1=y1+a(2*i+1)*cos(B.*(i))+a(2*i)*sin(B.*(i));endplot(B,y1,'r')holdonplot(B,H,'.')運(yùn)行magnetization_curve_fit.m文件，程序運(yùn)行結(jié)果如下圖所示。8I-16L4020In一80604020on-圖一擬合磁化曲線附圖說明：圖中藍(lán)色的散點(diǎn)是已知的150組磁通密度和磁化強(qiáng)度的描點(diǎn)圖，紅色曲線為用最小二乘法擬合出的函數(shù)曲線。由源程序段2可知，擬合函數(shù)總共有61項(xiàng)，其中a(1)為常數(shù)項(xiàng)，其余為三角函數(shù)項(xiàng)。由運(yùn)行所得圖像可見，上述程序進(jìn)行擬合的程度是很好的，通過增加擬合函數(shù)的項(xiàng)還可以進(jìn)一步提高擬合程度。擬合數(shù)據(jù)分析見EXCEL工作表“D23磁化曲線擬合數(shù)據(jù)”現(xiàn)將數(shù)據(jù)處理結(jié)果列表如下。

表電工硅鋼薄板（0?5mm）的磁化曲線擬合數(shù)據(jù)說明：B25=1.54T(D23),B、H為已知磁通密度和磁場強(qiáng)度，I丫為擬合后對(duì)應(yīng)的磁場強(qiáng)度單位：H-A/cmB-TB0.40.410.420.430.440.450.460.470.480.49H1.381.41.421.441.461.481.51.521.541.56H'1.38661.41581.4411.45941.47111.47861.48481.49311.5061.525誤差0.48%1.12%1.46%1.33%0.75%0.09%1.02%1.80%2.26%2.30%B0.50.510.520.530.540.550.560.570.580.59H1.581.61.621.641.661.691.711.741.761.78H'1.55051.58151.61621.65251.68771.721.74761.771.78731.8006誤差1.90%1.17%0.24%0.76%1.64%1.74%2.15%1.69%1.53%1.14%B0.60.610.620.630.640.650.660.670.680.69H1.811.841.861.891.911.941.9722.032.06H'1.81151.82221.83481.85121.8731.9011.93521.9752.01892.0654誤差0.08%0.98%1.37%2.10%1.98%2.05%1.80%1.27%0.55%0.26%B0.70.710.720.730.740.750.760.770.780.79H2.12.132.162.22.242.282.32.362.42.45H'2.11252.15822.20122.24032.27542.30682.33552.36312.39162.4229誤差0.59%1.31%1.87%1.80%1.56%1.16%1.52%0.13%0.35%1.12%B0.80.810.820.830.840.850.860.870.880.89H2.52.552.62.652.72.762.812.872.932.99H'2.45882.50092.54992.60612.6692.73742.80992.88442.95913.0322誤差1.68%1.96%1.96%1.68%1.16%0.83%0.00%0.50%0.98%1.39%B0.90.910.920.930.940.950.960.970.980.99H3.063.133.193.263.333.413.493.573.653.74H'3.10263.16943.23283.29333.35253.41213.47423.5413.61443.6959誤差1.37%1.24%1.32%1.01%0.67%0.06%0.45%0.82%0.98%1.19%B11.011.021.031.041.051.061.071.081.09H3.933.924.014.114.224.334.444.564.674.8H'3.78643.8863.99414.10964.23064.35534.48164.60794.73284.8558誤差3.79%0.87%0.40%0.01%0.25%0.58%0.93%1.04%1.33%1.15%B1.11.111.121.131.141.151.161.171.181.19H4.935.075.215.365.525.685.8466.166.33H'4.97725.09795.21985.34525.47665.61675.76795.93216.11016.3024誤差0.95%0.55%0.19%0.28%0.79%1.13%1.25%1.14%0.82%0.44%

B1.21.211.221.231.241.251.261.271.281.29H6.526.726.947.167.387.627.868.18.368.62H'6.50816.72586.95347.18837.42817.67067.91448.15898.40478.6535誤差0.18%0.09%0.19%0.39%0.65%0.66%0.69%0.72%0.53%0.39%B1.31.311.321.331.341.351.361.371.381.39H8.99.29.59.810.110.510.911.311.712.1H'8.90839.17269.45089.747610.06710.41410.79111.19911.64112.116誤差0.09%0.30%0.52%0.54%0.33%0.83%1.01%0.90%0.51%0.13%B1.41.411.421.431.441.451.461.471.481.49H12.613.113.614.214.815.516.317.118.119.1H'12.62413.16313.73414.33714.97415.64716.36517.13417.96718.876誤差0.19%0.48%0.98%0.96%1.16%0.94%0.40%0.20%0.74%1.19%B1.51.511.521.531.541.551.561.571.581.59H20.121.222.423.72526.728.530.432.635.1H'19.87620.98322.21323.58225.10326.78828.64630.68232.89935.296誤差1.13%1.03%0.84%0.50%0.41%0.33%0.51%0.92%0.91%0.56%B1.61.611.621.631.641.651.661.671.681.69H37.840.743.746.85053.456.860.46467.8H'37.86940.61343.52246.58949.80753.17356.68260.33464.12968.069誤差0.18%0.21%0.41%0.45%0.39%0.43%0.21%0.11%0.20%0.40%B1.71.711.721.731.741.751.761.771.781.79H7276.480.885.490.295100105110116H'72.15976.40180.79985.35890.07894.959100105.2110.56116.07誤差0.22%0.00%0.00%0.05%0.14%0.04%0.00%0.19%0.51%0.06%B1.81.811.821.83