控制系統(tǒng)與仿真

1、 實驗一Matlab的基本操作一、驗證所有例題內容例1.1：Time=111212345678910Time=111212345678910X_Data=2.323.43;4.375.98X_Data=2.32003.43004.37005.9800例1.2：g=1234;h=4321;s1=g+h,s2=g.*h,s3=g.Ah,s4=g.A2,s5=2.Ahs1=5555s2=4664s3=1894s4=14916s5=16842例1.3：A=20-1;132;B=17-1;423;201;M=A*B14-31713100.10000.1500-0.3500-0.20000.7000-1.

2、3000V,D=eig(B)V=-0.7094+0.0000i0.7444+0.0000i0.7444+0.0000i-0.6675+0.0000i-0.3599+0.0218i-0.3599-0.0218i-0.2263+0.0000i-0.5587-0.0607i-0.5587+0.0607iD=7.2680+0.0000i0.0000+0.0000i0.0000+0.0000i0.0000+0.0000i-1.6340+0.2861i0.0000+0.0000i0.0000+0.0000i0.0000+0.0000i-1.6340-0.2861iX=A/BX=0.4000-1.40003

3、.600001.5000-2.5000Y=BAY=-0.95001.35000.5500-0.15000.9000-0.7000-0.35001.1500det_B=det(B)det_B=20rank_A=rank(A)rank_A=2inv_B=inv(B)inv_B=0.10003、輸入A=715；256；315,B=111;222;333，在命令窗口中執(zhí)行下列表達式，掌握其含義：A(2,3)%矩陣A第一行第三列的兀素A(：,2)%矩陣A第一列的數(shù)據(jù)A(3,:)%矩陣A第一行的數(shù)據(jù)A(:,1:2:3)%矩陣A第一列和第三列的數(shù)據(jù)A(：,3).*B(:,2)%矩陣A的第三列和矩陣B的第二列

4、點乘A(:,3)*B(2,:)%矩陣A的第三列和矩陣B的第二行相乘A*B%矩陣A和矩陣B相乘A*B%矩陣A和矩陣B點乘AA2%矩陣A的乘方AH2%矩陣A的點乘方B/A%矩陣B右除矩陣AB/A%矩陣B點除矩陣AA=715;256;315;B=111;222;333;A(2,3)ans=6A(:,2)ans=151A(3,:)TOC o 1-5 h zans=315A(:,1:2:3)ans=752635A(:,3).*B(:,2)ans=51215A(:,3)*B(2,:)ans=101010121212101010A*Bans=242424303030202020A.*Bans=7154101

5、29315AA2ans=661766423370381346A42ans=49125425369125B/Aans=0.18420.2105-0.23680.36840.4211-0.47370.55260.6316-0.7105B./Aans=0.14291.00000.20001.00000.40000.33331.00003.00000.60004、輸入C=1:2:20,則C(i)表示什么？其中i=l,2,3,;10C=1:2:20C=135791113151719C(i)下標索引必須為正整數(shù)類型或邏輯類型。c(l)ans=1C(2)ans=3C(3)ans=5C(4)ans=7C(5)

6、ans=9C(6)ans=11C(7)ans=13C(8)ans=15C(9)ans=17C(10)ans=195、先求下列表達式的值，然后顯示Matlab工作空間的使用情況并保存全部變量。(1)_2sin8511+e2。(2)其中x1z=ln(x+i1+x2)，22e0.3ae-0.3aa+0.3(3)z=sin(a+0.3)+ln,a=3.0,2.9,2.8,.,2.8,2.9,3.0322提示：利用冒號表達式生成a向量，求各點的函數(shù)值時用點乘運算。zl=2*sin(85/360)/(l+(exp(l)人2)zl=0.0558x=21+2*i;-0.455x=2.0000+O.OOOOi1

7、.0000+2.0000i-0.4500+0.0000i5.0000+0.0000iz2=(log(x+sqrt(1+xA2)/2z2=0.7114-0.0253i0.8968+0.3658i0.2139+0.9343i1.1541-0.0044ia=-3:0.1:3a=Columns1through9-3.0000-2.9000-2.8000-2.7000-2.6000-2.5000-2.4000-2.3000-2.2000Columns10through18-2.1000-2.0000-1.9000-1.8000-1.7000-1.6000-1.5000-1.4000-1.3000Colu

8、mns19through27-1.2000-1.1000-1.0000-0.9000-0.8000-0.7000-0.6000-0.5000-0.4000Columns28through36-0.3000-0.2000-0.100000.10000.20000.30000.40000.5000Columns37through450.60000.70000.80000.90001.00001.10001.20001.30001.4000Columns46through541.50001.60001.70001.80001.90002.00002.10002.20002.3000Columns55

9、through612.40002.50002.60002.70002.80002.90003.0000m1=linspace(0.3,0.3,61)m1=Columns1through90.30000.30000.30000.30000.30000.30000.30000.30000.3000Columns10through180.30000.30000.30000.30000.30000.30000.30000.30000.3000Columns19through270.30000.30000.30000.30000.30000.30000.30000.30000.3000Columns28

10、through360.30000.30000.30000.30000.30000.30000.30000.30000.3000Columns37through450.30000.30000.30000.30000.30000.30000.30000.30000.3000Columns46through540.30000.30000.30000.30000.30000.30000.30000.30000.3000Columns55through610.30000.30000.30000.30000.30000.30000.3000m2=linspace(-0.3,-0.3,61)m2=Colum

11、ns1through9-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000Columns10through18-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000Columns19through27-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000Columns28through36-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3

12、000-0.3000-0.3000Columns37through45-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000Columns46through54-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000Columns55through61-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000-0.3000z2=(power(exp(l),ml.*a)-power(exp(l),m2.*a)/2.*sin(a+m

13、l)+log(a+ml)/2)z2=Columnslthrough40.7388+3.1416i0.7696+3.1416iColumns5through80.7822+3.1416i0.7602+3.1416iColumns9through120.6196+3.1416i0.5496+3.1416iColumns13through160.2775+3.1416i0.1680+3.1416iColumns17through20-0.2124+3.1416i-0.3566+3.1416iColumns21through24-0.8536+3.1416i-1.0497+3.1416iColumns

14、25through28-1.8436+3.1416i-2.2727+3.1416iColumns29through32-3.0017+0.0000i-2.3085+0.0000iColumns33through36-1.3575+0.0000i-1.1531+0.0000iColumns37through40-0.6567+0.0000i-0.5151+0.0000iColumns41through44-0.1374+0.0000i-0.0255+0.0000iColumns45through480.2663+0.0000i0.3478+0.0000iColumns49through520.5

15、379+0.0000i0.5815+0.0000iColumns53through560.6474+0.0000i0.6470+0.0000iColumns57through600.5777+0.0000i0.5327+0.0000iColumn610.3388+0.0000i0.7871+3.1416i0.7913+3.1416i0.7254+3.1416i0.6784+3.1416i0.4688+3.1416i0.3780+3.1416i0.0497+3.1416i-0.0771+3.1416i-0.5104+3.1416i-0.6752+3.1416i-1.2701+3.1416i-1.

16、5271+3.1416i-2.9837+3.1416i-37.0245+0.0000i-1.8971+0.0000i-1.5978+0.0000i-0.9723+0.0000i-0.8083+0.0000i-0.3819+0.0000i-0.2561+0.0000i0.0792+0.0000i0.1766+0.0000i0.4206+0.0000i0.4841+0.0000i0.6145+0.0000i0.6366+0.0000i0.6351+0.0000i0.6119+0.0000i0.4774+0.0000i0.4126+0.0000ii234-4_13-1A=34787,B=203365

17、73-276、已知:求下列表達式的值。A+6*B和A一B+八其中I為單位矩陣；A*B和A.*BA人3和A.人3A/B和ABA,B和A(1,3,:);BA2A=1234-4;34787;3657;B=13-1;203;3-27;A+6*Bans=1852-10467105215349I=eye(3);A-B+Ians=1231-3328840i671A*Bans=684462309-72596154-5241A.*Bans=12：0246802619-13049AA3ans=372262338244860424737014918860076678688454142118820A.A3ans=17

18、2839304-643930434365850327274625343A/Bans=16.4000-13.60007.600035.8000-76.200050.200067.0000-134.000068.0000ABans=-0.03130.3029-0.33240.0442-0.03230.10630.0317-0.11580.1558A,Bans=1234-413-13478720336573-27A(1,3,:);B9ans=1234-436574511101920-540實驗二Matlab的數(shù)值計算和符號運算一上機驗證實驗A、開啟PC機，進入MATLAB語言B、幫助命令的使用，査找

19、sqrt函數(shù)的使用方法答：helpsqrtsqrt-SquarerootThisMATLABfunctionreturnsthesquarerootofeachelementofthearrayX.B=sqrt(X)C、矩陣運算已知A=12;34;B=55;78;求AA2*B答：ans=105115229251矩陣除法。已知A=123;456;789;B=100;020;003;求A/B，AB答:A=123;456;789;B=100;020;003;A/Bans=1.00001.00001.00004.00002.50002.00007.00004.00003.0000AB警告：矩陣接近奇異

20、值，或者縮放錯誤。結果可能不準確。RCOND=1.541976e-18。ans=1.0e+16*-0.45041.8014-1.35110.9007-3.60292.7022-0.45041.8014-1.3511(3)矩陣的轉置及共軛轉置。已知A=15+i,2-i,1;6*i,4,9-i逑A，A答：A=15+i,2-i,l;6*i,4,9-i;A.ans=15.0000+l.OOOOi0.0000+6.0000i2.0000-1.0000i4.0000+0.0000i1.0000+0.0000i9.0000-1.0000iAans=15.0000-1.0000i0.0000-6.0000i2

21、.0000+1.0000i4.0000+0.0000i1.0000+0.0000i9.0000+1.0000i(4)使用冒號選出指定元素。已知A=123;456;789;求A中第3列前2個元素；A中所有第2行的元素；答:A=123;456;789;A(1:2,3)ans=36A(2,1:3)ans=456(5)方括號。用magic函數(shù)生成一個4階魔術矩陣，刪除該矩陣的第四列。答:A=magic(4)A=16231351110897612414151A(:,4)=A=16235111097641415D、多項式求多項式p(X)=x32X4的根答：P=1,0,-2,-4;roots(P)ans=2

22、.0000+0.0000i-1.0000+1.0000i-1.0000-1.0000i已知A=12350.9;51.756;3901;1234,求矩陣A的特征多項式;答:A=1.2350.9;51.756;3901;1234;B=poly(A)B=1.0000-6.9000-77.2600-86.1300604.5500P(s)=10000sM-69000sA3-7726OOsA2-861300s+6045500求矩陣多項式中未知數(shù)為20時的值；答：C=polyval(B,20)C=7.2778e+04把矩陣A作為未知數(shù)代入到多項式中；答：D=polyval(B,A)D=1.0e+03*0.3

23、801-0.4545-1.99510.4601-1.99510.2093-1.9951-2.8880-0.4545-4.89780.60450.43530.43530.0841-0.4545-1.1617二、上機練習實驗(1)利用help檢査roots指令的使用方法，然后求4xA4-3xA3+2xA2-x+1=0的所有根。答：helprootsroots-PolynomialrootsThisMATLABfunctionreturnsacolumnvectorwhoseelementsaretherootsofthepolynomialc.r=roots(c)P=4,-3,2,-1,1;roo

24、ts(P)ans=0.5917+0.4864i0.5917-0.4864i-0.2167+0.6158i-0.2167-0.6158i(2)令A是一個維度mxn的矩陣.解釋max(A)和min(max(A)分別是什么意思?答：A=rand(3,4)A=0.81470.91340.27850.96490.90580.63240.54690.15760.12700.09750.95750.9706max(A)ans=0.90580.91340.95750.9706min(max(A)ans=0.9058(3)令x是一個維度n的向量.解釋find(x08*max(x)是什么意思?答：find(x0.

25、8*max(x)的意思是從向量中找出大于最大值0.8倍的所有數(shù)據(jù)得位置。令x=2356和y=-l:2而z=x.Ay，解釋z的值是什么？答：x=2356;y=-1:2y=-1012z=x.Ayz=0.50001.00005.000036.0000試用解析解和數(shù)值解的方法求解微分方程x(t)=-2x(t)-3x(t)+exp(-5t)y(t)=2x(t)-3y(t)-4x(t)-4y(t)-sintx(0)=1,x(0)=2,y(0)=3,y(0)=4解析解：x,y=dsolve(D2x=(-2)*x-3*Dx+exp(-5*t),D2y=2*x-3*y-4*Dx-4*Dy-sint,x(0)=1

26、,Dx(0)=2,y(0)=3,Dy(0)=4)x=-(exp(-2*t)*(20*exp(t)*(3*exp(-4*t)/4-51/4)-20*exp(-3*t)+200)/60y=-(exp(-3*t)*(sint-(21*exp(-2*t)/2-sint*exp(3*t)+3*exp(t)*(20*exp(-3*t)/3-200/3)+6*exp(2*t)*(3*exp(-4*t)/4-51/4)-6*exp(2*t)*(sint/2+(exp(-4*t)*(12*t-8*sint*exp(5*t)+41)/16-465/16)+6*t*exp(2*t)*(3*exp(-4*t)/4-5

27、1/4)+171)/6計算y=sinx+sin2x+sin3x,在x=n/處得值。答：symsx;f=sin(x)+sin(2*x)+sin(3*x);subs(f,x,pi/6)ans=3A(1/2)/2+3/2Idx用符號方法求積分1+x4+x8答：symsx;f=1/(1+(xA4)+(xA8);int(f,x)ans=-(3A(1/2)*(atan(2*3A(1/2)*x)/(3*(2*xA2)/3-2/3)-atanh(2*3A(1/2)*x)/(3*(2*xA2)/3+2/3)/6x(esinx+1)一2(etanx1)lim(8)用符號方法求下列極限：xT0sin3x答：syms

28、x;f=(x*(power(exp(1),sin(x)+1)-2*(power(exp(1),tan(x)-1)/(power(sin(x),3);limit(f,x,O)ans=-Inf(9)用3次多項式方法插值計算1-100之間整數(shù)的平方根。N149162536496481100平方根12345678910答：n=(1:10).人2;f=sqrt(n);interpl(n,f,(l:100),cubic)ans=Columns1through71.00001.37291.7125Columns8through142.00002.24052.45512.64942.82923.00003.1

29、6363.31863.46613.60693.7422Columns15through213.87294.00004.12374.24354.35994.47304.5832Columns22through284.69074.79584.89885.00005.09935.19665.2921Columns29through355.38575.47775.56815.65705.74465.83095.9160Columns36through426.00006.08296.16476.24546.32496.40356.4810Columns43through496.55776.63346.7

30、0826.78236.85566.92817.0000Columns50through567.07127.14167.21137.28047.34877.41647.4835Columns57through637.55007.61597.68127.74597.81027.87397.9372Columns64through708.00008.06238.12428.18558.24648.30688.3668Columns71through778.42638.48548.54418.60248.66038.71788.7749Columns78through848.83178.88818.94429.00009.05559.11079.1655Columns85through919.22019.27449.32849.38219.43549.48849.5412Columns92through989.59359.64569.69739.74