现代控制理论作业1

现代控制理论作业作者：尹英杰时间：2010-5-19班级：2007级自动化题目一：离散系统，初值，当输入分别为=1\*GB2⑴=2\*GB2⑵=3\*GB2⑶时求{}K=1,2,3,4…300画图。解:当时：程序代码：G=[1,0.5;0,0.1];H=[0.3;0.4];X(:,1)=[1;2];fork=1:300,u=0;X(:,k+1)=G*X(:,k)+H*u;endk=1:1:301;plot(k,X(:,k));ylabel('X(k)');xlabel('k')图形为：数据为:X[K]K=1K=2K=3K=4K=5X1[K]22.12.112.1112.1111X2[K]0.20.020.0020.00020.00002K=6K=7K=8K=9K=102.111112.111112.1111112.1111112.1111110.0000022E-072E-082E-092E-10X[K]K=11K=12K=13K=14K=15X1[K]2.1111112.111112.1111112.1111112.111111X2[K]2E-102E-112E-122E-132E-14K=16K=17K=18K=19K=202.1111112.111112.1111112.1111112.1111112E-150000……………….X[K]K=291K=292K=293K=294K=295X1[K]2.1111112.111112.1111112.1111112.111111X2[K]00000K=296K=297K=298K=299K=3002.1111112.111112.1111112.1111112.11111100000当时：程序代码：G=[1,0.5;0,0.1];H=[0.3;0.4];X(:,1)=[1;2];fork=1:300,u=1;X(:,k+1)=G*X(:,k)+H*u;endk=1:1:301;plot(k,X(:,k));ylabel('X(k)');xlabel('k')图形为:数据为:X[K]K=1K=2K=3K=4K=5X1[K]2.32.93.433.9534.4753X2[K]0.60.460.4460.44460.44446K=6K=7K=8K=9K=104.997535.5197536.04197536.564197537.0864197530.4444464.44E-014.44E-014.44E-014.44E-01X[K]K=11K=12K=13K=14K=15X1[K]7.6086419758.13086428.653086429.1753086429.697530864X2[K]4.44E-014.44E-014.44E-014.44E-014.44E-01K=16K=17K=18K=19K=2010.2197530910.74197511.2641975311.7864197512.308641984.44E-010.44444440.4444444440.4444444440.444444444……………….X[K]K=291K=292K=293K=294K=295X1[K]153.8308642154.35309154.8753086155.3975309155.9197531X2[K]0.4444444440.44444440.4444444440.4444444440.444444444K=296K=297K=298K=299K=300156.4419753156.9642157.4864198158.008642158.53086420.4444444440.44444440.4444444440.4444444440.444444444当时：程序代码为：G=[1,0.5;0,0.1];H=[0.3;0.4];X(:,1)=[1;2];fork=1:300,u=2*sqrt(k);X(:,k+1)=G*X(:,k)+H*u;endk=1:1:301;plot(k,X(:,k));ylabel('X(k)');xlabel('k')图形为：数据为：X[K]K=1K=2K=3K=4K=5X1[K]2.60E+003.95E+005.60E+007.56E+009.77E+00X2[K]1.00E+001.23E+001.51E+001.75E+001.96E+00K=6K=7K=8K=9K=107.17E+001.22E+011.49E+011.78E+012.08E+011.08E+002.16E+002.33E+002.50E+002.65E+00X[K]K=11K=12K=13K=14K=15X1[K]2.74E+013.10E+013.47E+013.85E+014.25E+01X2[K]2.93E+003.06E+003.19E+003.31E+003.43E+00K=16K=17K=18K=19K=204.66E+015.08E+015.52E+015.97E+016.43E+013.54E+003.65E+003.76E+003.86E+003.96E+00……………….X[K]K=291K=292K=293K=294K=295X1[K]3.46E+033.48E+033.49E+033.51E+033.53E+03X2[K]1.52E+011.52E+011.52E+011.52E+011.53E+01K=296K=297K=298K=299K=3003.55E+033.57E+033.58E+033.60E+033.62E+031.53E+011.53E+011.53E+011.54E+011.54E+01题目2：离散系统，初值，当输入分别为=1\*GB2⑴=2\*GB2⑵=3\*GB2⑶时求{}K=1,2,3,4…300画图。解:当时：程序代码为：G=[1,0.5,0;0,0.1,0;0,0,1.3];H=[0.3;0.4;0.2];x(:,1)=[1;2;3];fork=1:300,u=0;x(:,k+1)=G*x(:,k)+H*u;endk=1:1:301;plot(k,x(:,k));ylabel('x(k)');xlabel('k')图形为：数据为：X[K]K=1K=2K=3K=4K=5X1[K]22.12.112.1112.1111X2[K]0.20.020.0020.00020.00002X3[K]3.95.076.5918.568311.13879K=6K=7K=8K=9K=102.111112.1111112.11111112.111111112.1111111110.0000022.00E-072.00E-082.00E-092.00E-1014.4804271.88E+012.45E+013.18E+014.14E+01X[K]K=11K=12K=13K=14K=15X1[K]2.1111111112.11111112.1111111112.1111111112.111111111X2[K]2.00E-112.00E-122.00E-132.00E-142.00E-15X3[K]5.38E+016.99E+019.09E+011.18E+021.54E+02K=16K=17K=18K=19K=202.1111111112.11111112.1111111112.1111111112.1111111110.00E+0000002.00E+02259.51248337.3662209438.5760871570.1489132……X[K]K=291K=292K=293K=294K=295X1[K]2.1111111112.11111112.1111111112.1111111112.111111111X2[K]00000X3[K]5.83249E+295.822E+285.75691E+295.48399E+293.12919E+29K=296K=297K=298K=299K=3002.1111111112.11111112.1111111112.1111111112.111111111000006.07E+291.9E+295.45E+299.091E+291.82E+29当时：程序代码为：G=[1,0.5,0;0,0.1,0;0,0,1.3];H=[0.3;0.4;0.2];x(:,1)=[1;2;3];fork=1:300,u=1;x(:,k+1)=G*x(:,k)+H*u;endk=1:1:301;plot(k,x(:,k));ylabel('x(k)');xlabel('k')图形为:数据为：X[K]K=1K=2K=3K=4K=5X1[K]2.30E+002.90E+003.43E+003.95E+004.48E+00X2[K]6.00E-014.60E-014.46E-014.45E-014.44E-01X3[K]4.10E+005.53E+007.39E+009.81E+001.29E+01K=6K=7K=8K=9K=105.00E+005.52E+006.04E+006.56E+007.09E+004.44E-014.44E-014.44E-014.44E-014.44E-011.70E+012.23E+012.92E+013.82E+014.99E+01X[K]K=11K=12K=13K=14K=15X1[K]7.61E+008.13E+008.65E+009.18E+009.70E+00X2[K]4.44E-014.44E-014.44E-014.44E-014.44E-01X3[K]6.50E+018.48E+011.10E+021.44E+021.87E+02K=16K=17K=18K=19K=201.02E+011.07E+011.13E+011.18E+011.23E+014.44E-014.44E-014.44E-014.44E-014.44E-012.43E+023.17E+024.12E+025.35E+026.96E+02……………….X[K]K=291K=292K=293K=294K=295X1[K]1.53E+021.54E+021.54E+021.55E+021.55E+02X2[K]4.44E-014.44E-014.44E-014.44E-014.44E-01X3[K]6.25E+297.13E+296.27E+298.15E+295.59E+29K=296K=297K=298K=299K=3001.56E+021.57E+021.57E+021.58E+021.59E+024.44E-014.44E-014.44E-014.44E-014.44E-017.50E+289E+296.67E+296.67E+296.67E+29当时：程序代码为：G=[1,0.5,0;0,0.1,0;0,0,1.3];H=[0.3;0.4;0.2];x(:,1)=[1;2;3];fork=1:300,u=2*sqrt(k);x(:,k+1)=G*x(:,k)+H*u;endk=1:1:301;plot(k,x(:,k));ylabel('x(k)');xlabel('k')图形为：数据为：X[K]K=1K=2K=3K=4K=5X1[K]2.60E+003.95E+005.60E+007.56E+009.77E+00X2[K]1.00E+001.23E+001.51E+001.75E+001.96E+00X3[K]4.30E+006.16E+008.70E+001.21E+011.66E+01K=6K=7K=8K=9K=101.22E+011.49E+011.78E+012.08E+012.40E+012.16E+002.33E+002.50E+002.65E+002.79E+002.26E+013.04E+014.07E+015.41E+017.16E+01X[K]K=11K=12K=13K=14K=15X1[K]2.74E+013.10E+013.47E+013.85E+014.25E+01X2[K]2.93E+003.06E+003.19E+003.31E+003.43E+00X3[K]9.44E+011.24E+021.63E+022.13E+022.79E+02K=16K=17K=18K=19K=204.66E+015.08E+015.52E+015.97E+0