控制系统数字仿真作业

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1、控制系统数字仿真作业学号：S309047020姓名：张宇2010年1月5号142.2将＝化成状态空间表达式，要求A阵为对角阵。解：＝＝＋=令：，则：将以上两式拉氏反变换：所以可得：y＝（4－2）2.3已知系统的状态空间描述为：A＝B＝C=求该系统的传递函数。解：====++=2.4求图2-20所示系统的状态空间描述。图2-20解：＝＝＝所以可以写出系统的状态空间描述为：A＝B＝C＝2.5分别用欧拉法、二阶龙格－库塔及四阶龙格－库塔法计算系统：在阶跃函数下的过渡过程141.选择相同的步距h＝0.005，试比较计算结果。2.选择不同的

2、步距：欧拉法h＝0.0001，二阶龙格－库塔法h＝0.005，四阶龙格－库塔法h＝0.05，试比较计算结果。解：=求得：=可以写出系统的状态空间方程为：即：=，=，=，利用MATLAB编写了程序，见附录1、附录2和附录3，1.选择相同的步距h＝0.005，得到的三者的图形如下：图1欧拉法图22阶龙格库塔法图34阶龙格库塔法时间（s）欧拉法二阶四阶时间（s）欧拉法二阶四阶0.0500.00416660.00411781.050.976460.977970.978410.100.385340.413450.41231.100.9693

3、0.968150.967830.151.07141.09461.09311.150.983360.980810.980120.201.51191.51921.5191.201.00311.00111.00060.251.48231.47881.48081.251.01351.01341.01340.301.13751.13231.13511.301.01041.01181.01220.350.799320.796160.797551.350.999551.00121.00160.400.692320.690040.688951.4

4、00.990480.991180.991360.450.821650.818770.816131.450.988690.988150.988020.501.03261.03031.02811.500.993240.992090.99180.551.16031.16081.16071.550.999190.998350.998140.601.1431.1471.14871.601.00211.00211.00210.651.0341.03881.04091.651.00091.00151.00160.700.932680.93480

5、.935721.700.997460.998140.998310.750.904630.902560.901881.750.994720.9950.995070.800.947530.942990.941471.800.994270.994040.993980.851.01221.00861.00751.850.99570.995230.995120.901.04891.04871.04871.900.997460.997130.997050.951.04111.0441.04491.950.998240.998230.99823

6、1.001.00681.01021.01122.000.997750.997990.99805从数据比较看出，三种方法均在0.2s达到峰值，其中欧拉法的峰值最小为1.5119，4阶龙格库塔法的最小为1.519，但4阶龙格库塔法的稳定时间最短，欧拉法的最长。2.选择不同的步距：欧拉法h＝0.0001，二阶龙格－库塔法h＝0.005，四阶龙格－库塔法h＝0.05，14图4欧拉法图52阶龙格库塔法图64阶龙格库塔法时间（s）欧拉法二阶四阶时间（s）欧拉法二阶四阶0.0500.0041670.345281.050.980790.96815

7、0.968740.100.349990.413451.02111.100.967730.980810.976250.151.03031.09461.49271.150.978321.00110.996150.201.49741.51921.50951.200.99881.01341.01190.251.50281.47881.18881.251.01281.01181.01430.301.17371.13230.835261.301.01281.00121.00550.350.822580.796160.688971.351.00

8、280.991180.994390.400.687730.690040.7871.400.99210.988150.988790.450.796990.818770.996321.450.9880.992090.990760.501.00881.0