单级旋转倒立摆系统.pdf

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1、现代控制理论课程综合设计单级旋转倒立摆系统1 引言单级旋转倒立摆系统一种广泛应用的物理模型，其物理模型如下：图示为单级旋转倒立摆系统原理图。其中摆的长度1l=1m，质量1m=，横杆的长度2l =1 m，质量2m=，重力加速度20.98/gms。以在水平方向对横杆施加的力矩M 为输入，横杆相对参考系产生的角位移1为输出。控制的目的是当横杆在水平方向上旋转时，将倒立摆保持在垂直位置上。图 1 单级旋转倒立摆系统模型单级旋转倒立摆可以在平行于纸面3600的范围内自由摆动。倒立摆控制系统的目的是使倒立摆在外力的推动下，摆杆仍然保持竖直向上状态。在横杆静止的状态下，由于受到重力的作用，倒立摆的稳定性在摆

2、杆微小的扰动下，就会使倒立摆的平衡无法复位，这时必须使横杆在平行于纸面的方向通过位移产生相应的加速度。作用力与物体位移对时间的二阶导数存在线性关系，故单级倒立摆系统是一个非线性系统。本文综合设计以以在水平方向对横杆施加的力矩M 为输入，横杆相对参考系产生的角位移1为输出，建立状态空间模型，在原有系统上中综合带状态观测器状态反馈系统，从而实现当横杆在旋转运动时，将倒立摆保持在垂直位置上。2 模型建立本文将横杆和摆杆分别进行受力分析，定义以下物理量：本文将横杆和摆杆分别进行受力分析，定义以下物理量：M 为加在横杆上的力矩；1m 为摆杆质量；1l 为摆杆长度；1I 为摆杆的转动惯量；2m 为横杆的质

3、量；2l 为横杆的长度；2I 为横杆的转动惯量；1为横杆在力矩作用下转动的角度；2为摆杆与垂直方向的夹角；N和 H分别为摆杆与横杆之间相互作用力的水平和垂直方向的分量。倒立摆模型受力分析如图2 所示。图 2 倒立摆模型受力分析摆杆水平方向受力平衡方程：2111222(0sin)2ldNmldt（12l 横杆的转动弧长即位移）摆杆垂直方向受力平衡方程：2111122(cos)22lldHm gmdt摆杆转矩平衡方程：22111222sincos22dllJHNdt横杆转矩平衡方程：21222dMNlJdt考虑到摆杆在设定点12,=0附近做微小振动，对上式进行线性化，即1mg2HN1l112l文档

4、编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文

5、档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1

6、文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M

7、1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4

8、M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E

9、4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6

10、E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M122sin，2cos1，20&，其中23mlJ，近似线性化得到，212222

11、222120.10.50.98010.50.5 130130dNdtHdHNdtdMNdt整理上式可得倒立摆的状态方程：21221114.71524110032MM?本文参数代入计算可得：12224.64211.05312.3799.474MM?&取状态变量如下：11213242xxxxx?&1122334400100004.642011.053000100012.37909.474xxxxMxxxx&故1211341000 xxyxx3稳定性和能控性分析稳定性分析文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H

12、3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1

13、H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO

14、1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 H

15、O1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9

16、HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9

17、 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X

18、9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1判断一个系统是否稳定，只需判断该系统传递函数的极点是否都在左半平面。编写 Matlab 语句可得该系统的传递函数，即A=0,1,0,0;0,0,0;0,0,0,1;0,0,0;B=0;0;C=1,0,0

19、,0;D=0;Gss=ss(A,B,C,D);G1=zpk(Gss)G1=(s+-s2 (s+Continuous-time zero/pole/gain model.从结果可以看出，传递函数存在一个在复平面右半侧的极点，故该系统是不稳定的。能控性分析判断系统是否完全能控，只需判断该系统能控性矩阵是否为满秩，即21LnCQBABA BA B若CrankQn，则该系统是完全能控的。根据Matlab 语句中 Qc=ctrb(A,B)，即A=0,1,0,0;0,0,0;0,0,0,1;0,0,0;B=0;0;C=1,0,0,0;Qc=ctrb(A,B);n1=rank(Qc)文档编码:CN10C3R

20、6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3

21、R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C

22、3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10

23、C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN1

24、0C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN

25、10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:C

26、N10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1n1=4从结果可以看出该系统是完全能控的，可以实现任意极点的配置。能观测性分析与判断能控性类似，

27、只需判断该系统能观测性矩阵是否为满秩，即01MnCCAQCA若0rankQn，该系统是完全能观测的。借用Matlab 语句中 Qo=obsv(A,C)，即A=0,1,0,0;0,0,0;0,0,0,1;0,0,0;B=0;0;C=1,0,0,0;Qo=obsv(A,C);n2=rank(Qo)n2=4从结果可以看出该系统是完全能观测的，故可以配置状态观测器4状态反馈分析4.1原系统 Simulink 仿真及分析根据现代控制原理，绘制原系统的状态模拟图，如图3 所示。My4x3x2x1x文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R

28、6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3

29、R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C

30、3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10

31、C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN1

32、0C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN

33、10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:C

34、N10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1图 3 原系统状态模拟图运用 MATLAB 中的 Simulink来对原系统进行仿真，首先可以得出原系统的Simulink 仿真模型如下图 4 所示图 4 原系统 Simulink仿

35、真图通过 Simulink 仿真可以得到原系统的零状态响应，其中初始值2=0.174，M=0，响应曲线如下图所示文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I

36、7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4

37、I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O

38、4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10

39、O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B1

40、0O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B

41、10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3

42、B10O4I7 ZH10V9S6E4M1图 5 原系统2和M零状态响应曲线从仿真波形可以看出，在初始扰动情况下，摆杆不会稳定到垂直位置，横杆会一直运动，故原系统不稳定，这与上文所述传递函数有左半平面极点符合。4.2状态反馈分析由于原系统是不稳定的，要使系统稳定，需要加入状态反馈，使系统的极点全部位于左半平面，状态反馈的结构图如图6 所示。BCBK()r t()u t()y t()x t()x t图 6 状态反馈系统的结构图控制系统的各种特性及其品质指标在很大程度上是由其闭环系统的零点和极点的位置决定。极点配置问题就是通过对状态反馈矩阵的选择，使其闭环系统的极点配置在所希望的位置上，从而达到期望

43、的性能指标的要求。极点配置是一个非常复杂的问题，是一个工程实践与理论相结合的问题。我们这里采用一种工程实践中经常用到的简便方法-主导极点法，其基本思路是先根据期望的性能指标和经验公式确定一对主导闭环极点，然后将另外的非主导极点放在复平面上远离主导极点的位置设倒立摆控制系统期望的性能指标为：阻尼系数=，调节时间ts=2s。亦即控制系统在任意给定的初始条件下，能够以适当的阻尼=（大约10%的超调），在2s 钟内将摆杆恢复到垂直平衡位置。根据控制理论的经验公式得到无阻尼自然频率为：文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9

44、 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X

45、9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2

46、X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R

47、2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6

48、R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R

49、6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3

50、R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1文档编码:CN10C3R6R2X9 HO1H3B10O4I7 ZH10V9S6E4M1n=4/（ts?）=4/=P=wn?由上述条件的很容易构建一个二阶系统，其两个极点为：p1=+2 j p2=-2 j它们就是需要的主导极点，控制系统的性能主要由这两个主导极点决定。另外两个非主