基于Matlab的非线性动态系统Lipschitz常数计算及GUI设计

论文总字数：36629字

目 录

1 绪论 1

1.1课程研究背景与意义 1

1.2本课题的研究目的 2

1.3本课题主要内容 2

1.4本课题使用的工具 2

2 Lipschitz常数计算 3

2.1 引言 3

2.2 Lipschitz连续条件的特征 3

2.3 Lipschitz常数计算方法 5

2.4以多变量函数解析式为模型的非线性系统lipschitz常数计算 7

2.5以状态空间方程为模型的非线性系统lipschitz常数计算 7

2.6以状态空间方程为模型的非线性系统的单边lipschitz常数计算 9

2.7 GUI设计 10

3 刚性二连杆机械臂系统模型建立、lipschitz常数计算和GUI设计 14

3.1 引言 14

3.2 模型建立 14

3.3 Lipschitz常数计算和GUI设计 17

4 柔性关节二连杆机械臂系统模型建立、lipschitz常数计算和GUI设计 20

4.1 引言 20

4.2 模型建立 20

4.3 Lipschitz常数计算和GUI设计 23

结论和展望 25

参考文献 26

致谢 28

附录 29

1 第二章GUI相关程序 29

1.1 计算以多变量函数解析式为模型的非线性系统lipschitz常数 29

1.2 计算以状态空间方程为模型的非线性系统lipschitz常数 29

1.3 计算以状态空间方程为模型的非线性系统单边lipschitz常数 30

2 第三章GUI相关程序 31

2.1 计算刚性二连杆机械臂系统lipschitz常数 31

2.2 计算刚性二连杆机械臂系统单边lipschitz常数 31

3 第四章GUI相关程序 32

3.1 计算柔性关节二连杆机械臂系统lipschitz常数 32

3.2 计算柔性关节二连杆机械臂系统单边lipschitz常数 33

基于Matlab的非线性动态系统Lipschitz常数计算及GUI设计

柳云凯

，China

Abstract: At present, in the analyses of nonlinear systems, many documents assume that the mathematical model of the system satisfies the Lipschitz continuous condition, and then analyze the stability of the system or design of the controller and the observer. So it is necessary for this method to solve the Lipschitz constant which makes Lipschitz continuous conditions set up. However, it is assumed that the Lipschitz constant is given directly according to experience after the nonlinear system conform to the Lipschitz continuity condition, which obviously can not meet the requirements of making further system analyses. In this paper, the Lipschitz constant calculation method for general nonlinear systems is studied, and the manipulator is taken as an example to verify and simulate it. In the first part, the calculation method of Lipschitz constant is summarized, the corresponding GUI is designed by Matlab and the simulation is carried out. In the second part, the dynamic model of the two link manipulator system under the rigid assumption is derived. The corresponding GUI is designed on the basis of the conclusion of the first part and the simulation is carried out. In the third part, the joint flexibility is considered on the basis of the second part, which make the dynamic model of the two link manipulator system improve. The corresponding GUI is designed and the simulation is carried out.

Keywords: Nonlinear system; Lipschitz constant; two link manipulator system; flexible joint

剩余内容已隐藏，请支付后下载全文，论文总字数：36629字