摘要倒立摆系统是一个典型的多变量、高阶次、不稳定、强耦合非线性系统。以固高直线倒立摆为被控对象，在建立一级与二级倒立摆的数学模型的基础上，设计了滑模变结构稳摆控制器，并针对其存在的抖振问题，对传统滑模控制算法进行了改进。针对传统滑模趋近运动项带来的抖振，提出了一种新型双幂趋近律，并采用符号函数连续化方法，对一级倒立摆滑模控制器进行改进，以抑制其抖振；将新型双幂趋近律和在线自调整系数引入二级倒立摆滑模控制器中，在保证算法鲁棒性的同时削弱了抖振。实验结果表明，所设计的算法能较好地抑制抖振，并保证了系统的强鲁棒性和抗干扰能力。63909

毕业论文关键词  倒立摆  滑模变结构控制  抖振抑制  在线自调整

毕业设计说明书（论文）外文摘要

Title  Study on sliding mode control of the linear inverted pendulum                                             

Abstract Inverted pendulum system is a typical multivariable, high-order, unstable, strong coupled and nonlinear system. Taking the inverted pendulum system of GoogolTech Company as the controlled object, based on the mathematical models of single and double inverted pendulum, sliding mode controller to stabilize the pendulum was designed. For the problem of chattering in the sliding mode control system, the traditional sliding mode control algorithm was improved. For the single inverted pendulum, to reduce the chattering of reaching in the traditional sliding mode control, a kind of new double-power reaching law was proposed, and sign function was made continuous replaced by another function to reduce the chattering. For the double inverted pendulum, self-adjusting factor and the new double-power reaching law were introduced into the sliding mode controller to ensure the robustness as well as the chattering reduction. Experimental results show that the algorithm designed can reduce the chattering and guarantee the good robustness and strong anti-jamming capability of the system.

Keywords  Inverted pendulum  sliding mode control  chattering reduction  self-adjusting

1  绪论 1

1.1  倒立摆控制的研究意义 1

1.2  倒立摆控制的研究现状 1

1.3  变结构控制理论的现状及发展 1

1.4  本文研究的主要内容 2

2  倒立摆系统及其数学模型 3

2.1  固高直线倒立摆系统概述 3

2.2  一级倒立摆数学建模 4

2.3  二级倒立摆数学建模 6

2.4  本章小结 9

3  滑模变结构控制的基本原理 10

3.1  滑动模态的定义及数学表达 10

3.2  滑动模态存在及可达条件 10

3.3  滑模变结构控制的定义 11

3.4  变结构控制的若干基本特性 11

3.5  本章小结 12

4  一级倒立摆系统的滑模变结构控制及其抖振抑制研究 13

4.1  传统滑模控制器设计 13

4.2  符号函数连续化法抖振抑制