环型二级倒立摆 LQR 控制作 者 ：系 别 ：专 业 ：学 号 ： 指导老师 ：日期：二零零六年五月二十日摘要控制理论进展过程中，某一理论的正确性以与实际应用中可行性，往往需要一个按其理论所设计的控制器去控制一个典型对象来验证其控制策略的效果。倒立摆就是这样一个较为理想的实验装置。倒立摆本身是一个自然不稳定体，在控制过程中能有效地反映控制中的许多问题。倒立摆的典型性在于:作为一个装置，其成本低廉，结构简单，便于模拟，数字实现不同方式控制;作为被控对象，又相当复杂，是高阶次、不稳定、非线性、强耦合系统，只有实行行之有效的控制方法方能使之稳定。本文在环型二级倒立摆系统进行数学建模的基础上得出系统的状态方程, 应用线性二次型最优控制策略, 对环型二级倒立摆进行ＬＱＲ控制器的设计与ＭＡＴＬＡＢ仿真实验，并给出了相应的实验结果。关键词: 倒立摆；ＬＱＲ；最优控制；状态方程AbstractThe inverted pendulum is an ideal equipment, which enables the possibility to validatethe validity and the feasibility of some control theories, The inverted pendulum is a natural unstable equipment and can effectively reflects many matters in the control process. The model of the inverted pendulum is: as an equipment, low cost, simple machinery, easy toperform all kinds of controls in simulation and digital; as a controlled object, quite complex,high orders, instability, non-linearity, strong coupling system. We can keep it stable throughsome control method.Inverted pendulum system is a complicated , nonlinear , unstable system of high order. Inthe paper, it is discussed how to model the system of double inverted pendulums by using dynamics equation and then to t transform into a control problem of linearitied system. The optimized cont rollingpolicy with LQR cont roller is established on the MATLAB platform. The relevant experiment is alsoprovided.Keywords: LQR; inverted pendulum; optimal control目 录１ 概述……………………………………………………………...
