单级倒立摆控的极点配置方法.doc

一级倒立摆控制的极点配置方法 摘要 倒立摆系统是一个典型的多变量、非线性、强耦合和快速运动的自然不稳定系统。因此倒立摆在研究双足机器人直立行走、火箭发射过程的姿态调整和直升机飞行控制领域中有重要的现实意义，相关的科研成果己经应用到航天科技和机器人学等诸多领域。 本文通过极点配置, 实现了用现代控制理论对一级倒立摆的控制。利用牛顿第二定律及相关的动力学原理等建立数学模型，对小车和摆分别进行受力分析，并采用等效小车的概念，列举状态方程，进行线性化处理想, 最后通过极点配置，得到变量系数阵。利用Simulink建立倒立摆系统模型，特别是利用Mask封装功能, 使模型更具灵活性，给仿真带来很大方便。实现了倒立摆控制系统的仿真。仿真结果证明控制器不仅可以稳定倒立摆系统，还可以使小车定位在特定位置。 倒立摆，数学建模，极点配置 THE POLE PLACEMENT CONTROL TO A SINGLE INVERTED PENDULUM Abstract Inverted pendulum system is multivariable, nonlinear, strong-coupling and instability naturally. The research of inverted pendulum has many important realistic meaning in the research such as, the walking of biped robot, the lunching process of rocket and flying control of helicopter, and many correlative productions has applications in the field of technology of space flight and subject of robot. Through the pole placement method, the control of the inverted pendulum is realized. We get the mathematic model according to the second law of Newton and the foundation of the dynamics, analysis the force of the cart and pendulum, and adopt the concept of the equivalent cart”. During writing the equitation of the system, the equitation has been processed by linear. At last，we get coefficient of the variability. The simulation of inverted pendulum system is done by the SIMULINK Tool box. Specially Mask function is applied, it makes simulation model more agility, the simulation work become more convenient. The result shows that it not only has quite goods ability, but also is able to make the cart of the pendulum moving to the place where it is appointed by us in advance along the orbit. Key words: inverted pendulum, mathematic model, pole placement 目 录 I Abstract II 1绪论 1 1.1倒立摆系统简介 1 1.2倒立摆的控制规律 2 1.3对倒立摆系统研究的意义 3 1.4倒立摆的发展状况 4 1.5论文的主要工作 5 2直线一级倒立摆的牛顿—欧拉方法建模 7 2.1微分方程的推导 7 3状态空间极点配置 10 3.1状态反馈及输出反馈的两种基本形式 10 3.1.1状态反馈 10 3.1.2输出反馈 11 3.2关于两种反馈的讨论 12 3.3状态反馈的优越性 14 3.4极点配置的提出 14 3.4.1期望极点的选择 14 3.4.2极点配置需要注意的问题 15 3.5理论分析 15 3.6极点配置的方法问题 16 3.7根据极点