文档介绍：基于极点配置的最优控制研究
摘要
随着科学技术的不断发展,自动控制系统已广泛应用于制造业自动化、交
通管理、办公自动化和决策支持系统,已几乎涉及生物、医学、生态、经济、
社会等所有领域。20 世纪 40 年代是自动控制技术和理论形成的关键时期,一
批科学家为了解决军事上提出的火炮空控制、飞机导航等技术问题,逐步形成
了分析和设计控制系统的理论和方法,而最优控制又是现代控制理论的一个最
重要最基本的组成部分。
最优控制的研究需要合适的数学模型,而二级倒立摆结构相对复杂,控制
难度相对大,控制算法也相对复杂,并且通常被用来检验各种控制策略的有效
性,许多抽象的控制概念,如系统稳定性、可控性、系统收敛速度、和系统抗
干扰能力等。因此,倒立摆系统可以成为最优控制研究中的一种较为理想的研
究对象。
本文分析了二次型最优控制方法与极点配置方法,介绍了按规定的主导极
点选择最优控制加权阵的原理,把二次型最优控制与极点配置方法结合起来,
得到了系统最优控制器。并以二级倒立摆为例,通过系统本身所存在的能量关
系,运用拉格朗日方程进行系统的数学表示即进行建模。将最优控制理论应用
于二级倒立摆系统,然后通过 matlab 仿真,说明了这种方法的合理性与科学
性。
关键词最优控制;二级倒立摆系统;极点配置
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哈尔滨理工大学学士学位论文
Optimal Control Based On The Pole Placement
Abstract
With the continuous development of science and technology, automatic control
system has been widely used in manufacturing automation, traffic management, office
automation and decision support system, involving almost biological, medical,
ecological, economic, social and other all areas. The 1940s is a theory of automatic
control technology and the critical period, a group of scientists in order to solve the
military's artillery air control, aircraft navigation and other technical issues, has
gradually developed a control system analysis and design of the theory and methods,
and the optimal Control of modern control theory is one of the most important basic
components.
Optimal Control of the research needs of a suitable model, and the two inverted
pendulum plicated structure, the relative difficulty of control, control
algorithm is plex, and often are used to test the effectiveness of various
control strategies, many of the abstract concept of control , Such as system stability,
controllability, the convergence rate system, and anti-jamming systems, and so on.
Therefore, the inverted pendulum system can e optimal control study in an ideal
object of study.
This paper analyses the quadratic optimal control method and pole placement
methods, in accordance with the regulations on the choice of the dominant pol