一级倒立摆的ID控制设计.doc

一级倒立摆的PID控制设计 摘 要 本文主要研究的是一级倒立摆的PID控制问题，并用遗传算法对其PID的参数进行了优化。倒立摆是典型的快速、多变量、非线性、强耦合、自然不稳定系统。由于在实际中有很多类似于倒立摆的系统，因此对它的研究在理论上和方法论上均有深远的意义。本文首先简单地介绍了倒立摆以及倒立摆的控制方法，并对其参数优化算法做了分类介绍。然后，介绍了遗传算法的基本理论和操作方法。接着建立了一级倒立摆的数学模型，并求出其状态空间描述。本文主要采用遗传算法来对PID的参数进行优化，得到较好的PID参数。最后，用Simulink对系统进行了仿真，验证了该方法的有效性，证明遗传算法是较为理想的参数优化方法。 关键词：PID控制器；倒立摆；遗传算法；MATLAB仿真 Abstract This paper mainly studies the PID control problem of the single inverted pendulum and optimizes PID parameters with Genetic Algorithms. Inverted pendulum is a typical fast, multivariable, nonlinear, strong-coupling and naturally unstable system. In reality there are many systems which are similar to inverted pendulum, so the research on it has profound significance both in theory and methodology. This paper first briefly introduces the inverted pendulum and the control methods of it, and makes a classified introduction of the optimization algorithm of the parameters. The basic theory and the method of operation of the Genetic Algorithms are also introduced in this paper. Then the mathematical model of the single inverted pendulum is set up and works out the description of its state and space. This paper mainly adopts the Genetic Algorithms to optimize the parameters of PID, in order to get the better PID parameters. Finally, using Simulink to do simulation of the system verifies the validity of this method and certifies that Genetic Algorithms is a ideal optimization method of the parameter. Keywords: PID controller; inverted pendulum; Genetic algorithm; MATLAB simulation 目 录 TOC \o 1-3 \h \z \u HYPERLINK \l _Toc358633307 1 绪论 PAGEREF _Toc358633307 \h 1 HYPERLINK \l _Toc358633308 1.1 倒立摆简介 PAGEREF _Toc358633308 \h 1 HYPERLINK \l _Toc358633309 1.2 倒立摆的控制方法 PAGEREF _Toc358633309 \h 2 HYPERLINK \l _Toc358633310 1.3 PID控制器参数整定方法 PAGEREF _Toc358633310 \h 3 HYPERLINK \l _Toc358633311 1.4 本文的主要任务 PAGEREF _Toc358633311 \h 5 HYPERLINK \l _Toc358633312 2 PID简介 PAGEREF _Toc358633312 \h 6 HYPERLINK \l _Toc358633313 2.1