倒立摆的研究.docVIP

摘 要 本文分别以旋转式倒立摆、小车倒立摆系统为控制对象，分别采用状态反馈控制、线性二次型调节器LQR控制、PID控制等控制器，对各控制器控制效果的比较研究，以确定哪种控制更适合解决这两种倒立摆装置的非线性控制问题。文中对三种典型的控制方法做了方法原理以及控制环境的对比，同时也对两种典型倒立摆模型做了原理介绍以及相应的数学建模。本次实验控制目标是使倒立摆在平衡点附近的运动成为一个稳定的运动，整个过程是一个动态平衡。 基于现代控制理论中的极点配置和线性二次型反馈控制（LQR）理论，分别设计完成了两种倒立摆的控制器，进行了MATLAB环境下的仿真实验与研究。在此基础上完成了旋转式倒立摆的实物控制实验。在倒立摆的控制的仿真实验中，两种倒立摆位移曲线最后都收敛于零位置，整个系统都是在一个小范围内动态稳定的。仿真和实验表明，由LQR方法所得到的反馈系数K更优于传统方法极点配置所得到的反馈系数K。关键词：倒立摆，状态反馈，PID，线性二次型反馈 ABSTRACT Rotary handstand pendulum, and car handstand pendulum system are set as the control object respectively. In order to decide which method is more suitable for solving nonlinear control problem of the two inverted pendulum, state feedback control, linear quadratic regulator conventional LQR control, PID control are used to compare the the control effects of different controllers.In this paper,the principle and the controlling environment of the three typical control methods are compared, simultaneously two typical inverted pendulum principle is introduced and the proposed model is the corresponding mathematical modeling. The goal of the experiment is to make experimental control in nearby movement balance handstand to become a stable movement, the whole process is a dynamic equilibrium. Based on modern control theory of poles and linear quadratic feedback control (conventional LQR) theory, two completed inverted pendulum are designed to do simulation experiment and research in the MATLAB software condition. In the controlling simulation experiment of inverted pendulum, curves of diatance of two handstand pendulum finally converge to zero,and the entire system are dynamically stable in a small range. The simulation and experiment show that the feedback coefficient K obtained by LQR is better than the coefficient K obtained by traditional pole-placing method. Keywords: Pendulum, State Feedback, PID, Linear Quadratic Feedback 目 录 摘 要 I ABSTRACT II 目 录 III 第一章 引言 1 1.1 倒立摆控制系统简介 1 1.1.1　倒立摆的发展历史及现状 1 1.1.2 两种倒立摆系统的简介 2 1.1.3 倒立摆系