论文总字数：22688字

摘 要

当今社会，已经进入信息时代的浪潮中。随着制造业技术和软件控制技术的发展，多自由度位移平台越来越多地应用于各类受软件控制的运动系统中。目前，在多自由度位移平台的研究与设计方面，西方发达国家已经有所进展和成就，而我国因起步较晚，和这些走在前面的国家还有很大的差距，我们还有很长的路要走。本文从多自由度位移平台的数学建模、控制算法、运动仿真进行研究，以期为多自由度位移平台的运动提供技术参考，达到节约人力成本，提高生产效率的目标。

本论文所做工作及成果如下：

1. 多自由度位移平台的数学建模

在位移平台上，以两个各能进行三个方向上旋转的多自由度转台为研究对象，建立多自由度位移平台上转台的数学模型。首先，介绍了建模所需的数理基础，比如点的位置和姿态以及点与点之间的坐标变换等；然后，有了数理基础准备工作之后，建立多自由度位移平台的坐标系；最后通过建模得到关于输出量与输入量的关系式，通过整理关系式来建立运动学方程组并求解，实现位置解算的功能。

1. 多自由度位移平台的运动仿真

在MATLAB中对建模得到的方程组进行化简整理，得到结果用输入量表示出来的方程组，然后赋位移初值，得到计算出来的角度变换量，再在多自由度位移平台上进行试验，观察转台转动的角度，是否与计算出来的角度差距在误差范围内。

1. 多自由度位移平台PLC控制系统设计

在PLC中，把输入量保存在寄存器中，通过PLC自带的指令系统，将寄存器中的数据进行加减乘除计算和三角函数变换，能够将MATLAB中的方程组表示出来，并将最后的结果输出出来。

1. 人机交互界面设计

在显示屏上设置12个数据输入、7个数据输出以及开始、复位按钮，通过把输入的12个数据放入PLC程序中，将PLC计算得到的7个数据输出到显示屏上，并能通过开始、复位按钮控制PLC程序，从而实现多自由度位移平台的控制。

关键词：多自由度位移平台，位置解算算法，PLC，显示屏

Abstract

Today's society has entered the wave of the information age. With the development of manufacturing technology and software control technology, multi-degree-of-freedom displacement platforms are increasingly used in various types of software-controlled motion systems. At present, in the research and design of the multi-degree-of-freedom displacement platform, Western developed countries have made some progress and achievements, and China has a long way to go because of its late start, and there is still a big gap between these countries that are ahead of the others and we still have a long way to go. The way to go. Studing the mathematical modeling, control algorithm and motion simulation of the multi-degree-of-freedom displacement platform is in order to provide a technical reference for the movement of the multi-degree-of-freedom displacement platform and achieve the goal of saving labor costs and increasing production efficiency.The work and achievements of this thesis are as follows:

1) Mathematical modeling of a multi-degree-of-freedom displacement platform

On the displacement platform, two multi-degree-of-freedom turntables, each capable of rotating in three directions, were studied, and a mathematical model of the turntable on a multi-degree-of-freedom displacement platform was established. Firstly, the mathematical foundations needed for modeling are introduced, such as the position and attitude of points and the coordinate transformation between points and points; then, with the basic preparations for mathematics and mechanics, the coordinate system of a multi-degree-of-freedom displacement platform is established; Through the modeling, the relationship between the output and the input is obtained, and the kinematics equations are established and solved by collating the relational expressions to realize the function of position solving.

2) Motion Simulation of Multi-DOF Displacement Platform

In MATLAB, the equations obtained by the modeling are simplified, and the equations are expressed by the input quantities. Then the initial values of the displacements are assigned, the calculated angle transformations are obtained, and the tests are performed on the multi-degree-of-freedom displacement platform. Observe that the rotation angle of the turntable is within the error range from the calculated angle.

3) Multi-degree-of-freedom displacement platform PLC control system design

In the PLC, the input amount is stored in a register. Through the PLC's own instruction system, the data in the register is added, subtracted, multiplied, and divided and the trigonometric function is transformed. The equations in MATLAB can be expressed and the final result can be expressed. Output it.

4) Man-machine interface design

12 data inputs, 7 data outputs, and start and reset buttons are set on the display screen. By putting the input 12 data into the PLC program, the 7 data calculated by the PLC are output to the display screen and can pass through. The start and reset buttons control the PLC program to achieve multi-freedom displacement platform control.

Keywords: multi-degree-of-freedom displacement platform, position solving algorithm, PLC, display

目录

摘要 I

Abstract III

第一章 绪论 1

1.1 课题研究的背景及意义 1

1.2 多自由度运动平台研究现状和发展趋势 2

1.2.1多自由度位移平台的机械结构 2

1.2.2多自由度位移平台位置解算 2

1.2.3多自由度位移平台控制策略 2

1.2.4 多自由度位移平台控制器 3

1.3 多自由度位移平台控制程序 5

1.3.1 三菱PLC程序 5

1.3.2 人机交互界面程序 5

1.4 本文研究内容及章节安排 5

第二章 多自由度位移平台数学建模及仿真分析 7

2.1 建立坐标系 7

2.1.1 自由度 8

2.1.2 位姿 8

2.2 位置解算算法 9

2.2.1 正逆运动学 10

2.2.2 坐标变换 10

2.2.3 欧拉角公式 12

2.2.4 位置解算 13

2.3 基于MATLAB的位置解算仿真分析 16

第三章 多自由度位移平台控制软件设计 18

3.1 PLC编程软件Gxworks2 18

3.2 PLC程序设计流程 18

3.3 软件程序设计 19

3.3.1 输入 19

3.3.2 运动学算法运算 19

3.3.3 转动量转换 21

3.3.4 转轴控制 21

3.3.5 输出 22

3.3.6 原点复位 23

第四章 多自由度位移平台人机交互软件设计 24

4.1 人机交互界面设计 24

4.2 人机交互程序设计 25

第五章 系统调试与结果论证 27

第六章 结果与展望 30

6.1 工作总结 30

6.2 后续研究工作展望 30

参考文献 31

致谢 33

绪论

课题研究的背景及意义

当今社会，已经进入信息时代的浪潮中。随着制造业技术和软件控制技术的发展，多自由度位移平台越来越多地应用于各类受软件控制的运动系统中。常用多自由度位移平台分为并联机构和串联机构两类，并联机构具有结构简单、运行精度高等特点，广泛应用于运动仿真控制系统中^[1]。本课题使用的正是并联机构的多自由度位移平台。

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