论文总字数：19704字

摘 要

起重机防摆系统在工业领域中的控制方面有很多应用，因其物理特征呈现为变量较多、耦合较强的特性，成为了非线性钻研领域里一个经典的模型。它是属于一种相当复杂，并且变化较多的系统。

起重机吊车体系里很难实现消除负载的摆动。从实际操作的角度来说，它对吊车体系迅速精准的搬运来说，难度相当之大；通常情况下我们用钢丝绳来连接吊车系统和负载。但在搬运过程中，负载会来回摆动，这是由于小车或者大车在不同情况下会有速度上的变化。我们发现，钢丝绳以及它所连接的挂钩和负载构成了一个体系，并且这个体系阻尼较小。所以负载需要很长期的衰减时间才会产生摆动响应。在实际情况中，一般要将负载快速准确的运到指定的地方，所以如果工作人员水平较高的话，他会将载重的物体平稳移动到正确地点。这个过程的速度必须很慢。并且在此之前，还要将运行速度调整到一个合适的值以后，或者载重的物体摆动格朗日运动方程。之后我们可以根据建立好的数学模型，来选择合理的方案来进行控制，并设计状态反馈控制器和PID控制器来搭建控制系统，从而实现精准的定位幅度较小以后，才能进行搬运操作。在这种情况下，如果负责操作的师傅不小心失误大意就会造成事故的发生，对生产率的提高反而没什么帮助。

为了加强吊车系统的安全性、提高工作效率以及达到便于实施等目的，我们有必要设计合适的控制方案来解决吊车系统存在的摆动问题。

在对系统的分析方面，本文首先通过对小车和负载受力分析，以小车的坐标位置、负载的摆角为输出量，以电机的拖动力为输入，建立桥式起重机的动力学数学模型，然后推导出桥式起重机的数学模型。这一推导过程需要使用到拉格朗日方程，在此基础上设计控制器实现小车的定位和荷载的消摆。

最后如何确定方案的可行性，就要通过Matlab/Simulink软件对完成的系统来进行比较和仿真。

关键词：桥式起重机 拉格朗日运动方程 控制器 状态反馈 PID控制

Abstract

The crane anti-sway system has many applications in the control of the industrial field. Because its physical characteristics are characterized by more variables and stronger coupling, it has become a classic model in the field of nonlinear drilling. It belongs to a rather complex and more varied system.

It is difficult to eliminate the load swing in crane crane system. From a practical point of view, it is very difficult for the crane to quickly and accurately carry the system; usually we use wire rope to connect the crane system and load.But in the process of handling, the load will swing back and forth. This is because the trolley or cart will change in speed under different conditions. We have found that the wire rope and the hooks and loads it is connected to form a system, and this system is less damped.So the load needs a very long decay time to produce the swing response. In the actual situation, the load is generally quickly and accurately transported to a designated place, so if the staff is at a high level, he will smoothly move the heavy load to the correct location. The speed of this process must be slow.And before this, it is necessary to adjust the operation speed to an appropriate value, or after the swing of the heavy object is small, the handling operation can be carried out. In this case, if the caretaker responsible for the operation accidentally carelessly causes accidents, it will not help the improvement of productivity.

In order to strengthen the safety of the crane system, improve the work efficiency, and achieve the purpose of easy implementation, it is necessary to design a suitable control scheme to solve the swing problem of the crane system.

In the analysis of the system, this paper first analyzes the load of the trolley and the load, and uses the coordinate position of the trolley and the swing angle of the load as the output, and takes the drag force of the motor as input to establish the dynamic mathematical model of the bridge crane. , and then deduced the mathematical model of the bridge crane.This derivation process requires the use of the Lagrangian equation of motion. Afterwards, we can choose a reasonable scheme to control according to the established mathematical model, and design the state feedback controller and PID controller to build the control system so as to achieve accurate positioning and prevent swing of weight.

Finally, how to determine the feasibility of the program, we must use Matlab/Simulink software to compare and simulate the completed system.

Key Words：Bridge Cranes; Lagrangian Motion Equations; Controllers;State feedback; PID control

目 录

摘 要 I

Abstract II

目 录 IV

第一章 绪 论 1

1.1 桥式起重机的研究背景及意义 1

1.2 桥式起重机的发展趋势 3

1.3 桥式起重机消摆控制研究现状 3

1.3.1国外桥式起重机消摆控制研究现状 3

1.3.2国内桥式起重机消摆控制研究现状 4

1.4本文主要内容及章节排布 5

第二章 桥式起重机动力学建模 6

2.1动力学模型建立方法 6

2.2受力模型建立及简化 6

2.2.1小车和荷载载的坐标及速度分量 8

2.2.2系统的动能和势能 9

2.3桥式起重机动力学系统方程的传递函数 10

2.4桥式起重机动力学系统的状态方程 11

2.5模型参数的选取 12

第三章 基于状态反馈的控制模型设计 13

3.1分析起重机防摆系统性能 13

3.1.1分析系统稳定性 13

3.1.2分析系统是否可控和可观 13

3.2状态反馈控制器设计 15

3.3控制算法 16

3.4极点配置 17

第四章 仿真分析 19

4.1系统仿真模型的建立 19

第五章 常规PID控制器的设计 26

5.1 PID控制器的结构 26

5.2 PID参数的整定 27

5.3 PID控制仿真分析 30

参 考 文 献 35

致 谢 37

第一章 绪 论

1.1 桥式起重机的研究背景及意义

在日常生活中，起重机的使用相当普遍。它一般被用来装卸物资，搬运材料，安装设施。它能够代替大量的劳动力，从而减轻劳动成本，提高工作效率。

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