论文总字数：28899字

摘 要

桥式起重机一般建模为一个单摆模型，即一个质点附在不计质量的刚性构件的末端。为了提高安全性和起重机操作的定位精度，许多控制系统已被开发出来以减少载荷的残留摆动。然而,在大尺寸载荷的情况下，桥式起重机模型将从一个单摆系统转变为一个双摆系统。本论文为了解决桥式起重机负载摆动的问题，提出了一种基于S曲线的速度轨迹来达到抑制负载的残留振动的目的。首先，我们需要根据拉格朗日运动方程推导出双摆桥式起重机系统的动力学模型，本文考虑的是桥式起重机的一个双摆模型，而非单摆模型，这种双摆模型在当前的一些大中型桥式起重机中尤为适用。然后，由于一开始建立的动力学模型是双摆桥式起重机的非线性模型，这儿需要一些数学操作得到一个线性解耦模型。接着，基于这种线性解耦模型可以将提出的S曲线速度轨迹代入求得两个摆角的表达式。再往下则需要MATLAB编程数值计算求得考虑了最短运输时间的最优S曲线速度轨迹。最后，在SIMULINK中建立仿真模型，并将所提出的S曲线速度轨迹作为输入，来观察这种方法能否达到消除吊具摆角的目的。

关键词：桥式起重机 双摆 S曲线 最优控制 消摆

Anti-swing control for double-pendulum overhead cranes based on an S-shaped curve

Abstract

An overhead crane is usually modeled as a simple pendulum with a point mass attached to the end of a mass-less rigid link. In order to improve the security and the positioning accuracy of crane operation, many of the control system has been developed in order to reduce the residual oscillations of the payload. However, in the case of large load, the bridge crane model may be transformed from a single pendulum system into a double pendulum system. In this paper, aiming at the problem of bridge crane load swing, put forward a kind of based on the speed of the S-shaped curve track to suppress the residual oscillations of the payload. First, we need to derive a dynamic model according to the Lagrange equation of motion,a double-pendulum model of bridge crane is considered in this paper , rather than a single pendulum model. The double pendulum model in the current is especially applicable in some large-size and medium-size bridge crane. Then, due to first established model of double-pendulum is a nonlinear model, here we need some mathematical operations to achieve a linear decoupling model. Then, based on the linear decoupling model , put forward the S-shaped curve of speed trajectory to the expression of two pendulum Angle. Next,it requires MATLAB numerical calculation for the optimum speed of S-shaped curve track considering the shortest transport time. Finally, the simulation model is established in SIMULINK, and the S-shaped curve of the proposed speed trajectory as input, to observe this method can achieve the goal of eliminating sling angular.

Key Word:overhead crane;double-pendulum;S-shaped curve;optimal control; sway suppression

目 录

摘 要 Ⅰ

Abstract II

第一章 绪论 1

1．1 课题研究背景和意义 1

1．2 国内外研究现状 2

1．3 论文主要研究内容 4

第二章 数学模型的建立与分析 6

2.1 桥式起重机的双摆模型 6

2.2 拉格朗日方程的特点 7

2.3 数学模型的建立 7

2.3.1 双摆桥式起重机的非线性模型 7

2.3.2 双摆桥式起重机的线性解耦模型 8

2.4 本章小结 10

第三章 基于S曲线的消摆控制方案的设计 11

3.1 S曲线速度轨迹的提出 11

3.2 摆角和的求解 12

3.2.1 摆角和的求解 12

3.2.2 系数的求解 13

3.3 残留摆动的抑制 16

3.4 本章小结 17

第四章 仿真 18

4.1 双摆桥式起重机的仿真模型 18

4.2 PID控制器的简介及仿真 19

4.2.1 PID控制器的简介 19

4.2.2 PID控制器的参数整定及仿真 19

4.3 最优化数值计算 21

4.4 仿真结果与比较 23

4.4.1 仿真结果 23

4 .4.2 仿真结果的分析 24

4.4.3 仿真的比较与分析 25

4.5 仿真结果不理想的原因分析 33

4.6 本章小结 34

第五章 总结与展望 35

5.1 全文总结 35

5.2 展望 35

参考文献 36

附录 38

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