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摘 要
大型桁架式桥梁检测车能够对大宽度的桥梁进行流动检测和养护,在工作时需要
把工作人员送到桥底,因此在空间中形成了一个很长的钢结构平台。由于材料的弹性,
在诸如工作人员行走、桥梁振动、风载荷等的扰动下,桥梁检测车的车身与工作平台
会产生振动。这种振动会降低工作平台的稳定性和舒适度。为了提高桁架式桥梁检测
车对外部环境扰动的适应能力并为工作人员创造更稳定的工作平台,本论文以某型号
的桁架式桥梁检测车为研究对象,展开对其振动控制的研究。建立桥检车在扰动下的
力学方程,用 PID 控制算法对主动悬架进行控制从而减小车身的振动,用 LQG 控制
算法对主动质量阻尼减振器进行控制从而减小工作平台的振动,把得到的受控状态下
的仿真结果与无控时的对比,显示出了较好的减振效果。
首先,对桥梁的模型进行简化,并根据欧拉-伯努利梁假设建立桥梁横向振动的力
学方程。求出匀速移动车辆对桥梁作用的广义力,用 MatLab 做出桥梁跨中振动的响
应曲线。
其次,用 PID 控制算法设计了主动悬架。列出微分方程形式的悬架振动力学方程,
用拉普拉斯变换求出传递函数。用 Simulink 仿真出车身在无控情况下的振动响应。设
计 PID 控制器比例、积分、微分环节的增益系数,用 Simulink 仿真,得出主动悬架对
车身振动的控制效果。
再次,用离散化的方法对工作平台力学模型进行简化,建立力学方程。简化行人
载荷的模型,用 MatLab 分别计算出行人在桁架各段行走所产生的振动响应。计算出
脉动风对桁架的载荷,用 MatLab 计算出桁架在风载荷下的振动响应。
最后,建立有主控力的工作平台力学方程。用 LQR 控制算法求出了反馈增益矩阵
K。设计 Kalman 滤波器,求出卡尔曼滤波增益。根据 LQG 控制算法用 Simulink 分别
建立桁架在行人激励和脉动风激励下的振动控制仿真模型。求出 LQG 控制算法下系
统的振动响应,与无控时的振动响应对比。
关键词:桁架式桥梁检测车,振型分析,主动减振,PID 控制,LQR 控制,LQG
控制,AMD
Abstract
Large truss bridge inspection vehicle can be used to detect and repair large-width
bridges. During the work, the workers need to be sent to the bottom of the bridge, thus
forming a long steel structure platform suspended in the space. Due to the elasticity of the
material, the vehicle body and working platform of the bridge inspection vehicle will
vibrate under the disturbance such as workers' walking, bridge vibration and wind load , etc.
These vibrations will reduce the stability and comfort of the working platform. In order to
improve the vehicle’s adaptability to external environment disturbances, and to create a
more stable working platform for the workers, this paper takes a certain model of truss
bridge inspection vehicle as research object and do research on its vibration control.
Establish mechanical equation of bridge inspection vehicle under disturbances. PID control
algorithm is designed for the active suspension to reduce the vibration of the vehicle body.
LQG control algorithm is designed for the active mass damper to reduce the vibration of the
working platform. The results comparison between the simulations in which control force is
applied and those in which have no control force shows a good damping effect.
Firstly, simplify the bridge to an equal-beam model, establish its mechanical equation
of transverse vibration, according to Euler-Bernoulli beam hypothesis. Obtain the
generalized force exerted by moving vehicle on bridge, use MatLab to make the response
curve of vibration at bridge mid-span.
Secondly, design PID control algorithm for active suspension. Establish differential
equations of the vehicle suspension, obtain system transfer function by Laplace transform.
Use Simulink to simulate vehicle body vibration response under disturbance. Design the
gain coefficients of proportional, integral and differential links of PID controller, use
Simulink to simulate the system with PID controller to see control effect of active
suspension.
Thirdly, simplify the mechanical model of working platform into distributed mass
model, and establish its mechanical equation. Simplify pedestrian load model, use MatLab
to calculate the vibration responses of pedestrians walking in each section of the platform.
Calculate the wind load applied to the platform, use MatLab to calculate the vibration
response of the platform under wind load.
Finally, establish the mechanical equation of working platform involved with control
force. Obtain feedback gain matrix K by using LQR control algorithm. Design Kalman
filter and calculate Kalman filter gain. According to LQG control algorithm, vibration
control models of working platform under pedestrian excitation and wind load excitation are
established in Simulink respectively. Make a comparison between under-control vibration
response and no control vibration response of the platform.
Key works: Truss bridge inspection vehicle, Mode analysis, Active damping, PID
control, LQR control, LQG control, AMD.
I
目 录
第一章 绪论 ...................................................................................................................... 1
1.1 研究的背景及意义 .............................................................................................. 1
1.2 国内外桥梁检测车发展及研究现状 .................................................................. 2
1.2.1 国内外桥梁检测车发展现状 ................................................................... 3
1.2.2 国内桥梁检测车研究现状 ....................................................................... 3
1.3 国内外主动、半主动减振研究现状 .................................................................. 5
1.4 存在的问题 .......................................................................................................... 7
1.5 研究的主要内容 .................................................................................................. 8
第二章 桥梁振动对桥检车的影响分析 ........................................................................ 11
2.1 建立桥梁横向振动力学模型 ............................................................................ 11
2.1.1 桥梁横向振动各阶振型 ......................................................................... 11
2.1.2 桥梁横向振动微分方程 ......................................................................... 14
2.2 来往车辆对桥面的振动激励 ............................................................................ 16
2.2.1 行驶车辆自重对桥梁振动的影响 ......................................................... 17
2.2.2 匀速移动力偶对桥梁振动的影响 ......................................................... 18
2.3 求解桥梁在激励下的响应 ................................................................................ 19
2.3.1 桥梁在两种激励下的响应 ..................................................................... 20
2.3.2 工程实例计算 ......................................................................................... 20
2.4 本章小结 ............................................................................................................ 22
第三章 主动悬架减振 .................................................................................................... 25
3.1 桥梁检测车悬架力学模型建立 ........................................................................ 25
3.2 悬架系统传递函数的建立 ................................................................................ 26
3.3 无控时桥检车的振动响应 ................................................................................ 27
3.4 主控力的计算 .................................................................................................... 28
3.4.1 PID 控制算法 .......................................................................................... 28
3.4.2 主动悬架 Simulink 仿真 ........................................................................ 29
3.5 随机扰动下主动悬架的减振效果分析 ............................................................ 32
3.6 本章小结 ............................................................................................................ 34
第四章 桁架振动的分析 ................................................................................................ 35
4.1 桁架式桥梁检测车基本结构与工作原理 ........................................................ 35
II
4.1.1 桁架式桥梁检测车基本结构 ................................................................. 35
4.1.2 桁架式桥梁检测车工作过程 ................................................................. 36
4.2 桥梁检测车臂架力学模型建立 ........................................................................ 38
4.2.1 臂架基本参数 ......................................................................................... 38
4.2.2 臂架力学模型的简化 ............................................................................. 40
4.2.3 臂架力学模型的建立 ............................................................................. 41
4.3 工作人员的行走对桁架的激励分析 ................................................................ 45
4.3.1 行人力学模型建立 ................................................................................. 45
4.3.2 行人激励分析 ......................................................................................... 46
4.4 风载荷对桁架的激励分析 ................................................................................ 49
4.5 本章小结 ............................................................................................................ 54
第五章 结构主动质量阻尼减振 .................................................................................... 55
5.1 主动质量阻尼减振 ............................................................................................ 55
5.1.1 主动质量阻尼器原理 ............................................................................. 55
5.1.2 被动调谐质量阻尼器参数确定 ............................................................. 56
5.2 主控力的计算 .................................................................................................... 57
5.2.1 桁架竖直方向振动的力学方程建立 ..................................................... 57
5.2.2 振动控制系统状态方程的建立 ............................................................. 58
5.2.3 系统能控性和稳定性分析 ..................................................................... 59
5.2.4 LQR 控制算法 ........................................................................................ 60
5.2.5 加权矩阵的选择 ..................................................................................... 61
5.3 LQG 控制算法基本原理 .................................................................................. 66
5.4 LQG 控制器设计 .............................................................................................. 68
5.4.1 系统的能观性 ......................................................................................... 68
5.4.2 Kalman 滤波器 ....................................................................................... 69
5.4.3 LQG 控制算法 Simulink 仿真 ............................................................... 70
5.5 本章小结 ............................................................................................................ 74
结论 .................................................................................................................................. 75
参考文献 .......................................................................................................................... 77
致谢 .................................................................................................................................. 81
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