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烟台大学硕士学位论文
I
摘要
近年来,随着科学技术和工业化进程的飞速发展,柔性机械臂因具有功耗低、自
身质量轻和运动速度快等特点,被广泛应用于机械制造业和航空航天等领域。然而,
由于柔性机械臂本身的物理特性,使得其建立的动力学模型参数非常复杂,难以实现
对其位置的高精度跟踪控制。针对此问题,本文基于单链杆柔性机械臂进行了如下的
研究:
(
1
)本文将柔性机械臂近似为
Euler–Bernoulli
梁进行建模分析。应用哈密顿原
理建立柔性机械臂偏微分方程动力学模型。运用假设模态法对柔性机械臂的偏微分
方程动力学模型进行降维,得到了常微分方程动力学模型并推导出状态空间方程表
达式。根据柔性机械臂的状态空间表达式建立了反映
Euler–Bernoulli
梁高阶模态的
柔性机械臂动力学模型。
(
2
)柔性机械臂高阶模态会对位置跟踪控制产生扰动影响,本文基于
Euler
–
Bernoulli
梁高阶模态的柔性机械臂动力学模型,设计状态观测器对高阶模态变量进
行观测,提出柔性机械臂位置输出反馈跟踪的自适应控制方法。在
MATLAB/Simulink
中进行仿真分析,通过与传统自适应控制方法进行比较,验证了输出反馈自适应控制
的有效性和可行性。
(
3
)柔性机械臂系统实际运行过程中,常因受到诸多不确定因素影响,而造成
位置跟踪偏差大,甚至引起柔性机械臂系统震荡并造成结构损坏。为了提高柔性机械
臂系统的安全性和鲁棒性,本文研究了状态约束的柔性机械臂位置跟踪控制问题,提
出了基于障碍李雅普诺夫函数的柔性机械臂位置输出反馈跟踪的自适应控制方法。
分别利用常值对数型和时变对数型障碍李雅普诺夫函数对柔性机械臂系统的输出进
行约束限制,运用
MATLAB/Simulink
软件对设计的两种控制器进行对比仿真分析,
验证了基于时变对数型障碍李雅普诺夫函数的反馈控制在柔性机械臂位置跟踪中的
可行性和有效性。
(
4
)针对柔性机械臂的状态空间方程因参数简化而导致模型精度降低的问题进
行研究。运用
Adams
虚拟样机仿真分析软件结合
MATLAB/Simulink
搭建联合仿真
摘要
II
实验平台,并对基于时变对数型障碍李雅普诺夫函数设计的位置跟踪控制器进行了
仿真分析,验证了该控制器对柔性机械臂实际控制结果的有效性。
关键词:柔性机械臂;
哈密顿原理;状态观测器;障碍李雅普诺夫函数
烟台大学硕士学位论文
III
Abstract
In recent years, with the rapid development of science and technology and
industrialization, flexible manipulators have been widely used in the fields of machinery
manufacturing and aerospace due to their low power consumption, lightweight, and fast
movement speed. However, due to the physical characteristics of the flexible manipulator
itself, the parameters of the established dynamic model are very complex, and it is difficult
to achieve high-precision tracking control of its position. The following study has been
conducted in this paper based on a single-link flexible manipulator.
(1) In this paper, the flexible manipulator is approximated as a Euler–Bernoulli beam
for modeling analysis. The partial differential equation dynamics model of the flexible
manipulator is established by applying the Hamiltonian principle. The hypothetical mode
method is used to reduce the dimension of the partial differential equation dynamic model
of the flexible manipulator, and the ordinary differential equation dynamic model is obtained
and the expression of the state space equation is derived. According to the state space
expression of the flexible manipulator, a dynamic model of the flexible manipulator
reflecting the higher-order modes of the Euler–Bernoulli beam is established.
(2) This paper focuses on the disturbance effects caused by high-order modes of
flexible manipulator on position tracking control. Based on the dynamic model of a flexible
manipulator using the Euler-Bernoulli beam high-order mode, a state observer is designed
to observe the high-order mode variables. An adaptive control method for position output
feedback tracking of flexible manipulator is proposed. Simulation analysis is conducted
using MATLAB/Simulink, and the effectiveness and feasibility of the output feedback
tracking control are verified by comparing it with traditional adaptive control methods.
(3) During the operation of a flexible manipulator system, it is often subject to various
uncertain factors, resulting in large position tracking errors and even causing oscillations
and structural damage to the system. In order to improve the safety and robustness of the
flexible manipulator system, this paper studies the constrained state of the position tracking
Abstract
IV
control problem of the flexible manipulator, and proposes an adaptive control method for
position output feedback tracking based on obstacle Lyapunov functions. By using both
constant and time-varying logarithmic obstacle Lyapunov functions to constrain the output
of the flexible manipulator system, two controllers are designed and compared through
simulation analysis using MATLAB/Simulink software. The feasibility and effectiveness of
the feedback controller based on time-varying logarithmic obstacle Lyapunov functions in
the position tracking of the flexible manipulator are verified.
(4) Research was conducted on the issue of reduced model accuracy due to parameter
simplification in the state space equation of a flexible manipulator. An integrated simulation
experimental platform was constructed using Adams virtual prototyping simulation
software combined with MATLAB/Simulink, and a feedback controller based on the time-
varying logarithmic barrier Lyapunov function was designed and simulated to verify the
effectiveness of the controller on the actual control results of the flexible manipulator.
Keywords
: flexible manipulator; hamilton's principle; state observer; barrier lyapunov
function
目 录
第 1 章 绪论............................................................................................... 1
1.1 研究的目的及意义 ........................................................................... 1
1.2 国内外研究现状 ............................................................................... 2
1.2.1 柔性机械臂建模理论研究 ......................................................... 2
1.2.2 柔性机械臂控制方法研究 ......................................................... 6
1.3 本文的主要结构安排 ..................................................................... 10
第 2 章 柔性机械臂系统的建模 ............................................................ 12
2.1 引言 ................................................................................................. 12
2.2 柔性机械臂的动力学模型建立 .................................................... 12
2.2.1 基于 Hamilton 的动力学建模 ............................................... 13
2.2.2 基于假设模态法的模型离散化 ............................................... 18
2.2.3 柔性机械臂的状态空间方程 ................................................... 24
2.3 本章小结 ......................................................................................... 24
第 3 章 基于输出反馈的柔性机械臂自适应位置跟踪控制 ................ 25
3.1 引言 ................................................................................................. 25
3.2 状态观测器设计 ............................................................................. 25
3.3 输出反馈自适应控制设计 ............................................................ 26
3.4 数值仿真与结果分析 ..................................................................... 30
3.4.1 状态观测器数值仿真与结果分析 ........................................... 30
3.4.2 输出反馈自适应控制的数值仿真与结果分析 ...................... 34
3.5 本章小结 ......................................................................................... 37
第 4 章 具有输出约束的柔性机械臂自适应位置跟踪控制 ................ 38
4.1 引言 ................................................................................................. 38
4.2 控制器设计 ..................................................................................... 38
4.2.1 基于常数对数型 BLF 位置跟踪控制 ..................................... 38
4.2.2 基于时变对数型 BLF 位置跟踪控制 ..................................... 42
4.3 数值仿真与结果分析 ..................................................................... 45
4.3.1 阶跃信号位置跟踪 ................................................................... 46
4.3.2 正弦信号位置跟踪 ................................................................... 47
4.4 本章小结 ......................................................................................... 48
第 5 章 柔性机械臂系统虚拟样机动力学建模与控制仿真 ................ 49
5.1 引言 ................................................................................................. 49
5.2 联合仿真流程 ................................................................................. 50
5.3 柔性机械臂联合仿真平台搭建 .................................................... 52
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