非线性动力学系统的多目标优化控制设计
发布时间：2021-07-17 09:19
动力学系统可以描述状态空间中的点随时间演化的运动规律,可以由一组微分（或差分）方程来表示。根据动力学系统方程的表达形式,可以将其分为线性系统和非线性系统两种。线性系统严格遵守叠加原理,系统输出与系统输入成比例关系。满足叠加原理的线性系统可以由一组线性常微分方程来描述。如果线性系统的参数不会随着时间的变化而变化,我们称其为线性时不变系统,即线性时不变系统既满足叠加原理又具有时不变的特性。对于通过时域来描述的带有控制的线性系统,有很多种追踪控制设计方法可以使得我们的系统沿着我们所设定的轨迹去运行,例如传统的比例积分微分（PID）设计方法,线性二次型最优控制设计方法（LQR）以及全状态反馈方法等。除了时域设计以外,还可以将线性时不变系统转换为频域中的表达方式来进行处理,常用的频域处理方法有多种,例如拉普拉斯变换（拉氏变换）,傅里叶变换,Z变换方法,根轨迹法,伯德图以及奈奎斯特稳定性准则等。这些频域处理方法通常使用诸如带宽,频率响应,特征值,增益,共振频率,极点和零点等术语来描述。由于线性控制设计不是本论文的研究重点,我们在此不做过多的叙述。非线性系统可以由一组非线性常微分方程进行描述,然而不...
【文章来源】：天津大学天津市 211工程院校 985工程院校 教育部直属院校
【文章页数】：178 页
【学位级别】：博士
【文章目录】：
中文摘要
ABSTRACT
Nomenclature
Abbreviation
Chapter 1 Introduction
1.1 Linear and Nonlinear Control
1.2 Time-delayed Dynamic System
1.3 Outline of the Thesis
Chapter 2 Methods for Control Design
2.1 Linear Control
2.1.1 PID Control
2.1.2 LQR Optimal Control
2.1.3 Pole Placement Method
2.2 Nonlinear Control
2.2.1 Sliding Mode Control
2.2.2 Example
2.3 Time Delay Control
2.3.1 Semi-Discretization
2.3.2 High-Order Control
2.3.3 Sliding Mode Control
Chapter 3 Multi-objective Optimization
3.1 Problem Statement
3.1.1 MOP Definition
3.1.2 Example
3.2 Genetic Algorithm
3.2.1 Introduction to Genetic Algorithm
3.2.2 Multi-objective Genetic Algorithm
3.3 Particle Swarm Optimization Algorithm
3.4 Simple Cell Mapping Method
3.4.1 Gradient-free Searching
3.4.2 Gradient-based Searching
3.4.3 The Hybrid Algorithm
3.4.4 Parallel Computing
Chapter 4 Multi-objective Optimal Sliding Mode Control
4.1 System Modeling
4.1.1 Geometric Deformation Analysis
4.1.2 Modeling with Euler-Lagrange Method
4.1.3 State Space Equations
4.2 Multi-objective Optimal Design
4.2.1 Stability Analysis
4.2.2 Stability on the Sliding Surface
4.2.3 Multi-objective Optimization
4.2.4 Numerical and Experimental Results
4.3 Robustness Study
4.3.1 Response of Nominal Model
4.3.2 Inertial Uncertainty of Rotary Arm
4.3.3 Inertial Uncertainty of Rotating Base
4.3.4 Stiffness Uncertainty
4.3.5 Effect of Estimation Error Bounds
4.4 A Post Processing of Multi-objective Optimal Design
4.4.1 Improved K-means Algorithm
4.4.2 Switching Algorithm
4.4.3 Examples
Chapter 5 Multiple Input Multiple Output System
5.1 Dynamical Modelling of a Helicopter Module
5.2 Control Formulation
5.3 MOP Design with Cell Mapping Method
5.3.1 Optimal Design Procedure
5.3.2 Numerical Results
5.4 MOP Design with Particle Swarm Optimization (PSO)
5.4.1 Numerical Results
5.5 A Comparison Study
Chapter 6 Control of Time Delay Dynamical Systems
6.1 Single Inverted Pendulum
6.1.1 LQR Control
6.1.2 Control with Semi-Discretization Method
6.1.3 High-Order Control
6.1.4 A Study of High-Order Control
6.2 Rotary Flexible Joint
6.2.1 Pole Placement
6.2.2 Sliding Mode Control
Chapter 7 Concluding Remarks
参考文献
发表论文和参加科研情况说明
致谢
【参考文献】：
期刊论文
[1]切换目标函数多目标非线性模型预测控制及其在化工过程中的应用（英文）[J]. 何德峰,余世明,俞立. Chinese Journal of Chemical Engineering. 2015(10)
[2]On Density-Based Data Streams Clustering Algorithms: A Survey[J]. Amineh Amini,Teh Ying Wah,Hadi Saboohi. Journal of Computer Science & Technology. 2014(01)
[3]A multi-objective optimal PID control for a nonlinear system with time delay[J]. Furui Xiong,Zhichang Qin,Carlos Hernndez,Yousef Sardahi,Yousef Narajani,Wei Liang,Yang Xue,Oliver Schtze,Jianqiao Sun. Theoretical & Applied Mechanics Letters. 2013(06)
[4]数据挖掘中聚类算法研究进展[J]. 周涛,陆惠玲. 计算机工程与应用. 2012(12)
[5]改进k-means聚类算法多模型建模的一种新的评价函数[J]. 周立芳,周芦文,赵豫红. 化工学报. 2007(08)
[6]Hierarchical Switching Control of Multiple Models Based on Robust Control Theory[J]. GAO FENG LI Ke-Qiang LIAN Xiao-Min (State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084). 自动化学报. 2006(03)
[7]免疫算法[J]. 王磊,潘进,焦李成. 电子学报. 2000(07)
本文编号：3287891
【文章来源】：天津大学天津市 211工程院校 985工程院校 教育部直属院校
【文章页数】：178 页
【学位级别】：博士
【文章目录】：
中文摘要
ABSTRACT
Nomenclature
Abbreviation
Chapter 1 Introduction
1.1 Linear and Nonlinear Control
1.2 Time-delayed Dynamic System
1.3 Outline of the Thesis
Chapter 2 Methods for Control Design
2.1 Linear Control
2.1.1 PID Control
2.1.2 LQR Optimal Control
2.1.3 Pole Placement Method
2.2 Nonlinear Control
2.2.1 Sliding Mode Control
2.2.2 Example
2.3 Time Delay Control
2.3.1 Semi-Discretization
2.3.2 High-Order Control
2.3.3 Sliding Mode Control
Chapter 3 Multi-objective Optimization
3.1 Problem Statement
3.1.1 MOP Definition
3.1.2 Example
3.2 Genetic Algorithm
3.2.1 Introduction to Genetic Algorithm
3.2.2 Multi-objective Genetic Algorithm
3.3 Particle Swarm Optimization Algorithm
3.4 Simple Cell Mapping Method
3.4.1 Gradient-free Searching
3.4.2 Gradient-based Searching
3.4.3 The Hybrid Algorithm
3.4.4 Parallel Computing
Chapter 4 Multi-objective Optimal Sliding Mode Control
4.1 System Modeling
4.1.1 Geometric Deformation Analysis
4.1.2 Modeling with Euler-Lagrange Method
4.1.3 State Space Equations
4.2 Multi-objective Optimal Design
4.2.1 Stability Analysis
4.2.2 Stability on the Sliding Surface
4.2.3 Multi-objective Optimization
4.2.4 Numerical and Experimental Results
4.3 Robustness Study
4.3.1 Response of Nominal Model
4.3.2 Inertial Uncertainty of Rotary Arm
4.3.3 Inertial Uncertainty of Rotating Base
4.3.4 Stiffness Uncertainty
4.3.5 Effect of Estimation Error Bounds
4.4 A Post Processing of Multi-objective Optimal Design
4.4.1 Improved K-means Algorithm
4.4.2 Switching Algorithm
4.4.3 Examples
Chapter 5 Multiple Input Multiple Output System
5.1 Dynamical Modelling of a Helicopter Module
5.2 Control Formulation
5.3 MOP Design with Cell Mapping Method
5.3.1 Optimal Design Procedure
5.3.2 Numerical Results
5.4 MOP Design with Particle Swarm Optimization (PSO)
5.4.1 Numerical Results
5.5 A Comparison Study
Chapter 6 Control of Time Delay Dynamical Systems
6.1 Single Inverted Pendulum
6.1.1 LQR Control
6.1.2 Control with Semi-Discretization Method
6.1.3 High-Order Control
6.1.4 A Study of High-Order Control
6.2 Rotary Flexible Joint
6.2.1 Pole Placement
6.2.2 Sliding Mode Control
Chapter 7 Concluding Remarks
参考文献
发表论文和参加科研情况说明
致谢
【参考文献】：
期刊论文
[1]切换目标函数多目标非线性模型预测控制及其在化工过程中的应用（英文）[J]. 何德峰,余世明,俞立. Chinese Journal of Chemical Engineering. 2015(10)
[2]On Density-Based Data Streams Clustering Algorithms: A Survey[J]. Amineh Amini,Teh Ying Wah,Hadi Saboohi. Journal of Computer Science & Technology. 2014(01)
[3]A multi-objective optimal PID control for a nonlinear system with time delay[J]. Furui Xiong,Zhichang Qin,Carlos Hernndez,Yousef Sardahi,Yousef Narajani,Wei Liang,Yang Xue,Oliver Schtze,Jianqiao Sun. Theoretical & Applied Mechanics Letters. 2013(06)
[4]数据挖掘中聚类算法研究进展[J]. 周涛,陆惠玲. 计算机工程与应用. 2012(12)
[5]改进k-means聚类算法多模型建模的一种新的评价函数[J]. 周立芳,周芦文,赵豫红. 化工学报. 2007(08)
[6]Hierarchical Switching Control of Multiple Models Based on Robust Control Theory[J]. GAO FENG LI Ke-Qiang LIAN Xiao-Min (State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084). 自动化学报. 2006(03)
[7]免疫算法[J]. 王磊,潘进,焦李成. 电子学报. 2000(07)
本文编号：3287891
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