非線性動力學系統(tǒng)的多目標優(yōu)化控制設計
發(fā)布時間：2021-07-17 09:19
動力學系統(tǒng)可以描述狀態(tài)空間中的點隨時間演化的運動規(guī)律,可以由一組微分（或差分）方程來表示。根據動力學系統(tǒng)方程的表達形式,可以將其分為線性系統(tǒng)和非線性系統(tǒng)兩種。線性系統(tǒng)嚴格遵守疊加原理,系統(tǒng)輸出與系統(tǒng)輸入成比例關系。滿足疊加原理的線性系統(tǒng)可以由一組線性常微分方程來描述。如果線性系統(tǒng)的參數不會隨著時間的變化而變化,我們稱其為線性時不變系統(tǒng),即線性時不變系統(tǒng)既滿足疊加原理又具有時不變的特性。對于通過時域來描述的帶有控制的線性系統(tǒng),有很多種追蹤控制設計方法可以使得我們的系統(tǒng)沿著我們所設定的軌跡去運行,例如傳統(tǒng)的比例積分微分（PID）設計方法,線性二次型最優(yōu)控制設計方法（LQR）以及全狀態(tài)反饋方法等。除了時域設計以外,還可以將線性時不變系統(tǒng)轉換為頻域中的表達方式來進行處理,常用的頻域處理方法有多種,例如拉普拉斯變換（拉氏變換）,傅里葉變換,Z變換方法,根軌跡法,伯德圖以及奈奎斯特穩(wěn)定性準則等。這些頻域處理方法通常使用諸如帶寬,頻率響應,特征值,增益,共振頻率,極點和零點等術語來描述。由于線性控制設計不是本論文的研究重點,我們在此不做過多的敘述。非線性系統(tǒng)可以由一組非線性常微分方程進行描述,然而不...
【文章來源】：天津大學天津市 211工程院校 985工程院校 教育部直屬院校
【文章頁數】：178 頁
【學位級別】：博士
【文章目錄】：
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
參考文獻
發(fā)表論文和參加科研情況說明
致謝
【參考文獻】：
期刊論文
[1]切換目標函數多目標非線性模型預測控制及其在化工過程中的應用（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]數據挖掘中聚類算法研究進展[J]. 周濤,陸惠玲. 計算機工程與應用. 2012(12)
[5]改進k-means聚類算法多模型建模的一種新的評價函數[J]. 周立芳,周蘆文,趙豫紅. 化工學報. 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). 自動化學報. 2006(03)
[7]免疫算法[J]. 王磊,潘進,焦李成. 電子學報. 2000(07)
本文編號：3287891
【文章來源】：天津大學天津市 211工程院校 985工程院校 教育部直屬院校
【文章頁數】：178 頁
【學位級別】：博士
【文章目錄】：
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
參考文獻
發(fā)表論文和參加科研情況說明
致謝
【參考文獻】：
期刊論文
[1]切換目標函數多目標非線性模型預測控制及其在化工過程中的應用（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]數據挖掘中聚類算法研究進展[J]. 周濤,陸惠玲. 計算機工程與應用. 2012(12)
[5]改進k-means聚類算法多模型建模的一種新的評價函數[J]. 周立芳,周蘆文,趙豫紅. 化工學報. 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). 自動化學報. 2006(03)
[7]免疫算法[J]. 王磊,潘進,焦李成. 電子學報. 2000(07)
本文編號：3287891
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