Baranyi TP-Model Transformation-Based-Control Design Frameworks

1. Auflage 2016
ISBN: 978-3-319-19605-3
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 245 Seiten

This book covers new aspects and frameworks of control, design, and optimization based on the TP model transformation and its various extensions. The author outlines the three main steps of polytopic and LMI based control design: 1) development of the qLPV state-space model, 2) generation of the polytopic model; and 3) application of LMI to derive controller and observer. He goes on to describe why literature has extensively studied LMI design, but has not focused much on the second step, in part because the generation and manipulation of the polytopic form was not tractable in many cases. The author then shows how the TP model transformation facilitates this second step and hence reveals new directions, leading to powerful design procedures and the formulation of new questions. The chapters of this book, and the complex dynamical control tasks which they cover, are organized so as to present and analyze the beneficial aspect of the family of approaches (control, design, and optimization). Additionally, the book aims to convey simple TP modeling; a new convex hull manipulation based possibilities for optimization; a general framework for stability analysis; standardized modeling and system description; relaxed and universal LMI based design framework; and a gateway to time-delayed systems.

Autoren/Hrsg.

Baranyi, Péter

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Acronyms and Abbreviations;14
4;The Key Messages of the Book;16
5;Outline of the Book;20
5.1;References;23
6;Part I Generalized TP Model Transformation;28
6.1;1 Basic Concepts;29
6.1.1;1.1 Notations;29
6.1.2;1.2 TP Function;30
6.1.3;1.3 TP Model of qLPV Systems;31
6.1.4;1.4 TP Model: TS Fuzzy Model;32
6.1.5;1.5 HOSVD and Quasi-HOSVD Based Canonical Form of TP Functions;34
6.1.6;References;36
6.2;2 Algorithms of the TP Model Transformation;37
6.2.1;2.1 Original TP Model Transformation;37
6.2.1.1;2.1.1 Numerical Example;40
6.2.2;2.2 Bi-Linear TP Model Transformation;43
6.2.2.1;2.2.1 Numerical Example;48
6.2.3;2.3 Enriched TP Model Transformation;50
6.2.3.1;2.3.1 Numerical Example;51
6.2.4;2.4 Convex TP Model Transformation: Convex Hull Manipulation;51
6.2.4.1;2.4.1 Numerical Example;54
6.2.4.1.1;2.4.1.1 SNNN Type TP Model;54
6.2.4.1.2;2.4.1.2 CNO Type TP Model;55
6.2.4.1.3;2.4.1.3 IRNO Type TP Model;61
6.2.5;2.5 Pseudo TP Model Transformation;61
6.2.6;2.6 Partial TP + Model Transformation;69
6.2.6.1;2.6.1 Numerical Example;70
6.2.7;2.7 Multi TP Model Transformation;74
6.2.7.1;2.7.1 Numerical Example;75
6.2.8;2.8 Generalized TP Model Transformation;78
6.2.9;2.9 Interpolation of the Weighting Functions;80
6.2.9.1;2.9.1 Numerical Example;81
6.2.10;2.10 Unifying the Weighting Functions;85
6.2.11;2.11 Operations Between TP Functions;86
6.2.12;2.12 Towards Approximation in Case of Non-TP Functions;87
6.2.13;References;88
7;Part II TP Model Transformation Based Control Design and Optimalization Frameworks;89
7.1;3 TP Model Transformation is a Gateway Between Identification and Design;90
7.1.1;References;91
7.2;4 TP Model Transformation Based Control Design Structure;93
7.2.1;References;95
7.3;5 General Stability Verification and Control Design;96
7.3.1;5.1 Key Idea;96
7.3.2;5.2 Example;97
7.3.3;5.3 Decoupling the Design, Optimization, and Stability Verification: Generalized Design Frameworks;100
7.3.3.1;5.3.1 Multi-Way Convex Manipulation;102
7.3.3.2;5.3.2 Main and Independent TP Model Component Analysis via the HOSVD Based Canonical Form;105
7.3.3.3;5.3.3 Convex Hull Manipulation;105
7.3.3.4;5.3.4 LMI Based System Design;106
7.3.3.5;5.3.5 Exact System Reconstruction: Unified TP Model Forms;107
7.3.3.6;5.3.6 LMI Based Stability Verification;109
7.3.4;References;109
7.4;6 TPI Model Transformation for the Class of Non-qLPV Models;110
7.4.1;6.1 Key Idea;110
7.4.2;6.2 TP I Model Transformation;111
7.4.3;6.3 Example of Re-identification;112
7.4.4;Reference;112
7.5;7 TP? Model Transformation for Systems Including Time Delay;113
7.5.1;7.1 TP? Model Transformation;113
7.5.2;7.2 Example of the TP? Model Transformation;114
7.5.3;References;115
8;Part III Analysis of the TP Model Based Design Frameworks via a Complex Example;116
8.1;References;116
8.2;8 qLPV Model of the 3DoF Prototypical Aeroelastic Wing Section;118
8.2.1;8.1 Equations of Motion;118
8.2.2;8.2 Including Stribeck Friction;121
8.2.3;Reference;122
8.3;9 TP Model Based Control Design;123
8.3.1;9.1 Exact and Convex TP Model of the 3DoF Aeroelastic Wing Section;123
8.3.2;9.2 Control Structure;124
8.3.3;9.3 Selecting LMIs;126
8.3.4;9.4 Results of the Control Design;127
8.3.4.1;9.4.1 Controller 1: Asymptotic Stabilization and Decay Rate Control;127
8.3.4.2;9.4.2 Controller 2: Constraint on the Control Value;127
8.3.4.3;9.4.3 Controller 3: State Feedback Control Including Stribeck Friction;128
8.3.4.4;9.4.4 Simulation;128
8.3.4.5;9.4.5 Evaluation;129
8.3.5;References;135
8.4;10 Convex Hull Manipulation Based Optimization;136
8.4.1;10.1 Convex Hull Manipulation Based Design Framework;136
8.4.1.1;10.1.1 Key Steps;137
8.4.1.2;10.1.2 Step 1: Convex TP Models;137
8.4.1.3;10.1.3 Step 2: Convex TP Model Interpolation;137
8.4.1.4;10.1.4 Step 3: LMI Based Design and Stability Verification;139
8.4.2;10.2 Numerical Simulations;139
8.4.2.1;10.2.1 Determination of the Feasibility Region;139
8.4.2.2;10.2.2 Results of the Numerical Simulations;140
8.5;11 Complexity Manipulation Based Optimization;149
8.5.1;11.1 The Control Design Framework;149
8.5.1.1;11.1.1 Main TP Model Component Analysis: HOSVD Based Canonical Form of the Model;150
8.5.1.2;11.1.2 LMI Based System Design;151
8.5.1.3;11.1.3 Exact System Reconstruction: Unified Weightings in the Polytopes;155
8.5.1.4;11.1.4 LMI Based Stability Verification;155
8.5.1.5;11.1.5 Maximizing Omega;155
8.5.2;11.2 Evaluation of the Benefits of the Proposed Control Design;156
8.5.3;References;162
8.6;12 TP Model Manipulation Influences the Control Performance and the Feasibility of LMI Based Design;163
8.6.1;12.1 Feasibility;163
8.6.1.1;12.1.1 Initialization of the Numerical Analysis;163
8.6.1.2;12.1.2 Results of the 2D Analysis: Feasibility and Convex Hull;164
8.6.1.3;12.1.3 Results of the 3D Analysis: Feasibility, Convex Hull, and Complexity;166
8.6.1.4;12.1.4 Results of the 4D Analysis: Feasibility, Convex Hull, Complexity, and Parameter Space;166
8.6.1.5;12.1.5 Summary;172
8.6.2;12.2 Control Performance;172
8.6.2.1;12.2.1 Control Performance Results of the Numerical Simulation;172
8.6.2.2;12.2.2 Evaluation and Comparison of the Derived Cases and the Best Solution;174
8.6.3;Reference;178
9;Part IV TP Model Based Control Design of the Dual-Excenter Vibration Actuator;179
9.1;References;180
9.2;13 qLPV Model of the Dual Excenter Vibration System;182
9.2.1;References;187
9.3;14 Convex TP Model of the Dual Excenter Vibration System;188
9.3.1;14.1 The Quasi-HOSVD Based Canonical Form: Approximation and Complexity Trade-Off;188
9.3.2;14.2 The Convex TP Model;189
9.4;15 Derivation of the Controller;196
9.4.1;15.1 LMI Based Controller Design;196
9.4.2;15.2 Simulation;199
9.4.3;Reference;201
10;Part V Control of the Impedance Model Including Varying Time Delay via TP? Model Transformation;202
10.1;16 Impedance Control for Force Reflecting Telemanipulation;203
10.1.1;16.1 Impedance Control with Feedback Delay;204
10.1.2;16.2 Control Structure for Stability Preservation;206
10.1.3;References;209
10.2;17 Impedance Model with Varying Feedback Delay in TP Model Form;211
10.2.1;17.1 The Quasi-HOSVD Based Canonical Form;211
10.2.1.1;17.1.1 Exact Quasi-HOSVD Based Canonical Form;211
10.2.1.2;17.1.2 Executing Trade-off by TP? Model Transformation;214
10.2.2;17.2 Manipulation of the Convex Hull;215
10.2.2.1;17.2.1 The Vertices of the Exact TP Model;220
10.2.2.1.1;17.2.1.1 SNNN Type Convex Hull;220
10.2.2.1.2;17.2.1.2 IRNO Type Convex Hull;223
10.2.2.1.3;17.2.1.3 CNO Type Convex Hull;224
10.2.2.2;17.2.2 The 5 Vertices of the Reduced TP Model;224
10.2.2.2.1;17.2.2.1 SNNN Type Convex Hull;224
10.2.2.2.2;17.2.2.2 IRNO Type Convex Hull;225
10.2.2.2.3;17.2.2.3 CNO Type Convex Hull;225
10.2.2.3;17.2.3 The 4 Vertices of the Reduced TP Model;226
10.2.2.3.1;17.2.3.1 SNNN Type Convex Hull;226
10.2.2.3.2;17.2.3.2 IRNO Type Convex Hull;226
10.2.2.3.3;17.2.3.3 CNO Type Convex Hull;226
10.2.2.4;17.2.4 The 3 Vertices of the Reduced TP Model;227
10.2.2.4.1;17.2.4.1 SNNN Type Convex Hull;227
10.2.2.4.2;17.2.4.2 IRNO Type Convex Hull;227
10.2.2.4.3;17.2.4.3 CNO Type Convex Hull;227
10.2.3;17.3 Validation of the Convex TP Model;227
10.2.3.1;17.3.1 Constant Time-Delay;228
10.2.3.2;17.3.2 Varying Time-Delay;230
10.2.4;Reference;231
10.3;18 TP? Transformation Based Control Design for Impedance Controlled Robot Gripper;232
10.3.1;18.1 The Control Problem;232
10.3.2;18.2 Execution of the TP? Model Transformation;233
10.3.3;18.3 LMI-Based Multi-Objective Controller and Observer Design;233
10.3.4;18.4 Resulting Controller and Observer Gains;234
10.3.4.1;18.4.1 Controller-Observer 1;235
10.3.4.2;18.4.2 Controller-Observer 2;235
10.3.4.3;18.4.3 Controller-Observer 3;236
10.3.5;18.5 Evaluation and Validation of the Control Design;236
10.3.6;References;245