TP-Model Transformation-Based-Control Design Frameworks (eBook)

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2016 | 1st ed. 2016
XXVI, 230 Seiten
Springer International Publishing (Verlag)
978-3-319-19605-3 (ISBN)

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TP-Model Transformation-Based-Control Design Frameworks - Péter Baranyi
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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.

Preface 6
Contents 8
Acronyms and Abbreviations 14
The Key Messages of the Book 16
Outline of the Book 20
References 23
Part I Generalized TP Model Transformation 28
1 Basic Concepts 29
1.1 Notations 29
1.2 TP Function 30
1.3 TP Model of qLPV Systems 31
1.4 TP Model: TS Fuzzy Model 32
1.5 HOSVD and Quasi-HOSVD Based Canonical Form of TP Functions 34
References 36
2 Algorithms of the TP Model Transformation 37
2.1 Original TP Model Transformation 37
2.1.1 Numerical Example 40
2.2 Bi-Linear TP Model Transformation 43
2.2.1 Numerical Example 48
2.3 Enriched TP Model Transformation 50
2.3.1 Numerical Example 51
2.4 Convex TP Model Transformation: Convex Hull Manipulation 51
2.4.1 Numerical Example 54
2.4.1.1 SNNN Type TP Model 54
2.4.1.2 CNO Type TP Model 55
2.4.1.3 IRNO Type TP Model 61
2.5 Pseudo TP Model Transformation 61
2.6 Partial TP + Model Transformation 69
2.6.1 Numerical Example 70
2.7 Multi TP Model Transformation 74
2.7.1 Numerical Example 75
2.8 Generalized TP Model Transformation 78
2.9 Interpolation of the Weighting Functions 80
2.9.1 Numerical Example 81
2.10 Unifying the Weighting Functions 85
2.11 Operations Between TP Functions 86
2.12 Towards Approximation in Case of Non-TP Functions 87
References 88
Part II TP Model Transformation Based Control Design and Optimalization Frameworks 89
3 TP Model Transformation is a Gateway Between Identification and Design 90
References 91
4 TP Model Transformation Based Control Design Structure 93
References 95
5 General Stability Verification and Control Design 96
5.1 Key Idea 96
5.2 Example 97
5.3 Decoupling the Design, Optimization, and Stability Verification: Generalized Design Frameworks 100
5.3.1 Multi-Way Convex Manipulation 102
5.3.2 Main and Independent TP Model Component Analysis via the HOSVD Based Canonical Form 105
5.3.3 Convex Hull Manipulation 105
5.3.4 LMI Based System Design 106
5.3.5 Exact System Reconstruction: Unified TP Model Forms 107
5.3.6 LMI Based Stability Verification 109
References 109
6 TPI Model Transformation for the Class of Non-qLPV Models 110
6.1 Key Idea 110
6.2 TP I Model Transformation 111
6.3 Example of Re-identification 112
Reference 112
7 TP? Model Transformation for Systems Including Time Delay 113
7.1 TP? Model Transformation 113
7.2 Example of the TP? Model Transformation 114
References 115
Part III Analysis of the TP Model Based Design Frameworks via a Complex Example 116
References 116
8 qLPV Model of the 3DoF Prototypical Aeroelastic Wing Section 118
8.1 Equations of Motion 118
8.2 Including Stribeck Friction 121
Reference 122
9 TP Model Based Control Design 123
9.1 Exact and Convex TP Model of the 3DoF Aeroelastic Wing Section 123
9.2 Control Structure 124
9.3 Selecting LMIs 126
9.4 Results of the Control Design 127
9.4.1 Controller 1: Asymptotic Stabilization and Decay Rate Control 127
9.4.2 Controller 2: Constraint on the Control Value 127
9.4.3 Controller 3: State Feedback Control Including Stribeck Friction 128
9.4.4 Simulation 128
9.4.5 Evaluation 129
References 135
10 Convex Hull Manipulation Based Optimization 136
10.1 Convex Hull Manipulation Based Design Framework 136
10.1.1 Key Steps 137
10.1.2 Step 1: Convex TP Models 137
10.1.3 Step 2: Convex TP Model Interpolation 137
10.1.4 Step 3: LMI Based Design and Stability Verification 139
10.2 Numerical Simulations 139
10.2.1 Determination of the Feasibility Region 139
10.2.2 Results of the Numerical Simulations 140
11 Complexity Manipulation Based Optimization 149
11.1 The Control Design Framework 149
11.1.1 Main TP Model Component Analysis: HOSVD Based Canonical Form of the Model 150
11.1.2 LMI Based System Design 151
11.1.3 Exact System Reconstruction: Unified Weightings in the Polytopes 155
11.1.4 LMI Based Stability Verification 155
11.1.5 Maximizing Omega 155
11.2 Evaluation of the Benefits of the Proposed Control Design 156
References 162
12 TP Model Manipulation Influences the Control Performance and the Feasibility of LMI Based Design 163
12.1 Feasibility 163
12.1.1 Initialization of the Numerical Analysis 163
12.1.2 Results of the 2D Analysis: Feasibility and Convex Hull 164
12.1.3 Results of the 3D Analysis: Feasibility, Convex Hull, and Complexity 166
12.1.4 Results of the 4D Analysis: Feasibility, Convex Hull, Complexity, and Parameter Space 166
12.1.5 Summary 172
12.2 Control Performance 172
12.2.1 Control Performance Results of the Numerical Simulation 172
12.2.2 Evaluation and Comparison of the Derived Cases and the Best Solution 174
Reference 178
Part IV TP Model Based Control Design of the Dual-Excenter Vibration Actuator 179
References 180
13 qLPV Model of the Dual Excenter Vibration System 182
References 187
14 Convex TP Model of the Dual Excenter Vibration System 188
14.1 The Quasi-HOSVD Based Canonical Form: Approximation and Complexity Trade-Off 188
14.2 The Convex TP Model 189
15 Derivation of the Controller 196
15.1 LMI Based Controller Design 196
15.2 Simulation 199
Reference 201
Part V Control of the Impedance Model Including Varying Time Delay via TP? Model Transformation 202
16 Impedance Control for Force Reflecting Telemanipulation 203
16.1 Impedance Control with Feedback Delay 204
16.2 Control Structure for Stability Preservation 206
References 209
17 Impedance Model with Varying Feedback Delay in TP Model Form 211
17.1 The Quasi-HOSVD Based Canonical Form 211
17.1.1 Exact Quasi-HOSVD Based Canonical Form 211
17.1.2 Executing Trade-off by TP? Model Transformation 214
17.2 Manipulation of the Convex Hull 215
17.2.1 The Vertices of the Exact TP Model 220
17.2.1.1 SNNN Type Convex Hull 220
17.2.1.2 IRNO Type Convex Hull 223
17.2.1.3 CNO Type Convex Hull 224
17.2.2 The 5 Vertices of the Reduced TP Model 224
17.2.2.1 SNNN Type Convex Hull 224
17.2.2.2 IRNO Type Convex Hull 225
17.2.2.3 CNO Type Convex Hull 225
17.2.3 The 4 Vertices of the Reduced TP Model 226
17.2.3.1 SNNN Type Convex Hull 226
17.2.3.2 IRNO Type Convex Hull 226
17.2.3.3 CNO Type Convex Hull 226
17.2.4 The 3 Vertices of the Reduced TP Model 227
17.2.4.1 SNNN Type Convex Hull 227
17.2.4.2 IRNO Type Convex Hull 227
17.2.4.3 CNO Type Convex Hull 227
17.3 Validation of the Convex TP Model 227
17.3.1 Constant Time-Delay 228
17.3.2 Varying Time-Delay 230
Reference 231
18 TP? Transformation Based Control Design for Impedance Controlled Robot Gripper 232
18.1 The Control Problem 232
18.2 Execution of the TP? Model Transformation 233
18.3 LMI-Based Multi-Objective Controller and Observer Design 233
18.4 Resulting Controller and Observer Gains 234
18.4.1 Controller-Observer 1 235
18.4.2 Controller-Observer 2 235
18.4.3 Controller-Observer 3 236
18.5 Evaluation and Validation of the Control Design 236
References 245

Erscheint lt. Verlag 28.4.2016
Zusatzinfo XXVI, 230 p. 120 illus., 52 illus. in color.
Verlagsort Cham
Sprache englisch
Themenwelt Technik Elektrotechnik / Energietechnik
Schlagworte LMI based Control Design • LMI-based Design • LMI based Optimization • Polytopic Modeling • qLPV State-space Modeling • Tensor Product Model Transformation • TP Model Transformation
ISBN-10 3-319-19605-7 / 3319196057
ISBN-13 978-3-319-19605-3 / 9783319196053
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