 | Baranyi P. Tensor product model transformation in polytopic model-based control / P.Baranyi, Y.Yam, P.Varlaki. - Boca Raton: CRC/ Taylor & Francis, 2014. - xiii, 248 p.: ill. - (Automation and control engineering series). - Bibliogr.: p.217-228. - Ind.: p.229-247. - ISBN 978-1-4398-1816-9
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Preface ......................................................... i
Acronyms and Abbreviations ................................... xiii
1 Introduction ................................................. 1
1.1 An overview ............................................. 1
1.2 TP model ................................................ 2
1.3 HOSVD-based computation ................................. 3
1.4 Convex optimization via LMIs/PDC framework .............. 4
1.5 Model convexity and convex hull manipulation ............ 5
1.6 Significant paradigm changes ............................ 6
1.7 Outline of the book ..................................... 7
I Tensor Product (TP) Model Formulation ........................ 9
2 TP Model .................................................... 11
3 TP Model Transformation ..................................... 21
3.1 Introduction to HOSVD .................................. 22
3.2 Transformation procedures .............................. 26
3.3 The extracted model .................................... 28
3.4 Addition of sampling grid lines ........................ 29
4 TP Canonical Model Form ..................................... 33
4.1 Definition ............................................. 33
4.2 Numerical reconstruction ............................... 35
4.3 The TORA example ....................................... 44
4.3.1 Equations of motion ............................. 45
4.3.2 TP canonical model .............................. 47
5 Approximation and Complexity Trade-Off ...................... 51
5.1 TP model form of bounded order ........................ 51
5.2 The nowhere dense property ............................. 52
5.3 Trade-off examples ..................................... 57
5.3.1 A mass-spring-damper system ..................... 57
5.3.2 A mass-spring-damper system with nonlinear
term ............................................ 59
5.4 Trade-off study on the TORA example .................... 60
6 TP Model Convexity Incorporation ............................ 65
6.1 TP model convexity ..................................... 66
6.2 Incorporation of convexity conditions .................. 69
6.2.1 Incorporating the SN condition .................. 70
6.2.2 Incorporating the NN condition .................. 71
6.2.3 Incorporating the NO condition .................. 72
6.2.4 Incorporating the RNO condition ................. 74
6.3 Alternate method for INO and RNO conditions ............ 75
6.3.1 The partial algorithm ........................... 76
6.3.2 The complete algorithm .......................... 78
6.4 The TORA example ....................................... 80
7 Introduction to the TPtool Toolbox .......................... 83
7.1 Generating the TP canonical model ...................... 83
7.2 Incorporating convexity conditions ..................... 86
8 Centralized Model Form ...................................... 91
8.1 The centralized model .................................. 91
8.1.1 Mathematical properties ......................... 92
8.1.2 Control properties .............................. 93
8.1.3 Computational advantages ........................ 93
8.2 Illustrating examples .................................. 93
9 Computational Relaxed TP Model Transformation ............... 99
9.1 SVD-based column equivalence .......................... 101
9.2 Modified transformation algorithm ..................... 104
9.3 Evaluation of computational reduction ................. 109
9.3.1 Discretization complexity ...................... 109
9.3.2 HOSVD computation .............................. 110
9.3.3 Tensor product computation ..................... 111
9.4 Examples .............................................. 112
9.4.1 A simple numerical example ..................... 112
9.4.2 The double inverted pendulum example ........... 112
II TP Model-Based Control System Design ...................... 117
10 Overview of TP Model-Based Design Strategy ................. 119
11 LMI Theorems under the PDC Framework ....................... 125
11.1 LMIs for control system design ........................ 125
11.1.1 Definition of LMIs ............................. 126
11.1.2 Constraints expressed via LMIs ................. 128
11.1.3 Generic problems for LMIs ...................... 130
11.2 LMI optimization under the PDC framework .............. 131
11.2.1 Lyapunov stability criteria .................... 132
11.2.2 Control design for stability ................... 133
11.2.3 Multiobjective control optimization ............ 134
11.2.4 Simultaneous observer/controller design ........ 135
11.3 TP model-based control design procedures .............. 137
11.4 LMI-based control design for the TORA example ......... 138
11.4.1 Control specifications ......................... 140
11.4.2 State feedback control design .................. 140
11.4.3 Observer-based output feedback control
design ......................................... 142
12 Convex Hull Manipulation ................................... 147
12.1 Nonlinear sensitivity of control solutions ............ 148
12.2 Conservativeness of control solutions ................. 150
III Control Design Examples ................................... 153
13 Control Design with TPtool Toolbox ......................... 155
14 2-D Prototypical Aeroelastic Wing Section with Structural
Nonlinearity ............................................... 157
14.1 Dynamics modeling ..................................... 158
14.2 The TP model .......................................... 162
14.3 State feedback control design ......................... 164
14.3.1 Controller for asymptotic stabilization ........ 165
14.3.2 Controller for decay rate control .............. 167
14.3.3 Controller for constraint on the control
value .......................................... 167
14.3.4 Comparison to other control solutions .......... 167
14.4 Observer-based output feedback control design ......... 171
14.4.1 An alternative TP model ........................ 171
14.4.2 Control system design .......................... 172
14.4.3 Control performance ............................ 173
14.5 Convex hull manipulation .............................. 173
14.6 Convex hull geometry .................................. 177
14.6.1 Effects on LMI-based controller performance .... 177
14.6.2 Effects on LMI-based observer performance ...... 178
15 3-D Prototypical Aeroelastic Wing Section with Structural
Nonlinearity ............................................... 181
15.1 Dynamics modeling ..................................... 182
15.2 The TP model .......................................... 185
15.3 LMI-based output feedback control design .............. 187
15.3.1 Controller 1: Asymptotic stabilization ......... 188
15.3.2 Controller 2: Constraint on the control
value .......................................... 190
15.3.3 Control performance ............................ 190
16 3-DoF Helicopter with Four Propellers ...................... 195
16.1 Dynamics Modeling ..................................... 195
16.1.1 A simplified model ............................. 199
16.1.2 Modeling of uncertainty ........................ 199
16.2 The TP model .......................................... 200
16.3 Control system design ................................. 202
16.4 Control performance ................................... 204
17 Heavy Vehicle Rollover Prevention Problem .................. 207
17.1 Problem introduction .................................. 207
17.2 A qLPV model for heavy vehicles ....................... 208
17.3 The TP model .......................................... 212
17.4 Control system design and performance ................. 212
References .................................................... 217
Index ......................................................... 229
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