Robust modal control with a toolbox for use with MATLAB / Jean-François Magni.

Format:

Book

Author/Creator:

Magni, Jean-François, 1954-

Language:

English

Subjects (All):

Control theory.

Automatic control.

MATLAB.

Physical Description:

xi, 312 pages : illustrations ; 24 cm + 1 CD-ROM (4 3/4 in.)

4 3/4 in.

Place of Publication:

New York : Kluwer Academic/Plenum, [2002]

System Details:

System requirements for accompanying computer disc: MATLAB 5.x or higher, the Optimization Toolbox, the Control System Toolbox.

text file

Summary:

Robust Modal Control covers most classical multivariable modal control design techniques that were shown to be effective in practice, and in addition proposes several new tools. The proposed new tools include: minimum energy eigenvector selection, low order observer-based control design, conversion to observer-based controllers, a new multimodel design technique, and modal analysis. The text is accompanied by a CD-ROM containing MATLABB. software for the implementation of the proposed techniques. The software is in use in aeronautical industry and has proven to be effective and functional. For more detail, please visit the author's webpage at http: //www.cert.fr/dcsd/idco/perso/Magni/booksandtb.html

Contents:

1. Modal Control: A Tutorial 9

1.1 Generalities and guide-lines for choosing eigenstructure to be assigned 11

1.1.1 List of symbols and abbreviations 12

1.1.2 System notations 13

1.1.3 Eigenstructure notations 14

1.1.4 Assignable eigenstructure 15

1.1.5 Definition of the concept of mode 17

1.1.6 Eigenvector assignment and decoupling 18

1.1.7 Projection of open-loop eigenvectors 22

1.1.8 Minimum energy assignment 24

1.2 Eigenstructure assignment I: Traditional approaches 27

1.2.1 State feedback or proportional output feedback 28

1.2.2 Pole assignment by output feedback 32

1.2.3 Insensitive state feedback design 34

1.2.4 Non-interactive control design 37

1.2.5 Dynamic feedforward 42

1.2.6 Dynamic extension for output feedback design 45

1.2.7 Observer definition 47

1.2.8 Observer-based output feedback 54

1.2.9 Observer-based state feedback 58

1.3 Eigenstructure assignment II: Multi-model approaches 63

1.3.2 Dynamic feedback with given structure 67

1.3.3 Definition of a frequency domain template 68

1.3.4 Multi-model eigenstructure assignment 69

1.3.5 Multi-model "phase control" 70

1.3.6 Controller order reduction 72

1.3.7 Illustrative example: multi-model assignment 73

1.3.8 Illustrative example: multi-model "phase control" 74

1.4 Eigenstructure assignment III: Feedback gain tuning 79

1.4.2 Constraints for pole shifting and gain structuring 82

1.4.3 Examples of files to be written by the user 88

1.4.4 Constraints for more advanced objectives 90

1.5 Modal analysis of a control law 95

1.5.1 Modal simulation and residuals 96

1.5.2 Modal controllability 99

1.5.3 Zeros and "almost zeros" 102

1.5.4 Miscellaneous tools 103

2. Some Control Design Problems 107

2.1 Recommendations and proposed design cycle 109

2.1.1 General recommendations 109

2.1.2 Multi-model sub-toolbox 111

2.1.3 Tuning sub-toolbox 112

2.1.4 Proposed design cycle for direct feedback design 113

2.1.5 Improvement of an existing feedback law 115

2.2 Single-model pole placement 117

2.2.1 From open-loop to closed-loop 118

2.2.2 Closed-loop eigenvalue insensitivity 122

2.2.3 Tuning of a dynamic controller 124

2.3 Decoupling 129

2.3.1 Non-interactive control by proportional feedback 130

2.3.2 Non-interactive control by dynamic feedforward 134

2.3.3 Observer-based non-interactive control 135

2.3.4 Illustration of Exact Loop Transfer Recovery 137

2.4 Multi-model eigenstructure assignment 139

2.4.1 Multi-model design with a proportional gain 140

2.4.2 Multi-model design with a dynamic gain 142

2.4.3 Multi-model design using the tuning procedure 145

2.5 Flexible systems control 149

2.5.1 Low and high frequency feedback designs 150

2.5.2 Single step dynamic feedback design 152

2.5.3 Generalized phase control 153

2.5.4 Iterative technique 155

2.5.5 Technique based on controllability analysis 157

2.6 Structured gain computation 159

2.6.1 Structured dynamic feedback 160

2.6.2 Controller order reduction 162

3. Toolbox Reference 167

3.1 List of available functions 169

3.2 Help messages 173

3.2.1 Function: ADD_CSTR 174

3.2.2 Function: ADD_DYN 175

3.2.3 Function: ADD_OBS 176

3.2.4 Function: AZER 178

3.2.5 Function: CHOI_EV 179

3.2.6 Function: CLEAN_EV 180

3.2.7 Function: COMP_DV 181

3.2.8 Function: CONTR_EV 183

3.2.9 Function: CRIT_CTR 183

3.2.10 Function: CRIT_K 185

3.2.11 Function: CSTR_DP 186

3.2.12 Function: CSTR_EIG 188

3.2.13 Function: CSTR_EV 190

3.2.14 Function: CSTR_INI 192

3.2.15 Function: CSTR_K 192

3.2.16 Function: CSTR_QUD 193

3.2.17 Function: DEFIN_VW 195

3.2.18 Function: DEMODATA 198

3.2.19 Function: DFB_INS 198

3.2.20 Function: DFB2OBS 199

3.2.21 Function: DFB_PROJ 201

3.2.22 Function: DIST_QUD 203

3.2.23 Function: DP_CSTR 204

3.2.24 Function: DYN2STA 205

3.2.25 Function: EIG_CSTR 206

3.2.26 Function: EIG_FB 207

3.2.27 Function: FB_DYN 208

3.2.28 Function: FB_PROP 209

3.2.29 Function: FB_TUN 211

3.2.30 Function: FB_VIEW 212

3.2.31 Function: FF_ASSGN 213

3.2.32 Function: FF_STAT 214

3.2.33 Function: KTF_CRIT 215

3.2.34 Function: KTF_CSTR 216

3.2.35 Function: LSIM_MOD 217

3.2.36 Function: OB_GENE 219

3.2.37 Function: OB_INS 221

3.2.38 Function: OBS2DFB 223

3.2.39 Function: PLOT_CON 224

3.2.40 Function: PLOT_RES 226

3.2.41 Function: PLOT_ZER 228

3.2.42 Function: RCAMDATA 229

3.2.43 Function: RCAMPOLE 231

3.2.44 Function: RCAMSTEP 232

3.2.45 Function: SFB_INS 233

3.2.46 Function: SFB_PROJ 236

3.2.47 Function: SOB_PROJ 237

3.2.48 Function: SORT_EV 239

3.2.49 Function: STA2DYN 239

3.2.50 Function: STR_CSTR 240

3.2.51 Function: STR_VIEW 242

3.2.52 Function: VICIN_EV 243

4. Appendix 1: Proofs of the Results Stated in the First Chapter 245

4.1 Results relative to eigenvector assignment 248

4.1.1 Proof of Lemmas 1.1.1 and 1.1.2 248

4.1.2 Proof of Lemma 1.2.4 249

4.1.3 Proof of Lemma 1.3.1 250

4.1.4 Linear Quadratic Programming 251

4.2 First order perturbations 255

4.2.1 Proof of Lemmas 1.2.2 and 1.4.1 255

4.2.2 Proof of Lemma 1.4.2 256

4.2.3 Proof of Lemma 1.3.2 259

4.2.4 Linear Quadratic Programming 260

4.3 Minimum energy assignment 262

4.3.1 The Hamiltonian solution to the Linear Quadratic Problem 262

4.3.2 Proof of Lemma 1.1.3 263

4.4 Pole assignment by output feedback 265

4.4.1 Technical preliminary results 265

4.4.2 Proof of Lemma 1.2.1 266

4.5 Non-interactive control design 268

4.6 Dynamic feedforward design 274

4.6.1 Rendering eigenvalues non controllable 274

4.6.2 Eigenvector pseudo-assignment 276

4.6.3 Proof of Lemma 1.2.3 277

4.7 Observers 278

4.7.1 Elementary observers: Proof of Lemma 1.2.5 278

4.7.2 Observer with Kalman filter structure: Proof of Lemma 1.2.7 280

4.7.3 Observer transfer function matrix: Proof of Lemma 1.2.6 281

4.7.4 Separation Principle: Proof of Lemma 1.2.8 282

4.7.5 Equivalent dynamic controller 284

5. Appendix 2: Additional Topics 289

5.1 Models used for demonstrations 289

5.1.1 A simplified flexible aircraft 289

5.1.2 A bank of linearized models of an aircraft (the RCAM) 290

5.2 Matrices CSTR and CRIT 295

5.3 Installation and system requirements 297.

Notes:

Includes bibliographical references (pages 303-307) and index.

ISBN:

0306467739

OCLC:

49277204