Multiple Models Approach in Automation

Multiple Models Approach in Automation......Page 2
Copyright......Page 3
Table of Contents......Page 4
Notations......Page 7
Introduction......Page 10
1.1. Introduction......Page 13
1.2. Techniques for obtaining multiple models......Page 14
1.2.1. Construction of multiple models by identification......Page 15
1.2.2. Multiple model construction by linearization......Page 20
1.2.3. Multiple model construction by mathematical transformation......Page 26
1.2.4. Multiple model representation using the neural approach......Page 34
1.3.1. Lyapunov approach......Page 41
1.3.2. Numeric tools: linear matrix inequalities......Page 43
1.3.3. Multiple model control techniques......Page 50
2.1. Introduction......Page 53
2.2. Stability analysis......Page 54
2.2.1. Exponential stability......Page 60
2.3. Relaxed stability......Page 61
2.4. Example......Page 64
2.5. Robust stability......Page 66
2.5.1. Norm-bounded uncertainties......Page 68
2.5.2. Structured parametric uncertainties......Page 69
2.5.3. Analysis of nominal stability......Page 72
2.5.4. Analysis of robust stability......Page 74
2.6. Conclusion......Page 75
3.1. Introduction......Page 76
3.2. Synthesis of multiple observers......Page 78
3.2.1. Linearization......Page 79
3.2.2. Pole placement......Page 81
3.2.3. Application: asynchronous machine......Page 83
3.2.4. Synthesis of multiple observers......Page 86
3.3. Multiple observer for an uncertain multiple model......Page 88
3.4. Synthesis of unknown input observers......Page 93
3.4.1. Unknown inputs affecting system state......Page 94
3.4.2. Unknown inputs affecting system state and output......Page 98
3.4.3. Estimation of unknown inputs......Page 99
3.5.1. Principle......Page 104
3.5.2. Multiple observers subject to unknown inputs and uncertainties......Page 107
3.6. Conclusion......Page 108
4.2. Full state feedback control......Page 109
4.2.1. Linearization......Page 111
4.2.2. Specific case......Page 113
4.2.3. a-stability: decay rate......Page 116
4.3. Observer-based controller......Page 123
4.3.1. Unmeasurable decision variables......Page 125
4.4. Static output feedback control......Page 129
4.4.1. Pole placement......Page 132
4.5. Conclusion......Page 136
5.1. Introduction......Page 137
5.2.1. Norm-bounded uncertainties......Page 139
5.2.2. Interval uncertainties......Page 141
5.3.1. Norm-bounded uncertainties......Page 147
5.3.2. Interval uncertainties......Page 157
5.4. Observer-based control......Page 160
5.5. Conclusion......Page 166
Conclusion......Page 167
A1.1. Definition of an LMI region......Page 169
A1.2. Interesting LMI region examples......Page 170
A1.2.3. Vertical band......Page 171
A1.2.5. Disk of radius R, centered at q,0......Page 172
A1.2.6. Conical sector......Page 173
Appendix 2 Properties of M-matrices......Page 174
A3.1.1. Definition of a vector norm......Page 176
A3.1.2. Definition of a system overvalued from a continuous process......Page 177
A3.1.3. Application......Page 179
A3.2. Vector norms and the principle of comparison......Page 180
A3.3. Application to stability analysis......Page 181
Bibliography......Page 182
Index......Page 192