Loop-shaping Robust Control

Title Page
......Page 2
Copyright
......Page 3
Table of Contents......Page 4
I.1 Presentation of the book......Page 7
I.2.1.1. Representation of LTISs......Page 10
I.2.1.2. Controllability and observability of LTISs......Page 12
I.2.1.3. Elementary operations on LTISs......Page 13
I.2.2.1. Definition......Page 15
I.2.2.2. Properties......Page 16
I.2.3.1. Definition......Page 17
I.2.3.2. Properties......Page 18
I.2.4.1. Definition......Page 19
I.2.4.2. Properties......Page 20
1.1.2. Sensitivity functions......Page 23
1.1.2.1. Output sensitivity functions......Page 24
1.1.2.2. Input sensitivity functions......Page 25
1.1.3. Declination of performance objectives......Page 27
1.1.4. Declination of the robustness objectives......Page 30
1.2.1. Phase and gain margins at the model’s output......Page 36
1.2.2. Phase and gain margins at the model’s input:......Page 38
1.3. Limitations inherent to bandwidth......Page 39
1.4.1. Example 1: sinusoidal disturbance rejection......Page 40
1.4.2. Example 2: reference tracking and friction rejection......Page 42
1.4.3. Example 3: issue of flexible modes and high-frequency disturbances......Page 47
1.4.4. Example 4: stability robustness in relation to system uncertainties......Page 51
1.5. Conclusion......Page 52
2.1.1. Definitions......Page 54
2.1.2. Practical calculation of normalized coprime factorizations......Page 56
2.1.3. Reconstruction of a transfer function from its coprime factors......Page 57
2.1.4. Set of stabilizing controllers ? Youla parameterization of stabilizing controllers......Page 58
2.2.1. Taking account of modeling uncertainties......Page 63
2.2.2.1. Reminder of the small-gain theorem......Page 64
2.2.2.2. Application to coprime factor plant descriptions......Page 65
2.2.3. Property of the equivalent “weighted mixed sensitivity? form......Page 67
2.2.4. Expression of the synthesis criterion in “4-blocks? equivalent form......Page 73
2.3.1. Expression of the problem by the Youla parameterization......Page 75
2.3.2.1. Maximum stability margin [GLO 88b]......Page 78
2.3.2.2. State-space representation of stabilizing controllers [GLO 89b]......Page 79
2.3.2.3. Proof by the standard H∞ approach......Page 81
2.4.1.1. Distance between two plants: the υ-gap......Page 98
2.4.1.2. Frequency extension of υ-gap......Page 99
2.4.2.2. Stabilization of a ball of plants......Page 100
2.4.2.3. Minimum stability margin for a ball of plants......Page 101
2.5.1. Motivation......Page 103
2.5.2. Loop-shaping H∞ synthesis [MCF 92]......Page 104
2.5.4. Phase margin and gain margin......Page 110
2.5.5. 4-blocks interpretation of the method......Page 111
2.5.6. Practical implementation......Page 113
2.5.7.1. Optimization of an existing controller......Page 121
2.5.7.2. Robust synthesis......Page 125
2.5.7.3. Robust multivariable synthesis......Page 131
2.6.1.1. Limitations of a posteriori discretization......Page 141
2.6.2. Discrete approach to loop-shaping H8 synthesis......Page 142
2.6.3.1. Implementation of discrete loop-shaping control......Page 148
3.1.1. Reference tracking......Page 156
3.1.2. Parameterization of 2-d.o.f. controllers [YOU 85]......Page 162
3.2.1. General formulation......Page 164
3.2.2. Simplification of the problem by the Youla parameterization......Page 166
3.2.3. Extension......Page 171
3.2.4. Setting of the weighting functions......Page 173
3.2.5. Associated performance robustness result......Page 175
3.3.1. General formulation......Page 177
3.3.2. Expression of the problem by Youla parameterization......Page 179
3.3.3. Associated performance robustness result......Page 182
3.3.4. Connection between the approach and loop-shaping synthesis......Page 184
3.4. Comparison of the two approaches......Page 186
3.5.1.1. Specifications......Page 187
3.5.1.2. Two-step approach......Page 191
3.5.1.3. One-step approach......Page 192
3.6.1. Principle......Page 195
3.6.2. Example......Page 200
4.1. Introduction......Page 207
4.2.1.1. Principle......Page 208
4.2.1.2. Optimization of the approach......Page 214
4.2.1.3. Observations......Page 215
4.2.2.1. Principle......Page 217
4.2.2.2. Fixed-order synthesis......Page 219
4.2.2.3. The limitations of LMI H∞ synthesis......Page 221
4.2.2.4. Toward new optimization tools......Page 224
4.2.2.5. Initialization of the algorithm......Page 230
4.2.2.7 Improving the rate of convergence for controller synthesis......Page 231
4.2.3. Example: fixed-order robust multivariable synthesis......Page 234
4.3.1. Weight setting on the basis of a frequency specification......Page 240
4.3.2. Optimal weight tuning using stochastic optimization and metaheuristics......Page 247
4.3.2.1. A systematic method for the declination of high-level specifications......Page 248
4.3.2.2. Optimal weight tuning with metaheuristics......Page 249
4.3.2.3. Taking into account the objectives of stability robustness......Page 251
4.3.2.5. Example: optimal weight tuning for the inertial line-of-sight stabilization problem......Page 252
4.4. Towards a new approach to loop-shaping fixed-order controller synthesis, etc.......Page 262
4.4.1. Taking account of objectives of stability robustness......Page 263
4.4.2. Taking account of objectives of performance robustness......Page 264
APPENDICES......Page 265
Appendix 1 Demonstrative Elements on the Optimizationof Robust Stabilization with Order Constraint......Page 266
Appendix 2 Establishment of Real LMIs for the Quasi-Convex Problem of Optimization of the Weighting Functions......Page 270
Bibliography......Page 273
Index......Page 277