1.1 Definitions and notations 140 -- 1.2 Equivalent electrical circuits 141 -- 1.3 Differential equation system 142 -- 2 Working out of the state-space equation system 146 -- 2.1 State-space equations in the fixed plane 147 -- 2.2 State-space equations in the complex plane 149 -- 2.3 State-space equation discretization 149 -- 2.4 Evolution matrix diagonalization 149 -- 2.4.1 Eigenvalues 150 -- 2.4.2 Transfer matrix calculation 152 -- 2.4.3 Transfer matrix inversion 153 -- 2.5 Projection of state-space vectors in the eigenvector basis 154 -- 3 Discretized state-space equation inversion 155 -- 3.1 Rotating reference frame 155 -- 3.2 State-space vector calculations in the eigenvector basis 155 -- 3.2.1 Calculation of third and fourth coordinates of the state-space equation 160 -- 3.2.2 Calculation of the first and the second coordinate of the state-space eigenvector 162 -- 3.3 Control calculation - Eigenstate-space equations inversion 162 -- 4 Control 165 -- 4.1 Constitution of the set-point state-space vector 165 -- 4.2 Constitution of the initial state-space vector 168 -- 4.3 Control process 169 -- 4.3.1 Real-time implementation 170 -- 4.3.2 Measure filtering 172 -- 4.3.3 Transition and input matrix calculations 174 -- 4.3.4 Kalman¿́¿s filter 176 -- 4.3.5 Synoptic of measurement, filtering and prediction 179 -- 4.4 Limitations 183 -- 4.4.1 Voltage limitation 184 -- 4.4.2 Current limitation 192 -- 4.4.3 Operating area and limits 193 -- 4.4.4 Set-point limit calculation 194 -- 4.5 Example of implementation 208 -- 4.5.1 Adjustment of torque - Limitations in traction mode 209 -- 4.5.2 Adjustment of torque - Limitations in electrical braking 212 -- 4.5.3 Free evolution - Short-circuit torque 214 -- 5 Conclusions on the IPM-SM 219 -- Chapter 4 - Inverter supply - LC Filter 220 -- 1 Electrical equations and equivalent circuit 220 -- 1.1 Definitions and notations 220 -- 1.2 Equivalent electrical circuit 221 -- 1.3 Differential equation system 222 -- 2 Working out of the state-space equation system 222.

2.1 State-space equations in a fixed frame 223 -- 2.2 State-space equations in the complex plane 224 -- 2.3 State-space equation discretization 224 -- 2.4 Evolution matrix diagonalization 225 -- 2.4.1 Eigenvalues 225 -- 2.4.2 Transfer matrix calculation 226 -- 2.4.3 Transfer matrix inversion 227 -- 3 Discretized state-space equation inversion 228 -- 3.1 Evolution matrix diagonalization 228 -- 3.2 State-space equation discretization 228 -- 3.3 State-space vector calculations in the eigenvector basis 229 -- 4 Control 231 -- 4.1 Constitution of the set-point state-space vector 231 -- 4.2 Constitution of the initial state-space vector 232 -- 4.3 Inversion - Line current control by the useful current 232 -- 4.4 Capacitor voltage control by the useful current 235 -- 4.5 General case - Control by the useful current 237 -- 4.6 Example of implementation 239 -- 4.6.1 Lack of capacitor voltage stabilization 239 -- 4.6.2 Capacitor voltage stabilization 240 -- 5 Conclusions on power LC filter stabilization 243 -- Conclusion 245 -- Appendix 1 - Calculation of vectorial PWM 248 -- 1 PWM types 248 -- 2 Work out of control voltage vector 249 -- 3 Other examples of a vectorial PWM 252 -- 3.1 Unsymmetrical vectorial PWM 252 -- 3.2 Symmetrical triangular wave based PWM 253 -- 3.3 Synchronous PWM 254 -- 4 Sampled shape of the voltage and current waves 255 -- Appendix 2 - Transfer matrix calculation 257 -- 1 First eigenvector calculation 257 -- 2 Second eigenvector calculation 258 -- 3 Third eigenvector calculation 260 -- 4 Fourth eigenvector calculation 262 -- 5 Transfer matrix calculation 263 -- Appendix 3 - Transfer matrix inversion 264 -- 1 Transfer matrix determinant calculation 265 -- 2 First row, first column 265 -- 3 First row, second column 266 -- 4 First row, third column 266 -- 5 First row, fourth column 266 -- 6 Second row, first column 267 -- 7 Second row, second column 267 -- 8 Second row, third column 267 -- 9 Second row, fourth column 268 -- 10 Third row, first column 268.

11 Third row, second column 268 -- 12 Third row, third column 268 -- 13 Third row, fourth column 268 -- 14 Fourth row, first column 269 -- 15 Fourth row, second column 269 -- 16 Fourth row, third column 269 -- 17 Fourth row, fourth column 269 -- 18 Inverse transfer matrix calculation 269 -- Appendix 4 - State-space eigenvector calculation 270 -- Appendix 5 - F and G matrices calculation 274 -- 1 Transition matrix calculation 274 -- 2 Discretized input matrix calculation 278 -- References 280 -- Index 284 --.

Acknowledgements v -- Contents vi -- Foreword x -- Foreword xii -- Preface xiv -- 1 Formulation of the motor control problem xiv -- 1.1 Electromagnetic torque xiv -- 1.2 Response time in tracking mode and on disturbances xv -- 1.3 Limitations xvi -- 2 Field orientation controls xviii -- 3 Sliding mode control families xviii -- 4 Objectives of a new motor control xx -- 5 Objectives of this work xxiii -- Capter 1 - Induction machine 1 -- 1 Electrical equations and equivalent circuits 1 -- 1.1 Definitions and notations 1 -- 1.2 Equivalent electrical circuits 2 -- 1.3 Differential equation system 4 -- 1.4 Interpretation of electrical relations 6 -- 2 State-space equation system working out 11 -- 2.1 State-space equations in the fixed plane 13 -- 2.2 State-space equations in the complex plane 16 -- 2.3 Complex state-space equation discretization 17 -- 2.4 Evolution matrix diagonalization 19 -- 2.4.1 Eigenvalues 19 -- 2.4.2 Transfer matrix algebraic calculation 20 -- 2.4.3 Transfer matrix inversion 21 -- 2.5 Projection of state-space vectors in the eigenvector basis 23 -- 3 Discretized state-space equation inversion 24 -- 3.1 Introduction of the rotating frame 24 -- 3.2 State-space vector calculations in the eigenvector basis 27 -- 3.3 Control calculation - eigenstate-space equation system inversion 34 -- 4 Control 35 -- 4.1 Constitution of the set-point state-space vector 35 -- 4.2 Constitution of the initial state-space vector 38 -- 4.3Control process 38 -- 4.3.1 Real-time implementation 38 -- 4.3.2 Measure filtering 41 -- 4.3.3 Transition and input matrix calculations 41 -- 4.3.4 Kalman¿́¿s filter, observation and prediction 42 -- 4.3.5 Synoptic of measurement, filtering and prediction 44 -- 4.4 Limitations 47 -- 4.4.1 Voltage limitation 48 -- 4.4.2 Current limitation 51 -- 4.4.3 Operating area and limits 51 -- 4.4.4 Set-point limit algebraic calculations 52 -- 4.5 Example of implementation 65 -- 4.5.1 Adjustment of flux and torque - Limitations in traction operation 65.

4.5.2 Adjustment of flux and torque - Limitations in electrical braking 68 -- 4.5.3 Free evolution - Short-circuit torque 70 -- 5 Conclusion on the induction machine control 74 -- Chapter 2 - Surface mounted permanent magnet synchronous motor. 76 -- 1 Electrical equations and equivalent circuit 77 -- 1.1 Definitions and notations: 77 -- 1.2 Equivalent electrical circuit 77 -- 1.3 Differential equation system 79 -- 2 Working out of the state-space equation system 80 -- 2.1 State-space equations in the fixed plane 81 -- 2.2 State-space equations in the complex plane 83 -- 2.3 Complex state-space equation discretization 84 -- 2.4 Evolution matrix diagonalization 85 -- 2.4.1 Eigenvalues 85 -- 2.4.2 Transfer matrix calculation 85 -- 2.4.3 Transfer matrix inversion 87 -- 2.5 Projection of state-space vectors in the eigenvector basis 88 -- 3 Discretized state-space equation inversion 88 -- 3.1 Introduction of the rotating frame 88 -- 3.2 State-space vector calculations in the eigenvector basis 89 -- 3.3 Control computation - Eigenstate-space equations inversion 95 -- 4 Control 98 -- 4.1 Constitution of set-point state-space vector 98 -- 4.2 Constitution of the initial state-space vector 99 -- 4.3 Control process 100 -- 4.3.1 Real-time implementation 100 -- 4.3.2 Measure filtering 102 -- 4.3.3 Transition and control matrix calculations 103 -- 4.3.4 Kalman's filter, observation and prediction 104 -- 4.3.5 Synoptic of measurement, filtering and prediction 106 -- 4.4 Limitations 110 -- 4.4.1 Voltage limitation 111 -- 4.4.2 Current limitation 114 -- 4.4.3 Operating area and limits 114 -- 4.4.4 Set-point limit calculations 115 -- 4.5 Example of implementation 128 -- 4.5.1 Adjustment of torque - Limitations in traction operation 129 -- 4.5.2 Adjustment of torque - Limitations in electrical braking 131 -- 4.5.3 Free evolution - Short-circuit torque 132 -- 5 Conclusion on SMPM-SM 138 -- Chapter 3 - Interior permanent magnet synchronous motor 139 -- 1 Electrical equations and equivalent circuits 140.