Direct Eigen Control for Induction Machines and Synchronous Motors

Alacoque was previously R&D manager at Alstom Traction in charge of product development in the field of telephone line insulation, traction motor control and wheel-rail adhension control. Prior to this he R&D manager of industrial electronic products for thermal controls and speed drives in CEM, Villeurbanne, then Technical Director of ACEP for power plant engineering. He later joined the R&D team of CORECI as manager for development of process control products. Jean Claude's research interests include discrete-time systems applied to machine control for railways traction during line voltage and wheel-rail adhesion disturbances and with voltage and current saturation. He has authored many technical papers and patents.

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 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