Direct Eigen Control for Induction Machines and Synchronous Motors

This is a unique book and the first to focus on direct eigen control for AC motors. It presents a clear and concise explanation of the new sampled vectorial method that is designed to control all AC motor types: induction machine (IM), surface mounted permanent magnet synchronous motor (SM–PMSM) and interior permanent magnet synchronous motor (IPM–SM).

This totally new control method supersedes the two well–known direct control solutions Direct Self Control (DSC) and Direct Torque Control (DTC or MPDTC) and takes into account all technical constraints and technical limits without overshoot or lagging. It can also be used to control input filter current and voltage of an inverter feeding an AC motor. The sampling period and voltage vector sequences can be chosen independently of control performances, allowing inverter PWM frequency and motor current harmonic level optimization.

Explained with the Kalman s Observer, the text describes how to practically implement, in real time, this method of dead–beat machine control in all three types of AC motors. Helpful additions include:

Straight–forward mathematical descriptions and solutions Full AC motor modeling by the discrete–time, state–space representation PWM optimization method Practical complex software implementation of the control Various examples that show the control performances in traction or braking mode Comprehensive simulations described in a way that is easy to understand and to reproduce on a computer, with simulation software files available on a companion website

Highly accessible, this is an essential reference for researchers in the field of drive control, postgraduate students studying electric machines, and electric engineers in the field of electric railways, electric cars, wind turbines, plane surface control, and military applications. Final year undergraduates and engineers in the field of machine tools, robots, and rolling mills, will also find it of value.

Foreword by Prof. Dr Ing. Jean–Luc Thomas xiii

Foreword by Dr Abdelkrim Benchaïb xv

Acknowledgements xvii

Introduction xix

1 Induction Machine 1

1. 1 Electrical Equations and Equivalent Circuits 1

1. 2 Working out the State–Space Equation System 9

1. 3 Discretized State–Space Equation Inversion 22

1. 4 Control 31

1. 5 Conclusion on the Induction Machine Control 63

2 Surface–Mounted Permanent–Magnet Synchronous Motor 65

2. 1 Electrical Equations and Equivalent Circuit 66

2. 2 Working out the State–Space Equation System 69

2. 3 Discretized State–Space Equation Inversion 76

2. 4 Control 84

2. 5 Conclusion on SMPM–SM 118

3 Interior Permanent Magnet Synchronous Motor 121

3. 1 Electrical Equations and Equivalent Circuits 122

3. 2 Working out the State–Space Equation System 127

3. 3 Discretized State–Space Equation Inversion 134

3. 4 Control 143

3. 5 Conclusions on the IPM–SM 189

4 Inverter Supply LC Filter 191

4. 1 Electrical Equations and Equivalent Circuit 191

4. 2 Working out the State–Space Equation System 193

4. 3 Discretized State–Space Equation Inversion 198

4. 4 Control 201

4. 5 Conclusions on Power LC Filter Stabilization 211

5 Conclusion 213

Appendix A Calculation of Vector PWM 217

A.1 PWM Types 218

A.2 Working out the Control Voltage Vector 218

A.3 Other Examples of Vector PWM 221

A.4 Sampled Shape of the Voltage and Current Waves 224

Appendix B Transfer Matrix Calculation 225

B.1 First Eigenvector Calculation 225

B.2 Second Eigenvector Calculation 227

B.3 Third Eigenvector Calculation 228

B.4 Fourth Eigenvector Calculation 230

B.5 Transfer Matrix Calculation 231

Appendix C Transfer Matrix Inversion 233

C.1 Transfer Matrix Determinant Calculation 234

C.2 First Row, First Column 234

C.3 First Row, Second Column 235

C.4 First Row, Third Column 235

C.5 First Row, Fourth Column 235

C.6 Second Row, First Column 236

C.7 Second Row, Second Column 236

C.8 Second Row, Third Column 236

C.9 Second Row, Fourth Column 237

C.10 Third Row, First Column 237

C.11 Third Row, Second Column 237

C.12 Third Row, Third Column 237

C.13 Third Row, Fourth Column 237

C.14 Fourth Row, First Column 238

C.15 Fourth Row, Second Column 238

C.16 Fourth Row, Third Column 238

C.17 Fourth Row, Fourth Column 238

C.18 Inverse Transfer Matrix Calculation 238

Appendix D State–Space Eigenvector Calculation 239

Appendix E F and G Matrix Calculations 245

E.1 Transition Matrix Calculation 245

E.2 Discretized Input Matrix Calculation 249

References 251

Index 253