About the Authors xiii -- Preface xv -- Acknowledgment xix -- List of Symbols and Acronyms xxi -- 1 Modeling of AC Drives and Power Converter 1 -- 1.1 Space Phasor Representation 1 -- 1.1.1 Space Vector for Magnetic Motive Force 1 -- 1.1.2 Space Vector Representation of Voltage Equation 4 -- 1.2 Model of Surface Mounted PMSM 5 -- 1.2.1 Representation in Stationary Reference Frame 5 -- 1.2.2 Representation in Synchronous Reference Frame 7 -- 1.2.3 Electromagnetic Torque 8 -- 1.3 Model of Interior Magnets PMSM 10 -- 1.3.1 Complete Model of PMSM 11 -- 1.4 Per Unit Model and PMSM Parameters 11 -- 1.4.1 Per Unit Model and Physical Parameters 11 -- 1.4.2 Experimental Validation of PMSM Model 12 -- 1.5 Modeling of Induction Motor 13 -- 1.5.1 Space Vector Representation of Voltage Equation of Induction Motor 13 -- 1.5.2 Representation in Stationary Reference Frame 17 -- 1.5.3 Representation in Reference Frame 17 -- 1.5.4 Electromagnetic Torque of Induction Motor 19 -- 1.5.5 Model Parameters of Induction Motor and Model Validation 19 -- 1.6 Modeling of Power Converter 21 -- 1.6.1 Space Vector Representation of Voltage Equation for Power Converter 22 -- 1.6.2 Representation in Reference Frame 22 -- 1.6.3 Representation in Reference Frame 23 -- 1.6.4 Energy Balance Equation 24 -- 1.7 Summary 25 -- 1.8 Further Reading 25 -- References 25 -- 2 Control of Semiconductor Switches via PWM Technologies 27 -- 2.1 Topology of IGBT Inverter 28 -- 2.2 Six-step Operating Mode 30 -- 2.3 Carrier Based PWM 31 -- 2.3.1 Sinusoidal PWM 31 -- 2.3.2 Carrier Based PWM with Zero-sequence Injection 32 -- 2.4 Space Vector PWM 35 -- 2.5 Simulation Study of the Effect of PWM 37 -- 2.6 Summary 40 -- 2.7 Further Reading 40 -- References 40 -- 3 PID Control System Design for Electrical Drives and Power Converters 41 -- 3.1 Overview of PID Control Systems Using Pole-assignment Design Techniques 42 -- 3.1.1 PI Controller Design 42 -- 3.1.2 Selecting the Desired Closed-loop Performance 43 -- 3.1.3 Overshoot in Reference Response 45.

3.1.4 PID Controller Design 46 -- 3.1.5 Cascade PID Control Systems 48 -- 3.2 Overview of PID Control of PMSM 49 -- 3.2.1 Bridging the Sensor Measurements to Feedback Signals (See the lower part of Figure 3.6) 50 -- 3.2.2 Bridging the Control Signals to the Inputs to the PMSM (See the top part of Figure 3.6) 51 -- 3.3 PI Controller Design for Torque Control of PMSM 52 -- 3.3.1 Set-point Signals to the Current Control Loops 52 -- 3.3.2 Decoupling of the Current Control Systems 53 -- 3.3.3 PI Current Controller Design 54 -- 3.4 Velocity Control of PMSM 55 -- 3.4.1 Inner-loop Proportional Control of q-axis Current 55 -- 3.4.2 Cascade Feedback Control of Velocity:P Plus PI 57 -- 3.4.3 Simulation Example for P Plus PI Control System 59 -- 3.4.4 Cascade Feedback Control of Velocity:PI Plus PI 61 -- 3.4.5 Simulation Example for PI Plus PI Control System 63 -- 3.5 PID Controller Design for Position Control of PMSM 64 -- 3.6 Overview of PID Control of Induction Motor 65 -- 3.6.1 Bridging the Sensor Measurements to Feedback Signals 67 -- 3.6.2 Bridging the Control Signals to the Inputs to the Induction Motor 67 -- 3.7 PID Controller Design for Induction Motor 68 -- 3.7.1 PI Control of Electromagnetic Torque of Induction Motor 68 -- 3.7.2 Cascade Control of Velocity and Position 70 -- 3.7.3 Slip Estimation 73 -- 3.8 Overview of PID Control of Power Converter 74 -- 3.8.1 Bridging Sensor Measurements to Feedback Signals 75 -- 3.8.2 Bridging the Control Signals to the Inputs of the Power Converter 76 -- 3.9 PI Current and Voltage Controller Design for Power Converter 76 -- 3.9.1 P Control of d-axis Current 76 -- 3.9.2 PI Control of q-axis Current 77 -- 3.9.3 PI Cascade Control of Output Voltage 79 -- 3.9.4 Simulation Example 80 -- 3.9.5 Phase Locked Loop 80 -- 3.10 Summary 82 -- 3.11 Further Reading 83 -- References 83 -- 4 PID Control System Implementation 87 -- 4.1 P and PI Controller Implementation in Current Control Systems 87 -- 4.1.1 Voltage Operational Limits in Current Control Systems 87.

4.1.2 Discretization of Current Controllers 90 -- 4.1.3 Anti-windup Mechanisms 92 -- 4.2 Implementation of Current Controllers for PMSM 93 -- 4.3 Implementation of Current Controllers for Induction Motors 95 -- 4.4 Current Controller Implementation for Power Converter 97 -- 4.4.1 Constraints on the Control Variables 97 -- 4.5 Implementation of Outer-loop PI Control System 98 -- 4.5.1 Constraints in the Outer-loop 98 -- 4.5.2 Over Current Protection for AC Machines 99 -- 4.5.3 Implementation of Outer-loop PI Control of Velocity 100 -- 4.5.4 Over Current Protection for Power Converters 100 -- 4.6 MATLAB Tutorial on Implementation of PI Controller 100 -- 4.7 Summary 102 -- 4.8 Further Reading 103 -- References 103 -- 5 Tuning PID Control Systems with Experimental Validations 105 -- 5.1 Sensitivity Functions in Feedback Control Systems 105 -- 5.1.1 Two-degrees of Freedom Control System Structure 105 -- 5.1.2 Sensitivity Functions 109 -- 5.1.3 Disturbance Rejection and Noise Attenuation 110 -- 5.2 Tuning Current-loop q-axis Proportional Controller (PMSM) 111 -- 5.2.1 Performance Factor and Proportional Gain 112 -- 5.2.2 Complementary Sensitivity Function 112 -- 5.2.3 Sensitivity and Input Sensitivity Functions 114 -- 5.2.4 Effect of PWM Noise on Current Proportional Control System 114 -- 5.2.5 Effect of Current Sensor Noise and Bias 116 -- 5.2.6 Experimental Case Study of Current Sensor Bias Using P Control 118 -- 5.2.7 Experimental Case Study of Current Loop Noise 119 -- 5.3 Tuning Current-loop PI Controller (PMSM) 123 -- 5.4 Performance Robustness in Outer-loop Controllers 128 -- 5.4.1 Sensitivity Functions for Outer-loop Control System 131 -- 5.4.2 Input Sensitivity Functions for the Outer-loop System 135 -- 5.5 Analysis of Time-delay Effects 136 -- 5.5.1 PI Control of q-axis Current 137 -- 5.5.2 P Control of q-axis Current 137 -- 5.6 Tuning Cascade PI Control Systems for Induction Motor 138 -- 5.6.1 Robustness of Cascade PI Control System 140 -- 5.6.2 Robustness Study Using Nyquist Plot 143.

5.7 Tuning PI Control Systems for Power Converter 147 -- 5.7.1 Overview of the Designs 147 -- 5.7.2 Tuning the Current Controllers 149 -- 5.7.3 Tuning Voltage Controller 150 -- 5.7.4 Experimental Evaluations 154 -- 5.8 Tuning P Plus PI Controllers for Power Converter 157 -- 5.8.1 Design and Sensitivity Functions 157 -- 5.8.2 Experimental Results 158 -- 5.9 Robustness of Power Converter Control System Using PI Current Controllers 159 -- 5.9.1 Variation of Inductance Using PI Current Controllers 160 -- 5.9.2 Variation of Capacitance on Closed-loop Performance 163 -- 5.10 Summary 167 -- 5.10.1 Current Controllers 167 -- 5.10.2 Velocity, Position and Voltage Controllers 168 -- 5.10.3 Choice between P Current Control and PI Current Control 169 -- 5.11 Further Reading 169 -- References 169 -- 6 FCS Predictive Control in d − q Reference Frame 171 -- 6.1 States of IGBT Inverter and the Operational Constraints 172 -- 6.2 FCS Predictive Control of PMSM 175 -- 6.3 MATLAB Tutorial on Real-time Implementation of FCS-MPC 177 -- 6.3.1 Simulation Results 179 -- 6.3.2 Experimental Results of FCS Control 181 -- 6.4 Analysis of FCS-MPC System 182 -- 6.4.1 Optimal Control System 182 -- 6.4.2 Feedback Controller Gain 184 -- 6.4.3 Constrained Optimal Control 185 -- 6.5 Overview of FCS-MPC with Integral Action 187 -- 6.6 Derivation of I-FCS Predictive Control Algorithm 191 -- 6.6.1 Optimal Control without Constraints 191 -- 6.6.2 I-FCS Predictive Controller with Constraints 194 -- 6.6.3 Implementation of I-FCS-MPC Algorithm 196 -- 6.7 MATLAB Tutorial on Implementation of I-FCS Predictive Controller 197 -- 6.7.1 Simulation Results 198 -- 6.8 I-FCS Predictive Control of Induction Motor 201 -- 6.8.1 The Control Algorithm for an Induction Motor 202 -- 6.8.2 Simulation Results 204 -- 6.8.3 Experimental Results 205 -- 6.9 I-FCS Predictive Control of Power Converter 209 -- 6.9.1 I-FCS Predictive Control of a Power Converter 209 -- 6.9.2 Simulation Results 211 -- 6.9.3 Experimental Results 214.

6.10 Evaluation of Robustness of I-FCS-MPC via Monte-Carlo Simulations 215 -- 6.10.1 Discussion on Mean Square Errors 216 -- 6.11 Velocity and Position Control of PMSM Using I-FCS-MPC 218 -- 6.11.1 Choice of Sampling Rate for the Outer-loop Control System 219 -- 6.11.2 Velocity and Position Controller Design 223 -- 6.12 Velocity and Position Control of Induction Motor Using I-FCS-MPC 224 -- 6.12.1 I-FCS Cascade Velocity Control of Induction Motor 225 -- 6.12.2 I-FCS-MPC Cascade Position Control of Induction Motor 226 -- 6.12.3 Experimental Evaluation of Velocity Control 228 -- 6.13 Summary 232 -- 6.13.1 Selection of sampling interval 233 -- 6.13.2 Selection of the Integral Gain 233 -- 6.14 Further Reading 234 -- References 234 -- 7 FCS Predictive Control in Reference Frame 237 -- 7.1 FCS Predictive Current Control of PMSM 237 -- 7.1.1 Predictive Control Using One-step-ahead Prediction 238 -- 7.1.2 FCS Current Control in Reference Frame 239 -- 7.1.3 Generating Current Reference Signals in Frame 240 -- 7.2 Resonant FCS Predictive Current Control 241 -- 7.2.1 Control System Configuration 241 -- 7.2.2 Outer-loop Controller Design 242 -- 7.2.3 Resonant FCS Predictive Control System 243 -- 7.3 Resonant FCS Current Control of Induction Motor 247 -- 7.3.1 The Original FCS Current Control of Induction Motor 247 -- 7.3.2 Resonant FCS Predictive Current Control of Induction Motor 250 -- 7.3.3 Experimental Evaluations of Resonant FCS Predictive Control 252 -- 7.4 Resonant FCS Predictive Power Converter Control 255 -- 7.4.1 FCS Predictive Current Control of Power Converter 255 -- 7.4.2 Experimental Results of Resonant FCS Predictive Control 260 -- 7.5 Summary 261 -- 7.6 Further Reading 262 -- References 262 -- 8 Discrete-time Model Predictive Control (DMPC) of Electrical Drives and Power Converter 265 -- 8.1 Linear Discrete-time Model for PMSM 266 -- 8.1.1 Linear Model for PMSM 266 -- 8.1.2 Discretization of the Continuous-time Model 267 -- 8.2 Discrete-time MPC Design with Constraints 268.

8.2.1 Augmented Model 269 -- 8.2.2 Design without Constraints 270 -- 8.2.3 Formulation of the Constraints 272 -- 8.2.4 On-line Solution for Constrained MPC 272 -- 8.3 Experimental Evaluation of DMPC of PMSM 274 -- 8.3.1 The MPC Parameters 274 -- 8.3.2 Constraints 275 -- 8.3.3 Response to Load Disturbances 275 -- 8.3.4 Response to a Staircase Reference 277 -- 8.3.5 Tuning of the MPC controller 278 -- 8.4 Power Converter Control Using DMPC with Experimental Validation 280 -- 8.5 Summary 281 -- 8.6 Further Reading 282 -- References 283 -- 9 Continuous-time Model Predictive Control (CMPC) of Electrical Drives and PowerConverter 285 -- 9.1 Continuous-time MPC Design 286 -- 9.1.1 Augmented Model 286 -- 9.1.2 Description of the Control Trajectories Using Laguerre Functions 287 -- 9.1.3 Continuous-time Predictive Control without Constraints 289 -- 9.1.4 Tuning of CMPC Control System Using Exponential Data Weighting and Prescribed Degree of Stability 292 -- 9.2 CMPC with Nonlinear Constraints 294 -- 9.2.1 Approximation of Nonlinear Constraint Using Four Linear Constraints 294 -- 9.2.2 Approximation of Nonlinear Constraint Using Sixteen Linear Constraints 294 -- 9.2.3 State Feedback Observer 297 -- 9.3 Simulation and Experimental Evaluation of CMPC of Induction Motor 298 -- 9.3.1 Simulation Results 298 -- 9.3.2 Experimental Results 300 -- 9.4 Continuous-time Model Predictive Control of Power Converter 301 -- 9.4.1 Use of Prescribed Degree of Stability in the Design 302 -- 9.4.2 Experimental Results for Rectification Mode 303 -- 9.4.3 Experimental Results for Regeneration Mode 303 -- 9.4.4 Experimental Results for Disturbance Rejection 304 -- 9.5 Gain Scheduled Predictive Controller 305 -- 9.5.1 The Weighting Parameters 305 -- 9.5.2 Gain Scheduled Predictive Control Law 307 -- 9.6 Experimental Results of Gain Scheduled Predictive Control of Induction Motor 309 -- 9.6.1 The First Set of Experimental Results 309 -- 9.6.2 The Second Set of Experimental Results 311 -- 9.6.3 The Third Set of Experimental Results 312.

9.7 Summary 312 -- 9.8 Further Reading 313 -- References 313 -- 10 MATLAB(R)/Simulink(R) Tutorials on Physical Modeling and Test-bed Setup 315 -- 10.1 Building Embedded Functions for Park-Clarke Transformation 315 -- 10.1.1 Park-Clarke Transformation for Current Measurements 316 -- 10.1.2 Inverse Park-Clarke Transformation for Voltage Actuation 317 -- 10.2 Building Simulation Model for PMSM 318 -- 10.3 Building Simulation Model for Induction Motor 320 -- 10.4 Building Simulation Model for Power Converter 325 -- 10.4.1 Embedded MATLAB Function for Phase Locked Loop (PLL) 325 -- 10.4.2 Physical Simulation Model for Grid Connected Voltage Source Converter 328 -- 10.5 PMSM Experimental Setup 332 -- 10.6 Induction Motor Experimental Setup 334 -- 10.6.1 Controller 334 -- 10.6.2 Power Supply 334 -- 10.6.3 Inverter 335 -- 10.6.4 Mechanical Load 335 -- 10.6.5 Induction Motor and Sensors 335 -- 10.7 Grid Connected Power Converter Experimental Setup 335 -- 10.7.1 Controller 335 -- 10.7.2 Inverter 336 -- 10.7.3 Sensors 336 -- 10.8 Summary 337 -- 10.9 Further Reading 337 -- References 337 -- Index 339.