About the Authors |
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xiii | |
Preface |
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xv | |
Acknowledgment |
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xix | |
List of Symbols and Acronyms |
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xxi | |
1 Modeling of AC Drives and Power Converter |
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1 | (26) |
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1.1 Space Phasor Representation |
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1 | (4) |
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1.1.1 Space Vector for Magnetic Motive Force |
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1 | (3) |
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1.1.2 Space Vector Representation of Voltage Equation |
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4 | (1) |
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1.2 Model of Surface Mounted PMSM |
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5 | (5) |
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1.2.1 Representation in Stationary Reference (α — β) Frame |
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5 | (2) |
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1.2.2 Representation in Synchronous Reference (d — q) Frame |
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7 | (1) |
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1.2.3 Electromagnetic Torque |
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8 | (2) |
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1.3 Model of Interior Magnets PMSM |
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10 | (1) |
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1.3.1 Complete Model of PMSM |
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11 | (1) |
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1.4 Per Unit Model and PMSM Parameters |
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11 | (2) |
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1.4.1 Per Unit Model and Physical Parameters |
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11 | (1) |
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1.4.2 Experimental Validation of PMSM Model |
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12 | (1) |
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1.5 Modeling of Induction Motor |
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13 | (8) |
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1.5.1 Space Vector Representation of Voltage Equation of Induction Motor |
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13 | (4) |
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1.5.2 Representation in Stationary α — β Reference Frame |
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17 | (1) |
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1.5.3 Representation in d — q Reference Frame |
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17 | (2) |
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1.5.4 Electromagnetic Torque of Induction Motor |
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19 | (1) |
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1.5.5 Model Parameters of Induction Motor and Model Validation |
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19 | (2) |
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1.6 Modeling of Power Converter |
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21 | (4) |
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1.6.1 Space Vector Representation of Voltage Equation for Power Converter |
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22 | (1) |
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1.6.2 Representation in α — β Reference Frame |
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22 | (1) |
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1.6.3 Representation in d — q Reference Frame |
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23 | (1) |
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1.6.4 Energy Balance Equation |
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24 | (1) |
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25 | (1) |
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25 | (1) |
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25 | (2) |
2 Control of Semiconductor Switches via PWM Technologies |
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27 | (14) |
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2.1 Topology of IGBT Inverter |
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28 | (2) |
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2.2 Six-step Operating Mode |
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30 | (1) |
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31 | (4) |
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31 | (1) |
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2.3.2 Carrier Based PWM with Zero-sequence Injection |
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32 | (3) |
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35 | (2) |
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2.5 Simulation Study of the Effect of PWM |
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37 | (3) |
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40 | (1) |
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40 | (1) |
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40 | (1) |
3 PID Control System Design for Electrical Drives and Power Converters |
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41 | (46) |
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3.1 Overview of PID Control Systems Using Pole-assignment Design Techniques |
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42 | (7) |
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3.1.1 PI Controller Design |
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42 | (1) |
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3.1.2 Selecting the Desired Closed-loop Performance |
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43 | (2) |
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3.1.3 Overshoot in Reference Response |
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45 | (1) |
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3.1.4 PID Controller Design |
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46 | (2) |
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3.1.5 Cascade PID Control Systems |
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48 | (1) |
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3.2 Overview of PID Control of PMSM |
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49 | (3) |
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3.2.1 Bridging the Sensor Measurements to Feedback Signals (See the lower part of Figure 3.6) |
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50 | (1) |
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3.2.2 Bridging the Control Signals to the Inputs to the PMSM (See the top part of Figure 3.6) |
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51 | (1) |
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3.3 PI Controller Design for Torque Control of PMSM |
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52 | (3) |
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3.3.1 Set-point Signals to the Current Control Loops |
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52 | (1) |
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3.3.2 Decoupling of the Current Control Systems |
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53 | (1) |
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3.3.3 PI Current Controller Design |
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54 | (1) |
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3.4 Velocity Control of PMSM |
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55 | (9) |
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3.4.1 Inner-loop Proportional Control of q-axis Current |
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55 | (2) |
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3.4.2 Cascade Feedback Control of Velocity:P Plus PI |
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57 | (2) |
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3.4.3 Simulation Example for P Plus PI Control System |
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59 | (2) |
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3.4.4 Cascade Feedback Control of Velocity: PI Plus PI |
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61 | (2) |
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3.4.5 Simulation Example for PI Plus PI Control System |
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63 | (1) |
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3.5 PID Controller Design for Position Control of PMSM |
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64 | (1) |
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3.6 Overview of PID Control of Induction Motor |
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65 | (3) |
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3.6.1 Bridging the Sensor Measurements to Feedback Signals |
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67 | (1) |
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3.6.2 Bridging the Control Signals to the Inputs to the Induction Motor |
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67 | (1) |
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3.7 PID Controller Design for Induction Motor |
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68 | (6) |
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3.7.1 PI Control of Electromagnetic Torque of Induction Motor |
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68 | (2) |
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3.7.2 Cascade Control of Velocity and Position |
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70 | (3) |
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73 | (1) |
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3.8 Overview of PID Control of Power Converter |
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74 | (2) |
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3.8.1 Bridging Sensor Measurements to Feedback Signals |
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75 | (1) |
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3.8.2 Bridging the Control Signals to the Inputs of the Power Converter |
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76 | (1) |
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3.9 PI Current and Voltage Controller Design for Power Converter |
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76 | (6) |
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3.9.1 P Control of d-axis Current |
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76 | (1) |
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3.9.2 PI Control of q-axis Current |
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77 | (2) |
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3.9.3 PI Cascade Control of Output Voltage |
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79 | (1) |
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80 | (1) |
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80 | (2) |
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82 | (1) |
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83 | (1) |
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83 | (4) |
4 PID Control System Implementation |
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87 | (18) |
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4.1 P and PI Controller Implementation in Current Control Systems |
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87 | (6) |
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4.1.1 Voltage Operational Limits in Current Control Systems |
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87 | (3) |
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4.1.2 Discretization of Current Controllers |
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90 | (2) |
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4.1.3 Anti-windup Mechanisms |
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92 | (1) |
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4.2 Implementation of Current Controllers for PMSM |
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93 | (2) |
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4.3 Implementation of Current Controllers for Induction Motors |
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95 | (2) |
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4.3.1 Estimation of ωs and θs |
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95 | (1) |
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96 | (1) |
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4.3.3 The Implementation Steps |
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97 | (1) |
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4.4 Current Controller Implementation for Power Converter |
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97 | (1) |
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4.4.1 Constraints on the Control Variables |
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97 | (1) |
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4.5 Implementation of Outer-loop PI Control System |
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98 | (2) |
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4.5.1 Constraints in the Outer-loop |
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98 | (1) |
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4.5.2 Over Current Protection for AC Machines |
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99 | (1) |
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4.5.3 Implementation of Outer-loop PI Control of Velocity |
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100 | (1) |
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4.5.4 Over Current Protection for Power Converters |
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100 | (1) |
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4.6 MATLAB Tutorial on Implementation of PI Controller |
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100 | (2) |
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102 | (1) |
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103 | (1) |
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103 | (2) |
5 Tuning PID Control Systems with Experimental Validations |
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105 | (66) |
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5.1 Sensitivity Functions in Feedback Control Systems |
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105 | (6) |
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5.1.1 Two-degrees of Freedom Control System Structure |
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105 | (4) |
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5.1.2 Sensitivity Functions |
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109 | (1) |
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5.1.3 Disturbance Rejection and Noise Attenuation |
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110 | (1) |
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5.2 Tuning Current-loop q-axis Proportional Controller (PMSM) |
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111 | (12) |
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5.2.1 Performance Factor and Proportional Gain |
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112 | (1) |
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5.2.2 Complementary Sensitivity Function |
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112 | (2) |
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5.2.3 Sensitivity and Input Sensitivity Functions |
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114 | (1) |
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5.2.4 Effect of PWM Noise on Current Proportional Control System |
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114 | (2) |
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5.2.5 Effect of Current Sensor Noise and Bias |
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116 | (2) |
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5.2.6 Experimental Case Study of Current Sensor Bias Using P Control |
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118 | (1) |
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5.2.7 Experimental Case Study of Current Loop Noise |
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119 | (4) |
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5.3 Tuning Current-loop PI Controller (PMSM) |
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123 | (5) |
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5.3.1 PI Controller Parameters in Relation to Performance Parameter γ |
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123 | (1) |
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5.3.2 Sensitivity in Relation to Performance Parameter γ |
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124 | (2) |
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5.3.3 Effect of PWM Error in Relation to γ |
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126 | (1) |
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5.3.4 Experimental Case Study of Current Loop Noise Using PI Control |
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126 | (2) |
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5.4 Performance Robustness in Outer-loop Controllers |
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128 | (8) |
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5.4.1 Sensitivity Functions for Outer-loop Control System |
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131 | (4) |
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5.4.2 Input Sensitivity Functions for the Outer-loop System |
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135 | (1) |
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5.5 Analysis of Time-delay Effects |
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136 | (2) |
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5.5.1 PI Control of q-axis Current |
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137 | (1) |
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5.5.2 P Control of q-axis Current |
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137 | (1) |
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5.6 Tuning Cascade PI Control Systems for Induction Motor |
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138 | (9) |
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5.6.1 Robustness of Cascade PI Control System |
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140 | (3) |
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5.6.2 Robustness Study Using Nyquist Plot |
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143 | (4) |
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5.7 Tuning PI Control Systems for Power Converter |
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147 | (10) |
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5.7.1 Overview of the Designs |
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147 | (2) |
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5.7.2 Tuning the Current Controllers |
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149 | (1) |
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5.7.3 Tuning Voltage Controller |
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150 | (4) |
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5.7.4 Experimental Evaluations |
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154 | (3) |
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5.8 Tuning P Plus PI Controllers for Power Converter |
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157 | (2) |
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5.8.1 Design and Sensitivity Functions |
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157 | (1) |
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5.8.2 Experimental Results |
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158 | (1) |
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5.9 Robustness of Power Converter Control System Using PI Current Controllers |
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159 | (8) |
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5.9.1 Variation of Inductance Using PI Current Controllers |
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160 | (3) |
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5.9.2 Variation of Capacitance on Closed-loop Performance |
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163 | (4) |
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167 | (2) |
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5.10.1 Current Controllers |
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167 | (1) |
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5.10.2 Velocity, Position and Voltage Controllers |
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168 | (1) |
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5.10.3 Choice between P Current Control and PI Current Control |
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169 | (1) |
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169 | (1) |
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169 | (2) |
6 FCS Predictive Control in d — q Reference Frame |
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171 | (66) |
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6.1 States of IGBT Inverter and the Operational Constraints |
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172 | (3) |
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6.2 FCS Predictive Control of PMSM |
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175 | (2) |
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6.3 MATLAB Tutorial on Real-time Implementation of FCS-MPC |
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177 | (5) |
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179 | (2) |
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6.3.2 Experimental Results of FCS Control |
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181 | (1) |
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6.4 Analysis of FCS-MPC System |
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182 | (5) |
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6.4.1 Optimal Control System |
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182 | (2) |
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6.4.2 Feedback Controller Gain |
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184 | (1) |
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6.4.3 Constrained Optimal Control |
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185 | (2) |
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6.5 Overview of FCS-MPC with Integral Action |
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187 | (4) |
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6.6 Derivation of I-FCS Predictive Control Algorithm |
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191 | (6) |
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6.6.1 Optimal Control without Constraints |
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191 | (3) |
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6.6.2 I-FCS Predictive Controller with Constraints |
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194 | (2) |
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6.6.3 Implementation of I-FCS-MPC Algorithm |
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196 | (1) |
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6.7 MATLAB Tutorial on Implementation of I-FCS Predictive Controller |
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197 | (4) |
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198 | (3) |
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6.8 I-FCS Predictive Control of Induction Motor |
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201 | (8) |
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6.8.1 The Control Algorithm for an Induction Motor |
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202 | (2) |
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204 | (1) |
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6.8.3 Experimental Results |
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205 | (4) |
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6.9 I-FCS Predictive Control of Power Converter |
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209 | (6) |
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6.9.1 I-FCS Predictive Control of a Power Converter |
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209 | (2) |
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211 | (3) |
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6.9.3 Experimental Results |
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214 | (1) |
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6.10 Evaluation of Robustness of I-FCS-MPC via Monte-Carlo Simulations |
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215 | (3) |
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6.10.1 Discussion on Mean Square Errors |
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216 | (2) |
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6.11 Velocity and Position Control of PMSM Using I-FCS-MPC |
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218 | (6) |
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6.11.1 Choice of Sampling Rate for the Outer-loop Control System |
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219 | (4) |
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6.11.2 Velocity and Position Controller Design |
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223 | (1) |
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6.12 Velocity and Position Control of Induction Motor Using I-FCS-MPC |
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224 | (8) |
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6.12.1 I-FCS Cascade Velocity Control of Induction Motor |
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225 | (1) |
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6.12.2 I-FCS-MPC Cascade Position Control of Induction Motor |
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226 | (2) |
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6.12.3 Experimental Evaluation of Velocity Control |
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228 | (4) |
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232 | (2) |
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6.13.1 Selection of sampling interval Δt |
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233 | (1) |
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6.13.2 Selection of the Integral Gain |
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233 | (1) |
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234 | (1) |
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234 | (3) |
7 FCS Predictive Control in α — β Reference Frame |
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237 | (28) |
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7.1 FCS Predictive Current Control of PMSM |
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237 | (4) |
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7.1.1 Predictive Control Using One-step-ahead Prediction |
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238 | (1) |
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7.1.2 FCS Current Control in α — β Reference Frame |
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239 | (1) |
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7.1.3 Generating Current Reference Signals in α — β Frame |
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240 | (1) |
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7.2 Resonant FCS Predictive Current Control |
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241 | (6) |
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7.2.1 Control System Configuration |
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241 | (1) |
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7.2.2 Outer-loop Controller Design |
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242 | (1) |
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7.2.3 Resonant FCS Predictive Control System |
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243 | (4) |
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7.3 Resonant FCS Current Control of Induction Motor |
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247 | (8) |
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7.3.1 The Original FCS Current Control of Induction Motor |
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247 | (3) |
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7.3.2 Resonant FCS Predictive Current Control of Induction Motor |
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250 | (2) |
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7.3.3 Experimental Evaluations of Resonant FCS Predictive Control |
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252 | (3) |
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7.4 Resonant FCS Predictive Power Converter Control |
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255 | (6) |
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7.4.1 FCS Predictive Current Control of Power Converter |
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255 | (5) |
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7.4.2 Experimental Results of Resonant FCS Predictive Control |
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260 | (1) |
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261 | (1) |
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262 | (1) |
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262 | (3) |
8 Discrete-time Model Predictive Control (DMPC) of Electrical Drives and Power Converter |
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265 | (20) |
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8.1 Linear Discrete-time Model for PMSM |
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266 | (2) |
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8.1.1 Linear Model for PMSM |
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266 | (1) |
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8.1.2 Discretization of the Continuous-time Model |
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267 | (1) |
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8.2 Discrete-time MPC Design with Constraints |
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268 | (6) |
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269 | (1) |
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8.2.2 Design without Constraints |
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270 | (2) |
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8.2.3 Formulation of the Constraints |
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272 | (1) |
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8.2.4 On-line Solution for Constrained MPC |
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272 | (2) |
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8.3 Experimental Evaluation of DMPC of PMSM |
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274 | (6) |
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274 | (1) |
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275 | (1) |
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8.3.3 Response to Load Disturbances |
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275 | (2) |
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8.3.4 Response to a Staircase Reference |
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277 | (1) |
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8.3.5 Tuning of the MPC controller |
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278 | (2) |
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8.4 Power Converter Control Using DMPC with Experimental Validation |
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280 | (1) |
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281 | (1) |
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282 | (1) |
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283 | (2) |
9 Continuous-time Model Predictive Control (CMPC) of Electrical Drives and Power Converter |
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285 | (30) |
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9.1 Continuous-time MPC Design |
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286 | (8) |
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286 | (1) |
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9.1.2 Description of the Control Trajectories Using Laguerre Functions |
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287 | (2) |
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9.1.3 Continuous-time Predictive Control without Constraints |
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289 | (3) |
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9.1.4 Tuning of CMPC Control System Using Exponential Data Weighting and Prescribed Degree of Stability |
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292 | (2) |
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9.2 CMPC with Nonlinear Constraints |
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294 | (4) |
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9.2.1 Approximation of Nonlinear Constraint Using Four Linear Constraints |
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294 | (1) |
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9.2.2 Approximation of Nonlinear Constraint Using Sixteen Linear Constraints |
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294 | (3) |
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9.2.3 State Feedback Observer |
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297 | (1) |
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9.3 Simulation and Experimental Evaluation of CMPC of Induction Motor |
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298 | (3) |
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298 | (2) |
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9.3.2 Experimental Results |
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300 | (1) |
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9.4 Continuous-time Model Predictive Control of Power Converter |
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301 | (4) |
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9.4.1 Use of Prescribed Degree of Stability in the Design |
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302 | (1) |
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9.4.2 Experimental Results for Rectification Mode |
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303 | (1) |
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9.4.3 Experimental Results for Regeneration Mode |
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303 | (1) |
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9.4.4 Experimental Results for Disturbance Rejection |
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304 | (1) |
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9.5 Gain Scheduled Predictive Controller |
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305 | (4) |
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9.5.1 The Weighting Parameters |
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305 | (2) |
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9.5.2 Gain Scheduled Predictive Control Law |
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307 | (2) |
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9.6 Experimental Results of Gain Scheduled Predictive Control of Induction Motor |
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309 | (3) |
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9.6.1 The First Set of Experimental Results |
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309 | (2) |
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9.6.2 The Second Set of Experimental Results |
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311 | (1) |
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9.6.3 The Third Set of Experimental Results |
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312 | (1) |
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312 | (1) |
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313 | (1) |
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313 | (2) |
10 MATLAB®/Simulink® Tutorials on Physical Modeling and Test-bed Setup |
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315 | (24) |
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10.1 Building Embedded Functions for Park-Clarke Transformation |
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315 | (3) |
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10.1.1 Park-Clarke Transformation for Current Measurements |
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316 | (1) |
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10.1.2 Inverse Park-Clarke Transformation for Voltage Actuation |
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317 | (1) |
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10.2 Building Simulation Model for PMSM |
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318 | (2) |
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10.3 Building Simulation Model for Induction Motor |
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320 | (5) |
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10.4 Building Simulation Model for Power Converter |
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325 | (7) |
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10.4.1 Embedded MATLAB Function for Phase Locked Loop (PLL) |
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325 | (3) |
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10.4.2 Physical Simulation Model for Grid Connected Voltage Source Converter |
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328 | (4) |
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10.5 PMSM Experimental Setup |
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332 | (2) |
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10.6 Induction Motor Experimental Setup |
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334 | (1) |
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334 | (1) |
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334 | (1) |
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335 | (1) |
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335 | (1) |
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10.6.5 Induction Motor and Sensors |
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335 | (1) |
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10.7 Grid Connected Power Converter Experimental Setup |
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335 | (2) |
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335 | (1) |
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336 | (1) |
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336 | (1) |
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337 | (1) |
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337 | (1) |
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337 | (2) |
Index |
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339 | |