PID and Predictive Control of Electrical Drives and Power Converters using MATLAB / Simulink

Liuping Wang is Professor of Control Engineering at RMIT University, Melbourne, Australia. She has been working on PID control systems and system identification for over 20 years and, together with her research group, Professor Wang has generated the research outcomes that have significantly improved the performance of computer numerical control (CNC) machines, leading to a new understanding of electric motor control and regenerative power supplies.  She has published numerous articles on the subject.Shan Chai, Dae Yoo, Lu Gan and Ki Ng are PhD students working under the supervision of Professor Wang and are part of the research team that has produced, and is producing, new approaches and new understanding of the electrical motor control and the control of regenerative power supplies.

• About the Authors xiiiPreface xvAcknowledgment xixList of Symbols and Acronyms xxi1 Modeling of AC Drives and Power Converter 11.1 Space Phasor Representation 11.1.1 Space Vector for Magnetic Motive Force 11.1.2 Space Vector Representation of Voltage Equation 41.2 Model of Surface Mounted PMSM 51.2.1 Representation in Stationary Reference Frame 51.2.2 Representation in Synchronous Reference Frame 71.2.3 Electromagnetic Torque 81.3 Model of Interior Magnets PMSM 101.3.1 Complete Model of PMSM 111.4 Per Unit Model and PMSM Parameters 111.4.1 Per Unit Model and Physical Parameters 111.4.2 Experimental Validation of PMSM Model 121.5 Modeling of Induction Motor 131.5.1 Space Vector Representation of Voltage Equation of Induction Motor 131.5.2 Representation in Stationary Reference Frame 171.5.3 Representation in Reference Frame 171.5.4 Electromagnetic Torque of Induction Motor 191.5.5 Model Parameters of Induction Motor and Model Validation 191.6 Modeling of Power Converter 211.6.1 Space Vector Representation of Voltage Equation for Power Converter 221.6.2 Representation in Reference Frame 221.6.3 Representation in Reference Frame 231.6.4 Energy Balance Equation 241.7 Summary 251.8 Further Reading 25References 252 Control of Semiconductor Switches via PWM Technologies 272.1 Topology of IGBT Inverter 282.2 Six-step Operating Mode 302.3 Carrier Based PWM 312.3.1 Sinusoidal PWM 312.3.2 Carrier Based PWM with Zero-sequence Injection 322.4 Space Vector PWM 352.5 Simulation Study of the Effect of PWM 372.6 Summary 402.7 Further Reading 40References 403 PID Control System Design for Electrical Drives and Power Converters 413.1 Overview of PID Control Systems Using Pole-assignment Design Techniques 423.1.1 PI Controller Design 423.1.2 Selecting the Desired Closed-loop Performance 433.1.3 Overshoot in Reference Response 453.1.4 PID Controller Design 463.1.5 Cascade PID Control Systems 483.2 Overview of PID Control of PMSM 493.2.1 Bridging the Sensor Measurements to Feedback Signals (See the lower part of Figure 3.6) 503.2.2 Bridging the Control Signals to the Inputs to the PMSM (See the top part of Figure 3.6) 513.3 PI Controller Design for Torque Control of PMSM 523.3.1 Set-point Signals to the Current Control Loops 523.3.2 Decoupling of the Current Control Systems 533.3.3 PI Current Controller Design 543.4 Velocity Control of PMSM 553.4.1 Inner-loop Proportional Control of q-axis Current 553.4.2 Cascade Feedback Control of Velocity:P Plus PI 573.4.3 Simulation Example for P Plus PI Control System 593.4.4 Cascade Feedback Control of Velocity:PI Plus PI 613.4.5 Simulation Example for PI Plus PI Control System 633.5 PID Controller Design for Position Control of PMSM 643.6 Overview of PID Control of Induction Motor 653.6.1 Bridging the Sensor Measurements to Feedback Signals 673.6.2 Bridging the Control Signals to the Inputs to the Induction Motor 673.7 PID Controller Design for Induction Motor 683.7.1 PI Control of Electromagnetic Torque of Induction Motor 683.7.2 Cascade Control of Velocity and Position 703.7.3 Slip Estimation 733.8 Overview of PID Control of Power Converter 743.8.1 Bridging Sensor Measurements to Feedback Signals 753.8.2 Bridging the Control Signals to the Inputs of the Power Converter 763.9 PI Current and Voltage Controller Design for Power Converter 763.9.1 P Control of d-axis Current 763.9.2 PI Control of q-axis Current 773.9.3 PI Cascade Control of Output Voltage 793.9.4 Simulation Example 803.9.5 Phase Locked Loop 803.10 Summary 823.11 Further Reading 83References 834 PID Control System Implementation 874.1 P and PI Controller Implementation in Current Control Systems 874.1.1 Voltage Operational Limits in Current Control Systems 874.1.2 Discretization of Current Controllers 904.1.3 Anti-windup Mechanisms 924.2 Implementation of Current Controllers for PMSM 934.3 Implementation of Current Controllers for Induction Motors 954.4 Current Controller Implementation for Power Converter 974.4.1 Constraints on the Control Variables 974.5 Implementation of Outer-loop PI Control System 984.5.1 Constraints in the Outer-loop 984.5.2 Over Current Protection for AC Machines 994.5.3 Implementation of Outer-loop PI Control of Velocity 1004.5.4 Over Current Protection for Power Converters 1004.6 MATLAB Tutorial on Implementation of PI Controller 1004.7 Summary 1024.8 Further Reading 103References 1035 Tuning PID Control Systems with Experimental Validations 1055.1 Sensitivity Functions in Feedback Control Systems 1055.1.1 Two-degrees of Freedom Control System Structure 1055.1.2 Sensitivity Functions 1095.1.3 Disturbance Rejection and Noise Attenuation 1105.2 Tuning Current-loop q-axis Proportional Controller (PMSM) 1115.2.1 Performance Factor and Proportional Gain 1125.2.2 Complementary Sensitivity Function 1125.2.3 Sensitivity and Input Sensitivity Functions 1145.2.4 Effect of PWM Noise on Current Proportional Control System 1145.2.5 Effect of Current Sensor Noise and Bias 1165.2.6 Experimental Case Study of Current Sensor Bias Using P Control 1185.2.7 Experimental Case Study of Current Loop Noise 1195.3 Tuning Current-loop PI Controller (PMSM) 1235.4 Performance Robustness in Outer-loop Controllers 1285.4.1 Sensitivity Functions for Outer-loop Control System 1315.4.2 Input Sensitivity Functions for the Outer-loop System 1355.5 Analysis of Time-delay Effects 1365.5.1 PI Control of q-axis Current 1375.5.2 P Control of q-axis Current 1375.6 Tuning Cascade PI Control Systems for Induction Motor 1385.6.1 Robustness of Cascade PI Control System 1405.6.2 Robustness Study Using Nyquist Plot 1435.7 Tuning PI Control Systems for Power Converter 1475.7.1 Overview of the Designs 1475.7.2 Tuning the Current Controllers 1495.7.3 Tuning Voltage Controller 1505.7.4 Experimental Evaluations 1545.8 Tuning P Plus PI Controllers for Power Converter 1575.8.1 Design and Sensitivity Functions 1575.8.2 Experimental Results 1585.9 Robustness of Power Converter Control System Using PI Current Controllers 1595.9.1 Variation of Inductance Using PI Current Controllers 1605.9.2 Variation of Capacitance on Closed-loop Performance 1635.10 Summary 1675.10.1 Current Controllers 1675.10.2 Velocity, Position and Voltage Controllers 1685.10.3 Choice between P Current Control and PI Current Control 1695.11 Further Reading 169References 1696 FCS Predictive Control in d − q Reference Frame 1716.1 States of IGBT Inverter and the Operational Constraints 1726.2 FCS Predictive Control of PMSM 1756.3 MATLAB Tutorial on Real-time Implementation of FCS-MPC 1776.3.1 Simulation Results 1796.3.2 Experimental Results of FCS Control 1816.4 Analysis of FCS-MPC System 1826.4.1 Optimal Control System 1826.4.2 Feedback Controller Gain 1846.4.3 Constrained Optimal Control 1856.5 Overview of FCS-MPC with Integral Action 1876.6 Derivation of I-FCS Predictive Control Algorithm 1916.6.1 Optimal Control without Constraints 1916.6.2 I-FCS Predictive Controller with Constraints 1946.6.3 Implementation of I-FCS-MPC Algorithm 1966.7 MATLAB Tutorial on Implementation of I-FCS Predictive Controller 1976.7.1 Simulation Results 1986.8 I-FCS Predictive Control of Induction Motor 2016.8.1 The Control Algorithm for an Induction Motor 2026.8.2 Simulation Results 2046.8.3 Experimental Results 2056.9 I-FCS Predictive Control of Power Converter 2096.9.1 I-FCS Predictive Control of a Power Converter 2096.9.2 Simulation Results 2116.9.3 Experimental Results 2146.10 Evaluation of Robustness of I-FCS-MPC via Monte-Carlo Simulations 2156.10.1 Discussion on Mean Square Errors 2166.11 Velocity and Position Control of PMSM Using I-FCS-MPC 2186.11.1 Choice of Sampling Rate for the Outer-loop Control System 2196.11.2 Velocity and Position Controller Design 2236.12 Velocity and Position Control of Induction Motor Using I-FCS-MPC 2246.12.1 I-FCS Cascade Velocity Control of Induction Motor 2256.12.2 I-FCS-MPC Cascade Position Control of Induction Motor 2266.12.3 Experimental Evaluation of Velocity Control 2286.13 Summary 2326.13.1 Selection of sampling interval 2336.13.2 Selection of the Integral Gain 2336.14 Further Reading 234References 2347 FCS Predictive Control in Reference Frame 2377.1 FCS Predictive Current Control of PMSM 2377.1.1 Predictive Control Using One-step-ahead Prediction 2387.1.2 FCS Current Control in Reference Frame 2397.1.3 Generating Current Reference Signals in Frame 2407.2 Resonant FCS Predictive Current Control 2417.2.1 Control System Configuration 2417.2.2 Outer-loop Controller Design 2427.2.3 Resonant FCS Predictive Control System 2437.3 Resonant FCS Current Control of Induction Motor 2477.3.1 The Original FCS Current Control of Induction Motor 2477.3.2 Resonant FCS Predictive Current Control of Induction Motor 2507.3.3 Experimental Evaluations of Resonant FCS Predictive Control 2527.4 Resonant FCS Predictive Power Converter Control 2557.4.1 FCS Predictive Current Control of Power Converter 2557.4.2 Experimental Results of Resonant FCS Predictive Control 2607.5 Summary 2617.6 Further Reading 262References 2628 Discrete-time Model Predictive Control (DMPC) of Electrical Drives and Power Converter 2658.1 Linear Discrete-time Model for PMSM 2668.1.1 Linear Model for PMSM 2668.1.2 Discretization of the Continuous-time Model 2678.2 Discrete-time MPC Design with Constraints 2688.2.1 Augmented Model 2698.2.2 Design without Constraints 2708.2.3 Formulation of the Constraints 2728.2.4 On-line Solution for Constrained MPC 2728.3 Experimental Evaluation of DMPC of PMSM 2748.3.1 The MPC Parameters 2748.3.2 Constraints 2758.3.3 Response to Load Disturbances 2758.3.4 Response to a Staircase Reference 2778.3.5 Tuning of the MPC controller 2788.4 Power Converter Control Using DMPC with Experimental Validation 2808.5 Summary 2818.6 Further Reading 282References 2839 Continuous-time Model Predictive Control (CMPC) of Electrical Drives and PowerConverter 2859.1 Continuous-time MPC Design 2869.1.1 Augmented Model 2869.1.2 Description of the Control Trajectories Using Laguerre Functions 2879.1.3 Continuous-time Predictive Control without Constraints 2899.1.4 Tuning of CMPC Control System Using Exponential Data Weighting and Prescribed Degree of Stability 2929.2 CMPC with Nonlinear Constraints 2949.2.1 Approximation of Nonlinear Constraint Using Four Linear Constraints 2949.2.2 Approximation of Nonlinear Constraint Using Sixteen Linear Constraints 2949.2.3 State Feedback Observer 2979.3 Simulation and Experimental Evaluation of CMPC of Induction Motor 2989.3.1 Simulation Results 2989.3.2 Experimental Results 3009.4 Continuous-time Model Predictive Control of Power Converter 3019.4.1 Use of Prescribed Degree of Stability in the Design 3029.4.2 Experimental Results for Rectification Mode 3039.4.3 Experimental Results for Regeneration Mode 3039.4.4 Experimental Results for Disturbance Rejection 3049.5 Gain Scheduled Predictive Controller 3059.5.1 The Weighting Parameters 3059.5.2 Gain Scheduled Predictive Control Law 3079.6 Experimental Results of Gain Scheduled Predictive Control of Induction Motor 3099.6.1 The First Set of Experimental Results 3099.6.2 The Second Set of Experimental Results 3119.6.3 The Third Set of Experimental Results 3129.7 Summary 3129.8 Further Reading 313References 31310 MATLAB®/Simulink® Tutorials on Physical Modeling and Test-bed Setup 31510.1 Building Embedded Functions for Park-Clarke Transformation 31510.1.1 Park-Clarke Transformation for Current Measurements 31610.1.2 Inverse Park-Clarke Transformation for Voltage Actuation 31710.2 Building Simulation Model for PMSM 31810.3 Building Simulation Model for Induction Motor 32010.4 Building Simulation Model for Power Converter 32510.4.1 Embedded MATLAB Function for Phase Locked Loop (PLL) 32510.4.2 Physical Simulation Model for Grid Connected Voltage Source Converter 32810.5 PMSM Experimental Setup 33210.6 Induction Motor Experimental Setup 33410.6.1 Controller 33410.6.2 Power Supply 33410.6.3 Inverter 33510.6.4 Mechanical Load 33510.6.5 Induction Motor and Sensors 33510.7 Grid Connected Power Converter Experimental Setup 33510.7.1 Controller 33510.7.2 Inverter 33610.7.3 Sensors 33610.8 Summary 33710.9 Further Reading 337References 337Index 339