Table of contents
1 Modeling of AC Drives and Power Converter
1.1 Space Phasor Representation
1.1.1 Space Vector for Magnetic Motive Force
1.1.2 Space Vector Representation of Voltage Equation
1.2 Model of Surface Mounted PMSM
1.2.1 Representation in Stationary Reference (𝛼 − 𝛽) Frame
1.2.2 Representation in Synchronous Reference (d − q) Frame
1.2.3 Electromagnetic Torque
1.3 Model of Interior Magnets PMSM
1.3.1 Complete Model of PMSM
1.4 Per Unit Model and PMSM Parameters
1.4.1 Per Unit Model and Physical Parameters
1.4.2 Experimental Validation of PMSM Model
1.5 Modeling of Induction Motor
1.5.1 Space Vector Representation of Voltage Equation of Induction Motor
1.5.2 Representation in Stationary 𝛼 − 𝛽 Reference Frame
1.5.3 Representation in d − q Reference Frame
1.5.4 Electromagnetic Torque of Induction Motor
1.5.5 Model Parameters of Induction Motor and Model Validation
1.6 Modeling of Power Converter
1.6.1 Space Vector Representation of Voltage Equation for Power Converter
1.6.2 Representation in 𝛼 − 𝛽 Reference Frame
1.6.3 Representation in d − q Reference Frame
1.6.4 Energy Balance Equation
1.7 Summary
1.8 Further Reading
References
2 Control of Semiconductor Switches via PWM Technologies
2.1 Topology of IGBT Inverter
2.2 Six-step Operating Mode
2.3 Carrier Based PWM
2.3.1 Sinusoidal PWM
2.3.2 Carrier Based PWM with Zero-sequence Injection
2.4 Space Vector PWM
2.5 Simulation Study of the Effect of PWM
2.6 Summary
2.7 Further Reading
References
3 PID Control System Design for Electrical Drives and Power Converters
3.1 Overview of PID Control Systems Using Pole-assignment Design Techniques
3.1.1 PI Controller Design
3.1.2 Selecting the Desired Closed-loop Performance
3.1.3 Overshoot in Reference Response
3.1.4 PID Controller Design
3.1.5 Cascade PID Control Systems
3.2 Overview of PID Control of PMSM
3.2.1 Bridging the Sensor Measurements to Feedback Signals (See the lower part of
Figure 3.6)
3.2.2 Bridging the Control Signals to the Inputs to the PMSM (See the top part of
Figure 3.6)
3.3 PI Controller Design for Torque Control of PMSM
3.3.1 Set-point Signals to the Current Control Loops
3.3.2 Decoupling of the Current Control Systems
3.3.3 PI Current Controller Design
3.4 Velocity Control of PMSM
3.4.1 Inner-loop Proportional Control of q-axis Current
3.4.2 Cascade Feedback Control of Velocity:P Plus PI
3.4.3 Simulation Example for P Plus PI Control System
3.4.4 Cascade Feedback Control of Velocity:PI Plus PI
3.4.5 Simulation Example for PI Plus PI Control System
3.5 PID Controller Design for Position Control of PMSM
3.6 Overview of PID Control of Induction Motor
3.6.1 Bridging the Sensor Measurements to Feedback Signals
3.6.2 Bridging the Control Signals to the Inputs to the Induction Motor
3.7 PID Controller Design for Induction Motor
3.7.1 PI Control of Electromagnetic Torque of Induction Motor
3.7.2 Cascade Control of Velocity and Position
3.7.3 Slip Estimation
3.8 Overview of PID Control of Power Converter
3.8.1 Bridging Sensor Measurements to Feedback Signals
3.8.2 Bridging the Control Signals to the Inputs of the Power Converter
3.9 PI Current and Voltage Controller Design for Power Converter
3.9.1 P Control of d-axis Current
3.9.2 PI Control of q-axis Current
3.9.3 PI Cascade Control of Output Voltage
Contents vii
3.9.4 Simulation Example
3.9.5 Phase Locked Loop
3.10 Summary
3.11 Further Reading
References
4 PID Control System Implementation
4.1 P and PI Controller Implementation in Current Control Systems
4.1.1 Voltage Operational Limits in Current Control Systems
4.1.2 Discretization of Current Controllers
4.1.3 Anti-windup Mechanisms
4.2 Implementation of Current Controllers for PMSM
4.3 Implementation of Current Controllers for Induction Motors
4.3.1 Estimation of 𝜔s and 𝜃s
4.3.2 Estimation of 𝜓rd
4.3.3 The Implementation Steps
4.4 Current Controller Implementation for Power Converter
4.4.1 Constraints on the Control Variables
4.5 Implementation of Outer-loop PI Control System
4.5.1 Constraints in the Outer-loop
4.5.2 Over Current Protection for AC Machines
4.5.3 Implementation of Outer-loop PI Control of Velocity
4.5.4 Over Current Protection for Power Converters
4.6 MATLAB Tutorial on Implementation of PI Controller
4.7 Summary
4.8 Further Reading
References
5 Tuning PID Control Systems with Experimental Validations
5.1 Sensitivity Functions in Feedback Control Systems
5.1.1 Two-degrees of Freedom Control System Structure
5.1.2 Sensitivity Functions
5.1.3 Disturbance Rejection and Noise Attenuation
5.2 Tuning Current-loop q-axis Proportional Controller (PMSM)
5.2.1 Performance Factor and Proportional Gain
5.2.2 Complementary Sensitivity Function
5.2.3 Sensitivity and Input Sensitivity Functions
5.2.4 Effect of PWM Noise on Current Proportional Control System
5.2.5 Effect of Current Sensor Noise and Bias
5.2.6 Experimental Case Study of Current Sensor Bias Using P Control
5.2.7 Experimental Case Study of Current Loop Noise
5.3 Tuning Current-loop PI Controller (PMSM)
5.3.1 PI Controller Parameters in Relation to Performance Parameter 𝛾
5.3.2 Sensitivity in Relation to Performance Parameter 𝛾
5.3.3 Effect of PWM Error in Relation to 𝛾
5.3.4 Experimental Case Study of Current Loop Noise Using PI Control
5.4 Performance Robustness in Outer-loop Controllers 128
5.4.1 Sensitivity Functions for Outer-loop Control System
5.4.2 Input Sensitivity Functions for the Outer-loop System
5.5 Analysis of Time-delay Effects
5.5.1 PI Control of q-axis Current
5.5.2 P Control of q-axis Current
5.6 Tuning Cascade PI Control Systems for Induction Motor
5.6.1 Robustness of Cascade PI Control System
5.6.2 Robustness Study Using Nyquist Plot
5.7 Tuning PI Control Systems for Power Converter
5.7.1 Overview of the Designs
5.7.2 Tuning the Current Controllers
5.7.3 Tuning Voltage Controller
5.7.4 Experimental Evaluations
5.8 Tuning P Plus PI Controllers for Power Converter
5.8.1 Design and Sensitivity Functions
5.8.2 Experimental Results
5.9 Robustness of Power Converter Control System Using PI Current Controllers
5.9.1 Variation of Inductance Using PI Current Controllers
5.9.2 Variation of Capacitance on Closed-loop Performance
5.10 Summary
5.10.1 Current Controllers
5.10.2 Velocity, Position and Voltage Controllers
5.10.3 Choice between P Current Control and PI Current Control
5.11 Further Reading
References
6 FCS Predictive Control in d − q Reference Frame
6.1 States of IGBT Inverter and the Operational Constraints
6.2 FCS Predictive Control of PMSM
6.3 MATLAB Tutorial on Real-time Implementation of FCS-MPC
6.3.1 Simulation Results
6.3.2 Experimental Results of FCS Control
6.4 Analysis of FCS-MPC System
6.4.1 Optimal Control System
6.4.2 Feedback Controller Gain
6.4.3 Constrained Optimal Control
6.5 Overview of FCS-MPC with Integral Action
6.6 Derivation of I-FCS Predictive Control Algorithm
6.6.1 Optimal Control without Constraints
6.6.2 I-FCS Predictive Controller with Constraints
6.6.3 Implementation of I-FCS-MPC Algorithm
6.7 MATLAB Tutorial on Implementation of I-FCS Predictive Controller
6.7.1 Simulation Results
6.8 I-FCS Predictive Control of Induction Motor
6.8.1 The Control Algorithm for an Induction Motor
6.8.2 Simulation Results
6.8.3 Experimental Results
6.9 I-FCS Predictive Control of Power Converter
6.9.1 I-FCS Predictive Control of a Power Converter
6.9.2 Simulation Results
6.9.3 Experimental Results
6.10 Evaluation of Robustness of I-FCS-MPC via Monte-Carlo Simulations
6.10.1 Discussion on Mean Square Errors
6.11 Velocity and Position Control of PMSM Using I-FCS-MPC
6.11.1 Choice of Sampling Rate for the Outer-loop Control System
6.11.2 Velocity and Position Controller Design
6.12 Velocity and Position Control of Induction Motor Using I-FCS-MPC
6.12.1 I-FCS Cascade Velocity Control of Induction Motor
6.12.2 I-FCS-MPC Cascade Position Control of Induction Motor
6.12.3 Experimental Evaluation of Velocity Control
6.13 Summary
6.13.1 Selection of sampling interval Δt
6.13.2 Selection of the Integral Gain
6.14 Further Reading
References
7 FCS Predictive Control in 𝜶 − 𝜷 Reference Frame
7.1 FCS Predictive Current Control of PMSM
7.1.1 Predictive Control Using One-step-ahead Prediction
7.1.2 FCS Current Control in 𝛼 − 𝛽 Reference Frame
7.1.3 Generating Current Reference Signals in 𝛼 − 𝛽 Frame
7.2 Resonant FCS Predictive Current Control
7.2.1 Control System Configuration
7.2.2 Outer-loop Controller Design
7.2.3 Resonant FCS Predictive Control System
7.3 Resonant FCS Current Control of Induction Motor
7.3.1 The Original FCS Current Control of Induction Motor
7.3.2 Resonant FCS Predictive Current Control of Induction Motor
7.3.3 Experimental Evaluations of Resonant FCS Predictive Control
7.4 Resonant FCS Predictive Power Converter Control
7.4.1 FCS Predictive Current Control of Power Converter
7.4.2 Experimental Results of Resonant FCS Predictive Control
7.5 Summary
7.6 Further Reading
References
8 Discrete-time Model Predictive Control (DMPC) of Electrical Drives
and Power Converter
8.1 Linear Discrete-time Model for PMSM
8.1.1 Linear Model for PMSM
8.1.2 Discretization of the Continuous-time Model
8.2 Discrete-time MPC Design with Constraints
8.2.1 Augmented Model
8.2.2 Design without Constraints
8.2.3 Formulation of the Constraints
8.2.4 On-line Solution for Constrained MPC
8.3 Experimental Evaluation of DMPC of PMSM
8.3.1 The MPC Parameters
8.3.2 Constraints
8.3.3 Response to Load Disturbances
8.3.4 Response to a Staircase Reference
8.3.5 Tuning of the MPC controller
8.4 Power Converter Control Using DMPC with Experimental Validation
8.5 Summary
8.6 Further Reading
References
9 Continuous-time Model Predictive Control (CMPC) of Electrical Drives and Power Converter
9.1 Continuous-time MPC Design
9.1.1 Augmented Model
9.1.2 Description of the Control Trajectories Using Laguerre Functions
9.1.3 Continuous-time Predictive Control without Constraints
9.1.4 Tuning of CMPC Control System Using Exponential Data Weighting and
Prescribed Degree of Stability
9.2 CMPC with Nonlinear Constraints
9.2.1 Approximation of Nonlinear Constraint Using Four Linear Constraints
9.2.2 Approximation of Nonlinear Constraint Using Sixteen Linear Constraints
9.2.3 State Feedback Observer
9.3 Simulation and Experimental Evaluation of CMPC of Induction Motor
9.3.1 Simulation Results
9.3.2 Experimental Results
9.4 Continuous-time Model Predictive Control of Power Converter
9.4.1 Use of Prescribed Degree of Stability in the Design
9.4.2 Experimental Results for Rectification Mode
9.4.3 Experimental Results for Regeneration Mode
9.4.4 Experimental Results for Disturbance Rejection
9.5 Gain Scheduled Predictive Controller
9.5.1 The Weighting Parameters
9.5.2 Gain Scheduled Predictive Control Law
9.6 Experimental Results of Gain Scheduled Predictive Control of Induction Motor
9.6.1 The First Set of Experimental Results
9.6.2 The Second Set of Experimental Results
9.6.3 The Third Set of Experimental Results
9.7 Summary
9.8 Further Reading
References
10 MATLAB®/Simulink® Tutorials on Physical Modeling and Test-bed Setup
10.1 Building Embedded Functions for Park-Clarke Transformation
10.1.1 Park-Clarke Transformation for Current Measurements
10.1.2 Inverse Park-Clarke Transformation for Voltage Actuation
10.2 Building Simulation Model for PMSM
10.3 Building Simulation Model for Induction Motor
10.4 Building Simulation Model for Power Converter
10.4.1 Embedded MATLAB Function for Phase Locked Loop (PLL)
10.4.2 Physical Simulation Model for Grid Connected Voltage Source Converter
10.5 PMSM Experimental Setup
10.6 Induction Motor Experimental Setup
10.6.1 Controller
10.6.2 Power Supply
10.6.3 Inverter
10.6.4 Mechanical Load
10.6.5 Induction Motor and Sensors
10.7 Grid Connected Power Converter Experimental Setup
10.7.1 Controller
10.7.2 Inverter
10.7.3 Sensors
10.8 Summary
10.9 Further Reading
References
Index
PID and Predictive Control of Electrical Drives and Power Converters using MATLAB/Simulink
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