You are previewing Control of Synchronous Motors.
O'Reilly logo
Control of Synchronous Motors

Book Description

Synchronous motors are indubitably the most effective device to drive industrial production systems and robots with precision and rapidity. Their control law is thus critical for combining at the same time high productivity to reduced energy consummation. As far as possible, the control algorithms must exploit the properties of these actuators. Therefore, this work draws on well adapted models resulting from the Park's transformation, for both the most traditional machines with sinusoidal field distribution and for machines with non-sinusoidal field distribution which are more and more used in industry. Both, conventional control strategies like vector control (either in the synchronous reference frame or in the rotor frame) and advanced control theories like direct control and predictive control are thoroughly presented. In this context, a significant place is reserved to sensorless control which is an important and critical issue in tomorrow's motors.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Introduction
  5. Chapter 1: Synchronous motor controls, Problems and Modeling
    1. 1.1. Introduction
    2. 1.2. Problems on the synchronous motor control
      1. 1.2.1. The synchronous motor control, a vector control
      2. 1.2.2. Direct/inverse model and modeling hypotheses
      3. 1.2.3. Control properties
    3. 1.3. Descriptions and physical modeling of the synchronous motor
      1. 1.3.1. Description of the motor in preparation for its modeling
      2. 1.3.2. Hypotheses on the motor
      3. 1.3.3. Notations
      4. 1.3.4. Main transformation matrices
      5. 1.3.5. Physical model of the synchronous motor
      6. 1.3.6. The two levels voltage inverter
      7. 1.3.7. Model of the mechanical load
    4. 1.4. Modeling in dynamic regime of the synchronous motor in the natural three-phase a-b-c reference frame
      1. 1.4.1. Model of the machines with non-salient poles and constant excitation
        1. 1.4.1.1. General properties
        2. 1.4.1.2. Case of a synchronous machine with sinusoidal field distribution
      2. 1.4.2. Exploitation of the model in the a-b-c reference frame in sinusoidal steady state, electromagnetic torque
        1. 1.4.2.1. Expression of the electromagnetic torque
        2. 1.4.2.2. Electromagnetic torque optimization: self-control
      3. 1.4.3. Extensions to the case of non-sinusoidal field distribution machines
        1. 1.4.3.1. Case of trapezoidal field distribution machines
        2. 1.4.3.2. Case of non-sinusoidal field distribution machines
    5. 1.5. Vector transformations and dynamic models in the a-ß and d-q reference frames (sinusoidal field distribution machines with non-salient and salient poles)
      1. 1.5.1. Factorized matrix modeling
      2. 1.5.2. Concordia transformation: a-ß reference frame
      3. 1.5.3. Park transformation, application to the synchronous salient pole motor
      4. 1.5.4. Note on the torque coefficients
    6. 1.6. Can we extend the Park transformation to synchronous motors with non-sinusoidal field distributions?
    7. 1.7. Conclusion
    8. 1.8. Appendices
      1. 1.8.1. Numerical values of the parameters
      2. 1.8.2. Nomenclature and notations
        1. 1.8.2.1. General notations
        2. 1.8.2.2. Single-phase variables in the natural reference frame (usually: first phase) and parameters
          1. 1.8.2.2.1. Stator variables
          2. 1.8.2.2.2. Stator parameters, inductances and resistances
          3. 1.8.2.2.3. Parameters and variables associated with excitation
        3. 1.8.2.3. Variables, vectors and matrices, after the Concordia and Park transformations
      3. 1.8.3. Acknowledgments
    9. 1.9. Bibliography
  6. Chapter 2: Optimal Supply and Synchronous Motors Torque Control: Designs in the a-b-c Reference Frame
    1. 2.1. Introduction: problems of the controls in a-b-c
    2. 2.2. Model in the a-b-c reference frame: extension of the steady state approach in transient regime
      1. 2.2.1. Case of sinusoidal field distribution machines
      2. 2.2.2. Case of trapezoidal field distribution machines (brushless DC motor)
      3. 2.2.3. Note on the electromagnetic torque for non-sinusoidal machines
    3. 2.3. Structures of torque controls designed in the a-b-c reference frame
      1. 2.3.1. Case of the sinusoidal distribution machine
      2. 2.3.2. Extension to brushless DC motors (case of trapezoidal field distribution machines)
      3. 2.4. Performances and criticisms of the control approach in the a-b-c reference frame
      4. 2.4.1. Case of a proportional control
      5. 2.4.2. Case of an integral and proportional (IP) current regulation
        1. 2.4.2.1. General information
        2. 2.4.2.2. First case: with a small gain
        3. 2.4.2.3. Second case: with a high gain
      6. 2.4.3. Interpretation in Park components of the IP controller designed in a-b-c
      7. 2.4.4. Advanced controllers: example of the resonant controller
    4. 2.5. Generalization: extension of the supplies to the case of non-sinusoidal distribution machines
      1. 2.5.1. Generalization of the modeling
      2. 2.5.2. A first (heuristic) approach of the solution
      3. 2.5.3. First generalization: optimization of the Joule losses (without constraint on the zero-sequence component current)
      4. 2.5.4. Application of this approach: optimization in the case where electromotive forces are sinusoidal
      5. 2.5.5. Second generalization: optimization of the Joule losses with constraint (the zero-sequence component current must be equal to zero)
      6. 2.5.6. Geometrical interpretation of the two optimal currents
    5. 2.6. Use of Fourier expansion to obtain optimal currents
      1. 2.6.1. Interest of the Fourier expansion (FS)
      2. 2.6.2. Modeling by Fourier series (with complex coefficients)
      3. 2.6.3. Properties of the results by the Fourier expansion
      4. 2.6.5. Second important case: the back-EMF only contain even order harmonics
      5. 2.6.6. General case, even and uneven order harmonics
      6. 2.6.7. Rules: to impose the torque, it is necessary to impose its different harmonics
      7. 2.6.8. General approach for the optimization (heuristic demonstration in one example)
        1. 2.6.8.1. First possibility: if we chooseM = 3
          1. 2.6.8.1.1. First case: all terms of (E) are real
          2. 2.6.8.1.2. Second case: (E) has all its imaginary terms
          3. 2.6.8.1.3. General case: the terms of (E) are not all real, nor all imaginary
        2. 2.6.8.2. Second possibility: let us look for a solution with less harmonics, for example with M = 2
      8. 2.6.9. General formulation of the optimization method
        1. 2.6.9.1. Objective
        2. 2.6.9.2. Discussion
        3. 2.6.9.3. Notations
        4. 2.6.9.4. Construction of the components of (K6q)t
        5. 2.6.9.5. Resolution
          1. 2.6.9.5.1. First case: all the terms of (E) are real.
          2. 2.6.9.5.2. Second case: all the terms of (E) are imaginary terms.
          3. 2.6.9.5.3. Application of a classical example [LEH 86]
          4. 2.6.9.5.4. General case: the terms of(E) are not all real, nor all imaginary terms
        6. 2.6.9.6. Comments: how to optimize the harmonics?
      9. 2.6.10. An important example: the sinusoidal field distribution machine
      10. 2.6.11. Application: obtaining a constant torque
        1. 2.6.11.1. Discussion
        2. 2.6.11.2. Example
      11. 2.6.12. Some results
    6. 2.7. Conclusion
    7. 2.8. Appendices
      1. 2.8.1. Digital parameters values
      2. 2.8.2. Nomenclature and notations
        1. 2.8.2.1. Regulations
        2. 2.8.2.2. Current optimization with non-sinusoidal back-EMF
        3. 2.8.2.3. Current optimization with non-sinusoidal back-EMF by FS
    8. 2.9. Bibliography
  7. Chapter 3: Optimal Supplies and Synchronous Motors Torque Controls. Design in the d-q Reference Frame
    1. 3.1. Introduction: on the controls designed in the Park d-q reference frame
    2. 3.2. Dynamic model (case of the salient pole machine and constant excitation)
    3. 3.3. First approach to determine of optimal current references (d-q reference frame)
    4. 3.4. Determination of the current controls designed in the d-q reference frame
      1. 3.4.1. Principle of control by model inversion: example of the proportional controller with compensations
      2. 3.4.2. Self-control
      3. 3.4.3. Some properties of efficient current regulation
      4. 3.4.4. Robustness problems of a proportional controller of the currents
    5. 3.5. New control by model inversion: example of an IP controller with compensations
      1. 3.5.1. Principle
      2. 3.5.2. Performances of the IP regulations for current loops
      3. 3.5.3. Robustness of the IP controllers for the current loops
        1. 3.5.3.1. First example: effect of an error on the estimate of the excitation flux
        2. 3.5.3.2. Second example: controller with compensation terms
      4. 3.5.4. Conclusion on the controls performances in the d-qreference frame
    6. 3.6. Optimal supply of the salient poles synchronous motors; geometrical approach of the isotorque curves
      1. 3.6.1. General information: a general approach with the torque surfaces
      2. 3.6.2. Preliminaries 1: case of synchronous machines, with magnets, with non-salient poles and with spatial distribution of the sinusoidal field
      3. 3.6.3. Preliminaries 2: case of synchronous machines with magnets, with non-salient poles and with spatial distribution of a non-sinusoidal field – first extension of the Park transformation
      4. 3.6.4. Remark: Analogy with the p-q theory
      5. 3.6.5. 3D visualization, case of non-salient pole machines
      6. 3.6.6. Generalization to the salient pole machines: case of synchronous magnet machines with sinusoidal field distribution
      7. 3.6.7. Visualization: case of an excited synchronous machine with salient poles
      8. 3.6.8. Case of a reluctance synchronous machine
        1. 3.6.8.1. Case of machines with mutual inductances
        2. 3.6.8.2. Case of three-phase machines with mutual inductances equal to zero
      9. 3.6.9. Case of synchronous machines with variable reluctance and non-sinusoidal spatial field distribution: second extension of the Park transformation
      10. 3.6.10. Visualization: torque surface of a reluctance synchronous machine
    7. 3.7. Conclusion
    8. 3.8. Appendices
      1. 3.8.1. Numerical parameters values
      2. 3.8.2. Nomenclature and notations
        1. 3.8.2.1. Indexes
        2. 3.8.2.2. Variables and parameters of the controls in the Park d-q reference frame
        3. 3.8.2.3. Specific functions for optimizations
    9. 3.9. Bibliography
  8. Chapter 4: Drive Controls with Synchronous Motors
    1. 4.1. Introduction
    2. 4.2. Principles adopted for speed controls: case of IP controllers
    3. 4.3. Speed controls designed in the a-b-c reference frame (application to a non-salient pole machine)
      1. 4.3.1. General information
      2. 4.3.2. IP speed controller with an IP current controller in the a-b-c reference frame
      3. 4.3.3. IP speed controller with a resonant current controller
    4. 4.4. Determination of the speed controls designed in the d-q reference frame (application to a salient pole machine)
      1. 4.4.1. General information
      2. 4.4.2. Introductory example: speed control with compensation or decoupling
      3. 4.4.3. Discussion on the speed controls
      4. 4.4.4. Examples of regulation choices. The interest of an IP controller: its limits
      5. 4.4.5. Examples of the regulation choices: IP controller with an anti-windup device
      6. 4.4.6. Examples of regulation choices: IP controller with limited dynamics
      7. 4.4.7. Example of an advanced regulation: P controller associated with an integral observer
        1. 4.4.7.1. General information, hypotheses, modeling
        2. 4.4.7.2. Design of the controller alone
        3. 4.4.7.3. Design of the observer
        4. 4.4.7.4. Global transfer function
        5. 4.4.7.5. Examples of transients and performances
    5. 4.5. Note on position regulations
    6. 4.6. Conclusion
    7. 4.7. Appendices
      1. 4.7.1. Numerical values of the parameters
      2. 4.7.2. Nomenclature and notations
        1. 4.7.2.1. Regulations in the a-b-c reference frame
        2. 4.7.2.2. Regulations in the d-q reference frame
    8. 4.8. Bibliography
  9. Chapter 5: Digital Implementation of Vector Control of Synchronous Motors
    1. 5.1. Introduction
    2. 5.2. Classical, analog and ideal torque control of a synchronous motor
      1. 5.2.1. Calculation of the current regulators
      2. 5.2.2. Determination of the current references
      3. 5.2.3. Parameters of the studied synchronous motor
      4. 5.2.4. Simulation results of the ideal analog vector control of synchronous motors
    3. 5.3. Digital implementation problem of the synchronous motor vector control
      1. 5.3.1. The interfaces, sources of restrictions
      2. 5.3.2. Time diagram
      3. 5.3.3. Digital implementation constraints of the vector control of synchronous motor
    4. 5.4. Discretization of the control system
      1. 5.4.1. Choice of the sampling period
      2. 5.4.2. Choice of the sampling instant
      3. 5.4.3. Implementation of the digital control
      4. 5.4.4. Simulation of the control with discrete regulators
    5. 5.5. Study of the delays introduced by the digital implementation of the vector control of the synchronous motor
      1. 5.5.1. Simulation results after introduction of the delays in the system
      2. 5.5.2. Calculation of the new regulators after taking into account the delays
      3. 5.5.3. Simulation after delays correction and system discretizatio
    6. 5.6. Quantization problems
      1. 5.6.1. Quantization affecting the current measures
      2. 5.6.2. Quantization at the level of the position measure
      3. 5.6.3. Calculation of the speed by digital differentiation
      4. 5.6.4. Quantization in the vector PWM of the voltage inverter
    7. 5.7. Delays in the reverse Park transformation
    8. 5.8. Conclusion
    9. 5.9. Bibliography
  10. Chapter 6: Direct Control of a Permanent Magnet Synchronous Machine
    1. 6.1. Introduction
    2. 6.2. Model of the permanent magnet synchronous machine in the d-q reference frame
      1. 6.2.1. State modeling
    3. 6.3. Conventional DTC with free switching frequency
      1. 6.3.1. General principle
      2. 6.3.2. Experimental application of DTC
        1. 6.3.2.1. The motor parameters
    4. 6.4. DTC at a fixed switching frequency
      1. 6.4.1. Principle of the control
      2. 6.4.2. Development of the reference vector Ψ#
        1. 6.4.2.1. Flux estimation
      3. 6.4.3. Experimental results of DTC on a period of fixed calculation
    5. 6.5. Predictive direct control
      1. 6.5.1. Introduction
      2. 6.5.2. General principle of predictive direct control
      3. 6.5.3. Application to the permanent magnet synchronous motor
        1. 6.5.3.1. Determination of the reference state vector
      4. 6.5.4. Experimental results
      5. 6.5.5. Predictive direct control by model inversion
        1. 6.5.5.1. Profile with an idle leg
        2. 6.5.5.2. Centered pulses
    6. 6.6. Conclusion
    7. 6.7. Bibliography
  11. Chapter 7: Synchronous Machine and Inverter Fault Tolerant Predictive Controls
    1. 7.1. Introduction
    2. 7.2. Topologies of three-phase fault tolerant machines
      1. 7.2.1. Restriction of the short-circuit current of permanent magnet machines
      2. 7.2.2. Restriction of the fault to the phase at fault alone
    3. 7.3. Topologies of fault tolerant converters
    4. 7.4. Fault tolerant controls
      1. 7.4.1. Modeling synchronous machines in preparation for fault tolerant control
      2. 7.4.2. Simulation of synchronous machines with fault tolerant control
      3. 7.4.3. Predictive control
      4. 7.4.4. Application
    5. 7.5. Conclusion
    6. 7.6. Bibliography
  12. Chapter 8: Characterization of Control without a Mechanical Sensor in Permanent Magnet Synchronous Machines
    1. 8.1. Introduction
      1. 8.1.1. State observation and disturbance observer
      2. 8.1.2. Interaction of the dynamics of control and observation
        1. 8.1.2.1. Linear case
        2. 8.1.2.2. Non-linear case
      3. 8.1.3. Poles placement for control and observation
    2. 8.2. Sensorless control of PMSM, thanks to an extended Kalman filter
      1. 8.2.1. A brief reminder on the Kalman filter (KF)
      2. 8.2.2. Application to the PMSM case
      3. 8.2.3. Simulation results
    3. 8.3. Comparison with the MRAS (model reference adaptive system) method
    4. 8.4. Experimental results comparison
    5. 8.5. Control without sensor of the PMSM with load torque observation
      1. 8.5.1. Control by state feedback on the currents
    6. 8.6. Starting the PMSM without a mechanical sensor
      1. 8.6.1. Equilibriums of the system without a mechanical sensor
      2. 8.6.2. Analysis by simulation
      3. 8.6.3. Modification of the control law for a global convergence
    7. 8.7. Conclusion
    8. 8.8. Bibliography
  13. Chapter 9: Sensorless Control of Permanent Magnet Synchronous Machines: Deterministic Methods, Convergence and Robustness
    1. 9.1. Introduction
    2. 9.2. Modeling PMSMs for mechanical sensorless control
      1. 9.2.1. State model
      2. 9.2.2. Reduced-order model
    3. 9.3. Convergence analysis of mechanical sensorless control laws
      1. 9.3.1. Proportional-type control law
      2. 9.3.2. Variable structure control law
    4. 9.4. Estimation of the back-EMF vector
    5. 9.5. Robustness of sensorless control of PMSM with respect to parameter uncertainties
      1. 9.5.1. Uncertainty on the stator inductances
      2. 9.5.2. Uncertainty on the torque coefficient
      3. 9.5.3. Uncertainty on the stator resistance
    6. 9.6. Sensorless control of PMSMs in the presence of uncertainties on the resistance
      1. 9.6.1. Online estimation of the resistance
      2. 9.6.2. Minimization of the sensitivity of the sensorless control with respect to the resistance
    7. 9.7. Conclusion
    8. 9.8. Appendix 1
    9. 9.9. Appendix 2
    10. 9.10. Bibliography
  14. List of Authors
  15. Index