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Electrical Actuators: Applications and Performance

Book Description

This helpful resource covers a large range of information regarding electrical actuators. In particular, robustness, a very problematic issue, is fully explored in a dedicated chapter. The text also deals with he estimate of non-measurable mechanical variables by examining the estimate of load moment, then observation of the positioning of a command without mechanical sensor. Finally, it examines the conditions needed to measure variables and real implementation of numerical algorithms. This is a key working resource for electrical engineers.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Introduction
  5. Part I. Measures and Identifications
    1. Chapter 1: Identification of Induction Motor in Sinusoidal Mode
      1. 1.1. Introduction
      2. 1.2. The models
        1. 1.2.1. Dynamic model of the induction machine
        2. 1.2.2. Establishment of the four parameter models
          1. 1.2.2.1. Total rotor leakage model
          2. 1.2.2.2. Total stator leakage model
          3. 1.2.2.3. Equivalence of total leakage models
        3. 1.2.3. Magnetic circuit saturation
        4. 1.2.4. Iron losses
        5. 1.2.5. Sinusoidal mode
        6. 1.2.6. Summary of the different models
        7. 1.2.7. Measurements
        8. 1.2.8. Use of the nameplates
      3. 1.3. Traditional methods from a limited number of measurements
        1. 1.3.1. Measurement of stator resistance
        2. 1.3.2. Total rotor leakage model
          1. 1.3.2.1. Usual method
            1. 1.3.2.1.1. Simplified calculation
            2. 1.3.2.1.2. Precise calculation
          2. 1.3.2.2. Use of any two measurements
        3. 1.3.3. Total stator leakage models
        4. 1.3.4. Saturation characteristic
        5. 1.3.5. Experimental results
          1. 1.3.5.1. Total rotor leakage model
          2. 1.3.5.2. Total stator leakage model
          3. 1.3.5.3. Saturation
      4. 1.4. Estimation by minimization of a criteria based on admittance
        1. 1.4.1. Estimation of parameters by minimization of a criterion
        2. 1.4.2. Choice of criterion
        3. 1.4.3. Implementation
        4. 1.4.4. Analysis of estimation errors
          1. 1.4.4.1. Method for error evaluation
          2. 1.4.4.2. Experiment design
          3. 1.4.4.3. Effect of measurement errors
            1. 1.4.4.3.1. Offset and error of gain on sensors
            2. 1.4.4.3.2. Stochastic measurement noise
          4. 1.4.4.4. Effect of model error
            1. 1.4.4.4.1. Iron losses
            2. 1.4.4.4.2. Saturation
          5. 1.4.4.5. Discussion
        5. 1.4.5. Experimental results
        6. 1.4.6. Optimal experiment design
          1. 1.4.6.1. Principle
          2. 1.4.6.2. Minimization of the effect of measurement noises
          3. 1.4.6.3. Minimization of the combined effect of measurement noise and iron losses
        7. 1.4.7. Conclusion on the method
      5. 1.5. Linear estimation
        1. 1.5.1. Principle
        2. 1.5.2. Case of the five parameter model
        3. 1.5.3. Study of precision
          1. 1.5.3.1. Measurement errors
            1. 1.5.3.1.1. Offset
            2. 1.5.3.1.2. Gain error
            3. 1.5.3.1.3. Stochastic errors
          2. 1.5.3.2. Error on stator resistance
          3. 1.5.3.3. Discussion
        4. 1.5.4. Experimental results
          1. 1.5.4.1. Experimental setup
          2. 1.5.4.2. Non-linear method
          3. 1.5.4.3. Linear method
          4. 1.5.4.4. Comparison
        5. 1.5.5. Conclusion on the “linearizing” method
      6. 1.6. Conclusion
      7. 1.7. Appendix
        1. 1.7.1. Expression of sensitivities
        2. 1.7.2. Characteristics of the machines used
      8. 1.8. Bibliography
    2. Chapter 2: Modeling and Parameter Determination of the Saturated Synchronous Machine
      1. 2.1. Modeling of the synchronous machine: general theory
        1. 2.1.1. Description of the machine studied and general modeling hypotheses
        2. 2.1.2. Fundamental circuit laws for the study of electrical machines
        3. 2.1.3. Equations of the machine in abc variables
        4. 2.1.4. Concordia transformation: equations of the machine in 0αβ variables
        5. 2.1.5. Park transformation: equations of the machine in 0dq variables
        6. 2.1.6. Connection between the machine and a three-phase link
        7. 2.1.7. Reduction of rotor circuits to the stator
        8. 2.1.8. Relative units (per-unit)
      2. 2.2. Classical models and tests
        1. 2.2.1. The synchronous non-saturated machine
          1. 2.2.1.1. Classical linear model (Park model)
          2. 2.2.1.2. Equivalent diagrams
          3. 2.2.1.3. Operational reactances in non-saturated mode
          4. 2.2.1.4. Internal and external parameters in non-saturated mode
        2. 2.2.2. General classical tests
          1. 2.2.2.1. Test of the synchronous machine in low-load steady state
            1. 2.2.2.1.1. No-load test (taking down of the direct-axis magnetic characteristic)
            2. 2.2.2.1.2. Short-circuit test
            3. 2.2.2.1.3. Loss determination (ohmic, magnetic, mechanical)
            4. 2.2.2.1.4. Low slip test (determination of longitudinal and transversal synchronous reactances)
          2. 2.2.2.2. Synchronous machine tests in transient state
            1. 2.2.2.2.1. Transient three-phase short-circuit test
            2. 2.2.2.2.2. Load shedding test
          3. 2.2.2.3. Transient standstill test
            1. 2.2.2.3.1. Direct current decay test
            2. 2.2.2.3.2. Frequency response static tests
        3. 2.2.3. Potier Method
          1. 2.2.3.1. Insufficiency of the linear theory
          2. 2.2.3.2. Potier Model
          3. 2.2.3.3. Experimental determination of Potier model parameters
          4. 2.2.3.4. Necessity for a more general theory in the presence of saturation and magnetic saliences
      3. 2.3. Advanced models: the synchronous machine in saturated mode
        1. 2.3.1. Elements of the von der Embse theory of saturated electrical machines: inductive circuits in the presence of magnetic saturation
        2. 2.3.2. General study of magnetic coupling in the presence of saturation
          1. 2.3.2.1. Transformer effect coupling
          2. 2.3.2.2. Cross-saturation coupling
            1. 2.3.2.2.1. General study
            2. 2.3.2.2.2. The UCL model
            3. 2.3.2.2.3. Isotropic inductance
        3. 2.3.3. Implementation of the model
          1. 2.3.3.1. Leakage flux
          2. 2.3.3.2. Operational reactances in saturated mode
          3. 2.3.3.3. Large-amplitude transients
      4. 2.4. Bibliography
    3. Chapter 3: Real-Time Estimation of the Induction Machine Parameters
      1. 3.1. Introduction
      2. 3.2. Objectives of parameter estimation
        1. 3.2.1. On control
        2. 3.2.2. Diagnosis
      3. 3.3. Fundamental problems
        1. 3.3.1. Identifiability, parameterization, and validation of the model
          1. 3.3.1.1. Identifiability and parameterization of the model
          2. 3.3.1.2. Validation of the model
          3. 3.3.1.3. Identifiability and parameterization of the induction motor model
        2. 3.3.2. Choice of the sampling period and digital problems
          1. 3.3.2.1. General case
          2. 3.3.2.2. Discretization of the IM dynamic model
            1. 3.3.2.2.1. Fourth-order state model
            2. 3.3.2.2.2. Reverse second order model
        3. 3.3.3. Monitoring and information analysis
          1. 3.3.3.1. Monitoring problem
          2. 3.3.3.2. Information analysis and global identification
            1. 3.3.3.2.1. Distance of structure and distance of state
            2. 3.3.3.2.2. Connection between distance of structure and distance of state
            3. 3.3.3.2.3. Hessian conditioning and parametric uncertainty
      4. 3.4. Least square methods
        1. 3.4.1. Principle of least squares and instrumental variables
          1. 3.4.1.1. Least squares and recursive least squares
          2. 3.4.1.2. Instrumental variables
          3. 3.4.1.3. Monitoring and parametric uncertainty
        2. 3.4.2. Application to the induction motor
          1. 3.4.2.1. Linear model in relation to parameters
          2. 3.4.2.2. Implementation of least squares
          3. 3.4.2.3. Experimental results
      5. 3.5. Extended Kalman filter
        1. 3.5.1. Principle
        2. 3.5.2. Tuning of Q and R matrices
        3. 3.5.3. Application to the induction motor
          1. 3.5.3.1. Complete order direct model of the induction motor
          2. 3.5.3.2. Reduced order model of the induction motor
          3. 3.5.3.3. Covariance matrix adjustment
          4. 3.5.3.4. Filter initialization and restart
          5. 3.5.3.5. Results
            1. 3.5.3.5.1. Simulation results
            2. 3.5.3.5.2. Experimental results
      6. 3.6. Extended Luenberger observer
        1. 3.6.1. Principle
          1. 3.6.1.1. Discrete time observer
          2. 3.6.1.2. Extended observer
          3. 3.6.1.3. Tuning (pole placement)
        2. 3.6.2. Estimation of induction machine velocity
          1. 3.6.2.1. Machine model
          2. 3.6.2.2. Extended Luenberger observer
          3. 3.6.2.3. Extended Kalman filter
          4. 3.6.2.4. Comparison between Kalman filter and Luenberger observer
      7. 3.7. Conclusion
      8. 3.8. Appendix: machine characteristics
      9. 3.9. Bibliography
  6. Part II. Observer Examples
    1. Chapter 4: Linear Estimators and Observers for the Induction Machine (IM)
      1. 4.1. Introduction
      2. 4.2. Estimation models for the induction machine
        1. 4.2.1. Park model for the induction machine
          1. 4.2.1.1. A dynamic model for observation
          2. 4.2.1.2. Reference frame changes
          3. 4.2.1.3. The model in the general reference
        2. 4.2.2. Different state models for flux estimation
          1. 4.2.2.1. State representation of a sinusoidal machine
          2. 4.2.2.2. State vector made up of stator currents and fluxes
          3. 4.2.2.3. State vector made up of stator currents and rotor fluxes
          4. 4.2.2.4. State vector made up of stator fluxes and rotor fluxes
        3. 4.2.3. Different study reference frames for flux estimation
          1. 4.2.3.1. Different study reference frames
          2. 4.2.3.2. Reference frames based on prior knowledge of angles
          3. 4.2.3.3. Reference frames based on subsequent knowledge of angles
          4. 4.2.3.4. Assessment of the different reference frames appropriate for the estimation of fluxes
      3. 4.3. Flux estimation
        1. 4.3.1. Introduction
        2. 4.3.2. Stator flux estimator
        3. 4.3.3. Rotor flux estimator
      4. 4.4. Flux observation
        1. 4.4.1. Full order deterministic observer
          1. 4.4.1.1. Principle
          2. 4.4.1.2. State equation of the observer
          3. 4.4.1.3. Observability
          4. 4.4.1.4. Calculation of observer gain
          5. 4.4.1.5. Example of observer robustness
      5. 4.5. Linear stochastic observers—Kalman–Bucy filters
        1. 4.5.1. Introduction
        2. 4.5.2. Kalman–Bucy filter model
        3. 4.5.3. Convergence of the Kalman filter
        4. 4.5.4. Simulation results and experimental results
      6. 4.6. Separate estimation and observation structures of the rotation speed
        1. 4.6.1. Introduction
        2. 4.6.2. General principles
        3. 4.6.3. Speed estimation and observation methods
          1. 4.6.3.1. Speed calculation by the self-piloting relation
          2. 4.6.3.2. Association of a mechanical observer to an estimator by frequency addition
          3. 4.6.3.3. Adaptive mechanism (MRAS)
          4. 4.6.3.4. Adaptive mechanism associated with a mechanical observer
      7. 4.7. Adaptive observer
        1. 4.7.1. Introduction
        2. 4.7.2. Determination of observer gains
        3. 4.7.3. Speed adaptation law
          1. 4.7.3.1. Verification of the third condition of the hyperstability theory
        4. 4.7.4. Simulation results and experimental results
      8. 4.8. Variable structure mechanical observer (VSMO)
        1. 4.8.1. Basic principle
        2. 4.8.2. Construction of the VSMO
        3. 4.8.3. Determination of variable structure observer gains
        4. 4.8.4. Presentation of observer performances
          1. 4.8.4.1. The shattering phenomenon
          2. 4.8.4.2. Rated speed operation
        5. 4.8.5. Low-speed operation
        6. 4.8.6. Robustness in relation to parametric variations
          1. 4.8.6.1. Mechanical parameter variations
      9. 4.9. Conclusion
      10. 4.10. Bibliography
    2. Chapter 5: Decomposition of a Determinist Flux Observer for the Induction Machine: Cartesian and Reduced Order Structures
      1. 5.1. Introduction
      2. 5.2. Estimation models for the induction machine
        1. 5.2.1. Park model of the induction machine
          1. 5.2.1.1. A dynamic model for control
          2. 5.2.1.2. Reference changes
          3. 5.2.1.3. The model in reference (αS, βS)
        2. 5.2.2. State models for Cartesian and reduced observers
          1. 5.2.2.1. State representation of an induction machine
          2. 5.2.2.2. State vector made up of stator currents and fluxes
          3. 5.2.2.3. State vector made up of stator currents and rotor fluxes
          4. 5.2.2.4. State vector made up of stator fluxes and rotor fluxes
        3. 5.2.3. Determination of the flux in the reference used by the control
          1. 5.2.3.1. Different study references
          2. 5.2.3.2. Flux estimators
          3. 5.2.3.3. Flux observers
      3. 5.3. Cartesian observers
        1. 5.3.1. Principle and structure of Cartesian observers
          1. 5.3.1.1. Breakdown of a complete observer
          2. 5.3.1.2. Coupled sub-observers
          3. 5.3.1.3. Characteristics of Cartesian observers
        2. 5.3.2. Different Cartesian observers
          1. 5.3.2.1. Cartesian observer associated with the stator current and stator flux
          2. 5.3.2.2. Cartesian observer associated with the stator current and rotor flux
          3. 5.3.2.3. Cartesian observer associated with the stator flux and rotor flux
        3. 5.3.3. Synthesis of the Cartesian observer linked to stator and rotor fluxes
          1. 5.3.3.1. Observability
          2. 5.3.3.2. Calculation of observer gains
          3. 5.3.3.3. Equivalence with a complete order observer
        4. 5.3.4. Discretization of the Cartesian observer linked to stator and rotor fluxes
          1. 5.3.4.1. Discretization of a complete order observer
          2. 5.3.4.2. Cartesian observer discretization
        5. 5.3.5. Validation of the Cartesian observer for stator and rotor fluxes
          1. 5.3.5.1. Specifications
          2. 5.3.5.2. Robustness test
        6. 5.3.6. Assessment on Cartesian observers
      4. 5.4. Reduced order observers
        1. 5.4.1. Principle and structure of reduced order observers
          1. 5.4.1.1. Principle of the reduced order observer
          2. 5.4.1.2. Breakdown of the complete observer
          3. 5.4.1.3. Characteristics of reduced order observers
        2. 5.4.2. Different reduced order observers
          1. 5.4.2.1. Reduced order stator flux observer
          2. 5.4.2.2. Reduced order rotor flux observer
        3. 5.4.3. Synthesis of the reduced order rotor flux observer
          1. 5.4.3.1. Observability
          2. 5.4.3.2. Gain calculation
        4. 5.4.4. Discretization of the reduced order rotor flux observer
        5. 5.4.5. Validation of the reduced order rotor flux observer
          1. 5.4.5.1. Specifications
          2. 5.4.5.2. Robustness test
        6. 5.4.6. Assessment on reduced order observers
      5. 5.5. Conclusion on Cartesian and reduced order observers
      6. 5.6. Appendix: parameters of the study induction machine
      7. 5.7. Bibliography
    3. Chapter 6: Observer Gain Determination Based on Parameter Sensitivity Analysis
      1. 6.1. Introduction
      2. 6.2. Flux observers
        1. 6.2.1. Rotor flux estimator
        2. 6.2.2. Reduced order flux observer
        3. 6.2.3. Full order flux observer
        4. 6.2.4. Choice of observer gains
        5. 6.2.5. Choice of the reference frame
      3. 6.3. Analysis method of the parametric sensitivity
        1. 6.3.1. Flux amplitude and phase error estimation
        2. 6.3.2. Influence of the magnetic saturation
        3. 6.3.3. Calculation algorithm of errors in the estimated flux
        4. 6.3.4. Variations of the stator current used
      4. 6.4. Choice of observer gains
        1. 6.4.1. Pole placement and parametric sensitivity
        2. 6.4.2. Optimal observer
      5. 6.5. Reduced order flux observer
        1. 6.5.1. Control strategy
        2. 6.5.2. Error in flux orientation and amplitude
        3. 6.5.3. Theoretical results
        4. 6.5.4. Experimental results
      6. 6.6. Full order flux observer
        1. 6.6.1. Control strategy
        2. 6.6.2. Error in flux orientation and amplitude
        3. 6.6.3. Theoretical results
        4. 6.6.4. Experimental results
      7. 6.7. Conclusion
      8. 6.8. Appendix: parameters of the squirrel-cage induction machine
      9. 6.9. Bibliography
    4. Chapter 7: Observation of the Load Torque of an Electrical Machine
      1. 7.1. Introduction
      2. 7.2. Characterization of a load torque relative to an axis of rotation
        1. 7.2.1. Introduction
        2. 7.2.2. Disruptions of the electrical machine torque
          1. 7.2.2.1. Generation of the electromagnetic torque
          2. 7.2.2.2. The cogging torque
          3. 7.2.2.3. Other disruptive torques non-linked to contact
        3. 7.2.3. Load torque disruptions by modification of contact actions
          1. 7.2.3.1. Low-speed friction
          2. 7.2.3.2. Non-linear friction simulation
      3. 7.3. Modal control of the actuator with load torque observation
        1. 7.3.1. Introduction
        2. 7.3.2. State representation of the actuator
        3. 7.3.3. Analysis of controllability and observability
        4. 7.3.4. Control law by state feedback
          1. 7.3.4.1. Control structure
          2. 7.3.4.2. Sizing of the control law
          3. 7.3.4.3. Limitation of the integral action
      4. 7.4. Observation of load torque
        1. 7.4.1. Introduction
        2. 7.4.2. Observer with integration in the loop
          1. 7.4.2.1. Principle
          2. 7.4.2.2. Open-loop operation
          3. 7.4.2.3. Closed-loop operation
          4. 7.4.2.4. Analytical characterization
        3. 7.4.3. Complete order observer
          1. 7.4.3.1. Considerations on observability
          2. 7.4.3.2. Construction
          3. 7.4.3.3. Analytical study
        4. 7.4.4. Reduced order two observer based on the measure of position
          1. 7.4.4.1. Construction
          2. 7.4.4.2. Analytical study
          3. 7.4.4.3. Experimental tests
        5. 7.4.5. Reduced order one observer based on speed measure
          1. 7.4.5.1. Construction
          2. 7.4.5.2. Analytical study
          3. 7.4.5.3. Experimental results of the reduced order one observer
        6. 7.4.6. Comparative study of different types of observers
      5. 7.5. Robustness of control law by state feedback with observation of the resistant torque
        1. 7.5.1. Introduction
        2. 7.5.2. Context of the study
        3. 7.5.3. Robustness of actuator position
          1. 7.5.3.1. Variations of inertia
          2. 7.5.3.2. Friction factor variations
        4. 7.5.4. Robustness of actuator rotation speed
          1. 7.5.4.1. Variations of inertia
          2. 7.5.4.2. Friction factor variations
          3. 7.5.4.3. Torque constant variations
        5. 7.5.5. Conclusions
      6. 7.6. Experimental results
        1. 7.6.1. Introduction
        2. 7.6.2. Results of modal control with pump torque observer
          1. 7.6.2.1. Mass lifting
          2. 7.6.2.2. Variation of the friction factor
          3. 7.6.2.3. Influence of the inertia variation
        3. 7.6.3. Non-linear friction influence
          1. 7.6.3.1. Static friction
          2. 7.6.3.2. Influence of static friction on control law with resistant torque compensation
      7. 7.7. Conclusion
      8. 7.8. Bibliography
    5. Chapter 8: Observation of the Rotor Position to Control the Synchronous Machine without Mechanical Sensor
      1. 8.1. State of the art
      2. 8.2. Reconstruction of the low-resolution position
        1. 8.2.1. Equivalent electromotive force measure
        2. 8.2.2. Reconstruction of the sum of electromotive forces using the machine neutral
        3. 8.2.3. Use of the extended Park reference
        4. 8.2.4. Use of a two-phase reference
      3. 8.3. Exact reconstruction by redundant observer
        1. 8.3.1. Principle and implementation of analytical redundancy
        2. 8.3.2. Adjustment of correction gains
          1. 8.3.2.1. First expression of εemfd , εemfq
          2. 8.3.2.2. Second expression of εemfd, εemfq
          3. 8.3.2.3. Adjustment of the analytical redundancy observer with filters
          4. 8.3.2.4. Adjustment of gains and filter in relation to the reference current
        3. 8.3.3. Sensitivity and robustness
        4. 8.3.4. Experimental results
      4. 8.4. Exact reconstruction by Kalman filter
        1. 8.4.1. Overview
        2. 8.4.2. Using the Kalman filter for the synchronous machine without mechanical sensor
        3. 8.4.3. Application for the synchronous machine
        4. 8.4.4. Gain adjustment
          1. 8.4.4.1. First tests
          2. 8.4.4.3. Initial matrix of P0 errors of estimation
          3. 8.4.4.4. Matrix of state noise Q
        5. 8.4.5. Assessment on the adjustment of Kalman filter factors
      5. 8.5. Comparison of reconstructions by Kalman filter or analytical redundancy observer
        1. 8.5.1. Influence of rating
        2. 8.5.2. Influence of the initial rotor position
        3. 8.5.3. Sensitivity to electric parameters
        4. 8.5.4. Influence and management of load torque
      6. 8.6. Bibliography
  7. List of Authors
  8. Index