MODELING AND HIGH-PERFORMANCE CONTROL OF ELECTRIC MACHINES

Transcription

1 MODELING AND HIGH-PERFORMANCE CONTROL OF ELECTRIC MACHINES JOHN CHIASSON IEEE PRESS ü t SERIES ON POWER ENGINEERING IEEE Press Series on Power Engineering Mohamed E. El-Hawary, Series Editor The Institute of Electrical and Electronics Engineers, Inc., New York WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION

2 I DC Machines, Controls, and Magnetics 1 1 The Physics of the DC Motor Magnetic Force Single-Loop Motor Torque Production Commutation of the Single-Loop Motor Faraday's Law The Surface Element Vector ds Interpreting the Sign of Back Emf in a Linear DC Machine Back Emf in the Single-Loop Motor Self-Induced Emf in the Single-Loop Motor Dynamic Equations of the DC Motor Microscopic Viewpoint Microscopic Viewpoint of the Single-Loop DC Motor T/fift Speed Tachometer for a DC Machine* Tachometer for the Linear DC Machine Tachometer for the Single-Loop DC Motor The Multiloop DC Motor* Increased Torque Production Commutation of the Armature Current Armature Reaction Field Flux Linkage and the Air Gap Magnetic Field Armature Flux Due to the External Magnetic Field Equations of the PM DC Motor Equations of the Separately Excited DC Motor Appendices 47 Rotational Dynamics 47 Gears 52 Problems 57 2 Feedback Control Model of a DC Motor Servo System 71 Sections marked with an asterisk (*) may be skipped without loss of continuity.

3 viii Contents 2.2 Speed Estimation Backward Difference Estimation of Speed Estimation of Speed Using an Observer Trajectory Generation Design of a State Feedback Tracking Controller Nested Loop Control Structure* Identification of the DC Motor Parameters* Least-Squares Approximation Error Index Parametric Error Indices Filtering of Noisy Signals* Filter Representations Causality Frequency Response Low-Pass Filters with Linear Phase Distortion Low-Pass Filtering of High-Frequency Noise Butterworth Filters Implementation of the Filter Discretization of Differential Equations Digital Filtering State-Space Representation Noncausal Filtering 126 Appendix - Classical Feedback Control 129 Tracking and Disturbance Rejection 129 General Theory of Tracking and Disturbance Rejection Internal Model Principle 149 Problems Magnetic Fields and Materials Introduction The Magnetic Field B and Gauss's Law Conservation of Flux Modeling Magnetic Materials Magnetic Dipole Moments The Magnetization M and Ampere's Law Relating B to M ^ The Magnetic Intensity Field Vector H The B-H Curve _ Computing B and H in Magnetic Circuits B is Normal to the Surface of Soft Magnetic Material Permanent Magnets* Hysteresis Loss Common Magnetic Materials 225 Problems 226

4 ix AC Machine Theory 235 Rotating Magnetic Fields Distributed Windings Approximate Sinusoidally Distributed B Field Conservation of Flux and 1/V Dependence Magnetic Field Distribution Due to the Stator Currents Sinusoidally Wound Phases Sinusoidally Wound Rotor Phase Sinusoidally Wound Stator Phases Sinusoidally Distributed Magnetic Fields Sinusoidally Distributed Rotating Magnetic Field Magnetomotive Force (mmf) Flux Linkage Azimuthai Magnetic Field in the Air Gap* Electric Field E 5a... ^.. ^ The Magnetic and Electric Fields B Sa, E Sa, B sfe, E Sb 276 Problems 277 The Physics of AC Machines Rotating Magnetic Field The Physics of the Induction Machine Induced Emfs in the Rotor Loops Magnetic Forces and Torques on the Rotor Slip Speed The Piiysics of the Synchronous Machine Two-Phase Synchronous Motor with a Sinusoidally Wound Rotor Emfs and Energy Conversion Synchronous Motor with a Salient Rotor Armature and Field Windings Microscopic Viewpoint of AC Machines* Rotating Axial Electric Field Due to the Stator Currents Induction Machine in the Stationary Coordinate System Faraday's Law and the Integral of the Force per Unit Charge Induction Machine in the Synchronous Coordinate System Synchronous Machine Steady-State Analysis of a Squirrel Cage Induction Motor* Rotor Fluxes, Emfs, and Currents Rotor Torque Rotor Magnetic Field 342

5 5.5.4 Comparison with a Sinusoidally Wound Rotor Problems 346 Mathematical Models of AC Machines The Magnetic Field B R (i Ra, i Rb, r, 6-0 R ) Leakage Flux Linkages in AC Machines Flux Linkages in the Stator Phases Flux Linkages in the Rotor Phases Torque Production in AC Machines Mathematical Model of a Sinusoidally Wound Induction Machine Total Leakage Factor The Squirrel Cage Rotor Induction Machine With Multiple Pole Pairs Mathematical Model of a Wound Rotor Synchronous Machine T> Mathematical Model of a PM Synchronous Machine The Stator and Rotor Magnetic Fields of an Induction Machine Rotate Synchronously* Torque, Energy, and Co-energy* Magnetic Field Energy Computing Torque From the Field Energy Computing Torque From the Co-energy 397 Problems 401 Symmetrie Balanced Three-Phase AC Machines Mathematical Model of a Three-Phase Induction Motor Steady-State Analysis of the Induction Motor Steady-State Currents and Voltages Steady-State Equivalent Circuit Model Rated Conditions Steady-State Torque Steady-State Power Transfer in the Induction Motor Mathematical Model of a Three-Phase PM Synchronous Motor Three-Phase, Sinusoidal, 60-Hz Voltages* Why Three-Phase? Why AC? Why Sinusoidal Voltages? Why 60 Hz? 474 Problems 475 Induction Motor Control Dynamic Equations of the Induction Motor 493

6 xi The Control Problem Field-Oriented and Input-Output Linearization Control of an Induction Motor Current-Command Field-Oriented Control Experimental Results Using a Field-Oriented Controller Field Weakening Input-Output Linearization Experimental Results Using an Input-Output Controller Observers Flux Observer Speed Observer Verghese Sanders Flux Observer* Optimal Field Weakening* Torque Optimization Under Current Constraints Torque Optimization Under Voltage Constraints Torque Optimization Under Voltage and Current Constraints Identification of the Induction Motor Parameters* Linear Overparameterized Model Nonlinear Least-Squares Identification Calculating the Parametric Error Indices Mechanical Parameters Simulation Results Experimental Results 560 Appendix 565 Elimination Theory and Resultants 565 Problems PM Synchronous Motor Control Field-Oriented Control Design of the Reference Trajectory and Inputs State Feedback Controller Speed Observer Experimental Results Current Command Control Optimal Field Weakening* Formulation of the Torque Maximization Problem Speed Ranges and Transition Speeds Two Examples Identification of the PM Synchronous Motor Parameters* Experimental Results PM Stepper Motors* Open-Loop Operation of the Stepper Motor 635

7 xii Contents Mathematical Model of a PM Stepper Motor High-Performance Control of a PM Stepper Motor. 641 Appendices 641 Two-Phase Equivalent Parameters 641 Current Plots 643 Problems Trapezoidal Back-Emf PM Synchronous Motors (BLDC) Construction Stator Magnetic Field B s.... u Stator Flux Linkage Produced by B^ Stator Flux Linkage Produced by B# Emf in the Stator Windings Produced by B# Torque Mathematical Model Operation and Control The Terminology "Brushless DC Motor" Microscopic Viewpoint of BLDC Machines* Axial Electric Field E fl Emf Induced in the Stator Phases 681 Problems 684 Trigonometrie Table and Identities 687 Trigonometrie Table 687 Trigonometrie Identities 688 References 691 Index 701