Control Methods for Electrical Machines

Transcription

1 Control Methods for Electrical Machines

2 Control Methods for Electrical Machines Edited by René Husson

3 First published in France in 2003 by Hermes Science/Lavoisier entitled Méthodes de commande des machines électriques LAVOISIER, 2003 First published in Great Britain and the United States in 2009 by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd John Wiley & Sons, Inc St George s Road 111 River Street London SW19 4EU Hoboken, NJ UK USA ISTE Ltd, The rights of René Husson to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act Library of Congress Cataloging-in-Publication Data Méthodes de commande des machines électriques. English Control methods for electrical machines / edited by René Husson. p. cm. Includes bibliographical references and index. ISBN Electric machinery--automatic control. 2. Electric machinery--mathematical models. I. Husson, René. II. Title. TK2391.M '042--dc British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN: Printed and bound in Great Britain by CPI/Antony Rowe Ltd, Chippenham, Wiltshire.

4 Table of Contents Preface... xi Chapter 1. Overview of Mechanical Transmission Problems... 1 Pascal FONTAINE and Christian CUNAT 1.1. Technological aspects General structures of the machines Mechanisms and movement Engine-machine Particular movements Friction elements of tribology Bibliography Chapter 2. Reminders of Solid Mechanics Jean-François SCHMITT and Rachid RAHOUADJ 2.1. Reminders of dynamics Kinematics of a rigid body Kinetic elements for a rigid body Koenig s theorems Newtonian dynamics Application example: dynamic balance of a rigid rotor Analytical dynamics (Euler-Lagrange) Linear energies in the neighborhood of the balance for a non-damped discrete system Equilibrium configuration without group motion Equilibrium configuration with group motion Vibratory behavior of a discrete non-damped system around an equilibrium configuration Analytical study of the vibratory behavior of a milling machine table Positioning the problem... 53

5 vi Control Methods for Electrical Machines Setting up the model Direct resolution of the eigenvalue problem Cancellation of the stiff mode and reduction of the problem Bibliography Chapter 3. Towards a Global Formulation of the Problem of Mechanical Drive Christian CUNAT, Mohamed HABOUSSI and Jean François GANGHOFFER 3.1. Presentation of the mechanical drive modeling problem Brief review on continuum mechanics Conservation laws Principle of virtual powers (PVP) Thermomechanics of continuous mediums Notions on strain Some material behaviors: elementary analog models Variational formulations in mechanics of the structures Bibliography Chapter 4. Continuous-time Linear Control Frédéric KRATZ 4.1. Introduction PID controllers Overview Various structures Selection criteria for the adjustments Control mode PID controllers Adjustment by trial and error Ziegler-Nichols method Cohen-Coon method Methods based on previous knowledge of a system model Presentation of the Bode method Presentation of the Phillips and Harbor method Linear state feedback control systems Formulation of the control problem The structure of the control law Reconstruction of the state The controller as a combination of state feedback and an observer Design of feedback gain matrix F Optimal control Optimal regulator at continuous time Stochastic optimal regulator at continuous time

6 Table of Contents vii Discrete time optimal regulator Stochastic time optimal regulator LQG/H2 control Choice of a control Bibliography Chapter 5. Overview of Various Controls Frédéric KRATZ 5.1. Introduction Internal model controller Introduction Passage of the structure of regulation to that of control by internal model Properties of the control by internal model Implementation Predictive control Introduction General principles of predictive control Sliding control Introduction Structure of the control law Equivalent method control Bang-bang control Control-based fuzzy logic Introduction Structure of the controlled loop Representation of fuzzy controllers Basic concepts of fuzzy logic Fuzzification The inference mechanism Defuzzification Neural network control Introduction Formal neurons Neural networks Parsimonious approximation Implementation of neural networks Bibliography Chapter 6. Sliding Mode Control Rachid OUTBIB and Michel ZASADZINSKI 6.1. Introduction Illustrative example

7 viii Control Methods for Electrical Machines 6.3. Basic concepts General features of non-linear systems Existence of a sliding mode Chattering phenomena Determination of sliding dynamics Case of more than one commutation surface Direct Lyapunov method Affine systems with regard to control Linear systems Equivalent control method Invariance condition Existence conditions Sliding mode for a perturbed system Canonical forms Imposing a surface dynamic A classic surface dynamic A particular case: dynamic with pure discontinuities The choice of sliding surface Introduction A specific linear surface choice Conclusion Notations Bibliography Chapter 7. Parameter Estimation for Knowledge and Diagnosis of Electrical Machines Jean-Claude TRIGEASSOU, Thierry POINOT and Smaïl BACHIR 7.1. Introduction Identification using output-error algorithms Introduction Least-squares algorithm in output-error Principle of the output-error method in the general case Sensitivity functions Convergence of the estimator Variance of the estimator Implementation Parameter estimation with a priori information Introduction Bayesian approach Minimization of the compound criterion Deterministic interpretation Implementation Parameter estimation of the induced machine Introduction

8 Table of Contents ix Modeling in the three-phase frame Park s transformation Continuous-time state-space model Output-error identification Output-error identification and a priori information Fault detection and localization based on parameter estimation Introduction Principle of the method Simulations Numerical simulations Conclusion Bibliography Chapter 8. Diagnosis of Induction Machines by Parameter Estimation Smaïl BACHIR, Slim TNANI, Gérard CHAMPENOIS and Jean-Claude TRIGEASSOU 8.1. Introduction Induction motor model for fault detection Stator faults modeling in the induction motor Rotor fault modeling Global stator and rotor fault model Diagnosis procedure Parameter estimation Implementation Conclusion Bibliography Chapter 9. Time-based Coordination Michel DUFAUT and René HUSSON 9.1. Introduction Brief description system Functional structure Some ideas on the manipulator system models Various model types Geometric models Kinematic models Dynamic models Coordination of motion Why coordinate movements? Step response of a controlled shaft Speed representation in a point-to-point movement Partially specified trajectories Conclusion Bibliography

9 x Control Methods for Electrical Machines Chapter 10. Multileaf Collimators Sabine ELLES and Bruno MAURY Radiotherapy The medical prescription Linear accelerators Multileaf collimators Geometric characteristics of multileaf collimators Technical characteristics Readout systems for leaf position checking Leaf command system Accuracy of command and leaf positioning Intensity modulated radiotherapy How to realize a modulated intensity beam with a multileaf collimator Discretization into static elementary beams Discretization into dynamic beams Conclusion Bibliography Chapter 11. Position and Velocity Coordination: Control of Machine-Tool Servomotors Patrick BOUCHER and Didier DUMUR Open architecture systems Historical overview Principle and advantages Modular architecture example Structure and implementation of control laws Cascaded structure Polynomial structure of controllers Conclusion Application to machines-tools axis drive control Classic control scheme Cascaded velocity-position predictive control of synchronous motors Multivariable flux-position predictive control of asynchronous motors Conclusions Bibliography List of Authors Index

10 Preface The control of electrical machines very much depends on the context and environment in which motors are considered. How a machine is used has a strong influence on its control laws. These are especially related to loading characteristics, variables requiring control, operating conditions and, consequently, to the models chosen. Loading intrinsically governs the choice of control laws and the way they are implemented. Common load torques are inertia torques, whether they are constant or variable, or possibly even randomly variable. Constant inertia torques are induced by rotating masses, which may be either symmetric homogenous, working as inertia flywheels, or dissymmetric heterogenous, causing torque fluctuations or vibrations. Inertia may vary due to a load geometrical distortion, as is the case in Watt regulators or hinged jibs, or to a change in the rotating mass, like in a winder. Generally, non-inertial load torques need to be considered on top of these. Gravity causes load torques that adds up to the inertia torques induced by movement, especially in handling devices. The viscosity of the ambient environment causes resisting torques proportional to speed (viscous friction torques). This is the case in fans, boat propellers and more generally in all lubricated devices such as main bearings. Dry frictions cause stress, determined by the surface roughness of materials in contact and by the traverse speed. Being highly complex to model, stress is tricky to take into account in equations. The result of this is ill-controlled torques as well as inaccurate positioning. Load driving by electrical motors is almost always operated through a transmission, the role of which is either to modify the range of accessible speeds and torques or to change the nature of the movement (rotation/translation). These transmitters alter the properties of loads quite significantly: not only do they

11 xii Control Methods for Electrical Machines adversely affect the order of magnitude of torques, but they also input nonlinearities that may compromise the operation of the system. This is why this work starts with a presentation of the main problems encountered in mechanical transmissions, which are covered by Chapters 1, 2 and 3. Chapters 4, 5, 6, 7 and 8 deal with the means available to drive a converter/motor/transmission/load unit. It intends to provide the reader the most useful and recent information on the techniques that make it possible to design the most accurate control laws for the problem that needs to be solved. Generally, in usual applications, we strive to control three mechanical variables: velocity, position or torque (separately or simultaneously). Therefore, automatic techniques are called for. Even though usual linear controls (continuous or discrete, IPD, etc.) are still frequently used (rightly, considering their benefits), more recent and effective methods in difficult cases can be implemented. Optimal controls (linear-quadratic, linear-quadratic-gaussian, etc.), adaptive controls (with or without the reference model), sliding mode controls or bang-bang controls help lead to more satisfying solutions, but often necessitate more comprehensive and more detailed models than linear control. Predictive controls, neural network and fuzzy logic controls help refine the control and improve the performance of dynamic system controls when the models are fairly unknown. Finally, since the models used in electrical machine control involve several disciplines (automatic control, electrical engineering, computer science and mechanics), a common representation mode appears to be appropriate. Bond graphs fulfill this role perfectly and can be very helpful as useful tools for control. This topic will not be addressed here, since a specialized piece of work of more than 300 pages 1 fully covers this issue. Control and model building are only applicable with accurate numeric values of parameters. Therefore, identification, applied to electrical machines, aims at providing these data. Although numerous methods of measurement make it possible to reach some variables, the majority of the models used in control reveal constants, which gather several electrical variables and are not directly measurable as a consequence. Moreover, the necessary values are dynamic values, which are impossible to obtain using traditional measurements. That is why a chapter is dedicated to the identification methods that are best adapted for our scope of activity. 1 Karnopp D., Margolis D., Rosenberg R. Systems Dynamic Modeling and Simulation of Mechatronic Systems, John Wiley & Sons, 2000; and Geneviève Dauphin-Tanguy, Les Bond Graph, Hermes Science Publications, 2000.

12 Preface xiii The correct operation of the electrical machine is a key factor for operating safety. This work tackles the subject through the diagnosis of the defects of the machine. This technique is based on the continuous identification of the system and on the monitoring of the variation of its parameters. Diagnosis and adaptive control are sectors in which identification techniques are paramount. Control techniques call upon traditional concepts in automatic control, such as stability, robustness and observers. The latter are essential to make use of some variables which are not accessible to measurement. However, such basic concepts are beyond the scope of this work. Indeed, developing them would require several chapters, the material of which could be found elsewhere, resulting in a global loss of generality and an unbalanced overview, with no obvious added value. Chapters 9, 10 and 11 relate to the control of systems animated by a set of electrical motors, which requires a coordination of the actions of each component. Each motor obeys by the same control laws as those that would be applied to it if considered separately; however, a coordination (subsequently a coupling) between motors is introduced at the set point-level. Allowing complex operations such as deformations of the curvature of large areas, simultaneous machining, movements of hinged jibs or variable geometry openings requires the introduction of several coordination modes. The most obvious is synchronization, which is a coordination based on time. Synchronization requires specific speeds or motions for each motor at certain times. The individual control laws of each actuator are thus coupled, either in a discrete way by an assignation method or in a continuous way when the durations of actions are imposed by the operating constraints of the system. Position is also a coupling variable in multi-motor systems. The set point given to one of them will interfere with those of the other motors. Such is the case, for instance, with the variable geometry openings used in medicine for the irradiation of tumours. The VLT (Very Large Telescope) is also an example, with its huge mirrors deforming under their own weight. They are placed on multiple small electrical jacks, which correct the radius of curvature very precisely, requiring the coupling in position of 1,000 motors. Finally, speed is also a coordination means for the control of a set of motors. Thus, on the machine tools (and many other devices), the feed and rotation speeds of pins are not independent and must be coordinated, like positions. This type of coordination also exists in assembly lines and conveying attachments: in such contexts, the velocity variations of a conveying belt must be reflected on all the others.

13 xiv Control Methods for Electrical Machines Working out a general theory at this level is a difficult task, that s why the third part of the work rather presents examples of multi-motors systems illustrating the main coordination types. Coordination by time: the robot, coordination by the position: the multileaf collimator, coordination by speed: the machine tools. Throughout this work, our main goal has been to explain the concepts covered in a way understandable to most readers. This book is especially dedicated to people faced with issues at the border of their area of expertise. We hope that the material presented here will help them to solve these problems and gain a better view of global complex system design. Our purpose has therefore been twofold: providing a tool allowing better communication between experts from different domains, while allowing engineers from any background to gain a broader insight into general scientific culture. René HUSSON