Control Methods for Electrical Machines E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 417

Veröffentlichungsjahr: 2013

Beschreibung

The type of control system used for electrical machines depends on the use (nature of the load, operating states, etc.) to which the machine will be put. The precise type of use determines the control laws which apply. Mechanics are also very important, because they affect performance. Another factor of essential importance in industrial applications is operating safety. Finally, the problem of how to control a number of different machines, whose interactions and outputs must be coordinated, is addressed and solutions are presented. These and other issues are addressed here by a range of expert contributors, each of whom are specialists in their particular field. This book is primarily aimed at those involved in complex systems design, but engineers in a range of related fields such as electrical engineering, instrumentation and control, and industrial engineering, will also find this a useful source of information.

Leseprobe

Table of Contents

Preface

Chapter 1. Overview of Mechanical Transmission Problems

1.1. Technological aspects

1.2. Bibliography

Chapter 2. Reminders of Solid Mechanics

2.1. Reminders of dynamics

2.2. Application example: dynamic balance of a rigid rotor

2.3. Analytical dynamics (Euler-Lagrange)

2.4. Linear energies in the neighborhood of the balance for a non-damped discrete system

2.5. Vibratory behavior of a discrete non-damped system around an equilibrium configuration

2.6. Analytical study of the vibratory behavior of a milling machine table

2.7. Bibliography

Chapter 3. Towards a Global Formulation of the Problem of Mechanical Drive

3.1. Presentation of the mechanical drive modeling problem

3.2. Brief review on continuum mechanics

3.3. Bibliography

Chapter 4. Continuous-time Linear Control

4.1. Introduction

4.2. PID controllers

4.3. PID controllers

4.4. Methods based on previous knowledge of a system model

4.5. Linear state feedback control systems

4.6. Optimal control

4.7. Choice of a control

4.8. Bibliography

Chapter 5. Overview of Various Controls

5.1. Introduction

5.2. Internal model controller

5.3. Predictive control

5.4. Sliding control

5.5. Bang-bang control

5.6. Control-based fuzzy logic

5.7. Neural network control

5.8. Bibliography

Chapter 6. Sliding Mode Control

6.1. Introduction

6.2. Illustrative example

6.3. Basic concepts

6.4. Direct Lyapunov method

6.5. Equivalent control method

6.6. Imposing a surface dynamic

6.7. The choice of sliding surface

6.8. Conclusion

6.9. Notations

6.10. Bibliography

Chapter 7. Parameter Estimation for Knowledge and Diagnosis of Electrical Machines

7.1. Introduction

7.2. Identification using output-error algorithms

7.3. Parameter estimation with a priori information

7.4. Parameter estimation of the induced machine

7.5. Fault detection and localization based on parameter estimation

7.6. Conclusion

7.7. Bibliography

Chapter 8. Diagnosis of Induction Machines by Parameter Estimation

8.1. Introduction

8.2. Induction motor model for fault detection

8.3. Diagnosis procedure

8.4. Conclusion

8.5. Bibliography

Chapter 9. Time-based Coordination

9.1. Introduction

9.2. Brief description system

9.3. Some ideas on the manipulator system models

9.4. Coordination of motion

9.5. Conclusion

9.6. Bibliography

Chapter 10. Multileaf Collimators

10.1. Radiotherapy

10.2. Multileaf collimators

10.3. Intensity modulated radiotherapy

10.4. Conclusion

10.5. Bibliography

Chapter 11. Position and Velocity Coordination: Control of Machine-Tool Servomotors

11.1. Open architecture systems

11.2. Structure and implementation of control laws

11.3. Application to machines-tools axis drive control

11.4. Conclusions

11.5. Bibliography

List of Authors

Index

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:

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© ISTE Ltd 2009

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 1988.

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 978-1-84821-093-6

1. Electric machinery--Automatic control. 2. Electric machinery--Mathematical models. I. Husson, René. II. Title.

TK2391.M48 2009

621.31′042--dc22

2008043200

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN: 978-1-84821-093-6

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 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 pages1 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.

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.

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

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.

Chapter 1

Overview of Mechanical Transmission Problems1

1.1. Technological aspects

The direct approach of a system of mechanical transmission of power may be delicate. In this chapter, we propose to assimilate a real mechanism to a discrete mechanical system. We will then identify its main components and propose a classification based on their efficiency (in section 1.1.1; see also [SPI 97]). The general theorems of mechanical application to these simple models after an easy mathematical treatment will highlight the relevant parameters governing machine performance and point to directions of thought in order to improve the command of those mechanisms (sections 1.1.2, 1.1.3 and 1.1.4; see also [SPI 97]). Finally, the main elements of tribology will be presented in section 1.1.5. Indeed, the study of friction and lubrication and their consequences constitutes an essential part in the conception and the functioning of machines.

1.1.1. General structures of the machines

These engines are connected with machines through transmission power systems or mechanisms such as gearings, belts or chains, clutches or brakes, systems connecting rod-crank or the sawnut systems, cams or eccentric, elastic coupling.

Any mechanism is put in motion by an entrance element called the leading or driving element, which supplies the driving energy. An exit element called the led or receiving element is the element by which the energy connected to loads goes out of the mechanism. The power circulates from the engine towards loads. The exit of a component constitutes the entrance of the next component.

1.1.1.1. Engine

In a power converter, the engine receives as an input an electrical power; as an output this power is always a mechanical power (couple and angular speed or strength and linear speed). The variation curve of the couple or the strength according to the speed is the curve of capacity of the engine, the characteristic of the engine. This conversion involves losses and therefore the notion of the engine’s efficiency is introduced.

1.1.1.2. Loads

Loads are the linear efforts and torques applied to the parts of the machine situated downstream of the studied part. Loads represent the resistances induced by the environment of the machine and result from their functioning. They are the loads of friction, gravity and slowness.

1.1.1.3. Energy efficiency

The classification of the numerous existing mechanisms can rely on the energy efficiency expression. By definition, the efficiency is the ratio of supplied energy to the necessary energy to supply.

Figure 1.1.Powers acting on a mechanism

The mechanism of Figure 1.1 receives the power P1 and supplies the mechanical power P2 to the receiver 2. The mechanism 1 being real, there is a Pp power being lost and transformed into heat in 1. The efficiency on the mechanism 1 is written:

The nature of the movement being assumed to be unchanged in 1 (here a rotation), we can write:

C1, C2 are the torques applied to 1, 2 respectively.

Ω1, Ω2, are the angular speeds of driveshaft 1, 2 respectively.

By making reference to a perfect mechanism, the efficiency of a real mechanism can be written as:

By dividing every term by C1 Ω1 and putting

the real mechanism can then be written as:

where ηc expresses losses by friction and ηω characterizes the internal gliding in the mechanism.

We can then write

This approach allows the classification of mechanisms into two big categories:

Non-positive mechanisms: the effort transmission is done by friction. There are mechanisms with friction such as the flat or trapezoidal belts, strip carrier, speed variators with friction, clutches with friction and brakes.