Reverse Engineering in Control Design E-Book

Daniel Alazard

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 191

Veröffentlichungsjahr: 2013

Beschreibung

Reverse Engineering in Control Design proposes practical approaches to building a standard H-infinity problem taking into account an initial controller. Such approaches allow us to mix various control objectives and to initialize procedures for a fixed-structure controller design. They are based on the Observer-Based Realization (OBR) of controllers. The interest of OBR from the controller implementation point of view is detailed and highlighted in this book through academic examples. An open-source toolbox is available to implement these approaches in Matlab®. Throughout the book academic applications are proposed to illustrate the various basic principles. These applications have been chosen by the author for their pedagogic contents and demo files and embedded Matlab® functions can be downloaded so readers can run these illustrations on their personal computers. Contents 1. Observer-based Realization of a Given Controller. 2. Cross Standard Form and Reverse Engineering. 3. Reverse Engineering for Mechanical Systems. Appendix 1. A Preliminary Methodological Example. Appendix 2. Discrete-time Case. Appendix 3. Nominal State-feedback for Mechanical Systems. Appendix 4. Help of Matlab® Functions. About the Authors Daniel Alazard is Professor in System Dynamics and Control at Institut Supérieur de l'Aéronautique et de l'Espace (ISAE), Toulouse, France - SUPAERO Graduate Program. His main research interests concern robust control, flexible structure control and their applications to various aerospace systems.

Leseprobe

Contents

Nomenclature

Introduction

Chapter 1 Observer-based Realization of a Given Controller

1.1. Introduction

1.2. Principle

1.3. A first illustration

1.4. Augmented-order controllers

1.5. Discussion

1.6. In brief

1.7. Reduced-order controllers case

1.8. Illustrations

1.9. Reference inputs in observer-based realizations

1.10. Disturbance monitoring and rejection

1.11. Minimal parametric description of a linear system

1.12. Selection of the observer-based realization

1.13. Conclusions

1.14. Bibliography

Chapter 2 Cross Standard Form and Reverse Engineering

2.1. Introduction

2.2. Definitions

2.3. Low-order controller case (nK ≤ n)

2.4. Augmented-order controller case (nK > n)

2.5. Illustration

2.6. Pseudo-cross standard form

2.7. Conclusions

2.8. Bibliography

Chapter 3 Reverse Engineering for Mechanical Systems

3.1. Introduction

3.2. Context

3.3. Model, specifications and initial controller

3.4. H∞ design based on the acceleration sensitivity function

3.5. Mixed H2/H∞ design based on the acceleration sensitivity function

3.6. Aircraft lateral flight control design

3.7. Conclusions

3.8. Bibliography

Conclusions and Perspectives

APPENDICES

Appendix 1 A Preliminary Methodological Example

A1.1. Bibliography

Appendix 2 Discrete-time Case

A2.1. Discrete-time predictor form

A2.2. Discrete-time estimator form

A2.3. Discrete-time cross standard form

Appendix 3 Nominal State-feedback for Mechanical Systems

A3.1. Recovering control law [3.4] using linear-quadratic approach

A3.2. Recovering control law [3.4] using eigenstructure assignment

A3.3. Recovering control law [3.4] using LMI

A3.4. Bibliography

Appendix 4 Help of Matlab® Functions

A4.1. Function cor2tfg

A4.2. Function cor2obr

A4.3. Function obr2cor

A4.4. Function obr2cor2ddl

A4.5. Function obcanon

A4.6. Function cor2tfga

A4.7. Function cor2obra

A4.8. Function obrmap

A4.9. Function h2hinfsol

List of Figures

Index

I would like to thank all my colleagues from the Institut Supérieur de l’Aéronautique et de l’Espace (ISAE) and from the Department of System Control and Flight Dynamics, ONERA (the French Aerospace Lab) for their help and support in this research. I would also like to thank all my PhD students, present and past, and more particularly to Olivier Voinot, Fabien Delmond, Nicolas Fezans and Nicolas Guy whose research works have fed this book.

Daniel Alazard

First published 2013 in Great Britain and the United States 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

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John Wiley & Sons, Inc.

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©ISTE Ltd 2013

The rights of Daniel Alazard to be identified as the author of this work have been asserted by him/her/them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2012955967

British Library Cataloguing-in-Publication Data

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

ISSN: 2051-2481 (Print)

ISSN: 2051-249X (Online)

ISBN: 978-1-84821-523-8

Nomenclature

Following notations are used throughout this book.

Introduction

The first objective of this book is to provide a general solution to the inverse H∞ and H2optimal control problems and to show how such a solution can be used to design controllers in a reverse engineering approach. Given an initial controller and a given plant, the solution to the inverseH∞/H2optimal control problem is a standard control problem, that is the two input ports–two output ports standard problem commonly used in the H∞ design framework, whose unique H∞ or H2 optimal controller is the given controller. This solution will be called the cross standard form (CSF). The reverse engineering approach consists of applying the CSF to a given controller in order to set up a standard control problem that can be completed to H2 handle H∞ or frequency-domain specifications. It will be shown that such an approach is quite attractive to mix various control design methods and to cope with various kinds of control specifications. Thus, reverse engineering is a suitable alternative to multi-objective control design that is still an open problem.

The second objective, which is strongly linked to the first objective, concerns the observer-based realization of controllers for implementation purposes. Full-order H∞ unstructured controllers are well-known to raise implementation problems such as:

– How the controller states can be initialized.

– How various controllers designed at various operating conditions can be switched or gain-scheduled; and so on.

When the model of a plant is described by a state space representation where the states have a physical meaning (and physical units: this is in particular the case in the field of mechanical engineering where the plant state vector is composed of the displacements along the various degrees of freedom and their time derivatives), an observer-based controller has a physical structure. Its state is an estimate of the plant state and has the same physical units. All the gains (state-feedback gains and state-estimator gains) have also a physical unit. This can reduce implementation problems in a significant way. It will be shown how an observer-based realization of a given controller for a given plant can be computed and implemented. Then, the link between observer-based realization and reverse engineering is straightforward: the observer-based realization of a controller allows a simple solution to the inverse optimal control problem to be proposed.

The third objective of this book concerns reverse engineering for mechanical systems and initial controllers designed to meet basic performance specifications, that is a prescribed second-order behavior for each degree of freedom and dynamic decoupling of degrees of freedom. The CSF, although a general solution to the inverse H∞ optimal control problem, leads to a standard problem where the closed-loop performance index cannot be always directly compared with other performance indexes. To solve this problem, a new standard H∞ problem weighting the acceleration sensitivity function is proposed as a starting point for the reverse engineering approach.

These three objectives are described in detail in Chapters 1–3. In Chapter 1, we present the procedure to compute the observer-based realization of a given controller and a given model. The application of this procedure to a very simple model of a launcher is proposed to illustrate the importance of observer-based controllers for gain-scheduling, controller switching, state and disturbance monitoring, and reference input tracking. In Chapter 2, the CSF is presented and also applied to the same academic example: a low-order controller is improved to fulfill a template on its frequency-domain response and to recover stability margins once the actuator dynamics is taken into account. Chapter 3 discusses reverse engineering for the particular class of mechanical systems. The extension of these results to the discrete-time case is given in the appendix. Concluding remarks and future works are proposed in the last chapter.

In the three chapters, academic applications are proposed to illustrate the various basic principles. These applications have been chosen for their pedagogic contents: demo files and embedded Matlab® functions can be downloaded from http://personnel.isae.fr/daniel-alazard/matlab-packages. Readers can run these illustrations on their personnel computer. More complex and more realistic applications related to this book are referenced for the reader who wishes to go further. The reader is also advised to read first the preliminary methodological example proposed in Appendix 1 to better understand the motivations of this book.

This book is aimed mainly for postgraduate students and control designers with a solid background in automatic control, mainly in:

– state-space representation of multivariable systems;

– linear–quadratic–gaussian (LQG), H2 and H∞ syntheses.

1

Observer-based Realization of a Given Controller

1.1. Introduction

Observer-based controllers (for instance, Linear Quadratic Gaussian (LQG) controllers) are quite interesting for different practical reasons and from the implementation point of view. Probably the key advantage of these controller structures lies in the fact that the controller states are meaningful variables as estimates of the physical plant states. It follows that the controller states can be used to monitor (online or offline) the performance of the system. Such a meaningful state also allows us to initialize the state of the controller or to update the controller state during control mode switching. Note that this simple property does not hold for general controllers with state-space description: