Reverse Engineering in Control Design

Daniel Alazard

• Publisher: Wiley-ISTE
• Year: 2013
• Print ISBN: 9781848215238
• eBook ISBN: 9781118602621
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Automotive Transportation & Engineering
• Index: Technology & Engineering

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.

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:

[1.1]

Another well-appreciated advantage comes from the ease of implementation of observer-based controllers. In addition to the plant data, only two static gains (the state-feedback and the state-estimator) define the entire controller dynamics. In return, this facilitates the construction of gain-scheduled or interpolated controllers. Indeed, assuming the plant model is available in real time, observer-based controllers will only require the storage of these two static gains of lower dimensions instead of the huge set of numerical data in [1.1] to update the controller dynamics at each sample of time. Note that if we are using an interpolating procedure to update the controller dynamics, the general representation in [1.1] is highly questionable from an implementation viewpoint and in many cases will lead to an insuperable computational effort. This was in our opinion a major impediment for a widespread use of modern control techniques, such as H_∞ and μ syntheses in realistic applications and particularly for problems necessitating the real-time adjustment of the controller gains. These approaches produce high-order controllers expressed under a meaningless state-space realization. Note also that this last point is relevant if a controller reduction has been performed after the design.

To overcome this problem a general procedure is proposed in this chapter to compute an observer-based realizations for an arbitrary given controller and a given plant (for both continuous and discrete time cases). Independently of the solver used for the control design, such a procedure allows us to provide a realization with a meaningful state vector. In [ALA 01] and [CUM 04], it is shown that observer-based realization are also convenient to isolate high level-tuning parameters (potentiometers) in a complex control law. As the observer-based realization exploits the model of the plant, we can also guess that such a realization is very convenient to update the controller to a change in the model or to build a parameter-dependent controller K(s, θ) from a parameter-dependent model G(s, θ).

Among other potential advantages of observer-based realization, we would like to point out the possibility to handle actuator saturation constraints by exploiting this information into the prediction equation. Since this matter is not covered in this book, the reader is referred to [TAR 97] and references therein for more details. More theoretical discussions on the implementation of gain-scheduled controllers which use the plant nonlinearity model are given in [LAW 95] and [KAM 95].

The practical solution to handle non-stationary problems (such as the launch vehicle control design during atmospheric flight) or nonlinear problems consists of designing a family of controllers at various flight instants or various flight conditions and then in interpolating (gain-scheduling) these various controllers. It is well-known that the non-station...

Table of contents

• Cover
• Contents
• Dedication
• Title page
• Copyright page
• Nomenclature
• Introduction
• Chapter 1: Observer-based Realization of a Given Controller
• Chapter 2: Cross Standard Form and Reverse Engineering
• Chapter 3: Reverse Engineering for Mechanical Systems
• Conclusions and Perspectives
• APPENDICES
• List of Figures
• Index