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2011 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

System Identification

An Introduction

verfasst von: Karel J. Keesman

Verlag: Springer London

Buchreihe : Advanced Textbooks in Control and Signal Processing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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SUCHEN

Über dieses Buch

System Identification shows the student reader how to approach the system identification problem in a systematic fashion. The process is divided into three basic steps: experimental design and data collection; model structure selection and parameter estimation; and model validation, each of which is the subject of one or more parts of the text.

Following an introduction on system theory, particularly in relation to model representation and model properties, the book contains four parts covering:

• data-based identification – non-parametric methods for use when prior system knowledge is very limited;

• time-invariant identification for systems with constant parameters;

• time-varying systems identification, primarily with recursive estimation techniques; and

• model validation methods.

A fifth part, composed of appendices, covers the various aspects of the underlying mathematics needed to begin using the text.

The book uses essentially semi-physical or gray-box modeling methods although data-based, transfer-function system descriptions are also introduced. The approach is problem-based rather than rigorously mathematical. The use of finite input–output data is demonstrated for frequency- and time-domain identification in static, dynamic, linear, nonlinear, time-invariant and time-varying systems. Simple examples are used to show readers how to perform and emulate the identification steps involved in various control design methods with more complex illustrations derived from real physical, chemical and biological applications being used to demonstrate the practical applicability of the methods described. End-of-chapter exercises (for which a downloadable instructors’ Solutions Manual is available from fill in URL here) will both help students to assimilate what they have learned and make the book suitable for self-tuition by practitioners looking to brush up on modern techniques.

Graduate and final-year undergraduate students will find this text to be a practical and realistic course in system identification that can be used for assessing the processes of a variety of engineering disciplines. System Identification will help academic instructors teaching control-related to give their students a good understanding of identification methods that can be used in the real world without the encumbrance of undue mathematical detail.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
The main topic of this textbook is how to obtain an appropriate mathematical model of a dynamic system on the basis of observed time series and prior knowledge of the system. Therefore first some background of dynamic systems and the modeling of these systems is presented.
Karel J. Keesman

Data-based Identification

Frontmatter
Chapter 2. System Response Methods
Abstract
In Chap. 2 the focus is on data-based or nonparametric identification methods that directly utilize specific responses of a linear, time-invariant (LTI) system, in particular the impulse, step, and sine-wave response. The first two signals directly provide estimates of the impulse response function g(t), while the sine-wave response forms the basis for the frequency domain methods described in Chap. 3.
Karel J. Keesman
Chapter 3. Frequency Response Methods
Abstract
Chapter 3 describes, for LTI systems, data-based or nonparametric identification methods that directly provide estimates of the impulse response function g(t) in the frequency domain, G(e jω ). In particular, the empirical transfer-function estimate (ETFE) and the critical point identification method are introduced. The frequency domain descriptions, given an estimate of the frequency function G(e jω ), are particularly suited for classical and robust controller design.
Karel J. Keesman
Chapter 4. Correlation Methods
Abstract
In many applications noise is clearly present. Under those circumstances, the reliability of the direct estimates of the impulse response function g(t) or frequency function G(e jω ) can be significantly reduced. Therefore, in Chap. 4 correlation methods, which are less sensitive to noise and thus very useful under practical circumstances, are presented. In particular, the so-called Wiener–Hopf relationship is derived from input–output data and analyzed with respect to its filter properties. The chapter finishes with spectral analysis methods that provide a transfer-function estimate using power spectra.
Karel J. Keesman

Time-invariant Systems Identification

Frontmatter
Chapter 5. Static Systems Identification
Abstract
In Chap. 5 we start with the identification of static linear systems, that is, no dynamics are involved. The output of a static system depends only on the input at the same instant and thus shows instantaneous responses. In particular, the so-called least-squares method is introduced. As will be seen in Chaps. 5 and 6, the least-squares method for the static linear case forms the basis for solving nonlinear and dynamic estimation problems. For the analysis of the resulting estimates, properties like bias and accuracy are treated. Special attention is paid to errors-in-variables problems, which allow noise in both input and output variables, to maximum likelihood estimation as a unified approach to estimation, in particular well-defined in the case of normal distributions, and to bounded-noise problems for cases with small data sets.
Karel J. Keesman
Chapter 6. Dynamic Systems Identification
Abstract
Chapter 6 focuses on the identification of dynamic systems, both linear and nonlinear. The selected model structure of linear dynamic systems and, in particular, the structure of the noise model appear to be of crucial importance for specific applications and the estimation methods to be used. In this chapter, it is stressed that both the linear and nonlinear model structures can be formulated in terms of (nonlinear) regression equations, which allow a unification of estimation problems. Special attention is paid to subspace identification for the direct estimation of the entries of the matrices A, B, C, and D in a discrete-time, linear state-space model formulation, to the identification of discrete-time linear parameter-varying models of nonlinear or time-varying systems, to the use of orthogonal basis functions for efficient calculation, and to closed-loop identification in LTI control system configurations.
Karel J. Keesman

Time-varying systems Identification

Chapter 7. Time-varying Static Systems Identification
Abstract
In Chap. 7 recursive estimation is introduced and applied to static, linear or nonlinear, systems with possibly time-varying parameters. The idea is as follows. On the basis of common prior knowledge, the model parameters in the linear regression models are considered as constant. Subsequently, the experimental data, using recursive estimation techniques, will tell how the estimates of the parameters vary with time. This idea can be easily extended to the case with a dynamic parameter model in the form of a linear dynamic state equation, which clearly illustrates the system theoretic concept of a model parameter as a (unobserved) state. Hence, the resemblance of the recursive least-squares parameter estimator to the well-known Kalman filter is emphasized. For the nonlinear case, the concept of extended Kalman filtering is introduced.
Karel J. Keesman
Chapter 8. Time-varying Dynamic Systems Identification
Abstract
Chapter 8 focuses on the recursive parameter estimation of dynamic systems, where, in general, the optimality of the estimation results of the linear regression models of Chap. 7 will no longer hold. Here the interchanging concept of parameter and state will be further worked out, using extended Kalman filtering and observer-based methods. And, again it will be applied to both the linear and nonlinear cases. The theory is illustrated by real-world examples, with most often a biological component in it, as these cases often show a time-varying behavior due to adaptation of the (micro)organisms.
Karel J. Keesman

Model Validation

Frontmatter
Chapter 9. Model Validation Techniques
Abstract
In the previous chapters, from data-based identification to time-invariant/time-varying system identification, many methods have been introduced to find an appropriate model structure, with or without using prior physical knowledge, from experimental data. However, the final step in a single system identification loop is model validation. In this step the user has to decide whether the identified model is appropriate or not. Chapter 9 therefore focuses on methods that support the user in making the right decisions about the validity of the mathematical model of the system. To be a little bit more precise, and in line with the Popperian philosophy, validation does not usually guarantee validity, but just tries to test adequacy or fails to establish invalidity. The use of prior knowledge, model experience, and experimental data in the model validation step are emphasized and basically illustrated by a couple of examples. After introducing the methods for model validation, a real-world application, related to perishable food storage, is extensively introduced and discussed in terms of model validation.
Karel J. Keesman
Backmatter
Metadaten
Titel
System Identification
verfasst von
Karel J. Keesman
Copyright-Jahr
2011
Verlag
Springer London
Electronic ISBN
978-0-85729-522-4
Print ISBN
978-0-85729-521-7
DOI
https://doi.org/10.1007/978-0-85729-522-4

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