Identification of Continuous-Time Systems

Linear and Robust Parameter Estimation

Allamaraju Subrahmanyam, Ganti Prasada Rao

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9781000732900
• Edition: 1
• Topic: Tecnologia e ingegneria
• Subtopic: Automazione in ingegneria

Models of dynamical systems are required for various purposes in the field of systems and control. The models are handled either in discrete time (DT) or in continuous time (CT). Physical systems give rise to models only in CT because they are based on physical laws which are invariably in CT. In system identification, indirect methods provide DT models which are then converted into CT. Methods of directly identifying CT models are preferred to the indirect methods for various reasons. The direct methods involve a primary stage of signal processing, followed by a secondary stage of parameter estimation. In the primary stage, the measured signals are processed by a general linear dynamic operation—computational or realized through prefilters, to preserve the system parameters in their native CT form—and the literature is rich on this aspect.

In this book: Identification of Continuous-Time Systems-Linear and Robust Parameter Estimation, Allamaraju Subrahmanyam and Ganti Prasada Rao consider CT system models that are linear in their unknown parameters and propose robust methods of estimation. This book complements the existing literature on the identification of CT systems by enhancing the secondary stage through linear and robust estimation.

In this book, the authors

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• provide an overview of CT system identification,

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• consider Markov-parameter models and time-moment models as simple linear-in-parameters models for CT system identification,

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• bring them into mainstream model parameterization via basis functions,

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• present a methodology to robustify the recursive least squares algorithm for parameter estimation of linear regression models,

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• suggest a simple off-line error quantification scheme to show that it is possible to quantify error even in the absence of informative priors, and

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• indicate some directions for further research.

This modest volume is intended to be a useful addition to the literature on identifying CT systems.

1

Introduction and Overview

1.1 Background

A system is a unified collection of entities or objects called subsystems. A system may occur naturally or be human engineered for a purpose. The objects are naturally interrelated or artificially made to interact. The collection functions together as a whole within certain spatial and temporal boundaries. A system is characterized by its structure, function, and environment. A dynamical system is a system whose state can change in time and space either spontaneously or by the action of external influence.

Dynamical systems are represented by their mathematical models—difference equations or differential equations. Differential equation models arise mostly from physical systems because the governing laws are basically formulated in continuous time (CT). Examples include Newton’s laws of mechanics and Faraday’s laws of electromagnetism. When a dynamic system is studied intermittently—in discrete time (DT)—the mathematical models are in the form of difference equations. CT and DT descriptions can be transformed into other domains for operational or computational convenience.

The behavior of a system is exhibited in its response to external inputs and is studied by solving the system model differential/difference equations with forcing functions. The reverse of such study is System Identification whose objective is to determine the dynamical system model that best fits the behavior under appropriate observations. System identification involves consideration of a set of (measurable) signals, a set of models, and a criterion (Zadeh 1962). System identification is then concerned with the determination of an appropriate (based on a criterion) mathematical model to describe the input–output behavior of the system under test on the basis of a given set of measured input and output signals and prior information.

For parametric identification of CT systems, an appropriate parameterization of the chosen model structure in a realistic time domain is crucial. The choice of model structure is governed—first by the nature of the system under test, and then by the intended application of the model.

The field of system identification has been surveyed in the past in general, both in CT and DT (Aström and Eykhoff 1971; Niederlinski and Hajdasinski 1979; Billings 1980; Young 1981; Unbehauen and Rao 1990, 1998; Pintelon et al. 1994). These include surveys of linear time-invariant (LTI) lumped dynamical stable CT systems (Young 1981; Unbehauen and Rao 1990, 1998; Pintelon et al. 1994). There are books dealing with CT identification of systems (Rao 1983; Saha and Rao 1983; Unbehauen and Rao 1987) and edited volumes of collected works of different authors (Sinha and Rao 1991; Garnier et al. 2001, 2008; Garnier and Young 2014) on the subject. Special issues of journals were devoted to CT approaches to identification and control (Rao and Unbehauen 1993; Young and Garnier 2014).

This book focuses on the identification of LTI lumped dynamical stable systems with CT processing of input–output signals; and hence, in the sequel we will consider LTI parametric transfer functions for modeling such systems.

CT systems have traditionally been modeled by linear differential equations in the time domain or by rational transfer functions in the complex variable “$s$” in the frequency domain. Howe...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Table of Contents
• List of Figures
• List of Tables
• Preface
• Acknowledgments
• Authors
• List of Abbreviations
• 1. Introduction and Overview
• 2. Markov Parameter Models
• 3. Time Moment Models
• 4. Robust Parameter Estimation
• 5. Error Quantification
• 6. Conclusions
• Bibliography
• Subject Index
• Author Index