Principles of System Identification Theory and Practice

PART I INTRODUCTION TO IDENTIFICATION AND MODELS FOR LINEAR DETERMINISTIC SYSTEMS

Introduction

Motivation

Historical developments

System Identification

Systematic identification

Flow of learning material

Software

A Journey into Identification

Identifiability

Signal-to-Noise ratio

Overfitting

A modeling example: liquid level system

Reflections and summary

Mathematical Descriptions of Processes: Models

Definition of a model

Classification of models

Models for Discrete-Time LTI Systems

Convolution model

Response models

Difference equation form

State-space descriptions

Illustrative example in MATLAB: estimating LTI models

Summary

Transform-Domain Models for Linear Time-Invariant Systems

Frequency response function

Transfer function form

Empirical transfer function (ETF)

Closure

Sampling and Discretization

Discretization

Sampling

Summary

PART II MODELS FOR RANDOM PROCESSES

Random Processes

Introductory remarks

Random variables and probability

Probability theory

Statistical properties of random variables

Random signals and processes

Time-series analysis

Summary

Time-Domain Analysis: Correlation Functions

Motivation

Auto-covariance function

White-noise process

Cross-covariance function

Partial correlation functions

Summary

Models for Linear Stationary Processes

Motivation

Basic ideas

Linear stationary processes

Moving average models

Auto-regressive models

Auto-regressive moving average models

Auto-regressive integrated moving average models

Summary

Fourier Analysis and Spectral Analysis of Deterministic Signals

Motivation

Definitions

Fourier representations of deterministic processes

Discrete Fourier Transform (DFT)

Summary

Spectral Representations of Random Processes

Introduction

Power spectral density of a random process

Spectral characteristics of standard processes

Cross-spectral density and coherence

Partial coherence

Spectral factorization

Summary

PART III ESTIMATION METHODS

Introduction to Estimation

Motivation

A simple example: constant embedded in noise

Definitions and terminology

Types of estimation problems

Estimation methods

Historical notes

Goodness of Estimators

Introduction

Fisher information

Bias

Variance

Efficiency

Sufficiency

Cramer-Rao’s inequality

Asymptotic bias

Mean square error

Consistency

Distribution of estimates

Hypothesis testing and confidence intervals

Empirical methods for hypothesis testing

Summary

Appendix

Estimation Methods: Part I

Introduction

Method of moments estimators

Least squares estimators

Non-linear least squares

Summary

Appendix

Estimation Methods: Part II

Maximum likelihood estimators

Bayesian estimators

Summary

Estimation of Signal Properties

Introduction

Estimation of mean and variance

Estimators of correlation

Estimation of correlation functions

Estimation of auto-power Spectra

Estimation of cross-spectral density

Estimation of coherence

Summary

PART IV IDENTIFICATION OF DYNAMIC MODELS - CONCEPTS AND PRINCIPLES

Non-Parametric and Parametric Models for Identification

Introduction

The overall model

Quasi-stationarity

Non-parametric descriptions

Parametric descriptions

Summary

Predictions

Introduction

Conditional expectation and linear predictors

One-step ahead prediction and innovations

Multi-step and infinite-step ahead predictions

Predictor model: An alternative LTI description

Identifiability

Summary

Identification of Parametric Time-Series Models

Introduction

Estimation of AR models

Estimation of MA models

Estimation of ARMA models

Summary

Identification of Non-Parametric Input-Output Models

Recap

Impulse response estimation

Step response estimation

Estimation of frequency response function

Estimating the disturbance spectrum

Summary

Identification of Parametric Input-Output Models

Recap

Prediction-error minimization (PEM) methods

Properties of the PEM estimator

Variance and distribution of PEM-QC estimators

Accuracy of parametrized FRF estimates using PEM

Algorithms for estimating specific parametric models

Correlation methods

Summary

Statistical and Practical Elements of Model Building

Introduction

Informative Data

Input design for identification

Data pre-processing

Time-delay estimation

Model development

Summary

Identification of State-Space Models

Introduction

Mathematical essentials and basic ideas

Kalman filter

Foundations for subspace identification

Preliminaries for subspace identification methods

Subspace identification algorithms

Structured state-space models

Summary

Case Studies

ARIMA model of industrial dryer temperature

Simulated process: developing an input-output model

Process with random walk noise

Multivariable modeling of a four-tank system

Summary

PART V ADVANCED CONCEPTS

Advanced Topics in SISO Identification

Identification of linear time-varying systems

Non-linear identification

Closed-loop identification

Summary

Linear Multivariable Identification

Motivation

Estimation of time delays in MIMO systems

Principal component analysis (PCA)

Summary

References

Index

Biography

Arun K. Tangirala an Associate Professor at the Department of Chemical Engineering, IIT Madras, India. He obtained his B. Tech. (Chemical Engineering) from IIT Madras, India and Ph.D. (Process Control & Monitoring) from the University of Alberta, Canada in the years 1996 and 2001, respectively. Dr. Tangirala specializes in process control, modelling, monitoring and multivariate data analysis. His research group is focused on solving some of the cutting edge problems in data-driven analysis and modelling. A recipient of different teaching and research awards, he has conducted several workshops and short-term courses on data analysis and process identification.

"This book is an encyclopedia of linear system identification. … A practicing engineer’s perfect guide to system identification and its applications."
—Bhushan Gopaluni, University of British Columbia, Vancouver, Canada

"Very good framework. … It reflects the core idea and dominant methods in this field."
—Fan Yang, Department of Automation, Tsinghua University, Beijing, China

"Students these days are looking to become knowledgeable about advanced topics as quickly and efficiently as possible, and therefore want to find that one-stop reference or course to bring them up to speed. This book is a welcome addition to the literature for students and teachers alike [who are] interested in doing just that in the field of system identification."
—William R. Cluett, Department of Chemical Engineering and Applied Chemistry, University of Toronto, Ontairo, Canada

"… nicely goes over all the key principles and concepts in way that is accessible to the average reader, yet touches upon the subtleties of the theoretical foundations. This book has the qualities to be an attractive entry point for anyone interested in this subject. In fact, the book is written in a way that it will draw the reader in with its simple and systematic exposition of this interesting and useful subject."
—Harish Palanthandalam-Madapusi, Indian Institute of Technology Gandhinagar, Ahmedabad

"The author is to be congratulated for writing this extensive textbook. It builds on the shoulders of the giants in the field like George Box and Ljung and provides the reader with an up-to-date, encyclopedic-like travelogue through the theory and practice of system identification. The author provides relatively simple examples in different places throughout the book to help the reader appreciate the problem without getting distracted by too much complexity. The majority of examples are accompanied by Matlab code to enable the reader to easily run simulations on his or her own and duplicate the author’s results. At the end of each chapter, the reader will find review questions to provoke reflection on what has just been read as well as exercises to gain practice and build confidence."
—IEEE Control Systems Magazine, April 2017 Issue