Identification of Physical Systems

Identification of a physical system deals with the problem of
identifying its mathematical model using the measured input and
output data. As the physical system is generally complex,
nonlinear, and its input-output data is corrupted noise,
there are fundamental theoretical and practical issues that need to
be considered.

Identification of Physical Systems addresses this need,
presenting a systematic, unified approach to the problem of
physical system identification and its practical
applications. Starting with a least-squares method, the
authors develop various schemes to address the issues of accuracy,
variation in the operating regimes, closed loop, and interconnected
subsystems. Also presented is a non-parametric signal or data-based
scheme to identify a means to provide a quick macroscopic picture
of the system to complement the precise microscopic picture given
by the parametric model-based scheme. Finally, a sequential
integration of totally different schemes, such as non-parametric,
Kalman filter, and parametric model, is developed to meet the speed
and accuracy requirement of mission-critical systems.

Key features:

• Provides a clear understanding of theoretical and practical
  issues in identification and its applications, enabling the reader
  to grasp a clear understanding of the theory and apply it to
  practical problems

• Offers a self-contained guide by including the background
  necessary to understand this interdisciplinary subject

• Includes case studies for the application of identification on
  physical laboratory scale systems, as well as number of
  illustrative examples throughout the book

Identification of Physical Systems is a comprehensive
reference for researchers and practitioners working in this field
and is also a useful source of information for graduate students in
electrical, computer, biomedical, chemical, and mechanical
engineering.

Autorentext

Rajamani Doraiswami, Professor Emeritus, Electrical and Computer Engineering Department, University of New Brunswick, USA
Rajamani Doraiswami is Professor Emeritus in the Department of Electrical and Computer Engineering at the University of New Brunswick.
Dr. Doraiswami is known internationally as an excellent researcher, has held an NSERC operating grant continually since 1981 and has published more than 60 papers in refereed journals and 90 conference papers. Dr. Doraiswami's research interests focus on control, signal processing, pattern classification and algorithms. One of his most successful collaborations has been in the development of laboratories for the teaching of analysis and design of control and signal processing systems in real-time. Chris Diduch is a Professor in the Department of Electrical and Computer Engineering at the University of New Brunswick. His research is in the fields of control systems and digital systems. Maryhelen Stevenson is a Professor in the Department of Electrical and Computer Engineering at the University of New Brunswick. Her research is in the fields of pattern classification, speech and signal processing, adaptive systems and time-frequency representations.

Zusammenfassung
Identification of a physical system deals with the problem of identifying its mathematical model using the measured input and output data. As the physical system is generally complex, nonlinear, and its inputoutput data is corrupted noise, there are fundamental theoretical and practical issues that need to be considered.

Identification of Physical Systems addresses this need, presenting a systematic, unified approach to the problem of physical system identification and its practical applications. Starting with a least-squares method, the authors develop various schemes to address the issues of accuracy, variation in the operating regimes, closed loop, and interconnected subsystems. Also presented is a non-parametric signal or data-based scheme to identify a means to provide a quick macroscopic picture of the system to complement the precise microscopic picture given by the parametric model-based scheme. Finally, a sequential integration of totally different schemes, such as non-parametric, Kalman filter, and parametric model, is developed to meet the speed and accuracy requirement of mission-critical systems.

Key features:

• Provides a clear understanding of theoretical and practical issues in identification and its applications, enabling the reader to grasp a clear understanding of the theory and apply it to practical problems
• Offers a self-contained guide by including the background necessary to understand this interdisciplinary subject
• Includes case studies for the application of identification on physical laboratory scale systems, as well as number of illustrative examples throughout the book
  Identification of Physical Systems is a comprehensive reference for researchers and practitioners working in this field and is also a useful source of information for graduate students in electrical, computer, biomedical, chemical, and mechanical engineering.

Inhalt

Preface xv

Nomenclature xxi

1 Modeling of Signals and Systems 1

1.1 Introduction 1

1.2 Classification of Signals 2

1.2.1 Deterministic and Random Signals 3

1.2.2 Bounded and Unbounded Signal 3

1.2.3 Energy and Power Signals 3

1.2.4 Causal, Non-causal, and Anti-causal Signals 4

1.2.5 Causal, Non-causal, and Anti-causal Systems 4

1.3 Model of Systems and Signals 5

1.3.1 Time-Domain Model 5

1.3.2 Frequency-Domain Model 8

1.4 Equivalence of InputOutput and State-Space Models 8

1.4.1 State-Space and Transfer Function Model 8

1.4.2 Time-Domain Expression for the Output Response 8

1.4.3 State-Space and the Difference Equation Model 9

1.4.4 Observer Canonical Form 9

1.4.5 Characterization of the Model 10

1.4.6 Stability of (Discrete-Time) Systems 10

1.4.7 Minimum Phase System 11

1.4.8 Pole-Zero Locations and the Output Response 11

1.5 Deterministic Signals 11

1.5.1 Transfer Function Model 12

1.5.2 Difference Equation Model 12

1.5.3 State-Space Model 14

1.5.4 Expression for an Impulse Response 14

1.5.5 Periodic Signal 14

1.5.6 Periodic Impulse Train 15

1.5.7 A Finite Duration Signal 16

1.5.8 Model of a Class of All Signals 17

1.5.9 Examples of Deterministic Signals 18

1.6 Introduction to Random Signals 23

1.6.1 Stationary Random Signal 23

1.6.2 Joint PDF and Statistics of Random Signals 24

1.6.3 Ergodic Process 27

1.7 Model of Random Signals 28

1.7.1 White Noise Process 29

1.7.2 Colored Noise 30

1.7.3 Model of a Random Waveform 30

1.7.4 Classification of the Random Waveform 31

1.7.5 Frequency Response and Pole-Zero Locations 31

1.7.6 Illustrative Examples of Filters 36

1.7.7 Illustrative Examples of Random Signals 36

1.7.8 Pseudo Random Binary Sequence (PRBS) 38

1.8 Model of a System with Disturbance and Measurement Noise 41

1.8.1 InputOutput Model of the System 41

1.8.2 State-Space Model of the System 44

1.8.3 Illustrative Examples in Integrated System Model 47

1.9 Summary 50

References 54

Further Readings 54

2 Characterization of Signals: Correlation and Spectral Density 57

2.1 Introduction 57

2.2 Definitions of Auto- and Cross-Correlation (and Covariance) 58

2.2.1 Properties of Correlation 61

2.2.2 Normalized Correlation and Correlation Coefficient 66

2.3 Spectral Density: Correlation in the Frequency Domain 67

2.3.1 Z-transform of the Correlation Function 69

2.3.2 Expressions for Energy and Power Spectral Densities 71

2.4 Coherence Spectrum 74

2.5 Illustrative Examples in Correlation and Spectral Density 76

2.5.1 Deterministic Signals: Correlation and Spectral Density 76

2.5.2 Random Signals: Correlation and Spectral Density 87

2.6…