Cover image for Control System Analysis and Identification with MATLAB : Block Pulse and Related Orthogonal Functions
Title:
Control System Analysis and Identification with MATLAB : Block Pulse and Related Orthogonal Functions
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Physical Description:
xxii, 364 pages : illustrations ; 24 cm
ISBN:
9781138303225

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33000000007296 TJ213 D43 2018 Open Access Book Book
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Summary

Summary

Key Features:

The Book Covers recent results of the traditional block pulse and other functions related material Discusses 'functions related to block pulse functions' extensively along with their applications Contains analysis and identification of linear time-invariant systems, scaled system, and sampled-data system Presents an overview of piecewise constant orthogonal functions starting from Ha ar to sample-and-hold function Includes examples and MATLAB codes with supporting numerical exampless.


Author Notes

Anish Deb(b.1951) did his B. Tech. (1974), M. Tech. (1976) and Ph.D. (Tech.) degree (1990) from the Department of Applied Physics, University of Calcutta. He started his career as a design engineer (1978) in industry and joined the Department of Applied Physics, University of Calcutta as Lecturer in 1983. In 1990, he became Reader and later became a Professor (1998) in the same Department.
He has retired from the University of Calcutta in November 2016 and presently is a Professor in the Department of Electrical Engineering, Budge Budge Institute of Technology, Kolkata.
His research interest includes automatic control in general and application of 'alternative' orthogonal functions like Walsh functions, block pulse functions, triangular functions etc., in systems and control. He has published more than seventy (70) research papers in different national and international journals and conferences. He is the principal author of the books 'Triangular orthogonal functions for the analysis of continuous time systems' published by Elsevier (India) in 2007 and Anthem Press (UK) in 2011, 'Power Electronic Systems: Walsh Analysis with MATLAB' published by CRC Press (USA) in 2014 and 'Analysis and Identification of Time-Invariant Systems, Time-Varying Systems and Multi-Delay Systems using Orthogonal Hybrid Functions: Theory and Algorithms with MATLAB' published by Springer (Switzerland) in 2016.

Srimanti Roy Choudhury(b.1984) did her B. Tech. (2006) from Jalpaiguri Government Engineering College, under West Bengal University of Technology and M. Tech. (2010) from the Department of Applied Physics, University of Calcutta.
During 2006 to 2007, she worked in the Department of Electrical Engineering of Jalpaiguri Government Engineering College as a part-time Faculty. She also acted as a visiting Faculty during 2012-2013 in the Department of Polymer Science & Technology and in 2015-2016 the Department of Applied Physics, University of Calcutta. Presently she is an Assistant Professor (from 2010) in the Department of Electrical Engineering, Budge Budge Institute of Technology, Kolkata.
Her research area includes control theory in general and application of 'alternative' orthogonal functions like Walsh functions, block pulse functions, triangular functions etc., in different areas of systems and control. She has been pursuing her Ph. D. in the Department of Applied Physics, University of Calcutta and is about to submit her Doctoral thesis in a couple of months.
She has published eight (8) research papers in different national and international journals and conferences. She is the second author of the book 'Analysis and Identification of Time-Invariant Systems, Time-Varying Systems and Multi-Delay Systems using Orthogonal Hybrid Functions: Theory and Algorithms with MATLAB' published by Springer (Switzerland) in 2016.


Table of Contents

List of Principal Symbolsp. xiii
Prefacep. xvii
Authorsp. xxi
1 Block Pulse and Related Basis Functionsp. 1
1.1 Block Pulse and Related Basis Functionsp. 1
1.2 Orthogonal Functions and Their Propertiesp. 2
1.2.1 Minimization of Mean Integral Square Error (MISE)p. 3
1.2.2 Haar Functionsp. 4
1.2.3 Rademacher Functionsp. 6
1.2.4 Walsh Functionsp. 7
1.2.4.1 Relation between Walsh Functions and Rademacher Functionsp. 9
1.2.4.2 Numerical Examplep. 10
1.2.5 Slant Functionsp. 11
1.2.6 Block Pulse Functions (BPF)p. 11
1.2.7 Relation among Haar, Walsh, and Block Pulse Functionsp. 14
1.2.8 Generalized Block Pulse Functions (GBPF)p. 16
1.2.8.1 Advantages of Using Generalized BPF over Conventional BPFp. 19
1.2.9 Pulse Width Modulated Generalized Block Pulse Functions (PWM-GBPF)p. 20
1.2.9.1 Conversion of a GBPF Set to a Pulse-Width Modulated (PWM) GBPF Setp. 20
1.2.9.2 Principle of Representation of a Time Function via a Pulse-Width Modulated (PWM) GBPF Setp. 22
1.2.10 Non-Optimal Block Pulse Functions (NOBPF)p. 23
1.2.11 Delayed Unit Step Functions (DUSF)p. 23
1.2.12 Sample-and-Hold Functions (SHF)p. 27
1.3 BPF in Systems and Controlp. 27
Referencesp. 30
Study Problemsp. 34
2 Function Approximation via Block Pulse Function and Related Functionsp. 35
2.1 Block Pulse Functions: Propertiesp. 35
2.1.1 Disjointednessp. 35
2.1.2 Orthogonalityp. 36
2.1.3 Additionp. 36
2.1.4 Subtractionp. 38
2.1.5 Multiplicationp. 39
2.1.6 Divisionp. 40
2.2 Function Approximationp. 40
2.2.1 Using Block Pulse Functionsp. 40
2.2.1.1 Numerical Examplesp. 41
2.2.2 Using Generalized Block Pulse Functions (GBPF)p. 42
2.2.2.1 Numerical Examplep. 42
2.2.3 Using Pulse-Width Modulated Generalized Block Pulse Functions (PWM-GBPF)p. 44
2.2.3.1 Numerical Examplep. 44
2.2.4 Using Non-Optimal Block Pulse Functions (NOBPF)p. 45
2.2.4.1 Numerical Examplep. 45
2.2.5 Using Delayed Unit Step Functions (DUSF)p. 46
2.2.5.1 Numerical Examplep. 47
2.2.6 Using Sample-and-Hold Functions (SHF)p. 47
2.2.6.1 Numerical Examplep. 47
2.3 Error Analysis for Function Approximation in BPF Domainp. 49
2.4 Conclusionp. 50
Referencesp. 51
Study Problemsp. 52
3 Block Pulse Domain Operational Matrices for Integration and Differentiationp. 55
3.1 Operational Matrix for Integrationp. 56
3.1.1 Nature of Integration of a Function in BPF Domain Using the Operational Matrix Pp. 60
3.1.2 Exact Integration and Operational Matrix Based Integration of a BPF Series Expanded Functionp. 61
3.1.3 Numerical Examplep. 62
3.2 Operational Matrices for Integration in Generalized Block Pulse Function Domainp. 63
3.2.1 Numerical Examplep. 65
3.3 Improvement of the Integration Operational Matrix of First Orderp. 67
3.3.1 Numerical Examplesp. 73
3.4 One-Shot Operational Matrices for Repeated Integrationp. 75
3.4.1 Numerical Examplep. 77
3.5 Operational Matrix for Differentiationp. 78
3.5.1 Numerical Examplep. 79
3.6 Operational Matrices for Differentiation in Generalized Block Pulse Function Domainp. 80
3.6.1 Numerical Examplep. 81
3.7 One-Shot Operational Matrices for Repeated Differentiationp. 81
3.7.1 Numerical Examplep. 82
3.8 Conclusionp. 84
Referencesp. 86
Study Problemsp. 87
4 Operational Transfer Functions for System Analysisp. 89
4.1 Walsh Operational Transfer Function (WOTF)p. 89
4.2 Block Pulse Operational Transfer Function (BPOTF) for System Analysisp. 91
4.2.1 Numerical Examplesp. 92
4.3 Oscillatory Phenomenon in Block Pulse Domain Analysis of First-Order Systemsp. 97
4.3.1 Numerical Examplep. 98
4.4 Nature of Expansion of the BPOTF of a First-Order Plantp. 100
4.5 Modified BPOTF (MBPOTF) Using All-Integrator Approach for System Analysisp. 101
4.5.1 First-Order Plantp. 102
4.5.2 Second-Order Plant with Imaginary Rootsp. 106
4.5.3 Second-Order Plant with Complex Rootsp. 107
4.6 Error Due to MBPOTF Approachp. 109
4.7 Conclusionp. 110
Referencesp. 111
Study Problemsp. 112
5 System Analysis and Identification Using Convolution and "Deconvolution" in BPF Domainp. 113
5.1 The Convolution Process in BPF Domainp. 113
5.1.1 Numerical Examplesp. 119
5.2 Identification of an Open Loop System via "Deconvolution"p. 121
5.2.1 Numerical Examplep. 123
5.3 Numerical Instability of the "Deconvolution" Operation: Its Mathematical Basisp. 124
5.4 Identification of a Closed Loop Systemp. 132
5.4.1 Numerical Examplep. 135
5.4.2 Discussion on the Reliability of Resultp. 136
5.5 Conclusionp. 138
Referencesp. 139
Study Problemsp. 140
6 Delayed Unit Step Functions (DUSF) for System Analysis and Fundamental Nature of the Block Pulse Function (BPF) Setp. 143
6.1 The Set of DUSF and the Operational Matrix for Integrationp. 144
6.1.1 Alternative Way to Derive the Operational Matrix for Integrationp. 147
6.1.2 Numerical Examplep. 149
6.2 Block Pulse Function versus Delayed Unit Step Function: A Comparative Studyp. 150
6.2.1 Function Approximation: BPF versus DUSFp. 150
6.2.2 Analytical Assessmentp. 152
6.2.2.1 Identification of the Last Member of the DUSF Setp. 152
6.2.2.2 Operational Matrix for Integrationp. 153
6.2.2.3 Operational Matrix for Integration and Related Transformation Matricesp. 157
6.3 Stretch Matrix in DUSF Domainp. 160
6.3.1 Stretch Matrices in Walsh and BPF Domainp. 162
6.3.2 Numerical Examplep. 163
6.4 Solution of a Functional Differential Equation Using DUSFp. 164
6.4.1 Numerical Examplep. 168
6.5 Conclusionp. 168
Referencesp. 171
Study Problemsp. 172
7 Sample-and-Hold Functions (SHFs) for System Analysisp. 175
7.1 Brief Review of Sample-and-Hold Functions (SHF)p. 176
7.2 Analysis of Control Systems with Sample-and-Hold Using the Operational Transfer Function Approachp. 176
7.2.1 Sample-and-Hold Matrix for SHE-Based Analysisp. 179
7.3 Operational Matrix for Integration in SHF Domainp. 181
7.3.1 Numerical Examplep. 184
7.4 One-Shot Operational Matrices for Repeated Integrationp. 184
7.5 System Analysis Using One-Shot Operational Matrices and Operational Transfer Functionp. 187
7.5.1 First Order Plantp. 187
7.5.2 nth Order Plant with Single Pole of Multiplicity np. 190
7.5.3 Second-Order Plant with Imaginary Rootsp. 191
7.5.4 Second-Order Plant with Complex Rootsp. 194
7.6 Error Analysis: A Comparison between SHF and BPFp. 195
7.6.1 Error Estimate for Sample-and-Hold Function Domain Approximationp. 196
7.6.2 Error Estimate for Block Pulse Function Domain Approximationp. 197
7.6.3 A Comparative Studyp. 197
7.7 Conclusionp. 198
Referencesp. 199
Study Problemsp. 200
8 Discrete Time System Analysis Using a Set of Delta Functions (DFs)p. 201
8.1 A Set of Mutually Disjoint Delta Functionsp. 201
8.2 Delta Function Domain Operational Matrices for Integrationp. 204
8.2.1 Numerical Examplep. 206
8.3 One-Shot Operational Matrices for Repeated Integrationp. 207
8.4 Analysis of Discrete SISO Systems Using One-Shot Operational Matrices and Delta Operational Transfer Functionp. 208
8.4.1 First-Order Plantp. 210
8.4.2 nth-Order Plant with Single Pole of Multiplicity np. 213
8.4.3 Second-Order Plant with Imaginary Rootsp. 214
8.4.4 Second-Order Plant with Complex Rootsp. 216
8.5 Conclusionp. 218
Referencesp. 218
Study Problemsp. 219
9 Non-Optimal Block Pulse Functions (NOBPFs) for System Analysis and Identificationp. 221
9.1 Basic Properties of Non-Optimal Block Pulse Functionsp. 221
9.1.1 Disjointednessp. 223
9.1.2 Orthogonalityp. 223
9.1.3 Additionp. 224
9.1.4 Subtractionp. 225
9.1.5 Multiplicationp. 227
9.1.6 Divisionp. 227
9.2 From "Optimal" Coefficients to "Non-Optimal" Coefficientsp. 228
9.3 Function Approximation Using Non-Optimal Block Pulse Functions (NOBPF)p. 229
9.3.1 Numerical Examplesp. 230
9.4 Operational Matrices for Integrationp. 231
9.5 The Process of Convolution and "Deconvolution"p. 232
9.6 Analysis of an Open-Loop System via Convolutionp. 233
9.6.1 First-Order Systemp. 233
9.6.2 Undamped Second-Order Systemp. 235
9.6.3 Underdamped Second-Order Systemp. 238
9.7 Identification of an Open-Loop System via "Deconvolution"p. 244
9.7.1 First-Order Systemp. 244
9.7.2 Undamped Second-Order Systemp. 245
9.7.3 Underdamped Second-Order Systemp. 249
9.8 Identification of a Closed-Loop System via "Deconvolution"p. 256
9.8.1 Using "Optimal" BPF Coefficientsp. 256
9.8.2 Using "Non-Optimal" BPF Coefficientsp. 257
9.9 Error Analysisp. 260
9.10 Conclusionp. 262
Referencesp. 263
Study Problemsp. 264
10 System Analysis and Identification Using Linearly Pulse-Width Modulated Generalized Block Pulse Functions (LPWM-GBPF)p. 267
10.1 Conversion of a GBPF Set to a LPWM-GBPF Setp. 268
10.2 Representation of Time Functions via LPWM-GBPF Setp. 269
10.3 Convolution Process in LPWM-GBPF Domainp. 269
10.3.1 Numerical Examplep. 278
10.4 Linear Feedback System Identification Using Generalized Convolution Matrix (GCVM)p. 281
10.4.1 Numerical Examplep. 282
10.5 Error Analysisp. 285
10.6 Conclusionp. 288
Referencesp. 289
Study Problemsp. 290
Appendix A Introduction to Linear Algebrap. 293
Appendix B Selected MATLAB Programsp. 303
Indexp. 361