Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
---|---|---|---|---|---|
Searching... | 33000000007296 | TJ213 D43 2018 | Open Access Book | Book | Searching... |
On Order
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 Symbols | p. xiii |
Preface | p. xvii |
Authors | p. xxi |
1 Block Pulse and Related Basis Functions | p. 1 |
1.1 Block Pulse and Related Basis Functions | p. 1 |
1.2 Orthogonal Functions and Their Properties | p. 2 |
1.2.1 Minimization of Mean Integral Square Error (MISE) | p. 3 |
1.2.2 Haar Functions | p. 4 |
1.2.3 Rademacher Functions | p. 6 |
1.2.4 Walsh Functions | p. 7 |
1.2.4.1 Relation between Walsh Functions and Rademacher Functions | p. 9 |
1.2.4.2 Numerical Example | p. 10 |
1.2.5 Slant Functions | p. 11 |
1.2.6 Block Pulse Functions (BPF) | p. 11 |
1.2.7 Relation among Haar, Walsh, and Block Pulse Functions | p. 14 |
1.2.8 Generalized Block Pulse Functions (GBPF) | p. 16 |
1.2.8.1 Advantages of Using Generalized BPF over Conventional BPF | p. 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 Set | p. 20 |
1.2.9.2 Principle of Representation of a Time Function via a Pulse-Width Modulated (PWM) GBPF Set | p. 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 Control | p. 27 |
References | p. 30 |
Study Problems | p. 34 |
2 Function Approximation via Block Pulse Function and Related Functions | p. 35 |
2.1 Block Pulse Functions: Properties | p. 35 |
2.1.1 Disjointedness | p. 35 |
2.1.2 Orthogonality | p. 36 |
2.1.3 Addition | p. 36 |
2.1.4 Subtraction | p. 38 |
2.1.5 Multiplication | p. 39 |
2.1.6 Division | p. 40 |
2.2 Function Approximation | p. 40 |
2.2.1 Using Block Pulse Functions | p. 40 |
2.2.1.1 Numerical Examples | p. 41 |
2.2.2 Using Generalized Block Pulse Functions (GBPF) | p. 42 |
2.2.2.1 Numerical Example | p. 42 |
2.2.3 Using Pulse-Width Modulated Generalized Block Pulse Functions (PWM-GBPF) | p. 44 |
2.2.3.1 Numerical Example | p. 44 |
2.2.4 Using Non-Optimal Block Pulse Functions (NOBPF) | p. 45 |
2.2.4.1 Numerical Example | p. 45 |
2.2.5 Using Delayed Unit Step Functions (DUSF) | p. 46 |
2.2.5.1 Numerical Example | p. 47 |
2.2.6 Using Sample-and-Hold Functions (SHF) | p. 47 |
2.2.6.1 Numerical Example | p. 47 |
2.3 Error Analysis for Function Approximation in BPF Domain | p. 49 |
2.4 Conclusion | p. 50 |
References | p. 51 |
Study Problems | p. 52 |
3 Block Pulse Domain Operational Matrices for Integration and Differentiation | p. 55 |
3.1 Operational Matrix for Integration | p. 56 |
3.1.1 Nature of Integration of a Function in BPF Domain Using the Operational Matrix P | p. 60 |
3.1.2 Exact Integration and Operational Matrix Based Integration of a BPF Series Expanded Function | p. 61 |
3.1.3 Numerical Example | p. 62 |
3.2 Operational Matrices for Integration in Generalized Block Pulse Function Domain | p. 63 |
3.2.1 Numerical Example | p. 65 |
3.3 Improvement of the Integration Operational Matrix of First Order | p. 67 |
3.3.1 Numerical Examples | p. 73 |
3.4 One-Shot Operational Matrices for Repeated Integration | p. 75 |
3.4.1 Numerical Example | p. 77 |
3.5 Operational Matrix for Differentiation | p. 78 |
3.5.1 Numerical Example | p. 79 |
3.6 Operational Matrices for Differentiation in Generalized Block Pulse Function Domain | p. 80 |
3.6.1 Numerical Example | p. 81 |
3.7 One-Shot Operational Matrices for Repeated Differentiation | p. 81 |
3.7.1 Numerical Example | p. 82 |
3.8 Conclusion | p. 84 |
References | p. 86 |
Study Problems | p. 87 |
4 Operational Transfer Functions for System Analysis | p. 89 |
4.1 Walsh Operational Transfer Function (WOTF) | p. 89 |
4.2 Block Pulse Operational Transfer Function (BPOTF) for System Analysis | p. 91 |
4.2.1 Numerical Examples | p. 92 |
4.3 Oscillatory Phenomenon in Block Pulse Domain Analysis of First-Order Systems | p. 97 |
4.3.1 Numerical Example | p. 98 |
4.4 Nature of Expansion of the BPOTF of a First-Order Plant | p. 100 |
4.5 Modified BPOTF (MBPOTF) Using All-Integrator Approach for System Analysis | p. 101 |
4.5.1 First-Order Plant | p. 102 |
4.5.2 Second-Order Plant with Imaginary Roots | p. 106 |
4.5.3 Second-Order Plant with Complex Roots | p. 107 |
4.6 Error Due to MBPOTF Approach | p. 109 |
4.7 Conclusion | p. 110 |
References | p. 111 |
Study Problems | p. 112 |
5 System Analysis and Identification Using Convolution and "Deconvolution" in BPF Domain | p. 113 |
5.1 The Convolution Process in BPF Domain | p. 113 |
5.1.1 Numerical Examples | p. 119 |
5.2 Identification of an Open Loop System via "Deconvolution" | p. 121 |
5.2.1 Numerical Example | p. 123 |
5.3 Numerical Instability of the "Deconvolution" Operation: Its Mathematical Basis | p. 124 |
5.4 Identification of a Closed Loop System | p. 132 |
5.4.1 Numerical Example | p. 135 |
5.4.2 Discussion on the Reliability of Result | p. 136 |
5.5 Conclusion | p. 138 |
References | p. 139 |
Study Problems | p. 140 |
6 Delayed Unit Step Functions (DUSF) for System Analysis and Fundamental Nature of the Block Pulse Function (BPF) Set | p. 143 |
6.1 The Set of DUSF and the Operational Matrix for Integration | p. 144 |
6.1.1 Alternative Way to Derive the Operational Matrix for Integration | p. 147 |
6.1.2 Numerical Example | p. 149 |
6.2 Block Pulse Function versus Delayed Unit Step Function: A Comparative Study | p. 150 |
6.2.1 Function Approximation: BPF versus DUSF | p. 150 |
6.2.2 Analytical Assessment | p. 152 |
6.2.2.1 Identification of the Last Member of the DUSF Set | p. 152 |
6.2.2.2 Operational Matrix for Integration | p. 153 |
6.2.2.3 Operational Matrix for Integration and Related Transformation Matrices | p. 157 |
6.3 Stretch Matrix in DUSF Domain | p. 160 |
6.3.1 Stretch Matrices in Walsh and BPF Domain | p. 162 |
6.3.2 Numerical Example | p. 163 |
6.4 Solution of a Functional Differential Equation Using DUSF | p. 164 |
6.4.1 Numerical Example | p. 168 |
6.5 Conclusion | p. 168 |
References | p. 171 |
Study Problems | p. 172 |
7 Sample-and-Hold Functions (SHFs) for System Analysis | p. 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 Approach | p. 176 |
7.2.1 Sample-and-Hold Matrix for SHE-Based Analysis | p. 179 |
7.3 Operational Matrix for Integration in SHF Domain | p. 181 |
7.3.1 Numerical Example | p. 184 |
7.4 One-Shot Operational Matrices for Repeated Integration | p. 184 |
7.5 System Analysis Using One-Shot Operational Matrices and Operational Transfer Function | p. 187 |
7.5.1 First Order Plant | p. 187 |
7.5.2 nth Order Plant with Single Pole of Multiplicity n | p. 190 |
7.5.3 Second-Order Plant with Imaginary Roots | p. 191 |
7.5.4 Second-Order Plant with Complex Roots | p. 194 |
7.6 Error Analysis: A Comparison between SHF and BPF | p. 195 |
7.6.1 Error Estimate for Sample-and-Hold Function Domain Approximation | p. 196 |
7.6.2 Error Estimate for Block Pulse Function Domain Approximation | p. 197 |
7.6.3 A Comparative Study | p. 197 |
7.7 Conclusion | p. 198 |
References | p. 199 |
Study Problems | p. 200 |
8 Discrete Time System Analysis Using a Set of Delta Functions (DFs) | p. 201 |
8.1 A Set of Mutually Disjoint Delta Functions | p. 201 |
8.2 Delta Function Domain Operational Matrices for Integration | p. 204 |
8.2.1 Numerical Example | p. 206 |
8.3 One-Shot Operational Matrices for Repeated Integration | p. 207 |
8.4 Analysis of Discrete SISO Systems Using One-Shot Operational Matrices and Delta Operational Transfer Function | p. 208 |
8.4.1 First-Order Plant | p. 210 |
8.4.2 nth-Order Plant with Single Pole of Multiplicity n | p. 213 |
8.4.3 Second-Order Plant with Imaginary Roots | p. 214 |
8.4.4 Second-Order Plant with Complex Roots | p. 216 |
8.5 Conclusion | p. 218 |
References | p. 218 |
Study Problems | p. 219 |
9 Non-Optimal Block Pulse Functions (NOBPFs) for System Analysis and Identification | p. 221 |
9.1 Basic Properties of Non-Optimal Block Pulse Functions | p. 221 |
9.1.1 Disjointedness | p. 223 |
9.1.2 Orthogonality | p. 223 |
9.1.3 Addition | p. 224 |
9.1.4 Subtraction | p. 225 |
9.1.5 Multiplication | p. 227 |
9.1.6 Division | p. 227 |
9.2 From "Optimal" Coefficients to "Non-Optimal" Coefficients | p. 228 |
9.3 Function Approximation Using Non-Optimal Block Pulse Functions (NOBPF) | p. 229 |
9.3.1 Numerical Examples | p. 230 |
9.4 Operational Matrices for Integration | p. 231 |
9.5 The Process of Convolution and "Deconvolution" | p. 232 |
9.6 Analysis of an Open-Loop System via Convolution | p. 233 |
9.6.1 First-Order System | p. 233 |
9.6.2 Undamped Second-Order System | p. 235 |
9.6.3 Underdamped Second-Order System | p. 238 |
9.7 Identification of an Open-Loop System via "Deconvolution" | p. 244 |
9.7.1 First-Order System | p. 244 |
9.7.2 Undamped Second-Order System | p. 245 |
9.7.3 Underdamped Second-Order System | p. 249 |
9.8 Identification of a Closed-Loop System via "Deconvolution" | p. 256 |
9.8.1 Using "Optimal" BPF Coefficients | p. 256 |
9.8.2 Using "Non-Optimal" BPF Coefficients | p. 257 |
9.9 Error Analysis | p. 260 |
9.10 Conclusion | p. 262 |
References | p. 263 |
Study Problems | p. 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 Set | p. 268 |
10.2 Representation of Time Functions via LPWM-GBPF Set | p. 269 |
10.3 Convolution Process in LPWM-GBPF Domain | p. 269 |
10.3.1 Numerical Example | p. 278 |
10.4 Linear Feedback System Identification Using Generalized Convolution Matrix (GCVM) | p. 281 |
10.4.1 Numerical Example | p. 282 |
10.5 Error Analysis | p. 285 |
10.6 Conclusion | p. 288 |
References | p. 289 |
Study Problems | p. 290 |
Appendix A Introduction to Linear Algebra | p. 293 |
Appendix B Selected MATLAB Programs | p. 303 |
Index | p. 361 |