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E-raamat: Control System Analysis and Identification with MATLAB(R): Block Pulse and Related Orthogonal Functions

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  • Formaat: 386 pages
  • Ilmumisaeg: 09-Oct-2018
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351399562
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Control System Analysis and Identification with MATLAB(R): Block Pulse and Related Orthogonal FunctionsSuurem pilt
  • Formaat: 386 pages
  • Ilmumisaeg: 09-Oct-2018
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351399562
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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 Haar to sample-and-hold function





Includes examples and MATLAB codes with supporting numerical exampless.
List of Principal Symbols xiii
Preface xvii
Authors xxi
1 Block Pulse and Related Basis Functions 1(34)
1.1 Block Pulse and Related Basis Functions
1(1)
1.2 Orthogonal Functions and Their Properties
2(25)
1.2.1 Minimization of Mean Integral Square Error (MISE)
3(1)
1.2.2 Haar Functions
4(2)
1.2.3 Rademacher Functions
6(1)
1.2.4 Walsh Functions
7(4)
1.2.4.1 Relation between Walsh Functions and Rademacher Functions
9(1)
1.2.4.2 Numerical Example
10(1)
1.2.5 Slant Functions
11(1)
1.2.6 Block Pulse Functions (BPF)
11(3)
1.2.7 Relation among Haar, Walsh, and Block Pulse Functions
14(2)
1.2.8 Generalized Block Pulse Functions (GBPF)
16(4)
1.2.8.1 Advantages of Using Generalized BPF over Conventional BPF
19(1)
1.2.9 Pulse-Width Modulated Generalized Block Pulse Functions (PWM-GBPF)
20(3)
1.2.9.1 Conversion of a GBPF Set to a Pulse-Width Modulated (PWM) GBPF Set
20(2)
1.2.9.2 Principle of Representation of a Time Function via a Pulse-Width Modulated (PWM) GBPF Set
22(1)
1.2.10 Non-Optimal Block Pulse Functions (NOBPF)
23(1)
1.2.11 Delayed Unit Step Functions (DUSF)
23(4)
1.2.12 Sample-and-Hold Functions (SHF)
27(1)
1.3 BPF in Systems and Control
27(3)
References
30(4)
Study Problems
34(1)
2 Function Approximation via Block Pulse Function and Related Functions 35(20)
2.1 Block Pulse Functions: Properties
35(5)
2.1.1 Disjointedness
35(1)
2.1.2 Orthogonality
36(1)
2.1.3 Addition
36(2)
2.1.4 Subtraction
38(1)
2.1.5 Multiplication
39(1)
2.1.6 Division
40(1)
2.2 Function Approximation
40(9)
2.2.1 Using Block Pulse Functions
40(2)
2.2.1.1 Numerical Examples
41(1)
2.2.2 Using Generalized Block Pulse Functions (GBPF)
42(2)
2.2.2.1 Numerical Example
42(2)
2.2.3 Using Pulse-Width Modulated Generalized Block Pulse Functions (PWM-GBPF)
44(1)
2.2.3.1 Numerical Example
44(1)
2.2.4 Using Non-Optimal Block Pulse Functions (NOBPF)
45(1)
2.2.4.1 Numerical Example
45(1)
2.2.5 Using Delayed Unit Step Functions (DUSF)
46(1)
2.2.5.1 Numerical Example
47(1)
2.2.6 Using Sample-and-Hold Functions (SHF)
47(9)
2.2.6.1 Numerical Example
47(2)
2.3 Error Analysis for Function Approximation in BPF Domain
49(1)
2.4 Conclusion
50(1)
References
51(1)
Study Problems
52(3)
3 Block Pulse Domain Operational Matrices for Integration and Differentiation 55(34)
3.1 Operational Matrix for Integration
56(7)
3.1.1 Nature of Integration of a Function in BPF Domain Using the Operational Matrix P
60(1)
3.1.2 Exact Integration and Operational Matrix Based Integration of a BPF Series Expanded Function
61(1)
3.1.3 Numerical Example
62(1)
3.2 Operational Matrices for Integration in Generalized Block Pulse Function Domain
63(4)
3.2.1 Numerical Example
65(2)
3.3 Improvement of the Integration Operational Matrix of First Order
67(8)
3.3.1 Numerical Examples
73(2)
3.4 One-Shot Operational Matrices for Repeated Integration
75(3)
3.4.1 Numerical Example
77(1)
3.5 Operational Matrix for Differentiation
78(2)
3.5.1 Numerical Example
79(1)
3.6 Operational Matrices for Differentiation in Generalized Block Pulse Function Domain
80(1)
3.6.1 Numerical Example
81(1)
3.7 One-Shot Operational Matrices for Repeated Differentiation
81(3)
3.7.1 Numerical Example
82(2)
3.8 Conclusion
84(2)
References
86(1)
Study Problems
87(2)
4 Operational Transfer Functions for System Analysis 89(24)
4.1 Walsh Operational Transfer Function (WOTF)
89(2)
4.2 Block Pulse Operational Transfer Function (BPOTF) for System Analysis
91(6)
4.2.1 Numerical Examples
92(5)
4.3 Oscillatory Phenomenon in Block Pulse Domain Analysis of First-Order Systems
97(3)
4.3.1 Numerical Example
98(2)
4.4 Nature of Expansion of the BPOTF of a First-Order Plant
100(1)
4.5 Modified BPOTF (MBPOTF) Using All-Integrator Approach for System Analysis
101(8)
4.5.1 First-Order Plant
102(4)
4.5.2 Second-Order Plant with Imaginary Roots
106(1)
4.5.3 Second-Order Plant with Complex Roots
107(2)
4.6 Error Due to MBPOTF Approach
109(1)
4.7 Conclusion
110(1)
References
111(1)
Study Problems
112(1)
5 System Analysis and Identification Using Convolution and "Deconvolution" in BPF Domain 113(30)
5.1 The Convolution Process in BPF Domain
113(8)
5.1.1 Numerical Examples
119(2)
5.2 Identification of an Open Loop System via "Deconvolution"
121(3)
5.2.1 Numerical Example
123(1)
5.3 Numerical Instability of the "Deconvolution" Operation: Its Mathematical Basis
124(8)
5.4 Identification of a Closed Loop System
132(6)
5.4.1 Numerical Example
135(1)
5.4.2 Discussion on the Reliability of Result
136(2)
5.5 Conclusion
138(1)
References
139(1)
Study Problems
140(3)
6 Delayed Unit Step Functions (DUSF) for System Analysis and Fundamental Nature of the Block Pulse Function (BPF) Set 143(32)
6.1 The Set of DUSF and the Operational Matrix for Integration
144(6)
6.1.1 Alternative Way to Derive the Operational Matrix for Integration
147(2)
6.1.2 Numerical Example
149(1)
6.2 Block Pulse Function versus Delayed Unit Step Function: A Comparative Study
150(10)
6.2.1 Function Approximation: BPF versus DUSF
150(2)
6.2.2 Analytical Assessment
152(8)
6.2.2.1 Identification of the Last Member of the DUSF Set
152(1)
6.2.2.2 Operational Matrix for Integration
153(4)
6.2.2.3 Operational Matrix for Integration and Related Transformation Matrices
157(3)
6.3 Stretch Matrix in DUSF Domain
160(4)
6.3.1 Stretch Matrices in Walsh and BPF Domain
162(1)
6.3.2 Numerical Example
163(1)
6.4 Solution of a Functional Differential Equation Using DUSF
164(4)
6.4.1 Numerical Example
168(1)
6.5 Conclusion
168(3)
References
171(1)
Study Problems
172(3)
7 Sample-and-Hold Functions (SHFs) for System Analysis 175(26)
7.1 Brief Review of Sample-and-Hold Functions (SHF)
176(1)
7.2 Analysis of Control Systems with Sample-and-Hold Using the Operational Transfer Function Approach
176(5)
7.2.1 Sample-and-Hold Matrix for SHF-Based Analysis
179(2)
7.3 Operational Matrix for Integration in SHF Domain
181(3)
7.3.1 Numerical Example
184(1)
7.4 One-Shot Operational Matrices for Repeated Integration
184(3)
7.5 System Analysis Using One-Shot Operational Matrices and Operational Transfer Function
187(8)
7.5.1 First Order Plant
187(3)
7.5.2 nth Order Plant with Single Pole of Multiplicity n
190(1)
7.5.3 Second-Order Plant with Imaginary Roots
191(3)
7.5.4 Second-Order Plant with Complex Roots
194(1)
7.6 Error Analysis: A Comparison between SHF and BPF
195(3)
7.6.1 Error Estimate for Sample-and-Hold Function Domain Approximation
196(1)
7.6.2 Error Estimate for Block Pulse Function Domain Approximation
197(1)
7.6.3 A Comparative Study
197(1)
7.7 Conclusion
198(1)
References
199(1)
Study Problems
200(1)
8 Discrete Time System Analysis Using a Set of Delta Functions (DFs) 201(20)
8.1 A Set of Mutually Disjoint Delta Functions
201(3)
8.2 Delta Function Domain Operational Matrices for Integration
204(3)
8.2.1 Numerical Example
206(1)
8.3 One-Shot Operational Matrices for Repeated Integration
207(1)
8.4 Analysis of Discrete SISO Systems Using One-Shot Operational Matrices and Delta Operational Transfer Function
208(10)
8.4.1 First-Order Plant
210(3)
8.4.2 nth-Order Plant with Single Pole of Multiplicity n
213(1)
8.4.3 Second-Order Plant with Imaginary Roots
214(2)
8.4.4 Second-Order Plant with Complex Roots
216(2)
8.5 Conclusion
218(1)
References
218(1)
Study Problems
219(2)
9 Non-Optimal Block Pulse Functions (NOBPFs) for System Analysis and Identification 221(46)
9.1 Basic Properties of Non-Optimal Block Pulse Functions
221(7)
9.1.1 Disjointedness
223(1)
9.1.2 Orthogonality
223(1)
9.1.3 Addition
224(1)
9.1.4 Subtraction
225(2)
9.1.5 Multiplication
227(1)
9.1.6 Division
227(1)
9.2 From "Optimal" Coefficients to "Non-Optimal" Coefficients
228(1)
9.3 Function Approximation Using Non-Optimal Block Pulse Functions (NOBPF)
229(2)
9.3.1 Numerical Examples
230(1)
9.4 Operational Matrices for Integration
231(1)
9.5 The Process of Convolution and "Deconvolution"
232(1)
9.6 Analysis of an Open-Loop System via Convolution
233(11)
9.6.1 First-Order System
233(2)
9.6.2 Undamped Second-Order System
235(3)
9.6.3 Underdamped Second-Order System
238(6)
9.7 Identification of an Open-Loop System via "Deconvolution"
244(12)
9.7.1 First-Order System
244(1)
9.7.2 Undamped Second-Order System
245(4)
9.7.3 Underdamped Second-Order System
249(7)
9.8 Identification of a Closed-Loop System via "Deconvolution"
256(4)
9.8.1 Using "Optimal" BPF Coefficients
256(1)
9.8.2 Using "Non-Optimal" BPF Coefficients
257(3)
9.9 Error Analysis
260(2)
9.10 Conclusion
262(1)
References
263(1)
Study Problems
264(3)
10 System Analysis and Identification Using Linearly Pulse-Width Modulated Generalized Block Pulse Functions (LPWM-GBPF) 267(26)
10.1 Conversion of a GBPF Set to a LPWM-GBPF Set
268(1)
10.2 Representation of Time Functions via LPWM-GBPF Set
269(1)
10.3 Convolution Process in LPWM-GBPF Domain
269(12)
10.3.1 Numerical Example
278(3)
10.4 Linear Feedback System Identification Using Generalized Convolution Matrix (GCVM)
281(4)
10.4.1 Numerical Example
282(3)
10.5 Error Analysis
285(3)
10.6 Conclusion
288(1)
References
289(1)
Study Problems
290(3)
Appendix A: Introduction to Linear Algebra 293(10)
Appendix B: Selected MATLAB Programs 303(58)
Index 361
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.
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