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Transfer function identification from impulse response via a new set of orthogonal hybrid functions (HF)

APPLIED MATHEMATICS AND COMPUTATION 2012年第9期218卷 4760-4787页

作者： Deb, Anish Sarkar, Gautam Mandal, Priyaranjan Biswas, Amitava Ganguly, Anindita Biswas, Debasish Jadavpur Univ Dept Mech Engn Kolkata 700032 India Univ Calcutta Dept Appl Phys Kolkata 700009 India Acad Technol Dept Elect Engn Aedconagar 712121 Hooghly India Techno India Coll Technol Dept Elect Engn Kolkata 700156 India

The present work proposes a new set of hybrid functions (HF) which evolved from the synthesis of sample-and-hold functions (SHF) and triangular functions (TF). Traditional block pulse functions (BPF) still continue to be attractive to many researchers in the arena of control theory. Block pulse functions also gave birth to a few useful variants. Two such variants are SHF and TF. The former is efficient for analyzing sample-and-hold control systems, while triangular functions established their superiority in obtaining piecewise linear solution of various control problems. After developing the basic theory of HF, a few square integrable functions are approximated via this set in a piecewise linear manner. For such approximation, it is shown, the mean integral square error (MISE) is much less than block pulse function based approximation. The operational matrices for integration in HF domain are also derived. Finally, this new set is employed for solving identification problem from impulse response data. The results are compared with the solutions obtained via BPF, SHF, TF, etc. and many illustrations are presented. (C) 2011 Elsevier Inc. All rights reserved.

关键词： sample-and-hold functions Triangular functions Hybrid functions Function approximation Operational matrices Identification

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Computation of Convolution via A New Set of Orthogonal Hybrid functions (HF) for Linear Control System Analysis and Identification

Computation of Convolution via A New Set of Orthogonal Hybri...

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Annual IEEE India Conference (INDICON)

作者： Deb, Anish Sarkar, Gautam Ganguly, Anindita Biswas, Amitava Univ Calcutta Dept Appl Phys 92 APC Rd Kolkata 700009 India St Thomas Coll Engn Technol Dept Elect Engn Kolkata 700023 India Acad Technol Dept Elect Engn Hooghly W Bengal India

ISBN: (纸本)9781467322706;9781467322713

The present work proposes application of a new set of orthogonal hybrid functions (HF) which evolved from the synthesis of orthogonal sample-and-hold functions (SHF) and orthogonal triangular functions (TF). This HF set is employed for determining the result of convolution of two time functions and the result has been used for solving linear control system analysis and synthesis problems. The theory is supported by examples and the results are compared with the exact solutions.

关键词： sample-and-hold functions Triangular functions Hybrid functions Analysis Synthesis

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Numerical solution of third order linear differential equations using generalized one-shot operational matrices in orthogonal hybrid function domain

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APPLIED MATHEMATICS AND COMPUTATION 2012年第4期219卷 1485-1514页

作者： Deb, Anish Ganguly, Anindita Sarkar, Gautam Biswas, Amitava Jadavpur Univ Dept Mech Engn Kolkata 700032 India Univ Calcutta Dept Appl Phys Kolkata 700009 W Bengal India Acad Technol Dept Elect Engn Hooghly India

The present work proposes a new set of orthogonal hybrid functions (HF) which evolved from synthesis of orthogonal sample-and-hold functions (SHF) and triangular functions (TF). The HF set is used to approximate a time function in a piecewise linear manner. For such approximation, the mean integral square error (MISE) is much less than block pulse function based approximation which always provides staircase solutions and it is found that HF based approximation is a strong contender of approximations based upon orthogonal polynomials like Legendre polynomials. The respective MISE's and elapsed times for MISE computations for these three kinds of approximations are also studied in detail. The one-shot operational matrices for integration of different orders in HF domain are also derived. These matrices are employed for more accurate multiple integration. An example is treated to determine efficiency of these matrices. Finally, these matrices are employed for solving third order non-homogeneous differential equations followed by a numerical example. The results, obtained via MATLAB, are compared with the exact solution as well as the results obtained via 4th order Runge-Kutta method. (C) 2012 Elsevier Inc. All rights reserved.

关键词： sample-and-hold functions Triangular functions Hybrid functions Function approximation Operational matrices Differential equation

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Numerical Algorithm for the Solution of Third Order Differential Equations in Orthogonal Hybrid Function (HF) Domain

Numerical Algorithm for the Solution of Third Order Differen...

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Annual IEEE India Conference - Engineering Sustainable Solutons

作者： Deb, Anish Ganguly, Anindita Sarkar, Gautam Biswas, Amitava Univ Calcutta Dept Appl Phys Kolkata 700009 W Bengal India Jadavpur Univ Dept Mech Engn Kolkata 700032 India Acad Technol Dept Elect Engn Hooghly India

ISBN: (纸本)9781457711091

关键词： Hybrid functions sample-and-hold functions Triangular functions Function approximation Operational matrices Differential equation

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