Journal ArticleDOI
A new set of orthogonal functions and its application to the analysis of dynamic systems
TLDR
It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution.Abstract:
The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been computed and their relation with the BPF domain integral operational matrix is shown. It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution. As a further study, the newly proposed sets have been applied to the analysis of dynamic systems to prove the fact that it introduces less mean integral squared error (MISE) than the staircase solution obtained from BPF domain analysis, without any extra computational burden. Finally, a detailed study of the representational error has been made to estimate the upper bound of the MISE for the TF approximation of a function f ( t ) of Lebesgue measure.read more
Citations
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Journal ArticleDOI
Solving Linear Time Varying Systems by Orthonormal Bernstein Polynomials
TL;DR: In this paper, the authors present a method to find the solution of time-varying systems using orthonormal Bernstein polynomials, which is based upon expanding various time functions in the system as their truncated OBNs.
Proceedings ArticleDOI
Numerical implementation a stochastic operational matrix based on triangular functions for solving a stochastic nonlinear differential equation
Numerical solution of fuzzy linear volterra-fredholm integral equations by triangular functions method
Maryam Mosleh,Mahmood Otadi +1 more
TL;DR: A numerical method based on an m-set of general, orthogonal triangular functions is proposed to approximate the solution of linear Volterra-Fredholm fuzzy integral equations and a theorem is proved for convergence analysis.
Proceedings ArticleDOI
Application of Triangular Orthogonal Function in Chemical Process Simulation
TL;DR: Triangular basis functions (TBF), a linear piecewise constant basis function (PCBF) are being applied here to offer an attractive solution in Chemical process simulation as discussed by the authors, which is the simulation of an auto-catalytic reaction, multiple reactions in CSTR, and a jacketed heater processes were taken up for TBF based simulation studies.
Journal ArticleDOI
Review of Five Sets of Piecewise Constant Orthogonal Functions for Function Approximation, Integration and Solution of First Order Differential Equation Using These Function Sets
Anindita Ganguly,Himadri Basu +1 more
TL;DR: With the help of integration operational matrices the authors can solve an nth order differential equation which is of importance for solving control engineering problems although a first order ordinary differential equation has been dealt with in this paper.
References
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Book
Modern control engineering
TL;DR: This comprehensive treatment of the analysis and design of continuous-time control systems provides a gradual development of control theory and shows how to solve all computational problems with MATLAB.
Journal ArticleDOI
Zur Theorie der orthogonalen Funktionensysteme
TL;DR: In der Theorie der Reihenentwicklung der reellen Funktionen spielen die sog. orthogonalen Funktionensysteme eine fuhrende Rolle.
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Identification of continuous-time systems
G.P. Rao,Heinz Unbehauen +1 more
TL;DR: Continuous-time model-based system identification as mentioned in this paper is a well-established field in the field of control systems and is concerned with the determination of particular models for systems that are intended for a certain purpose such as control.
Journal ArticleDOI
Walsh operational matrices for fractional calculus and their application to distributed systems
C.F. Cheng,Y.T. Tsay,Tao Wu +2 more
TL;DR: In this paper, the Walsh operational matrix for performing integration and solving state equations is generalized to fractional calculus for investigating distributed systems and a new set of orthogonal functions is derived from Walsh functions.