Real interpolation method for transfer function approximation of distributed parameter system

• Published in: Telkomnika 2019-08, Vol.17 (4), p.1941-1947
• Main Authors: Tin, Phu Tran, Tran, Minh, Vu, Le Anh, Dung, Nguyen Quang, Trang, Tran Thanh
• Format: Article
• Language: English
• Subjects: Acoustics; Applied mathematics; Approximation; Automation; Control theory; Distributed parameter systems; Identification; International conferences; Interpolation; Laplace transforms; Linear equations; Lumped parameter systems; Mathematical models; Methods; Neural networks; Ordinary differential equations; Partial differential equations; Polynomials; Process parameters; System theory; Transfer functions
• ISSN: 1693-6930; 2302-9293
• DOI: 10.12928/telkomnika.v17i4.11088

A mathematical description of this class of systems is represented by partial differential equations (PDEs), which lead to the infinite-dimensional model as well as to irrational transfer function representations [1, 2]. [...]due to the mathematical complexity, analysis of DPS is much more complicated than in the case of lumped parameter systems (LPS), where spatial effects are averaged. The transfer functions of these systems typically have the form such as formula (1). Because of the presence of fractional and/or transcendental components in the transfer function, which not allow using method and means of lumped parameters systems. .. For fixed ð???ð??? both numerator and denominator polynomials are linear combinations of the unknown process parameters. [...]the set of (6) represents a linear system of equations having N linear equations, one obtains N coefficients of the rational approximation (4). According to the considered model (10): ð???1(∞)→0 and ð???1(0)=1, we have chosen the approximation model (4) with ð???0=1,ð???0=1 and the order of denominator of transfer function must be higher than the order of numerator. According to the model (11): Limð???→0ð???2(ð???)=0.5 and limð???→∞ð???2(ð???)=0. we have chosen approximation model (3) with ð???0=0.5,ð???0=1 and the order of denominator of the transfer function must be higher than the order of numerator.