Application of fractional order transfer functions to modeling of high — Order systems

Abstract

The paper presents an application of elementary fractional order transfer funtions to efective modeling of high order control plants. An example of modeling experimental heat plant is also given.

Application of modified least squares method for order reduction of commensurate higher order fractional systems

“…A subsequent set of equations obtained on assessing (7) and ( 9) to preserve 'v' Markov parameters of the original system in its reduced model.…”

“…The concept of non-integer order operators was deliberated first in the year 1974, in New Haven, Connecticut, USA [1].Many honored mathematicians notably Euler, Laplace, Fourier, Abel, Liourille, Riemann and Lauret focused on fractional calculus [2]. The dynamics of Fractional systems include differential or intergral operators of non integers systems [3].It handles with the adaptation of dynamic systems to achieve a desired reference model having its performance with a set of specifications.In the last decades of the last century there was continuing growth of the applications of fractional calculus mainly promoted by the engineering applications in the field of feedback control, systems theory and singal processing.Among the many applications of fractional controller to engineering problem Position control of a single link flexible robot , Automatic control of a hydraulic canal , Mechtronics , control of Power Electronic Buck converter applying fractional order control can be mentioned [4,5,6,7] . Any linear time invariant systems can be classified as integer and non -integer systems.The non integer systems further classified as Commensurate and noncommensurate systems.…”

A Study on Fractional Power-Law Applications and Approximations

“…The dynamic behavior of fractional transfer functions can be approximated using integer transfer functions or digital transfer functions [21,22]. Approximations are helpful in numerical methods for solving fractional differential equations.…”

Reduction of High Dimensional Noninteger Commensurate Systems Based on Differential Evolution

“…Researchers in a wide range of engineering disciplines are very interested in noninteger fractional-order (FO) systems [2,3] because their mathematical representations of various physical phenomena, such as electrochemical processes, long-distance lines, dielectric polarisation, viscoelastic materials, coloured noise, and even chaos, have shown to be more accurate. Some of these include the control of a single-link robot, an automatic control system for a hydraulic canal, and the power electronic buck converter [4]. Modelling, analysis, and control of fractional-order systems have received a great deal of theoretical and practical attention [5,6].…”