Brief paper: Rational approximations in the simulation and implementation of fractional-order dynamics: A descriptor system approach

Authors:
Mohammad Saleh Tavazoei;Mohammad Haeri
Affiliations:
Advanced Control System Lab, Electrical Engineering Department, Sharif University of Technology, Tehran, Iran;Advanced Control System Lab, Electrical Engineering Department, Sharif University of Technology, Tehran, Iran
Venue:
Automatica (Journal of IFAC)
Year:
2010

Citing 4
Cited 6

Singular Control Systems

Singular Control Systems
Design equations for fractional-order sinusoidal oscillators: Four practical circuit examples

International Journal of Circuit Theory and Applications
Analysis of undamped oscillations generated by marginally stable fractional order systems

Signal Processing
Stability Preservation Analysis for Frequency-Based Methods in Numerical Simulation of Fractional Order Systems

SIAM Journal on Numerical Analysis

Stability preservation analysis in direct discretization of fractional order transfer functions

Signal Processing
The Minimal State Space Realization for a Class of Fractional Order Transfer Functions

SIAM Journal on Control and Optimization
Brief paper: Stability and resonance conditions of elementary fractional transfer functions

Automatica (Journal of IFAC)
Fractional integro-differential calculus and its control-theoretical applications. II. Fractional dynamic systems: Modeling and hardware implementation

Automation and Remote Control
Robust decentralized control of perturbed fractional-order linear interconnected systems

Computers & Mathematics with Applications
Robust asymptotical stability of fractional-order linear systems with structured perturbations

Computers & Mathematics with Applications

Quantified Score

Hi-index	22.15

Visualization

Abstract

This paper deals with issues related to the use of rational approximations in the simulation of fractional-order systems and practical implementations of fractional-order dynamics and controllers. Based on the mathematical formulation of the problem, a descriptor model is found to describe the rational approximating model. This model is analyzed and compared with the original fractional-order system under the aspects which are important in their simulation and implementation. From the results achieved, one can determine in what applications the use of rational approximations would be unproblematic and in what applications it would lead to fallacious results. In order to clarify this point, some examples are presented in which the effects of using rational approximations are investigated.