Comparison between Commensurate and Non-commensurate Fractional Systems

Abstract

This article deals with fractional systems that represent better physical process and guarantee a very small number of parameters that can reduces the computation time. It focuses in particular on the state-space representation which highlights the state variables and allows to study the internal behavior of the system taking into account the initial state. Moreover, this representation adapts better to the multiple input multiple-output case. It also discusses the discretization of fractional system to finally adapt the Model Predictive Control to apply it and shows its efficiency and performance in these systems. The main objective of this article is to compare the commensurate and noncommensurate fractional models performance, calculation time and ease of use.

System identification of photovoltaic system based on fractional-order model

“…The fractional-order model is considered in this paper. A generalized fractional-order dynamic system can be represented by the next equation [32]:…”

Robust fractional-order fixed-structure controller design for uncertain non-commensurate fractional plants using fractional Kharitonov theorem

“…Over the last few years, many practical and theoretical contributions have shown the significance of fractional systems in various disciplines such as electricity, economics, biology, chemistry, automation and signal processing. 1 Some of the most studied physical phenomena are listed in the work by Oustaloup et al 2 The attenuation of water movement on dikes, in particular those with cavities or depressions trapping air pockets that can be compressed by water, is one of these phenomena. Modelling the viscoelasticity of substances intermediate between solids and liquids involves some hereditary properties which indicates the advantages of employing fractional derivatives over classical derivatives.…”

Non-commensurate fractional linear systems: New results

“…The last 30 years of Fractional Calculus [5] , [14] , [15] brought a remarkable progress and became popular in many scientific and technical areas [4] , [6] , [7] , [8] , [9] , [16] due to its ability to better describe many natural phenomena. The fact that fractional models represent systems which require lower number of parameter than those of integer order is a point in favor of fractional systems (see [2] ). This is due to their capacity of supplying us with more reliable time and frequency representations.…”