Abstract
This article deals with fractional systems that rep-resent 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 non-commensurate fractional models performance, calculation time and ease of use.
Highlights
Over the last few years, many theoretical and practical contributions showed the importance of fractional systems and their interest in different applications of modeling, identification and control of physical systems
The results have shown that fractional model represents systems with much lower number of parameters than those of integer model
The use of fractional models becomes more and more frequent given the efficiency they provide in the discription of certain physical systems
Summary
Over the last few years, many theoretical and practical contributions showed the importance of fractional systems and their interest in different applications of modeling, identification and control of physical systems. Several control strategies have been developed and adapted for fractional systems such as the PID controller, sliding mode control and predictive control. In different disciplines such as electricity, chemistry, biology, economics, automation and signal processing. Some researchers have compared the fractional models with the classical integer models. The results have shown that fractional model represents systems with much lower number of parameters than those of integer model. The most studied physical phenomena and most used during modeling or identification are mentioned in [1]
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