Next Article in Journal
Emergence of Fractional Kinetics in Spiny Dendrites
Next Article in Special Issue
Fractional Derivatives with the Power-Law and the Mittag–Leffler Kernel Applied to the Nonlinear Baggs–Freedman Model
Previous Article in Journal / Special Issue
Fractional Velocity as a Tool for the Study of Non-Linear Problems
Article Menu

Export Article

Open AccessArticle
Fractal Fract 2018, 2(1), 5; https://doi.org/10.3390/fractalfract2010005

Comparison between the Second and Third Generations of the CRONE Controller: Application to a Thermal Diffusive Interface Medium

1
UMR 5218 CNRS, IMS Laboratory, University of Bordeaux, 33405 Talence Cedex, France
2
Biomedical Technologies Department, Faculty of Public Health, Lebanese German University, Sahel Alma, Jounieh 1200, Lebanon
3
MART Learning, Education and Research Center, Chananiir 1200, Lebanon
4
Faculty of Engineering, Lebanese University, Tripoli 1300, Lebanon
*
Author to whom correspondence should be addressed.
Received: 19 December 2017 / Revised: 9 January 2018 / Accepted: 12 January 2018 / Published: 17 January 2018
(This article belongs to the Special Issue The Craft of Fractional Modelling in Science and Engineering)
Full-Text   |   PDF [3409 KB, uploaded 18 January 2018]   |  

Abstract

The control of thermal interfaces has gained importance in recent years because of the high cost of heating and cooling materials in many applications. Thus, the main focus in this work is to compare the second and third generations of the CRONE controller (French acronym of Commande Robuste d’Ordre Non Entier), which means a non-integer order robust controller, and to synthesize a robust controller that can fit several types of systems. For this study, the plant consists of a rectangular homogeneous bar of length L, where the heating element in applied on one boundary, and a temperature sensor is placed at distance x from that boundary (x is considered very small with respect to L). The type of material used is the third parameter, which may help in analyzing the robustness of the synthesized controller. The originality of this work resides in controlling a non-integer plant using a fractional order controller, as, so far, almost all of the systems where the CRONE controller has been implemented were of integer order. Three case studies were defined in order to show how and where each CRONE generation controller can be applied. These case studies were chosen in such a way as to influence the asymptotic behavior of the open-loop transfer function in the Black–Nichols diagram in order to point out the importance of respecting the conditions of the applications of the CRONE generations. Results show that the second generation performs well when the parametric uncertainties do not affect the phase of the plant, whereas the third generation is the most robust, even when both the phase and the gain variations are encountered. However, it also has some limitations, especially when the temperature to be controlled is far from the interface when the density of flux is applied. View Full-Text
Keywords: CRONE controller; homogeneous plan diffusive interface; semi-infinite medium; robust control CRONE controller; homogeneous plan diffusive interface; semi-infinite medium; robust control
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Moreau, X.; Abi Zeid Daou, R.; Christophy, F. Comparison between the Second and Third Generations of the CRONE Controller: Application to a Thermal Diffusive Interface Medium. Fractal Fract 2018, 2, 5.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Fractal Fract EISSN 2504-3110 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top