Abstract
This chapter deals with the control of the temperature across a finite diffusive interface medium using the CRONE controller (French acronym: Commande Robuste d’Ordre Non Entier). In fact, the plant transfer function presents two special properties: a fractional integrator of order 0.5 and a delay factor of a fractional order (when controlling the temperature far from the boundary where the density of flux is applied). The novel approach of this work resides by the use of a fractional controller that would control a fractional order plant. Also note that the choice of the CRONE generation is important as this controller is developed in three generations: the first generation CRONE strategy is particularly appropriate when the desired open-loop gain crossover frequency ω u is within a frequency range where the plant frequency response is asymptotic (this frequency band will be called a plant asymptotic-behavior band). As for the second generation, it is defined when ω u is within a frequency range where the plant uncertainties are gain-like along with a constant phase variation. Concerning the third generation, it would be applied when both a gain and a phase variations are observed when dealing with plant’s uncertainties. This generation will not be treated in this chapter due to some space constraints. Thus, this chapter will present some case scenarios which will lead to the use of the first two CRONE generations when using three different plants: the first one is constituted of iron, the second of aluminum and the third of copper with variable lengths L and several placements of the temperature sensor x. Simulation results will show the temperature variation across the diffusive interface medium in both time and frequency domains using Matlab and Simulink. These results show how the temperature behaves at different positions for the three materials in use.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abi Zeid Daou, R., & Moreau, X. (2015). Fractional calculus: Applications. New York: Nova.
Abi Zeid Daou, R., Moreau, X., Assaf, R., & Christohpy, F. (2012). Analysis of HTE fractional order system in the thermal diffusive interface—part 1: Application to a semi-infinite plane medium. In International Conference on Advances in Computational Tools for Engineering Applications, Lebanon.
Assaf, R., Moreau, X., Abi Zeid Daou, R., & Christohpy, F. (2012). Analysis of HTE fractional order system in HTE thermal diffusive interface—part 2: Application to a finite medium. In International Conference on Advances in Computational Tools for Engineering Applications, Lebanon.
Azar, A. T., & Serrano, F. (2014). Robust IMC-PID tuning for cascade control systems with gain and phase margin specifications. Neural Computing and Applications, 25(5).
Azar, A. T., & Serrano, F. (2015). Design and modeling of anti wind up PID controllers. Complex System Modelling and Control Through Intelligent Soft Computations, 319.
Azar, A. T., & Zhu, Q. (2015). Advances and applications in sliding mode control systems. Study in computational intelligence (Vol. 576). Springer.
Battaglia, J., Cois, O., Puigsegur, L., & Oustaloup, A. (2001). Solving an inverse heat conduction problem using a non-integer identified model. International Journal of Heat and Mass Transfer, 44(14), 2671–2680.
Boulkroune, A., Bouzeriba, A., Bouden, T., & Azar, A. T. (2016). Fuzzy adaptative synchronization of uncertain fractional-order chaotic systems. Control: Advances in Chaos Theory and Intelligent. 337.
Charef, A., & Fergani, N. (2010). PIλDμ controller tuning for desired closed-loop response using impulse response. In Workshop on Fractional Derivation and Applications, Spain.
Cois, O. (2002). Systèmes linéaires non entiers et identification par modèle non entier: application en thermique. Bordeaux: Université Bordeaux I.
CRONE Group. (2005). CRONE control design module. Bordeaux: Bordeaux University.
Lin, J. (2001). Modélisation et identification de systèmes d’ordre non entier. Poitiers: Université de Poitiers.
Magin, R., Ortigueira, M., Podlubny, I., & Trujillo, J. (2011). On the fractional signals and systems. Signal Processing, 91(3), 350–371.
Malti, R., Sabatier, J., & Akçay, H. (2009). Thermal modeling and identification of an aluminium rod using fractional calculus. In 15th IFAC Symposium on System Identification, France.
Miller, K., & Ross, B. (1993). An introduction to the fractional calculus and fractional differential equations. New York: Wiley.
Oldham, K., & Spanier, J. (1974). The fractional calculus. New York: Academic Press.
Oustaloup, A. (1975). Etude et Réalisation d’un systme d’asservissement d’ordre 3/2 de la fréquence d’un laser à colorant continu. Bordeaux: Universitu of Bordeaux.
Poinot, T., & Trigeassou, J. (2004). Identification of fractional systems using an output-error technique. Nonlinear Dynamics, 38(1), 133–154.
Trigeassou, J.-C., Poinot, T., Lin, J., Oustaloup, A., & Levron, F. (1999). Modeling and identification of a non integer order system. In European Control Conference. Karlsruhe: IFAC.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Moreau, X., Abi Zeid Daou, R., Christophy, F. (2017). Control of the Temperature of a Finite Diffusive Interface Medium Using the CRONE Controller. In: Azar, A., Vaidyanathan, S., Ouannas, A. (eds) Fractional Order Control and Synchronization of Chaotic Systems. Studies in Computational Intelligence, vol 688. Springer, Cham. https://doi.org/10.1007/978-3-319-50249-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-50249-6_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-50248-9
Online ISBN: 978-3-319-50249-6
eBook Packages: EngineeringEngineering (R0)