Thierry Poinot

Fractional modelling and identification of thermal systems

Heat transfer in homogeneous media obeys to diffusion phenomenon which can be modelled with the help of fractional systems. In this paper, we use a parsimonious black box model based on an original fractional integrator whose order 12 acts only over a limited spectral band. We carried out simulations of front face thermal experimentations which consist in measuring the temperature at the surface of a material where a random heat flux is applied. We consider the characterization of the thermal behaviour of a wall or a sphere. These simulations show the ability of the fractional model, thanks to an output error identification technique, to obtain accurate estimation of diffusion interface temperature evolution as well as frequency response using time data series for the two considered geometries. Experimental results are given in the case of the sphere.

A method for modelling and simulation of fractional systems

An original method for modelling and simulation of fractional systems is presented in this article. The basic idea is to model the fractional system by a state-space representation, where conventional integration is replaced by fractional one with the help of non-integer integrator. This operator is itself approximated by a N dimensional system composed of an integrator and of a phase-lead filter. This method is compared to other techniques like direct discretization of the fractional derivator and diffusive representation. Numerical simulations exhibit the general applicability and flexibility of this new approach to different types of fractional models and to non-conventional non-integer derivation with limited spectral range.

Approximation and identification of diffusive interfaces by fractional models

Heat transfer problems obey to diffusion phenomenon. In this paper we show that they can be modelled with the help of fractional systems. The simulation is based on a fractional integrator operator where the non-integer behaviour acts only over a limited spectral band. Starting with frequency considerations derived from the analysis of a diffusion problem, a more general approximation of the fractional system is proposed. A state-space model is presented that gives an accurate simulation for transients, and with which it is possible to carry out an output-error technique to estimate the model parameters. Numerical simulations of the heat transfer problem are used to illustrate the improvements of the proposed model.

Estimation of thermal parameters using fractional modelling

Heat transfer problems in homogeneous medium obey to diffusion phenomenon. In this paper, we study heat conduction through a sphere which can be modelled with the help of fractional systems. We use models based on an original fractional integrator whose order 12 acts only over a limited spectral band. Simulations of front face thermal characterization consisting in measuring the inner surface temperature of the sphere where a random heat flux is applied are carried out. These simulations allow to validate the ability of the proposed estimation algorithms not only to rebuild the inner surface temperature but also to identify with a good accuracy the heat conductivity and diffusivity. Monte-Carlo simulations are also performed in order to provide statistical properties of the thermo-physical parameter estimates.

Parameter Estimation of Fractional Systems: Application to the Modeling of a Lead-Acid Battery

Abstract Black box modeling of diffusion processes can be performed by fractional systems. The simulation of these particular systems is based on a new fractional integrator, with limited spectral range for non integer order. Parameter estimation of this class of systems is performed by an OE identification technique. This paper presents the application of this new methodology to the modeling of the dynamics of a lead-acid battery.

Continuous-Time Linear Parameter-Varying Identification of a Cross Flow Heat Exchanger: A Local Approach

In this paper, the problem of deriving a dynamical model of a cross flow heat exchanger is considered. In order to take into account the dependency of the systems dynamics on the hot and the cold mass flow rates in an explicit way, an input-output linear parameter-varying (LPV) model is used. A local approach composed of three steps is carried out to identify this LPV model. A parameter estimation scheme is introduced in which cost functions are minimized by using specific nonlinear programming methods. In this study, a finite volume physical model simulator is exploited to simulate and to generate the data. Simulations are performed to demonstrate the benefits of the suggested approach.

Modeling the oxidation of atrazine by H2O2/UV. Estimation of kinetic parameters

Abstract A kinetic model for the oxidation of atrazine by H2O2/UV in dilute aqueous solutions ([Atrazine]0 < 2 μM) has been tested in a batch reactor. In this model, direct photolysis and oxidation by hydroxyl radicals are assumed to be the main reactions in the decomposition of atrazine by H2O2/UV. The data showed that the model can be used to predict the effects of some parameters (hydrogen peroxide dose, pH, bicarbonate alkalinity, …) and to estimate values of quantum yield of photolysis, rate constants for the reaction of hydroxyl radicals with atrazine and of the scavenging term (SkiSi) of natural waters.

Parameter estimation of fractional models : Application to the modeling of diffusive systems

Abstract Black box modeling of diffusion processes can be performed by fractional models. The simulation of these particular models is based on a new fractional integrator, with limited spectral range. Parameter estimation of this class of systems is performed by an OE identification technique. This paper presents the application of this new methodology to the modeling of different diffusive systems dealing with electrochemistry, heat transfer and electromagnetism.

Fractional Modelling and Identification of a Thermal Process

Heat transfer problems are subject to diffusion phenomenon, and can be modelled with the help of fractional systems. The simulation of these particular systems is based on a fractional integrator, where the non-integer behaviour occurs only within a limited spectral band. A first model, based on the use of one fractional integrator, has been already defined and tested on a thermal pilot. Starting from frequency considerations derived from the analysis of a diffusion problem, a more general approximation of the fractional system is proposed here. The new model is based on the use of two fractional integrator operators. This makes it possible to define a state-space model for simulation of transients, and to use an output-error technique in order to estimate the parameters of the model. Experimental results obtained for a thermal process illustrate the improvements obtained using the proposed model.

MODELLING AND SIMULATION OF FRACTIONAL SYSTEMS USING A NON INTEGER INTEGRATOR

An original method for modelling and simulation of fractional systems is presented in this paper. The basic idea is to model the fractional system by a state-space representation, where conventional integration is replaced by a fractional one with the help of a non integer integrator. This operator is itself approximated by a N + 1 dimensional system composed of an integrator and of a phase-lead filter. This method is compared to other techniques like direct discretization of the fractional derivator and diffusive representation. Numerical simulations exhibit the general applicability and flexibility of this new approach to different types of fractional models and to non conventional non integer derivation with limited spectral range.