Jean-Denis Gabano

Fractional modeling of ultracapacitors dynamic behavior

Abstract In this paper, we present an identification algorithm based on a porous impedance model which allows to characterize an ultracapacitor. We simulate experiments which consist in applying a current sequence charging an ultracapacitor and measuring the induced voltage drop change across its terminals. The analysis of the porous part of the impedance shows that the charging process can be modeled with the help of a fractional model made of a classical integrator in parallel with a fractional integrator of order 1/2, whose action is blocked outside a limited spectral band. Numerical simulations show the ability of the fractional model, thanks to an output error identification technique, to obtain accurate estimation of the voltage drop change evolution as well as the impedance frequency response using time data series. Furthermore, the fractional parameter estimates allow to provide accurate values of the capacity and the high frequency internal equivalent series resistance.

Fractional Identification Algorithms Applied to Thermal Parameter Estimation

Abstract In this paper, we present a simulator of the heat flow through a wall in order to validate and compare different fractional identification algorithms. Indeed, heat transfer in homogeneous medium obeys to diffusion phenomenon which can be modelled with the help of fractional systems. We use models based on an original fractional integrator whose order 1/2 acts only over a limited spectral band. Simulations of front face thermal characterization consisting in measuring the temperature at the surface of a material 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 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 thermophysical parameter estimates.

Comparison of Two LPV Fractional Models Used for Ultracapacitor Identification

Abstract This paper deals with the comparison of two LTI fractional models allowing the identification of an ultracapacitor impedance using input current data and output induced low level voltage variation measurements around an initial bias voltage in the time domain. Both models are issued from the analysis of the porous nature of the electrodes. The first one, based on a 1-pore model structure has already been developped in previous works and will be used as a reference model. The second one, based on a multipore model, leads to a new more complex fractional model based on the sum of two fractional integrators of non integer order. The interest of this new modeling is discussed. For both models, the double layer capacitance depends on the voltage. So, in order to explicitly take into account the dependence of the system dynamics on the operating voltage, fractional continuous LPV models are used and determined thanks to a local approach composed of two steps. First, the local LTI fractional model parameters are estimated thanks to an output-error technique at different bias voltages. Secondly, the parameter estimates dependence with respect to the operating voltage is obtained by using cubic spline interpolation. The resulting LPV fractional models performances are compared on an experimental ultracapacitor bench.

Fractional modeling applied to non destructive thermal characterization

Abstract In this paper, we present a simulator of front face thermal characterization experiment, consisting in measuring the temperature at the surface of a thin slab where a random heat flux is applied, in order to validate and compare different fractional identification algorithms. Indeed, heat transfer in homogeneous medium obeys to diffusion phenomenon which can be modeled with the help of fractional systems. We use models based on an original continuous fractional integrator whose order 1/2 acts only over a limited spectral band. These models are obtained thanks to series expansion of the slab thermal impedance which lead to multiple 0.5 derivative order systems. Simulations taking into account the influence of heat losses across each face are performed and show the interest to take them into account so as to obtain accurate heat conductivity and diffusivity estimates.

Frequential Moments: Application to Linear System Identification

Abstract A new class of linear system invariant is presented. An estimation of frequential moments is performed by a least squares algorithm. The linears relationships between moments and transfer function parameters are also used to estimate local frequency models.