Régis Ouvrard

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.

On embedded FIR filter models for identifying continuous-time and discrete-time transfer functions: the RPM approach

For identifying a continuous-time (CT) transfer function model, data filtering is a solution which provides the necessary unmeasurable input--output derivative approximations. In discrete-time (DT) system identification, the well-known ARX model can be used successfully if the estimate is performed with suitable prefiltered data. This article describes the reinitialised partial moment (RPM) model which embeds implicitly a finite impulse response filter in both CT and DT domains. With knowledge of the important role of data prefiltering in standard methods, this RPM model embedded filter gives particular properties to this original tool. Although both the CT RPM model and the DT RPM model present an embedded filter, the formulation and the implementation in the CT and the DT domains are different. Therefore, the aim of this article is to present a tutorial on the RPM models and to give an overview of all the applications.

CONTINUOUS-TIME MODEL IDENTIFICATION USING REINITIALIZED PARTIAL MOMENTS - APPLICATION TO POWER AMPLIFIER MODELING

Abstract An application of continuous-time system identification to the modeling of a power amplifier used in mobile communication is proposed. Generally, electronic components modeling uses discrete-time black-box models. In order to keep physical knowledge and easy interpretation of estimated model, a continuous-time transfer function model is chosen to represent amplifier transmittance. Hence, parameter estimation is performed by the reinitialized partial moments method. This estimation method has been chosen because of its insensitivity to initial conditions and rough system a priori knowledge. Then, power amplifier continuous-time model allows immediate physical interpretation to the electronics engineer.

A counter flow water to oil heat exchanger: MISO quasi linear parameter varying modeling and identification

Abstract This paper presents a dynamic model of a counter flow water to oil heat exchanger when all inputs (inlet temperatures of the fluids and the mass flow rates) are simultaneously varying. Although interesting results about modeling of heat exchanger by linear parameter varying (LPV) can be found in [25] , several problems remain to be solved such as the structure estimation or a proper initial MISO model for the optimization algorithms. This paper introduces a new model structure called quasi LPV model which simulates accurately the temperature and flow transients in a counter flow heat exchanger (COFHX). The quasi LPV model is compared to a realistic numerical model of a counter flow heat exchanger adjusted with the test rig heat exchanger of the University of Valenciennes in France. Comparisons indicate that the developed quasi LPV model is capable of predicting the transient performance of the heat exchangers satisfactorily.

A Pseudo-Output Error Algorithm To Improve Global Convergence

In this work, a new off-line optimization approach is proposed to improve the global convergence. This algorithm, called pseudo-output error algorithm, is based on the introduction of a stationary filter in the sensitivity functions of the Newton algorithm. The convergence of the proposed algorithm is studied and analyzed. A comparison with Newton algorithm is performed to evaluate its performance. The results of the simulations show that the pseudo-output error algorithm converges to true parameters describing the system to be identified. Whereas, the Newton algorithm might converge to a secondary minimum for the same input-output data and initialized parameters

Identification of 2D Roesser models by using linear fractional transformations

In this paper, the problem of identifying a 2D linear time-invariant Roesser model is tackled. Based on the strong relation between the linear fractional representation and the nD Roesser model, a gradient-based optimization algorithm is suggested to estimate the state-space matrices of a standard Roesser model in the black-box as well as the gray-box model identification frameworks. Contrary to the developments available in the literature, no specific restriction (to the 2D causal, recursive and separable-in-denominator (CRSD) state-space models) is required by the non-linear programming technique developed in this article. The efficiency of this method is illustrated through two simulation examples: a CRSD state-space model and a 2D Roesser model of a co-current flow heat exchanger.

Identification and control of a wastewater treatment pilot by catalytic ozonation

This paper deals with the control of a wastewater treatment pilot by catalytic ozonation. In general, catalytic ozonation processes operate with a deliberate ozone overproduction to obtain a treated water which respects the discharge standards. But, in this case, the oxygen consumption is not optimal and the operating costs are important. The objective of this study focuses on the optimization of the catalytic ozonation pilot. A continuous-time transfer function model is identified to represent the pilot behavior, and an internal model control is proposed to obtain a significant abatement of the pollutant. In this application, the pollutant abatement is represented by the absorbance.

Continuous-Time Identification of Linear Parameter Varying Model using an Output-Error Technique

Abstract In this paper, a practical solution for the identification of Continuous-Time (CT) Input-Output (IO) Linear Parameter Varying (LPV) systems is proposed. For this particular class, we formulate an output error identification problem and present a parameter estimation scheme in which a prediction error based cost function is minimized using nonlinear programming. Because the cost function possesses local minima, the success of any iterative parameter estimation algorithm depends on appropriate initial seeds. One approach would be to generate an initial estimate using CT Reinitialized Partial Moments (RPM) models extended to CT IO LPV systems. We assume that the inputs, outputs and scheduling parameters are directly measurable, and that the functional dependence of the system coefficients on the parameters is of a polynomial form. The performance of the proposed method is evaluated by Monte Carlo simulation analysis.

Combining least-squares and gradient-based algorithms for the identification of a co-current flow heat exchanger

ABSTRACT Because of the high-dimensional nature of partial differential equations (PDEs), identifying accurate models of processes, the behaviour of which is governed by PDEs, is a challenging problem which still deserves a lot of attention. We address the problem of identifying a grey-box model of a heat exchanger by combining equation-error and output-error-based algorithms. First, in order to estimate rough but reliable values of the sought physical parameters characterising the heat exchanger behaviour, we use the interesting properties of the reinitialised partial moments (RPMs) developed initially for ordinary differential equations to deal with the problem of inaccessible partial derivatives of the PDE. Such an adaptation of the RPM features to PDEs leads to a direct continuous-time system identification problem for which convex least-squares solutions can be found. Second, thanks to a description of the heat exchanger dynamics with a 2D linear time-invariant Roesser model, the aforementioned rough estimates are used as reliable initial guesses for the nonlinear optimisation of a standard non-convex cost function introduced to estimate the state-space matrices of the Roesser model we want to identify. The efficiency of this two-step approach in terms of physical parameter estimation is validated through the simulation of a co-current flow heat exchanger.

Continuous-time model identification of wells interaction on the Hydrogeological Experimental Site of Poitiers

In hydrogeology, estimating aquifer permeability is an important issue. This can be useful in understanding the flow of pollutants from one area of an aquifer to another. For this aquifer analysis sake, the Hydrogeological Experimental Site of Poitiers (France) covering a limestone aquifer is an appropriate instrumented test bed enabling measurement of hydraulic responses of a series of observation wells due to a step-type pumping out excitation at a given well. Given the input-output data, black-box continous-time modeling is quite a straight forward process as shown in this paper. The aim is then to be able to use the identified parameters to classify the different wells according to how sensitive they are to the one having been excited. A correlation between black-box parameters and hydrogeological ones is then established.