Stéphane Victor

Parameter and differentiation order estimation in fractional models

This paper deals with continuous-time system identification using fractional differentiation models. An adapted version of the simplified refined instrumental variable method is first proposed to estimate the parameters of the fractional model when all the differentiation orders are assumed known. Then, an optimization approach based on the use of the developed instrumental variable estimator is presented. Two variants of the algorithm are proposed. Either, all differentiation orders are set as integral multiples of a commensurate order which is estimated, or all differentiation orders are estimated. The former variant allows to reduce the number of parameters and can be used as a good initial hit for the latter variant. The performances of the proposed approaches are evaluated by Monte Carlo simulation analysis. Finally, the proposed identification algorithms are used to identify thermal diffusion in an experimental setup.

Advances in System Identification Using Fractional Models

This paper presents an up to date advances in time-domain system identification using fractional models. Both equation-error and output-error-based models are detailed. In the former models, prior knowledge is generally used to fix differentiation orders; model coefficients are estimated using least squares. The latter models allow simultaneous estimation of models coefficients and differentiation orders, using non linear programming. As an example, a thermal system is identified using a fractional model and compared to a rational one.

An optimal instrumental variable method for continuous-time fractional model identification

Abstract this paper deals with continuous-time system identification using fractional differentiation models in a noisy output context. The simplified refined instrumental variable for continuous-time systems ( srivc ) is extended to fractional models. Monte Carlo simulation analysis are used to demonstrate the performance of the proposed optimal instrumental variable scheme.

Robust path tracking using flatness for fractional linear MIMO systems: A thermal application

This paper deals with robust path tracking using flatness principles extended to fractional linear MIMO systems. As soon as the path has been obtained by means of the fractional flatness, a robust path tracking based on CRONE control is presented. Flatness in path planning is used to determine the controls to apply without integrating any differential equations when the trajectory is fixed (in space and in time). Several developments have been made for fractional linear SISO systems using a transfer function approach. For fractional systems, especially in MIMO, developments are still to be made. Throughout this paper, flatness principles are applied using polynomial matrices for fractional linear MIMO systems. To illustrate the robustness performances, a third-generation multi-scalar CRONE controller is compared to a PID one.

System Identification Using Fractional Models: State of the Art

This paper presents a state of the art of actual achievements in time-domain system identification using fractional models. It starts with some general aspects on time and frequency-domain representations, time-domain simulation, and stability of fractional models. Then, an overview on system identification methods using fractional models is presented. Both equation-error and output-error-based models are detailed. In the former models, prior knowledge is generally used to fix differentiation orders; model coefficients are estimated using least squares. The latter models allow simultaneous estimation of model’s coefficients and differentiation orders, using non linear programming. A real thermal example is identified using a fractional model and compared to a rational one.Copyright

Instrumental variable method with optimal fractional differentiation order for continuous-time system identification

this paper deals with continuous-time system identification using fractional differentiation models in a noisy output context. The simplified refined instrumental variable for continuous-time fractional systems (srivcf) is extended to optimize the commensurate order with a gradient-based method as the coosrivcf algorithm. Simulation analysis is used to demonstrate the performance of the proposed optimal instrumental variable scheme combined with order optimization.

Flatness for linear fractional systems with application to a thermal system

This paper is devoted to the study of the flatness property of linear time-invariant fractional systems. In the framework of polynomial matrices of the fractional derivative operator, we give a characterization of fractionally flat outputs and a simple algorithm to compute them. We also obtain a characterization of the so-called fractionally 0-flat outputs. We then present an application to a two dimensional heated metallic sheet, whose dynamics may be approximated by a fractional model of order 1/2. The trajectory planning of the temperature at a given point of the metallic sheet is obtained thanks to the fractional flatness property, without integrating the system equations. The pertinence of this approach is discussed on simulations.

Path tracking with flatness and CRONE control for Fractional Systems: thermal application

Abstract Flatness principles using polynomial matrices, well-suited for trajectory planning, are studied for fractional systems. Once a path has been defined by flatness for a real fractional system, a robust path tracking based on CRONE control is presented. Flatness in path planning is used to determine the controls to apply without integrating any differential equations.

FROM SYSTEM IDENTIFICATION TO PATH PLANNING USING FRACTIONAL APPROACH: A THERMAL APPLICATION EXAMPLE

This paper presents a global fractional approach from system identification to path planning; these results will be ap plied to a typical fractional application: a thermal diffusion in an aluminium rod. The objective is to follow a desired path using fractional linear flatness. However, models of true systems are not always known. Through a black box identification using a fractional model, the temperature versus the heat flux of an a luminium rod is modeled. The coosrivcf algorithm enables to optimize as well the parameter coefficients and the commensura te order. The fractional flat output generates the input comman d so that the system follows that desired path.

Instrumental Variable Identification of Hybrid Fractional Box-Jenkins Models

Abstract this paper deals with continuous-time system identification using fractional differentiation models in a colored noisy output context. An optimal instrumental variable method for identifying fractional models in a hybrid Box-Jenkins form is described. The relationship between the measured input and the output is a fractional continuous-time transfer function, and the noise is a discrete-time AR or ARMA process.