Mathieu Merveillaut

On observability and pseudo state estimation of fractional order systems

In this paper, fractional order system observability is discussed. A representation of these systems that involves a classical linear integer system and a system described by a parabolic equation is used to define the system real state and to conclude that the system state is approximately observable. However, it is also shown that the pseudo state space representation, usually encountered in the literature for fractional systems, can be used to design Luenberger like observers that permits an estimation of important variables in the system. Such an observer is finally used in order to estimate the temperature in a thermal system from a temperature measure at a different abscissa.

On Observability of Fractional Order Systems

In this paper, fractional order system observability is discussed. A representation of these systems that involves a classical linear integer system and a system described by a parabolic equation is used to define the system real state and to conclude that the system state cannot be observed. However, it is also shown that the state space like representation usually encountered in the literature for fractional systems, can be used to design Luenberger like observers that permit an estimation of important variables in the system.© 2009 ASME

CRONE Observer of Nonlinear SISO Systems

CRONE control, robust control methodology based on fractional differentiation, is applied to state observer design. State observation can indeed be viewed as a regulation problem given that the goal of a state observer is to cancel the observation error in spite of measurement noise, disturbances and plant perturbations. This conclusion has been used recently to define a new class of state observers known in the literature as “dynamic observers” or “input-output observer”. It is based on the observation error dynamic feedback. In this paper, this idea is used to define the CRONE observer design methodology for nonlinear SISO systems. As for CRONE control, fractional differentiation in the definition of an equivalent open loop transfer function permits the reduction of the number of parameters to be optimised.Copyright

On the Implementation of a Limited Frequency Band Integrator and Application to Energetic Material Ignition Prediction

This paper describes an algorithm for the implementation a fractional order integrator. This algorithm is based on a fractional integrator transfer function approximation by a recursive distribution of poles and zeros. This algorithm is then used to predict the ignition of energetic materials. For these materials, the ignition under low velocity impact can be predicted through the fractional integration of a local function of pressure and of shear strain rate inside the material. It is shown that the proposed algorithm allows obtaining accurate results with a low computational complexity.