Computation of flat outputs for fractional systems : a Thermal Application

In trajectory planning, flatness is used to compute inputs generating suitable trajectories, without using any integration. The extension of linear flat outputs to linear controllable time-invariant fractional systems is put forward by means of polynomial matrix formalism, leading to the notion of fractional flatness. The so-called defining matrices, which are transformations that express all system variables in function of the flat outputs and a finite number of their time derivatives, are introduced and characterized in this fractional context. Fractional flatness is then applied to the trajectory planning of a real thermal experiment.