Flatness principle extension to linear fractional MIMO systems: Thermal application

This paper concerns the application of flatness principle to fractional MIMO systems in the pseudo-state-space representation. The aim here is to compute linear flat outputs for linear controllable time-invariant systems in polynomial matrix form. The defining matrices expressed with the system variables in terms of a linear flat output and its derivatives define the kernel of a polynomial matrix. Flatness in path planning is used to determine the controls to apply without integrating any differential equations when the trajectory is fixed. Several developments have been made for LTI systems, however concerning fractional differentiation systems, especially in MIMO, developments are still to be made. The aim of this paper is to apply flatness principle using polynomial matrices for linear fractional MIMO systems.