Flatness control of a fractional thermal system.

*(English)* Zbl 1126.93335
Sabatier, J. (ed.) et al., Advances in fractional calculus. Theoretical developments and applications in physics and engineering. Dordrecht: Springer (ISBN 978-1-4020-6041-0/hbk; 978-1-4020-6042-7/e-book). 493-509 (2007).

Summary: This paper concerns the application of flatness principle to fractional systems. In path planning, the flatness concept is used when the trajectory is fixed (in space and in time), to determine the controls inputs to apply without having to integrate any differential equations. A lot of developments have been made but, in the case of non-integer differential systems (or fractional systems), few developments are still to be made. So, the aim of this paper is to apply flatness principle to a fractional system. As soon as the path has been obtained by flatness, a new robust path tracking based on CRONE control is presented Firstly, flatness principle definitions used in control’s theory are reminded. The fractional systems dynamic inversion is studied. A robust path tracking based on CRONE control is presented. Finally, simulations on a thermal testing bench model, with two different controllers (PID and CRONE), illustrate the path tracking robustness.

##### MSC:

93B35 | Sensitivity (robustness) of control systems |

26A33 | Fractional derivatives and integrals (real functions) |