Periodic disturbance rejection for fractional-order dynamical systems

Abstract

Abstract This paper proposes a simple fractional-order derivative controller, based on an adaptive orthogonal signals generator, which permits both to reconstruct an unknown multi-sinusoidal disturbance and cancel its effect on the system output. An interesting feature is that the disturbance is removed by the generated internal signals with no additional dynamics in the cancellation algorithm. An opportune choice of the fractional-order controller guarantees the closed-loop stability of the system if the location of the plant frequency response at the estimated frequencies belongs to a halfplane passing through the origin of the complex plane, i.e. no information about the order of the system to be controlled, the relative degree, the nature of its poles and zeros, is required. The case of multi-sinusoidal disturbance is also analyzed. Simulations are presented that highlight the performances of the proposed method.