Periodic disturbance rejection with unknown frequency and unknown plant structure

This paper deals with asymptotic rejection of a multi-sinusoidal signal for linear single-input single-output stable systems with unknown structure. An adaptive orthogonal signals generator is used to both reconstruct the 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. A fractional-order controller is designed which guarantees the closed-loop stability of the system if the location of the plant frequency response at the estimated frequencies lies in a half-plane 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 and comparisons with existing approaches are presented that highlight the performances of the proposed method.