Two-layer observer based control for a class of uncertain systems with multi-frequency disturbances

A novel disturbance estimation approach is presented for a class of uncertain systems subject to multiple-sinusoidal disturbances with unknown frequencies. Different from existing results on disturbance observer based control (DOBC), a new methodology with a two-layer observer structure is developed to effectively estimate and reject the disturbances. In the proposed control architecture, an auxiliary observer is derived to generate a disturbance representation in a parametric uncertainty form. Furthermore, the unknown parameters can be reduced to a constant vector with the dimension of the number of harmonic components in the disturbances. Then an augmented observer is designed to estimate the corresponding unknown parameters of the disturbances. As a result, the uncertain systems with disturbances constituting of multiple unknown-frequency sinusoidal components can be controlled within the DOBC framework, where asymptotic stability can be guaranteed. The proposed approach is successfully validated on a robotic manipulating example.