Estimation of unknown multi-sinusoidal disturbance using delay-dependent observer

A disturbance estimation approach is presented for a class of nonlinear systems subject to multiple-sinusoidal disturbances with unknown frequencies. The auxiliary observer yields an disturbance representation in a parametric uncertainty form. Furthermore, the unknown parameters can be reduced to a constant vector, the dimension of which is the same as the number of sinusoidal component. Then a delay-dependent observer is designed to approach the disturbance precisely. This result can be generalized to the case of nonlinear uncertain systems in disturbance observer-based control (DOBC) frame. Simulations on a single-link robotic manipulator demonstrate the advantages of the proposed scheme.