Design of High-gain Observer-based High-order Internal Model Disturbance Observer

This paper presents a high-gain observer-based high-order internal model disturbance observer considering a single-frequency sinusoidal disturbance and mth-order polynomial-in-time disturbances. Two Q-filters in the disturbance observer structure serve different roles: one has disturbance compensation capability, and the other performs the implementation of the inverse dynamics. In specific, since the block of the Q-filter with the inverse dynamics has a high-gain observer structure, it is designed as the high-gain observer to facilitate state feedback control design. On the other hand, the disturbance compensation Q-filter incorporates the modeled part of the disturbance to eliminate it completely. Using the singular perturbation theory, it is demonstrated that the overall closed-loop system with the proposed disturbance observer completely compensates for the effect of modeled disturbances and behaves like the nominal closed-loop system. Furthermore, robust stability conditions under model uncertainties are provided. The effectiveness of the proposed disturbance observer is validated through simulation.