Performance Recovery and Stability Analysis of Disturbance Observer Under Unmodeled Dynamics

Feedback system design is often achieved by neglecting the unmodeled dynamics, such as the actuator and sensor, to reduce design complexity. It is based on an assumption that the unmodeled dynamics are fast enough to be negligible. However, it may cause severe problems for the stability or performance of the overall system, especially, when the controller contains the fast dynamics or uses the high-gain feedback term. A disturbance observer has been widely employed in many industrial applications due to its simple structure and powerful ability to reject disturbances and compensate plant uncertainties. However, since the disturbance observer contains fast dynamics in its structure, the analysis of the effect of the unmodeled dynamics on the disturbance observer-based control is mandatory. This paper reveals the robustness and disturbance rejection performance of the disturbance observer based on the singular perturbation theory and proposes its design guideline for robust stability in the presence of unmodeled dynamics. In addition, this paper presents that the disturbance observer recovers a nominal performance designed for a nominal model of the plant.