Robust Stability Condition and Simplified Design of Filter-embedded Disturbance Observer

Embedding a filter is one of the simplest ways to enhance the disturbance attenuation performance of feedback control systems. In this paper, we introduce the filter-embedded disturbance observer (FDOB) and present a rigorous stability analysis of the FDOB. The proposed robust stability condition for the closed-loop system with the FDOB shows that if the filter to be embedded is stable and has zero relative degree with unity high-frequency gain, then the FDOB can be designed by simply adding the filter to a well-designed conventional disturbance observer (DOB) that guarantees closed-loop robust stability, and by adjusting the time constant of the Q-filter of the conventional DOB. It is also highlighted that the FDOB can be implemented by integrating the filter into the Q-filter of the conventional DOB, maintaining the add-on structure of the conventional DOB. In addition, it is shown that internal models of disturbances can be directly embedded into the filter of FDOB, which does not affect the design of the Q-filter. Simulation results on a motor control system are provided to validate the theoretical results.