Lemmas on Determination of Minimum Bandwidth of Q-filter for Robust Stability of Feedback Loop with Disturbance Observers

Abstract

As the disturbance observer (DOB)-based controller has been widely applied in practice, various aspects of the disturbance observer have been theoretically studied. In particular, robust stability of the linear closed-loop system with single-input single-output (SISO) Q-filter-based DOB has been rigorously analyzed, and finally, a necessary and sufficient condition for robust stability was obtained under the premise that the bandwidth of Q-filter is large. However, even the most recent study about the design of Q-filter-based DOB for robust stability does not offer a practical method for the determination of the Q-filter's bandwidth. In this paper, we present several lemmas regarding the determination of the bandwidth, from which a procedure is developed that can exactly compute the threshold of the bandwidth, so that robust stability (against parametric variations of the plant within a prescribed range) is lost if the bandwidth of the Q-filter becomes lower than that. The proposed procedure is implemented in a MATLAB toolbox named DO-DAT, which is now available at https://do- dat.github.io.