A study of disturbance observers with unknown relative degree of the plant

Robust stability of the disturbance observer (DOB) control system is studied when the relative degree of the plant is not the same as that of the nominal model. The study reveals that the closed-loop system can easily become unstable with sufficiently fast Q-filter when the relative degree of the plant is not known. In a few cases of unknown relative degree, however, robust stability can be obtained, and we present a design guideline of the nominal model, as well as the Q-filter, for that purpose. Moreover, a universal design of DOB is given for a plant whose relative degree is uncertain but less than or equal to four.