A note on disturbance observer with unknown relative degree of the plant

The disturbance observer (DOB)-based controller has been widely applied to real applications since it is able to recover, in spite of plant uncertainties and input disturbances, the performance of the nominal system. In this paper, we study robust stability of the DOB control system when the relative degree of the plant P is greater than or equal to that of nominal model P
_n
. Based on the standing assumption that the bandwidth of the Q-filter is sufficiently large, our study reveals the following: (1) If the relative degree difference is equal to one, then robust stabilization can be achieved by careful selection of the Q-filter and P
_n
. (2) If the relative degree difference is greater than one, then robust stabilization is not possible no matter how Q-filter and P
_n
are chosen.