Reduced order type-k disturbance observer based on a generalized Q-filter design scheme

As a robust control scheme, a disturbance observer (DOB) has been widely employed in industrial applications to reject the effect of disturbances and plant uncertainties. The disturbance rejection performance of DOB is mainly determined by the design of two Q-filters, which are the core components of DOB structure. Despite the different roles of each Q-filter, they have been typically designed to have the same structure. In this paper, we generalize Q-filters´ structures based on the observation about each Q-filter´s objective and derive a robust stability condition for the proposed DOB based control system. In addition, following the generalized Q-filter design scheme, a reduced order type-k DOB is proposed to enhance the disturbance rejection performance and reduce the order of type-k DOB compared with the conventional one. Finally, a constructive Q-filter design procedure for guaranteeing robust stability of the closed-loop system is proposed under parametric uncertainties of plant which belong to an arbitrarily large compact set.