Rejection of polynomial-in-time disturbances via disturbance observer with guaranteed robust stability

The type-k disturbance observer, known as 'high order disturbance observer', is a variant of disturbance observer which contains an internal model for polynomial-in-time disturbances so that it can reject those disturbances exactly as well as unmodelled low frequency disturbances approximately. This paper presents a systematic design procedure for the type-k disturbance observer so that the closed-loop system is robustly internally stable and at the same time polynomial-in-time disturbances are rejected exactly. To develop the procedure, we employ the Kharitonov theorem and a root-locus based design tool to deal with the uncertain plant parameters explicitly, and as a result it is guaranteed that one can always find a solution step by step even if the uncertain parameters belong to an arbitrarily large (but bounded) set.