Relation between generalized proportional integral observer and linear disturbance observer based control

Among di fferent disturbance compensation based control methods, the way of estimating disturbances is the core. This paper studies the relationship between two frequently used observer, i.e., generalized proportional integral observer (GPIO) and linear disturbance observer (DOB). By rigorously calculating the transfer function of GPIO, it is revealed that GPIO is exactly an optimal linear DOB. In details, by carefully designing the order and parameters of Q-filter in DOB, the estimating performance of GPIO and linear DOB is the same. The presented theoretical result further shows the relationship between extended state observer and linear DOB, which generalizes the existing results.