State space analysis of the relation between two types of disturbance observers

This paper analyzes the structures and the internal dynamic characteristics of two types of disturbance observers. The disturbance observer is used to estimate and compensate the disturbance and the variation of the inputs caused by uncertainties. The exosystem-model-based disturbance observer is constructed against the augmented system with the disturbance generating model and the nominal plant model (Johnson (1972)). There is also the inverse-model-based disturbance observer, which is constructed with the inverse model of the nominal plant model (Ohishi et al. (1983)). The differences and advantages between these two types of disturbance observers have yet to be fully understood. Accordingly, this paper aims to clarify the relation between two types of disturbance observers from the viewpoint of state-space representation. First, the paper shows the explicit realization of the inverse-model-based disturbance observer. Then, a detailed analysis of the relation between the inverse-model-based and exosystem-model-based disturbance observers is given. This analysis shows the correspondence between the observer gains and the dynamics of the disturbance generating model.