Minimum-order exosystem-model-based disturbance observer and the relation among the disturbance observers

The authors aim to show the relation among the disturbance observers. This paper considers disturbance observers, which are constructed to estimate the steady disturbance affecting the outputs of the plants with the same inputs and outputs. For such disturbance observers, Shikada and Sebe showed that the inverse-model-based disturbance observer could be realized as a full-order Luenberger-type observer for the nominal model. On the other hand, the exosystem-model-based disturbance observer is a full-order observer for the augmented system consisting of the nominal plant model and the exosystem model. Accordingly, the order of the exosystem-model-based disturbance observer is higher than that of the inverse-model-based disturbance observer. As a final remaining problem to clarify the relation of the disturbance observers, this paper constructs the minimum-order exosystem-model-based disturbance observer to fill the gap in their order. Furthermore, this paper also clarifies the one-to-one correspondence to the Luenberger-type disturbance observer for the nominal plant model. This correspondence shows that the minimum-order exosystem-model-based disturbance observer can achieve the same characteristics as the inverse-model-based disturbance observer. Finally, this paper summarizes the obtained relation among the disturbance observers in one inclusion relation. The obtained inclusion relation shows that all types of disturbance observers can be interpreted as one of the exosystem-model-based disturbance observers.