Design of Dynamic Deadbeat Controllers Using an Observer or a Dual Observer in Discrete Time Linear Multivariable Systems

Abstract

This paper considers the problem of designing the minimum time dynamic deadbeat controllers, using an observer or a dual observer. As a preliminary, optimal controller and observer are defined and obtained. Then, the existence of a dynamic deadbeat controller is examined, and a separation theorem is proved. This theorem states that the minimum time dynamic deadbeat controller is given by the optimal controller combined with the optimal observer. These results are dualized to yield the corresponding result in the case of using the dual observer, i.e., the result on the minimum time dual deadbeat controller. Finally, a method is presented for finding reduced order controllers by applying the results on linear function observers.