Generalized pole placement for systems requiring fast sampling

In this paper, we present a controller design applicable to sampled-data discrete-time systems which require fast sampling in the relative sense. It is based upon the ¿-operator, and uses a Generalized Predictive Controller [1] (GPC)-like structure which we had previously developed in [2]. Here, by using, in addition, the key elements of the novel approach of [3], the controller of [2] is further developed to incorporate the very useful properties of Generalized Pole-Placement in the sense defined in [3]. The result is an adaptive discrete-time conitroller applicable to systems requiring fast (relative) sampling, and which possesses the nice properties attained by the approach of [3]; it is effectively a ¿-operator redesign of the Generalized Pole Placement (GPP) controller. We remark that it is indeed a ¿-operator redesign, as opposed to simply a ¿-operator realization, of the GPP. This redesign requires the use of the auxiliary developments from [2], and might not have been possible without them. In addition, the re-design takes into account the properties of the ¿-operator as a discrete-time operator in its own right.