A multiestimation discrete-time adaptive control incorporating fractional order holds and multirate sampling with stabilization of the discrete plant zeros

Abstract

A multiestimation scheme with a discrete-time matching controller for linear time-invariant (LTI) continuous-time plant with unknown parameters is presented. The scheme incorporates several discretization models running in parallel. Each of these models is calculated from a different combination of the correcting gain beta in a fractional order hold (FROH) and the set of gains to reconstruct the plant input under multirate sampling with fast input sampling. The estimated discrete unstable zeros are avoided through an appropriate design of the multirate gains so that the reference model might be freely chosen with no zeros constrains. Since the plant parameters are unknown, they have to be estimated. However, only the active model is updated by using a least squares algorithm. The rest of possible models are updated by first calculating an estimated continuous transfer function, which results to be identical for all the models. A tracking performance index is used to select the model with the best behavior.