A new approach to the study of controlled systems: Multiestimation adaptive discrete control with multirate sampling

The purpose of this paper is to improve the transient response and the inter‐sample behavior of a model reference adaptive control system by an appropriate selection of the fractional order hold (FROH) gain β and the multirate gains used in the control reconstruction signal through a fully freely chosen reference model even when the continuous plant possesses unstable zeros.

A multiestimation adaptive control scheme for linear time‐invariant continuous‐time plant with unknown parameters is presented. The set of discrete adaptive models is calculated from a different combination of the correcting gain β in a FROH and the set of gains to reconstruct the plant input under multirate sampling with fast input sampling. Then the scheme selects online the model with the best continuous‐time tracking performance which includes a measure of the inter‐sample ripple, which is improved. 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 constraints on potential unstable zeros.

The scheme is able to select online the discretization model with the best continuous‐time tracking performance without an appropriate initialization.

The switching mechanism among the different models should maintain in operation the active discretization model at least for a minimum residence time in order to guarantee closed‐loop stability. The inter‐sample behavior is improved, but it is not always completely removed.

The transient response and the inter‐sample behavior are improved by using this multiestimation‐based discrete controller compared with a single estimation‐based one. The implementation of discrete controllers makes it easier and cheaper to implement and also more reliable than continuous‐time controllers.

The main innovation of the paper compared with previous background work is that the reference output is supplied by a stable continuous transfer function. Then the scheme is able to partly regulate the continuous‐time tracking error while the controller is essentially discrete‐time and operated by a FROH in general.