On the equivalence of inversion-based control architectures

Inversion-based control architectures are feedforward-feedback schemes in which the feedforward control is determined by stable input-output inversion. The main architectures of this type are the plant and the closed-loop inversion architectures. For scalar, linear, nonminimum-phase systems these architectures are shown to be equivalent for any disturbance and any plant perturbation for which the feedback controller ensures closed-loop stability. This equivalence - deduced by using a behavioral approach - also holds in practice when a careful truncation of the preaction control occurs. New output-error-based rules to set the preaction and postaction times of a stable inverse input are introduced. Still holding the equivalence, these rules help in choosing the preferable architecture at the implementation stage. An example with simulation comparisons highlights the paper findings. (c) 2023 European Control Association. Published by Elsevier Ltd. All rights reserved.