On the equivalence of model inversion architectures for control applications

The main inversion-based control architectures are the plant and closed-loop inversion architectures. For scalar continuous-time linear systems, these architectures are shown to be fully equivalent for both the minimum and nonminimum-phase cases when exact stable inverses are used. This equivalence, deduced by using a behavioral approach, dictates that the two architectures deliver the same performances for any disturbance and mis-modeling affecting the controlled plant. A simulation example highlights that the equivalence still holds in practice when a careful truncation of the preaction control is performed.