Continuous-time linear predictive control and flatness: a module-theoreticsetting with examples

A general flatness-based framework for linear continuous-time predictive co ntrol is presented. The mathematical setting, which is valid for multivaria ble systems, is provided by the algebraic theory of modules where a control lable system corresponds to a finitely generated free module over a princip al ideal ring. Any basis of this free module is a hat output which yields a n easy calculation of the predicted trajectory. This formalism permits one to handle non-minimum phase systems, system constraints, and to deal with a dditive perturbations. Three concrete case studies, namely a de motor, a fl exible system, and a cement mill, are analysed and simulations are given. T hese examples are written in such a way that any reader who is not familiar with module theory may nevertheless grasp the proposed control strategy.