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

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