Continuous-time non-linear flatness-based predictive control: an exact feedforward linearisation setting with an induction drive example

A general flatness-based framework for non-linear continuous-time predictive control is presented. It extends the results of Fliess and Marquez (2000 Fliess, M and Marquez, R. 2000. Continuous-time Linear Predictive Control and Flatness: A Module-theoretic Setting with Examples. International Journal of Control, 73: 606–623. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) to the non-linear case. The mathematical setting, which is valid for multivariable systems, is provided by the theory of flatness-based exact feedforward linearisation introduced by the authors (Hagenmeyer and Delaleau 2003b Hagenmeyer, V and Delaleau, E. 2003b. Exact Feedforward Linearization Based on Differential Flatness. International Journal of Control, 76: 537–556. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). Thereby differential flatness does not only yield an easy calculation of the predicted trajectories considering the respective system constraints, but allows to use simple linear feedback parts in a two-degree-of-freedom control structure. Moreover, this formalism permits one to handle non-minimum phase systems, and furthermore to deal with parameter uncertainties and exogenous perturbations. Respective robustness analysis tools are available. Finally, an induction drive example is discussed in detail and experimental results for this fast electro-mechanical system are presented.