Exact feedforward linearization based on differential flatness

Abstract

This article deals with the trajectory aspect of differential flatness from a feedforward point of view. The notion of exact feedforward linearization based on differential flatness is introduced: a differentially flat system, to which a nominal feedforward deduced from flatness is applied, is equivalent, by change of coordinates, to a linear multivariable Brunovsk@ form if the initial condition is consistent with the one considered in the design of the nominal trajectory. In its second part, the new notion states that there exist unique solutions in the vicinity of the desired trajectory when applying a nominal feedforward to the corresponding flat system. To the end of stabilizing the desired trajectory, the information from the Brunovský form is used to design the combination of the nominal feedforward and an additional feedback part. In the case of extended PID controls for the latter, stability is proven using a theorem by Kelemen. Thus the overall control structure turns out to be quite simple and effective for industrial application. Simulations of a DC drive example and experimental results of a magnetic levitation system illustrate its performance.