Nonlinear Control of Flat Systems Using a Non-Flat Output with Dynamic Extension

Abstract

If a nonlinear system is differentially flat and a flat output is known, the design of a linearizing feedback law is straightforward. For state-space systems, this corresponds to the input-to-state linearization. Otherwise, i.e., if the system is not flat or no flat output can be found, we could carry out an input-output linearization provided the system is minimum phase. In this case, only certain parts of the systems dynamics are assigned by the control law. From a theoretical point of view, this method is based on the Byrnes-Isidori normal form. A less common approach is the usage of the non-flat output in order to carry out a linearization in connection with the generalized controller canonical form [8]. The linearization is achieved by a dynamic extension. The existence of an alternative linearization method may be advantageous from a computational point of view and gives additional degrees of freedom, e.g., allowing for a higher-order of the desired closed-loop dynamics. Both approaches are illustrated on the nonlinear boost converter model.