On the relations between different flatness based design methods for tracking controllers

Flatness based tracking controllers (see e.g. (M. Fliess et al., 1995), (P. Martin et al., 1997), (J. Levine, 1999), (H. Sira-Ramirez and S.K. Agrawal, 2004)) are a very important tool for nonlinear controller design. Such tracking controllers achieve an exact linearization of the tracking error dynamics. In (V. Hagenmeyer and E. Delaleau, 2003) a different flatness based tracking controller has been proposed based on the notion of feedforward linearization. This contribution clarifies the relations between these two flatness based tracking controllers and the tracking controller design for flat systems which has been proposed in (J. Deutscher, 2003), (F. Antritter et al., 2004). This approach uses a differential operator representation of the linearized tracking error dynamics and yields a linear time varying feedback. Similarities and differences of the different controllers are pointed out and are illustrated for a magnetic levitation system.