Dr. Felix Antritter

Universität der Bundeswehr München, Germany

For differentially flat linear and nonlinear control systems there exists a so-called flat output which allows a differential parameterization of the states and inputs of the system. This parameterization simplifies, e.g., the feedforward controller design for a rest-to-rest-maneuver to an algebraic problem. Also the tracking contoller design is very convenient for differentially flat systems, since a feedback controller, which achieves linear tracking error dynamics, can be computed by means of the parameterization.

The drawback of the flatness based approach is the fact that there is no finitely terminating algorithm for checking differential flatness of a given systems and to compute a flat output, at least for general nonlinear systems. For linear systems flatness is equivalent to controllability and can therefore be checked algebraically. Also for nonlinear single-input systems, differential flatness can be checked. The computation of the flat output, however, needs the solution of a system of PDEs. For nonlinear multi-input systems, non-flatness can be proven for some systems using the ruled manifold criterion. In this course the necessary and sufficient conditions introduced by J. Levine are presented. The evaluation of these conditions for nonlinear multi-input systems is rather computationally involved. A software tool is discussed which allows to evaluate the conditions according to a sequential procedure.