A Simple Algorithm for the Construction of Flat Outputs
Sprache des Vortragstitels:
Since the introduction of flatness for lumped parameter systems into control about 15 years ago, this approach has become quite popular in theory of lumped parameter systems. Also extensions to distributed parameter systems are known, particulary for trajectory planning. Apart from many progresses the "simple" problem, how to construct a flat output, has remained open. Although several special results are known, a general method to determine the flat output for nonlinear systems with more than one input, if it exists, is currently not available. This contribution proposes an elimination theory based approach to construct flat outputs for nonlinear lumped parameter systems with an arbitrary number of inputs. The main concept is the gradual reduction of the system to simpler ones such that one can decide for the final system, whether it admits a flat output. If the final system admits one, then a flat output for the initial system can be constructed in a straightforward manner. Since elimination of variables leads to implicit systems in general, this contribution deals with implicit dynamic systems. To complete the talk some examples will demonstrate, how the proposed approach can be used to construct flat outputs. Furthermore, the well known VTOL problem can be downloaded from http://regpro.mechatronik.uni-linz.ac.at/about/staff/schoeberl/.