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On the Exact Linearization and Control of Flat Discrete-time Systems | | Bernd Kolar
; Johannes Diwold
; Conrad Gstöttner
; Markus Schöberl
; | | Date: |
1 Jan 2022 | | Abstract: | The paper addresses the exact linearization of flat nonlinear discrete-time
systems. Two main questions are investigated: The first one is how to determine
which forward-shifts of a given flat output can be chosen in principle as a new
input, and the second one is how to actually introduce this new input by a
suitable feedback. With respect to the choice of a feasible input, easily
verifiable conditions are derived. Introducing such a new input requires a
feedback which may in general depend not only on this new input itself but also
on its forward-shifts. Hence, there occur similarities to the class of
quasi-static feedbacks, which have already proven to be useful for the exact
linearization of flat systems in the continuous-time case. For systems with a
flat output that does not depend on forward-shifts of the input, it is shown
how to systematically construct a new input such that the total number of the
corresponding forward-shifts of the flat output is minimal. Furthermore, it is
shown that in this case the calculation of a linearizing feedback is
particularly simple, and the subsequent design of a discrete-time
flatness-based tracking control is discussed. The presented theory is
illustrated by the discretized models of a wheeled mobile robot and a 3DOF
helicopter. | | Source: | arXiv, 2201.00189 | | Services: | Forum | Review | PDF | Favorites | |
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