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On the Exact Linearization and Control of Flat Discrete-time Systems

Bernd KolarJohannes DiwoldConrad Gst\\"ottnerMarkus Sch\\"oberl
摘要
The paper addresses the exact linearization of flat nonlinear discrete-timesystems. Two main questions are investigated: The first one is how to determinewhich forward-shifts of a given flat output can be chosen in principle as a newinput, and the second one is how to actually introduce this new input by asuitable feedback. With respect to the choice of a feasible input, easilyverifiable conditions are derived. Introducing such a new input requires afeedback which may in general depend not only on this new input itself but alsoon its forward-shifts. Hence, there occur similarities to the class ofquasi-static feedbacks, which have already proven to be useful for the exactlinearization of flat systems in the continuous-time case. For systems with aflat output that does not depend on forward-shifts of the input, it is shownhow to systematically construct a new input such that the total number of thecorresponding forward-shifts of the flat output is minimal. Furthermore, it isshown that in this case the calculation of a linearizing feedback isparticularly simple, and the subsequent design of a discrete-timeflatness-based tracking control is discussed. The presented theory isillustrated by the discretized models of a wheeled mobile robot and a 3DOFhelicopter.
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