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arXiv · 2110.12995

Tracking Control for $(x,u)$-Flat Systems by Quasi-Static Feedback of Classical States

Conrad Gstöttner·Bernd Kolar·Markus Schöberl
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Abstract

It is well known that for flat systems the tracking control problem can be solved by utilizing a linearizing quasi-static feedback of generalized states. If measurements (or estimates) of a so-called generalized Brunovsk\'y state are available, a linear, decoupled and asymptotically stable tracking error dynamics can be achieved. However, from a practical point of view, it is often desirable to achieve the same tracking error dynamics by feedback of a classical state instead of a generalized one. This is due to the fact that the components of a classical state typically correspond to measurable physical quantities, whereas a generalized Brunovsk\'y state often contains higher order time derivatives of the (fictitious) flat output which are not directly accessible by measurements. In this paper, a systematic solution for the tracking control problem based on quasi-static feedback and measurements of classical states only is derived for the subclass of $(x,u)$-flat systems.

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Conrad Gstöttner, Bernd Kolar, Markus Schöberl. 2021-10-25. Tracking Control for $(x,u)$-Flat Systems by Quasi-Static Feedback of Classical States. https://doi.org/10.3842/sigma.2024.071

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