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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Authors: Gstöttner, Conrad, Kolar, Bernd, Schöberl, Markus
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212349
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Tracking Control for (, )-Flat Systems by Quasi-Static Feedback of Classical States. Conrad Gstöttner, Bernd Kolar and Markus Schöberl. SIGMA 20 (2024), 071, 27 pages

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 Brunovský 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 Brunovský 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 (, )-flat systems.