Abstract
Adaptive structures where actuators are incorporated into a building structure have the potential to reduce resource consumption in construction industry drastically. However, the performance of static load compensation depends to a large extend on the actuator placement. This paper presents optimal actuator placement for systems with distributed parameters based on the Gramian compensability matrix. To provide a general framework for different kind of loads, static loads are discretized as Dirac impacts. The resulting optimal actuator placement is robust against unknown load amplitudes, as load profiles are only considered qualitatively in the cost function. Further, the optimal control input for a given load results directly from the optimization problem. The procedure is illustrated for a Kirchhoff-Love plate and integrated fluidic actuators.
Zusammenfassung
Adaptive Strukturen, bei denen Aktoren in das Tragwerk integriert werden, zeigen großes Potential, den Ressourcenverbrauch im Bausektor drastisch zu verringern. Dabei hängt die Performance eines adaptiven Tragwerks maßgeblich von der Platzierung der Aktoren ab. In diesem Beitrag wird eine Methode zur optimalen Aktorplatzierung für verteiltparametrische Systeme basierend auf der Gramschen Kompensierbarkeitsmatrix vorgestellt. Um eine allgemeine Darstellung verschiedener statischer Lasten zu gewährleisten, werden diese als Dirac-Stöße diskretisiert. Die resultierenden optimalen Aktorpositionen sind robust gegenüber unbekannten Lastamplituden, da Lastprofile nur qualitativ berücksichtigt werden. Weiterhin leitet sich der optimale Eingang für eine gegebene Lastverteilung aus dem Optimierungsproblem ab. Die Methode wird am Beispiel einer Kirchhoff-Love Platte mit integrierten Fluidaktoren veranschaulicht.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: 279064222 – SFB 1244, B04
Funding statement: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 279064222 – SFB 1244, B04.
About the authors
Theresa Kleine received the B. Sc. degree and M. Sc. degree in engineering cybernetics from the University of Stuttgart, Stuttgart, Germany, in 2016 and 2019, respectively. Since 2019, she has been a research assistant at the Institute for System Dynamics, University of Stuttgart, where she is also working towards the Ph. D. degree. Her current research interests include modeling, design and control of electromagnetic systems.
Julia Wagner received her B. Sc. degree in medical engineering as a joint degree from the Universities of Stuttgart and Tübingen, Germany, in 2014. She finished her M. Sc. degree in the same course from the University of Stuttgart, Germany, in 2017. Since 2017, she is a research assistant and a Ph. D. candidate at the Institute for System Dynamics at the University of Stuttgart. Her main research interests are analysis and control of adaptive structures, a comprehensive understanding of their system dynamics and the couplings to other disciplines.
Michael Böhm received the Dipl.-Ing. degree and the Dr.-Ing. degree in engineering cybernetics from the University of Stuttgart, Stuttgart, Germany, in 2011 and 2017, respectively. Since 2017, he has been the head of the construction systems engineering group at the Institute for System Dynamics. His current research interests include dynamic modeling and control of mechanical systems and distributed parameter systems with applications to civil engineering.
Oliver Sawodny received his Dipl.-Ing. degree in electrical engineering from the University of Karlsruhe, Karlsruhe, Germany, in 1991 and his Ph. D. degree from the University of Ulm, Ulm, Germany, in 1996. In 2002, he became a Full Professor at the Technical University of Ilmenau, Ilmenau, Germany. Since 2005, he has been the Director of the Institute for System Dynamics, University of Stuttgart, Stuttgart, Germany. His current research interests include methods of differential geometry, trajectory generation, and applications to mechatronic systems. He received important paper awards in major control application journals such as Control Engineering Practice Paper Prize (IFAC, 2005) and IEEE Transaction on Control System Technology Outstanding Paper Award (2013).
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