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Optimal Actuator Placement for Dynamical Systems
Author(s) -
Schäfer Carsten,
Ulbrich Stefan
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310227
Subject(s) - controllability , controllability gramian , control theory (sociology) , actuator , context (archaeology) , gramian matrix , computer science , noise (video) , state space representation , mathematics , physics , algorithm , control (management) , artificial intelligence , image (mathematics) , biology , paleontology , eigenvalues and eigenvectors , quantum mechanics
Vibrations occur in many industrial areas and produce undesirable side effects. To avoid respectively suppress these effects actuators can be attached to the structure. Actuators can transfer forces into the structure, which can be used to control the system behavior of the structure in order to achieve, for example, vibration absorption, noise reduction and/or exact positioning. The appropriate positioning of actuators is of significant importance for the controllability of the structure. We present a method for determining the optimal actuator placement. We consider applications, where the dynamics of a system can be described by a finite dimensional, controllable and observable state‐space model. The concept of controllability by Kálmán forms the basis for the definition of controllability measures. In this context, the controllability gramian plays an important role. In our approach actuators are placed in such a way that the selected controllability measure becomes maximal. This leads to an optimization problem with binary and continuous variables and linear matrix inequalities. The numerical results show the optimal actuator placement for a two dimensional flexible clamped plate. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)