13 March 2003 Approximate normal stresses for the boundary control of flexible structures
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When trying to control flexible structures by means of model-based control strategies, the necessary model reduction by means of discretization schemes may completely change the behavior of the 'true' or reference structure to be controlled. For example, the exact pointwise displacement control of a beam, once discretized by standard low-degree finite elements, is the solution of an ill-posed problem, resulting in wildly oscillating controls and suggesting the beam be less and less controllable when the mesh gets refined, whereas the continuous, or reference, model is exactly controllable, and although the mentioned finite elements yield a converging approximation of the statics and of the free dynamics of the structure. Moreover, the closed-loop spectrum associated with optimal control may get closer to the imaginary axis when the mesh is refined, even in cases when the reference model is uniformly exponentially stable.
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Frederic Bourquin, "Approximate normal stresses for the boundary control of flexible structures", Proc. SPIE 4763, European Workshop on Smart Structures in Engineering and Technology, (13 March 2003); doi: 10.1117/12.508684; https://doi.org/10.1117/12.508684

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