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Coupled Systems Mechanics Volume 13, Number 1, January 2024 , pages 73-93 DOI: https://doi.org/10.12989/csm.2024.13.1.073 |
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Time varying LQR-based optimal control of geometrically exact Reissner's beam model |
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Suljo Ljukovac, Adnan Ibrahimbegovic and Maida Cohodar-Husic
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| Abstract | ||
| In this work, we propose combining an advanced optimal control algorithm with a geometrically exact beam model. For simplicity, the 2D Reissner beam model is chosen to represent large displacements and rotations. The difficulty pertains to the nonlinear nature of beam kinematics affecting the tangent stiffness matrix, making it non-constant, which compromises direct use of optimal control methods for linear problems. Thus, we seek to accommodate a time varying control using linear-quadratic regulator (LQR) algorithm with the proposed geometrically nonlinear beam model. We provide a detailed theoretical formulation and its numerical implementation in a variational format form. Several illustrative numerical examples are provided to confirm an excellent performance of the proposed methodology. | ||
| Key Words | ||
| geometrically exact kinematics; linear-quadratic regulator; optimal control; Reissner's beam | ||
| Address | ||
| Suljo Ljukovac: University of Technology Compiègne-Alliance Sorbonne University, Laboratoire Roberval, Centre de Recherche Royallieu, Rue du Docteur Schweitzer, Compiègne, 60200, Hauts-de-France, France; Faculty of Civil Engineering, University of Sarajevo, Patriotske Lige 30, Sarajevo, 71000, Bosnia & Herzegovina Adnan Ibrahimbegovic: University of Technology Compiègne-Alliance Sorbonne University, Laboratoire Roberval, Centre de Recherche Royallieu, Rue du Docteur Schweitzer, Compiègne, 60200, Hauts-de-France, France; Institut Universitaire de France, 1 Rue Descartes, Paris, 75000, France Maida Cohodar-Husic: Faculty of Mechanical Engineering, University of Sarajevo, Vilsonovo Setaliste 9, Sarajevo, 71000, Bosnia & Herzegovina | ||
