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Control for (highly) flexible geometrically exact 2D Reissner beam by energy shaping of distributed port-Hamiltonian system.

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Title: Control for (highly) flexible geometrically exact 2D Reissner beam by energy shaping of distributed port-Hamiltonian system.
Authors: Ljukovac, Suljo1,2 (AUTHOR) suljo.ljukovac@utc.fr, Ibrahimbegovic, Adnan1,3 (AUTHOR) adnan.ibrahimbegovic@utc.fr
Source: Multibody System Dynamics. Jun2026, Vol. 67 Issue 2, p437-465. 29p.
Subjects: Distributed parameter systems, Hamiltonian systems, Curved beams, Control theory (Engineering), Damping (Mechanics), Nonlinear control theory
Abstract: The main focus of this work is control of large overall motion of (highly) flexible Reissner beam that can represent in geometrically exact manner large displacements, large rotations and large strains. This nonlinear control problem is cast in distributed port-Hamiltonian framework, extending the previous works (Duindam et al. in Modeling and Control of Complex Physical Systems: The Port-Hamiltonian Approach, Springer, Berlin, 2009) dealing with finite dimensional systems (such as rigid components of multibody system interconnected with flexible joints) to infinite dimensional system with Hamiltonian density (Ljukovac et al. in Int. J. Numer. Methods Eng. 126, 2025). The nonlinear control is performed by defining the desired state of the flexible system through energy-shaping of distributed port-Hamiltonian, previously introduced for lumped-parameter system (Ortega et al. in IEEE Control Syst. Mag. 21:18–33, 2001; Brogliato et al. in Dissipative Systems Analysis and Control: Theory and Aplications, Springer, Cham, 2020). We first show how to perform the energy shaping for internal energy density by bringing the flexible beam with large overall motion into deformed configuration that is in static equilibrium, which is also the closest to the desired configuration of Reissner beam after large overall motion. We then show how to perform the energy shaping for kinetic energy, with the illustration provided for the choice of uniform rotational motion, which also requires the corresponding choice of internal energy defined by Casimir functional (Marsden et al. in Hamiltonian Reduction by Stages, Springer, Berlin, 2007). We finally discuss different procedures for damping injection that will stabilize the system to configurations with desired Hamiltonian, including viscous damping, frictional damping and energy decaying of high frequency modes for Reissner nonlinear beam. The results of illustrative numerical simulations of large overall motion of (very) flexible geometrically exact beam confirm the good performance of the proposed approach. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:The main focus of this work is control of large overall motion of (highly) flexible Reissner beam that can represent in geometrically exact manner large displacements, large rotations and large strains. This nonlinear control problem is cast in distributed port-Hamiltonian framework, extending the previous works (Duindam et al. in Modeling and Control of Complex Physical Systems: The Port-Hamiltonian Approach, Springer, Berlin, 2009) dealing with finite dimensional systems (such as rigid components of multibody system interconnected with flexible joints) to infinite dimensional system with Hamiltonian density (Ljukovac et al. in Int. J. Numer. Methods Eng. 126, 2025). The nonlinear control is performed by defining the desired state of the flexible system through energy-shaping of distributed port-Hamiltonian, previously introduced for lumped-parameter system (Ortega et al. in IEEE Control Syst. Mag. 21:18–33, 2001; Brogliato et al. in Dissipative Systems Analysis and Control: Theory and Aplications, Springer, Cham, 2020). We first show how to perform the energy shaping for internal energy density by bringing the flexible beam with large overall motion into deformed configuration that is in static equilibrium, which is also the closest to the desired configuration of Reissner beam after large overall motion. We then show how to perform the energy shaping for kinetic energy, with the illustration provided for the choice of uniform rotational motion, which also requires the corresponding choice of internal energy defined by Casimir functional (Marsden et al. in Hamiltonian Reduction by Stages, Springer, Berlin, 2007). We finally discuss different procedures for damping injection that will stabilize the system to configurations with desired Hamiltonian, including viscous damping, frictional damping and energy decaying of high frequency modes for Reissner nonlinear beam. The results of illustrative numerical simulations of large overall motion of (very) flexible geometrically exact beam confirm the good performance of the proposed approach. [ABSTRACT FROM AUTHOR]
ISSN:13845640
DOI:10.1007/s11044-025-10139-0