A Lagrangian approach to nonlinear modeling of anti-roll tanks |
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Authors: | Christian Holden Tristan Perez Thor I Fossen |
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Institution: | 1. Department of Engineering Cybernetics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway;2. School of Engineering, Discipline of Mechanical and Mechatronics, The University of Newcastle, University Drive, Callaghan, NSW 2308, Australia;3. Centre for Ships and Ocean Structures, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway |
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Abstract: | This paper presents two novel nonlinear models of u-shaped anti-roll tanks for ships, and their linearizations. In addition, a third simplified nonlinear model is presented. The models are derived using Lagrangian mechanics. This formulation not only simplifies the modeling process, but also allows one to obtain models that satisfy energy-related physical properties. The proposed nonlinear models and their linearizations are validated using model-scale experimental data. Unlike other models in the literature, the nonlinear models in this paper are valid for large roll amplitudes. Even at moderate roll angles, the nonlinear models have three orders of magnitude lower mean square error relative to experimental data than the linear models. |
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