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Research Papers

Analytical Stability Analysis of Surface Vessel Trajectories for a Control-Oriented Model

[+] Author and Article Information
Alan M. Whitman

Department of Mechanical Engineering, Villanova University, Villanova, PA 19085alan.whitman@villanova.edu

Hashem Ashrafiuon1

Center for Nonlinear Dynamics and Control, Department of Mechanical Engineering, Villanova University, Villanova, PA 19085hashem.ashrafiuon@villanova.edu

Kenneth R. Muske

Department of Chemical Engineering, Villanova University, Villanova, PA 19085

1

Corresponding author.

J. Comput. Nonlinear Dynam 6(3), 031010 (Feb 01, 2011) (10 pages) doi:10.1115/1.4002976 History: Received May 10, 2010; Revised October 28, 2010; Published February 01, 2011; Online February 01, 2011

An analytical stability analysis of the steady trajectory for a surface vessel with various damping models is presented in this work. The analysis is based on a control-oriented, three degrees-of-freedom model that considers vessel motion only in the horizontal plane. The goal of this study is to understand the vessel trajectories predicted by this reduced order model for model-based control design. Straight line and circular motion stability conditions for each trajectory are derived and presented for the various damping models. The results of this analysis show that either a straight line or a circular steady trajectory is possible, depending on the magnitude of the surge force and the form of the damping model used to represent viscous drag, vortex shedding, and losses due to the surface wake generated by the vessel motion. However, the straight line motion is much less likely for the vessel considered in this work.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Planar surface vessel schematic

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Figure 2

Comparison of different vessel model responses to a small constant propulsive force

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Figure 3

Comparison of different vessel model responses to a large constant propulsive force

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Figure 4

Comparison of terminal velocities for different drag models

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Figure 7

Comparison of simulated and experimental motion

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Figure 5

Diameter of circular motion as a function of propulsive force for various α values

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Figure 6

Comparison of exact and approximate solutions for α=1/2

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