Abstract
In this paper, the stability of an umbilical–ROV system under nonlinear oscillations in heave motion is analyzed using numerical methods for the uncontrolled and controlled cases comparatively. Mainly the appearance of the so-called taut–slack phenomenon on the umbilical cable produced by interactions of monochromatic waves and an operated ROV is specially focused. Nonlinear elements were considered as nonlinear drag damping, bilinear restoring force and saturation of the actuators. Free-of-taut/slack stability regions are investigated in a space of physical bifurcation parameters involving a set of both operation and design parameters. They indicate a wide diversity in qualitative behaviors, both in the periodicity and possible routes to chaos from the stability regions to outside. For detection of periodicity of the nonlinear oscillations inside and outside the stability regions, a method based on Cauchy series is developed. The first part of the results is dedicated to the stability of the uncontrolled dynamics. These results suggest the design of a control system that is able to counteract hefty hauls of the cable during the sinking/lifting operation under perturbation. A combination of a force and cinematic controller based on nonlinear model–reference control is proposed. Through a comparative study of the stability regions for uncontrolled and controlled dynamics, it is shown that the control system can extend considerably these regions without appearance of the taut–slack phenomenon despite the presence of wave perturbations. The limits between the taut and taut–slack zones are defined by the wave steepness and the available energy of the actuators.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
AQWA: AQWA Reference Manual, Version 5.3A. Century Dynamics Ltd., UK (2002)
Behbahani-Nejad, M., Perkins, N.C.: Hydrodynamic and geometric stiffening effects on the out-of-plane waves of submerged cables. Nonlinear Dyn. 13(3), 243–257 (1997)
Dmitrieva, I., Lougovsky, V.: Non-linear harmonic, subharmonic and chaotic motion of offshore structures. In: Proceedings of the 8th International Conference on the Behaviour of Offshore Structures, Vol. 2, pp. 205–218, Delft, The Netherlands, (1997)
Feng, Z., Allen, R.: Evaluation of the effects of the communication cable on the dynamics of an underwater flight vehicle. Ocean Eng. 31, 1019–1035 (2003)
Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer-Verlag, Berlin (1997)
El-Hawary, F.: The Ocean Engineering Handbook. CRC Press, Boca Raton, Florida, USA (2001)
Ellermann, K., Kreuzer, E., Markiewicz, M.: Nonlinear dynamics of floating cranes. Nonlinear Dyn. 27(2), 107–183 (2002)
Fossen, T.I.: Guidance and Control of Ocean Vehicles. Wiley, Chichester, UK (1994)
Huang, S.: Stability analysis of the heave motion of marine cable-body systems. Ocean Eng. 26, 531–546 (1999)
Huang, S., Vassalos, D.: Heave response of a thetered subsea unit during the lunch and recovery process. In: Proceedings of the 2nd International Offshore and Polar Engineering Conference, San Francisco, (1992)
Indiveri, G.: Modelling and Identification of Underwater Robotic Systems, Ph.D. University of Genova (1998)
Jordán, M.A.: On-line identification and convergence analysis of excitation-force and drag-force models for moored floating structures. Ocean Eng. 33, 1161–1213 (2006)
Jordán, M.A., Beltrán-Aguedo, R.: Nonlinear identification of mooring lines in dynamic operation of floating structures. Ocean Eng. 31, 455–482 (2004)
Jordán, M.A., Beltrán-Aguedo, R.: Optimal identification of potential-radiation hydrodynamics for moored floating structures: A new general approach in state space. Ocean Eng. 31, 1859–1914 (2004)
Jordán, M.A., Bustamante, J.L.: Diseño de un observador no-lineal para Robots subacuáticos en operación de ascenso/descenso. In: Proceedings of the III Jornadas Argentinas de Robótica, San Juan, June 3–4, (2004)
Kijima, K., Fossen, T.I. (eds.): Control Applications in Marine Systems. Pergamon Press (2000)
Kleczka, W., Kreuzer, E.: On the systematic analytic-numeric bifurcation analysis. Nonlinear Dyn. 7, 149–163 (1995)
Papazoglou, V.J., Mavrakos, A., Triantaffilou, M.S.: Nonlinear cable response and model testing in water. J. Sound Vib. 140(1), 103–115 (1990)
Plaut, R.H., Farmer, A.L., Holland, M.M.: Bouncing-ball model of ‘dry’ motions of a tethered buoy. J. Vib. Acoustics 123(3), 333–339 (2001)
Rosenwasser, E.N.: Oscillations of Non-Linear Systems. Nauka, Moscow (1969)
Smith, R.J: Taut–slack dynamics of a vertically suspended subsea unit. In: Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering (OMAE), Vol. 1, pp. 873–884 (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jordán, M.A., Bustamante, J.L. Numerical stability analysis and control of umbilical–ROV systems in one-degree-of-freedom taut–slack condition. Nonlinear Dyn 49, 163–191 (2007). https://doi.org/10.1007/s11071-006-9120-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-006-9120-2