Stochastic Control of Sensitive Nonlinear Motions of an Ocean Mooring System

[+] Author and Article Information
Paul E. King

 U.S. Department of Energy, Albany Research Center, Albany, OR 97321

Solomon C. Yim

Coastal and Ocean Engineering Program, Department of Civil and Construction Engineering, Oregon State University, Corvallis, OR 97331solomon.yim@oregonstate.edu

J. Offshore Mech. Arct. Eng 129(1), 29-38 (Oct 03, 2006) (10 pages) doi:10.1115/1.2428323 History: Received October 14, 2005; Revised October 03, 2006

Complex sensitive motions have been observed in ocean mooring systems consisting of nonlinear mooring geometries. These physical systems can be modeled as a system of first-order nonlinear ordinary differential equations, taking into account geometric nonlinearities in the restoring force, quadratic viscous drag, and harmonic excitation. This study examines the controllability of these systems utilizing an embedded approach to noise filtering and online controllers. The system is controlled using small perturbations about a selected unstable cycle and control is instigated for periodic cycles of varying periodicities. The controller, when applied to the system with additive random noise in the excitation, has marginal success. However, the addition of an iterated Kalman filter applied to the system increases the regime under which the controller behaves under the influence of noise. Because the Kalman filter is applied about locally linear trajectories, the feedback of the nonlinearities through the filter has little effect on the overall filtering system.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Schematic of a moored structure subject to current and wave excitation

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Figure 2

Chaotic response of the mooring system showing: (a) the Poincaré section; (b) the phase space portrait; (c) the frequency spectrum; and (d) a time series plot

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Figure 3

Schematic of feedback control of a general plant represented as a set of differential equations

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Figure 4

Control of the ocean mooring system (a),(b) primary resonance; (c)-(d) 12 subharmonic; and (e)–(f) 1∕3 subharmonic

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Figure 5

Multi-plane control is achieved by constructing r separate control planes distributed evenly throughout phase space as exhibited here for r=8 for the mooring system

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Figure 6

Effects of noise on the chaotic mooring system attractor as seen through the Poincaré section of the mooring system for a SNR of: (a) 2.42; (b) 2.07; (c) 1.81; and (d) 1.48

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Figure 7

Effects of additive noise on mooring system control for the Period-1cycle and the SNR of: (a) 2.42; (b) 2.07; (c) 1.81; and (d) 1.48

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Figure 8

Application of the multi-plane control on the mooring system for the Period-1 case and for a SNR of: (a) 2.42; (b) 2.07; (c) 1.81; and (d) 1.48

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Figure 9

Effects of the number of control planes used versus the noise level for the mooring system

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Figure 10

Kalman filter approach to control of the discrete time, nonlinear system

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Figure 11

Application of the IKF to the nonlinear mooring system

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Figure 12

Unstable periodic orbit and iterates under the influence of the IKF for three of the Period-1cycles found within the mooring system



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