Cables, Submarine--Mathematical models

Technology movement toward deeper waters necessitates the control of vertically tethered systems that are used for installing, repairing, and maintaining underwater equipment. This has become an essential ingredient for the future success of the oil industry as the near-shore oil reservoirs are nearly depleted. Increased operation depths cause large oscillations and snap loadings in these longer cables. Research on this topic has been limited, and includes only top feedback control. The controllers developed in this thesis utilize top, bottom and combined top and bottom feedback. They are implemented on a discrete finite element lumped mass cable model. Comparison between PID, LQG and H infinity for all feedback combinations reveal that the Hinfinity controller with both top and bottom feedback has the best performance, while LQG has a more consistent and reliable performance for all feedback cases.

This thesis develops a novel variable length cable model to simulate the behavior of submerged cables with variable unstretched length and a PC based simulation that integrates the governing cable equations. The general model is developed from continuous cable equations that are discretized using a finite element method with linear elements. Two systems of equations were developed, one for a variable length elastic element and the other for a constant length elastic element. A cable transition model is developed to ensure dynamic compatibility when a variable length element is divided or combined. The model proved to be an efficient and reliable tool to predict the behavior of underwater cables with variable length.