Determining Parameters for a Lagrangian Mechanical System Model of a Submerged Vessel Maneuvering in Waves

In this dissertation, an approach for determining parameters for a nonlinear Lagrangian mechanical system model of a submerged vessel maneuvering near waves is presented. The nonlinear model with determined parameters is capable of capturing nonlinear effects neglected by other linear models, and therefore can be applied to improve maneuvering performance and expand the operating envelope for submerged vessels operating in elevated sea states.

To begin, a first principles Lagrangian nonlinear maneuvering (LNM) model for a surface-affected submerged vessel derived by using Lagrangian mechanics cite{BattistaPhD2018} is reformulated to allow the application of data from a medium fidelity potential flow code. In the reformulation process, the order of integration and differentiation in the integro-differential parameters are switched and partial derivatives of the Lagrangian function are computed with readily available data from the panel code solution. As a result, all model parameters can be computed individually using the panel code, wherein the need for additional numerical discretization is circumvented in the computation process through use of solutions already performed by the basic panel code, enabling higher accuracy and lower computational cost. Furthermore, incident wave effects are incorporated into the reformulated LNM model to yield a Lagrangian nonlinear maneuvering and seakeeping (LNMS) model. The LNMS model is numerically validated by confirming the proposed methods and by comparing steady and unsteady hydrodynamic force calculations from the LNMS model against panel code computations for various vessel motions in calm water and in plane progressive waves. Finally, methods for computing physically intuitive components of the model parameters, as well as methods for making approximations of the terms accounting for memory effects are presented, leading to a model formulation amenable to control design.

By applying the methods proposed in this dissertation, each and every parameter of the Lagrangian mechanical system model of a submerged vessel maneuvering in waves can be obtained accurately and with computational efficiency by using a potential flow panel code. The resulting nonlinear motion model provides higher model fidelity than existing unified maneuvering and seakeeping models, especially in applications such as nonlinear control design and simulation.