Optimal Stochastic Path Control of Surface Ships in Shallow Water

Abstract

The control of a surface ship along a prescribed straight_line path is formulated as a stationary linear, state_variable control problem. The open-loop characteristics of this problem are studied using data for a Mariner type ship at two speeds and varying water ratio and for the tanker Tokyo Maru at one speed and varying water ratio using data obtained by Fujino. Optimal stochastic control systems using a Kalman-Bucy filter and a state_feedback controller are designed for both vessels at various conditions. These designs are developed to control the ship when subject to random, zero-mean disturbances. The design disturbances are the yaw moment and sway force due to a passing ship which are modeled by first-order shaping filters in the design derivation. The selection of a set of measurements adequate to provide effective path control is studied. System performance is studied by the evaluation of the Root Mean Square (RMS) response of the controlled ship to the modeled design disturbances and by digital computer simulation of the response of the controlled ship to initial condition errors and the specific disturbances due to a passing ship. The effects of vessel speed and water depth on the design and performance of these controllers are studied in detail. These results yield guidance for the selection of design conditions for the design of constant_gain controllers and provide an assessment of the need for adaptive controllers which can adjust the gains to remain optimal as the ship characteristics change with vessel speed and water depth. A sensitivity study is presented to show quantitatively which of the system coefficients which change with water depth can be assumed constant and which of the coefficients must be considered variables in an adaptive path control system design.