Modeling and Parameter Estimation of Planing and Semi-Planing Marine Vessels under Colored Disturbances

Abstract

A linear grey-box Multiple Input Multiple Output (MIMO) model describing ship attitude motion is derived from established nonlinear equations for ship motion. The model describes how five control surfaces: two fins, two interceptors and a rudder control the roll, pitch and yaw dynamics of a vessel. The model is developed for ship stabilization control design and consists of 15 parameters, neglecting the translational states surge, sway and heave. These neglected states are concluded to introduce errors in the model through residual correlation analysis, but the model is considered adequate for control design through empirical frequency domain validation using SPAFDR. To ensure the model is applicable to the different operating states of a planing vessel (displacement, hump and planing), it is validated at the operating states respective speed of a test vessel: 10, 15 and 20 kt. Input-output data is collected in open-loop system identification experiments. To make this possible, an excitation signal for MIMO system identification is proposed as a modified PRBS7 signal. The excitation signal is applied periodically to separate the ship’s deterministic output from the noise. The noise is analyzed, modeled as an ARMA process and concluded to be time-variant. Parameter estimation of the proposed ship model is performed using a batch Prediction Error Method (PEM) in the presence of colored noise. Furthermore, two recursive parameter estimation algorithms are implemented and tested on data with colored noise (specifically a Recursive Output Error Model and a Recursive Instrumental Variable State Varying Filter) to allow for parameter estimation on limited hardware, lacking the ability to use batch estimation methods.