Identification of parameters of mathematical non-linear model of vessel longitudinal motion

The article considers the important task of modern control theory to construct an adequate mathematical model of a specific dynamic object or vessel movement, that is, its identification (structural or parametric). It is proposed to construct a nonlinear model of the longitudinal motion of the ship. Practical data were obtained experimentally, a brief description of the experimental platform for an unmanned boat and equipment used in the study of the object dynamic characteristics is given. It is noted that the boat is characterized by three modes of movement: displacement, transitional and planning. The relationship between the thrust of the propeller and the speed of the boat is determined. To solve the identification problem in the work, it is proposed to use the apparatus of power series. The power series coefficients are determined experimentally. The problem of selecting the coefficients of a power series can be solved using the least squares method. In order to avoid the cumbersome calculations there were used numerical optimization methods applying the capabilities of the MS Excel computing environment. The solution to the problem was obtained by using a different number of members of the power series ($N = 1, 3, 5$). The efficiency of the proposed approach is justified.