Abstract
The paper presents the possibilities of using B-splines to determine a mathematical model in the form of linear differential equations describing the change of the motion parameters of floating objects depending on the values of the control signals. The elaborated identification system is a collection of algorithms including: approximation of input and output signals, optimal selection of differential equation coefficients and model verification. The basic spline functions were used to approximate the values of the input and output signals. The developed method was illustrated by an example of identification of underwater submarine motion equations describing the change in draft depth and trim angle depending on the difference between buoyancy force and ship’s weight.
Highlights
SummaryThe paper presents the possibilities of using B-splines to determine a mathematical model in the form of linear differential equations describing the change of the motion parameters of floating objects depending on the values of the control signals
In [14] the smoothing splines were used for signals description
The algorithm presented in this paper enables the identification of dynamic systems described by the differential equations of the n-th order
Summary
The paper presents the possibilities of using B-splines to determine a mathematical model in the form of linear differential equations describing the change of the motion parameters of floating objects depending on the values of the control signals. The elaborated identification system is a collection of algorithms including: approximation of input and output signals, optimal selection of differential equation coefficients and model verification. The basic spline functions were used to approximate the values of the input and output signals. The developed method was illustrated by an example of identification of underwater submarine motion equations describing the change in draft depth and trim angle depending on the difference between buoyancy force and ship’s weight.
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