Systematic Approach to Mathematical Modelling of a Submarine Dynamics
at the Periscope Depth
A0114Sadko Mandzuka Brodarski Institute
Operating at the periscope depth below a seaway, a submarine is in an
unstable condition. As a free surface is approached, the wave forces
increase, trying to pull the submarine to the surface . To counter
these forces, the submarine's ballast may be changed and/or control
surfaces are used. Because of the stochastic nature of waves, the
manual operation of the submarine for longer periods at the periscope
depth exhausts the submarine control operators. Improved periscope
depth performance is therefore imperative [2,3].
As a submarine approaches the free surface, several complexities are
introduced into the mathematical modelling of its dynamics. The
approach used in this paper is first to establish a dynamic model
appropriate for a deeply submerged submarine at moderate speeds. The
forces and moments resulting from the seaway will then be superimposed
on that model to provide a reasonable approximation to the submarine
motion below waves. In the published submarine periscope depth
control research, [4,5], these disturbances were modelled by the
simple affine form. The main disadvantage of this approach is a poor
correspondence with the real situation. The dynamic model is
inadequate, and there is no phase information between Zwave (t), Mwave
(t) and v (t). The seawave spectra are described in the mathematical
form using different kinds of spectra . Unfortunately, the
equations arising from such descriptions are difficult to manipulate
in analytical investigations. Following the linear theory, using
spectral factorisation techniques, the sea spectrum was modelled by
transfer function representation (colour filter). The model of the
depth-attenuation factor by the first order lag is a reasonable
choice.A new presented high-frequency mathematical model of a
submarine dynamic at the periscope depth is writen in the form of
color filter. The numerical and simulation examples given in this
paper are based on the mathematical model of the dynamic of new
Croatian Navy midget submarine VELEBIT.
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