Sea wave modelling for motion control applications
DOI:
https://doi.org/10.3329/jname.v11i1.17768Keywords:
Shaping filter, White noise, Rational polynomial, Least square fitting, State space model,Abstract
The modelling of sea environment is important in designing an effective motion control system for any marine vehicle. Inadequate representation of the components of a typical random sea might lead to poor performance of the control system. A multiple output system such as the one having components of wave elevation and slope, facilitates designing the control system taking into account the different degrees of freedom. The method of modelling the sea environment presented here, provides the basis for the design of motion control systems for multiple degree of freedom cases, which give rise to excitation forces and moments acting on the marine vehicle. The method used here models the sea environment using Gaussian white noise and shaping filter to generate a multiple output form of the random sea state. In the first step a given standard wave spectrum is approximated using a rational polynomial, the coefficients of the polynomial are obtained by least square fitting method to best match the spectrum. The established rational polynomial is then decomposed to get the transfer function of the shaping filter. The wave slope spectrum is similarly approximated using the same rational polynomial. The transfer functions of the two components of amplitude and slope, representing the filters are combined to generate a state space form. Using the white noise as input, the state space form obtains the wave elevation and slope as outputs. By performing spectral analysis using Welch method, the quality of the obtained output is checked against the targetted spectrum. The application of the simulated wave slope spectrum in a closed loop state space model is demonstrated as applied to the roll stabilization characteristics of a stationary ship using a passive tank.
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