Reliability of Switched Model-Based Controller for Vessel Dynamic Positioning With Switching Under Estimated Motion Frequency

In switched-control methodology, which integrates several controllers handling different environmental conditions for dynamic positioning (DP) systems in marine vessels, the supervisor uses the estimated wave peak frequency (WPF) to classify the existing environmental condition so as to switch to the appropriate controller. The WPF is assumed to be the same as the peak frequency of the vessel’s response spectrum at wave frequency estimated by fast Fourier transform (FFT) of the measured position and heading. Using a short window width leads to error in the WPF estimation whereas a longer width causes a significant time lag in control activation. This paper addresses the effect of uncertainty in the estimation of WPF by FFT on the reliability of the switched-controller based DP vessel. The probability of the supervisor switching to a wrong controller due to WPF estimation error is first evaluated for four different environmental conditions. The failure probabilities of the system with and without WPF uncertainty are then evaluated and compared. Numerical simulation based on a supply vessel shows that the increase in failure probability of the switched-controller DP system due to the uncertainty in the estimated WPF by FFT is not significant compared with the failure probability of a perfect switched-controller DP system.