On roll stabilization using a canting keel

This article investigates the modeling and control of a canting keel mechanism for roll reduction in marine vessels, examining two distinct configurations through simulation and experimental validation. A comprehensive nonlinear mathematical model of the system describing the roll motion of a vessel equipped with the canting keel, derived from first principles and accounting for the influence of unbalanced loading and waves, is provided. In the positively buoyant configuration of the keel, known as "airkeel (AK)", the system is shown to exhibit nonminimum phase (NMP) behavior arising from locally unstable zero dynamics, which, in turn, poses significant challenges for controller design. This issue is addressed by selecting proper coordinates that allow the supertwisting control (STC) algorithm to mitigate both matched and unmatched disturbances in conjunction with an extended state observer (ESO). The effectiveness of the proposed scheme is demonstrated in simulation through several case studies involving roll damping, unbalanced loading, and disturbances caused by waves generated by a stochastic model. The results are then objectively validated by experiments conducted on a small-scale model boat within an indoor test setting that emulates uneven loading conditions, as well as a field test examining the impact of sea waves on rolling behavior. The findings indicate that by appropriately selecting control parameters, the vessel's roll response can be tailored to its operational mode, thereby optimizing system performance and enhancing disturbance rejection.