Feedback stabilization of high-speed planing vessels by a controllable transom flap

This paper focuses on the mitigation of porpoising instability of high-speed planing vessels using controllable transom flap and dynamic feedback. A control oriented model that captures both steady-state and dynamic characteristics is presented and used to facilitate the model-based control design. A nonlinear controller is developed based on the feedback linearization method to achieve asymptotic stability of the planing boat, thus avoiding porpoising at high speeds. We first show that the full-state nonlinear dynamic model describing the ship motion is not feedback linearizable. A state transformation is then constructed to decompose the model into a linearizable subsystem and a nonlinear internal dynamic subsystem. A reduced order state feedback is shown next to stabilize the planing vessel motion around the equilibrium point. Analysis of the region of attraction is also performed to provide an assessment of the effective safe operating range around the equilibrium point.