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

Planing vessels suffer from porpoising instability at high forward speeds. Controllable transom flaps can be used to control the heave/pitch motion of the planing craft. In this paper, a nonlinear controller is designed based on the feedback linearization method to achieve asymptotic stability of the planning 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.