The absolute stabilization and optimal control of hydrofoil watercrafts

Abstract

Hydrofoil watercrafts have a technology through which immersed wings are mounted under the hull. In the longitudinal movement case, these transversal wings are developing a carrying capacity which lifts the ship, thus decreasing the wet surface. The hydrodynamic lag decreases too, reaching economic fuel consumption as well. The paper deals with the analytic and graphic-numeric study, specifying the stable movement regime in the vicinity of the critical (equilibrium) points v1, v2, v3. The asymptotical stability is highlighted by using the Liapunov criteria, too. The practical control (self-stabilization) is obtained by using an automate speed controller (scanner), depending on wings flaps and the ship attack angle compared to the horizontal. It may be observed that (1) is in the category of cuspidal-returns from the Catastrophes Theory and bifurcations. Transversal waves or wind disturbances causes a ship flutter effect. For hydrofoil dynamics, an optimal control is finally applied, using the minimal time criterion related to Lev Pontryagin’s extremum principle.

Keywords

• hydrofoil
• longitudinal movement
• asymptotical stability
• catastrophes theory
• mathematical model