Extended Kalman Filter as Observer for a Hydrofoiling Watercraft : Modelling of a new hydrofoiling concept, based on the Spherical Inverted Pendulum Model

Abstract: Hydrofoiling in general has the potential to revolutionize watercraft in the future since it allows smoother and faster transport on water with less energy consumption than traditional planning hulls. Even if the concept of hydrofoiling has been around since the last century, development in control theory and material science together with increased computing power has led to a growing interest for the technology. Especially in water sports such as speed sailing and surfing due to its superiority in speed and comfort. Researchers and students at the Engineering Mechanics Department at KTH, Royal Institute of Technology, Stockholm are working on a new type of watercraft, utilizing only one single hydrofoil with the intention to minimize drag for faster and smoother rides in various wave and weather conditions. The difficulties lie in understanding the relationship between actuators and the mechanics. This thesis is a continuation work from a previous thesis which designed a control strategy based on a model with 4 degrees of freedom (DOF). Due to simplifications and linearizations, the 4 DOF model was not rich enough to meet the performance requirements. This thesis presents a 6 DOF model by deriving the mechanical equations for the spherical inverted pendulum and actuation from the hydrofoiling module. The inverted pendulum model is a well-known control problem that can be solved with different strategies. By showing that the hydrofoiling concept can be modelled as an inverted pendulum, it is also shown that it can be controlled as an inverted pendulum. The derived model is used together with an Extended Kalman Filter to create an observer. The observer is validated with a spherical inverted pendulum model in Matlab and the block diagram environment, Simulink. Simulation results show that the 6 DOF model is able to produce accurate state estimation of the watercraft even in the presence of stochastic measurement noise. It is also concluded that viscous forces, that arise from the watercraft being partly surrounded by water and partly by air, need further investigation.