Passivity-based Control of a Hydrokinetic Energy Kite with a Multi-element Tether

This paper studies passivity-based control of a tethered underwater kite used for energy generation. The mathematical formulation of the motion of a 6-degee-of-freedom(DOF) rigid kite is coupled with the continuous governing equations of a flexible tether. The tether is spatially discretized as N-frame elements so that the intrinsic infinite-dimensional set of partial differential equations (PDEs) is reduced to a finite second-order set of ordinary differential equations (ODEs). Using this formulation, a Lyapunov-stability analysis is conducted to establish operational conditions on the system parameters and states to achieve a certain level of internal and input-output stability and to provide proof of system trajectory boundedness. Previous passivity-based control schemes on tethered kite systems are used to establish a baseline scheme for the control logic that can accommodate the previously defined tether dynamics. A Lyapunov-based feedback linearization control is imposed on the rotational dynamics of the rigid kite according to overall stability and boundness conditions. Baseline simulation results that compare energy generation levels for decoupled-rigid kite dynamics, tether drag influenced-kite dynamics, and the tether-kite full dynamics are presented.