Nonlinear optimal control of a ballast-stabilized floating wind turbine via externally stabilised Hamiltonian dynamics

Abstract

We consider the problem of controlling a ballaststabilized offshore wind turbine. We formulate an optimal control problem with the objective of maximising the power generation while minimising structural fatigue of the wind turbine. Due to the nonlinear nature of the model, obtaining a solution to the above control task poses a severe challenge. Recalling that solutions of the optimal control problem are characterised by a certain (unstable) invariant manifold of the underlying Hamiltonian system, we demonstrate that nonlinear control strategies which approximate the solution of the optimal control problem can be constructed through the introduction of an externally stabilised Hamiltonian system. This observation enables the construction of an algorithm to compute (with relatively low computational complexity) an approximate solution of the optimal control problem, without ignoring nonlinearities in the control design. This approach has several benefits, as demonstrated via simulations on a ballast-stabilized offshore wind turbine.