Generation of feasible and optimal reference trajectories is crucial in tracking Nonlinear Model Predictive Control. Especially, for stability and optimality in presence of a time varying parameter, adaptation of the tracking trajectory has to be implemented. General approaches are real-time generation of trajectories or switching between a discrete set of precomputed trajectories. In order to circumvent the operational efforts of these methods for a special type of dynamical systems, we propose time warping as an alternative approach. This algorithm implements online generation of tracking trajectories by warping a single precomputed reference. In detail, warpable systems, feasibility and optimality of trajectories and the controller implementation are discussed. Finally, as an application example, simulation results of a tethered kite system for airborne wind energy generation are presented.
Classical wind turbines suffer from a significant problem: while their power output scales with the square of the height, the mass does so cubically; as a result, material costs are high and the technology becomes non-competitive. Considering that the bulk of the power is generated by the outer parts of the rotor blades, AWE tries to extract wind power by means of tethered kite or airplanes (“wings”) while avoiding these high material costs. The conceptual idea is to fly these “wings” in a crosswind motion with the help of a strong cable and extract power by means of pumping cycles or small generators on board.
In this context and in collaboration with the company Skysails, this Masters thesis focuses on two research areas: computation of optimal trajectories for energy maximization by means of an OCP and design and implementation of NMPC on a real AWE system.
Using as a basis a previous research on periodic optimal trajectories, this thesis contributes to the field of optimal control and airborne wind energy with a set of four ideas: new safety conditions to augment the extracted power; the study of dynamic invariants within the periodic OCP; a proposed tethered kite model in natural coordinates and a performance comparison between the introduced model, a quaternion parameterization, and a model based on Euler angles; and the generation of different flight topologies to enhance the power efficiency.
Furthermore, in its second research domain, this thesis strengthens the field of airborne wind energy and control theory with the following three contributions: the design of a NMPC scheme on a real AWE system to track generated optimal trajectories; NMPC stability and robustness against real life perturbations such as wind gusts, delays in control inputs, parameter mismatches and realistic estimation errors; and development of the theory of warping systems, a manifold of dynamical systems for which an algorithm to perform online generation of optimal trajectories is proposed.