Nonlinear Control and Estimation of a Tethered Kite in Changing Wind Conditions

Abstract

K ITE systems have been identified as a potential means for generating power from high-altitude winds [1–3]. Many early concepts for extracting wind energy from high altitudes focused on placing a generator in the prevalent winds [4,5]. This has the major drawback of wasting a significant amount of power just to maintain the system at the desired altitude. Alternatively, keeping the generator on the ground and using a light lifting body to generate tension in the cable allows converting the wind energy into mechanical work. This line of thinking has stimulated a lot of interest in tethered kites because of the relative ease with which different concepts can be tested. There are currently two major design concepts that have been suggested for power generation based onmechanical transmission of the wind energy: 1) horizontal-axis generators that are driven by alternating the cable length and 2) vertical-axis generators that are driven by a torque created by the tether tension. The first concept controls themotion of the lifting body in such away that high tension is created during payout of the cable and low tension is generated during the reel-in phase. The difference in tension allows net power to be generated. The vertical-axis concept requires flying the kite in a way that maximizes the torque on the generator. Both of these concepts require that the kite can be controlled to fly suitable trajectories. Tomake power generation through kites a reality, it is necessary to implement a control system that can autonomously control the kite system in a robust manner. Currently, research in this area is limited by the unavailability of sufficient data to allow accurate kite models to be constructed. Recent work has focused on the extraction of experimental data to help model identification and model development [6]. In [7], a multiplate representation of the kite was used that allowed for control by movement of the tether attachment points on the kite. However, the high flexibility of most kite systems makes modeling a challenge when viewed from a control engineer’s perspective. Highly detailed models can be developed using fluid– structure interaction methodologies, but these would be too slow to enable control system development. This work builds on the work presented in [3],which details the design of nonlinear optimal powergenerating trajectories for kite systems. This paper is aimed at developing a preliminary control system for manipulating the trajectory of a tethered kite. We employ a very simple approximation of the kite dynamics by considering only the forces generated by the system. The goal is to create a means for stabilizing the kite motion around a particular set of reference trajectories under varying wind conditions. In a practical system, the wind speed is not known in general, and it fluctuates in both magnitude and direction. The control system must be capable of handling changes in wind speed and direction. In this Note, we describe the development of a nonlinear feedback controller that stabilizes the kite motion using a set of noisy measurements of the system. Numerical simulations are used to demonstrate the effectiveness of the controller for tracking power-generation trajectories. This work shows that the loop can be closedwith the kite using inexact feedback and nonlinear optimal control with a representative tether dynamic model.