Sean Costello

Real-Time Optimization for Kites

Over the past decade, a large number of academics and start-ups have devoted them- selves to developing kites, or airplanes on tethers, as a renewable energy source. Determining the trajectories the kite should follow is a modeling and optimization challenge. We present a dynamic model and analyse how uncertainty affects the resulting optimization problem. We show how measurements can be used to rapidly correct the model-based optimal trajectories in real time. This novel real-time optimization approach does not rely on intensive online computation. Rather, it uses knowledge of the structure of the optimal solution, which can be studied offline.

Directional real-time optimization applied to a kite-control simulation benchmark

This paper applies a novel two-layer optimizing control scheme to a kite-control benchmark problem. The upper layer is a recent real-time optimization algorithm, called Directional Modifier Adaptation, which represents a variation of the popular Modifier Adaptation algorithm. The lower layer consists of a path-following controller that can follow arbitrary paths. Application to a challenging benchmark scenario in simulation shows that this two-layer scheme is capable of substantially improving the performance of a complex system affected by significant stochastic disturbances, measurement noise and plant-model mismatch, while respecting operational constraints.

Improved path following for kites with input delay compensation

In kite power systems, substantial input delay between the actuator and the tethered kite can severely hinder the performance of the control algorithm, limiting the capability of the system to track power-optimal loops. We propose a method that deals with this impediment by using a data-based adaptive filter that predicts future states despite variations in wind conditions, other exogenous disturbances and model mismatch. Moreover, we exploit the geometry of the path on a hemisphere to enhance the guidance algorithm for such kites at a fixed length tether. The objective is to improve the automatic crosswind operation of an airborne wind energy system. To test this under realistic conditions, a small-scale prototype was employed for a series of experiments. The robustness to disturbances and the performance of the algorithm in path following was evaluated for a number of different paths.

Analysis of the maximum efficiency of kite-power systems

This paper analyzes the maximum power that a kite, or system of kites, can extract from the wind. First, a number of existing results on kite system efficiency are reviewed. The results that are generally applicable require significant simplifying assumptions, usually neglecting the effects of inertia and gravity. On the other hand, the more precise analyses are usually only applicable to a particular type of kite-power system. Second, a novel result is derived that relates the maximum power output of a kite system to the angle of the average aerodynamic force produced by the system. This result essentially requires no limiting assumptions, and as such it is generally applicable. As it considers average forces that must be balanced, inertial forces are implicitly accounted for. In order to derive practically useful results, the maximum power output is expressed in terms of the system overall strength-to-weight ratio, the tether angle, and the tether drag through an efficiency factor. The result is a simpl...

Modifier Adaptation for Run-to-Run Optimization of Transient Processes

Dynamic optimization can be used to determine optimal input profiles for dynamic processes. Due to plant-model mismatch and disturbances, the optimal inputs determined through model-based optimization will, in general, not be optimal for the plant. Modifier adaptation is a methodology that uses measurements to achieve optimality in the presence of uncertainty. Modifier-adaptation schemes have been developed for the real-time optimization of plants operating at steady state. In this paper, the concept of modifier adaptation is extended to transient plants such as batch processes. Two different schemes are proposed, and their performance is illustrated via the simulation of a semi-batch reaction system.

Real-Time Optimizing Control of an Experimental Crosswind Power Kite

The contribution of this paper is to propose and experimentally validate an optimizing control strategy for power kites flying crosswind. The algorithm ensures the kite follows a reference path (control) and also periodically optimizes the reference path (efficiency optimization). The path-following part of the controller is capable of consistently following a reference path, despite significant time delays and wind variations, using position measurements only. The path-optimization part adjusts the reference path in order to maximize line tension. It uses a real-time optimization algorithm that combines off-line modeling knowledge and on-line measurements. The algorithm has been tested comprehensively on a small-scale prototype, and this paper focuses on experimental results.

Extension of modifier adaptation for controlled plants using static open-loop models

Model-based optimization methods suffer from the limited accuracy of the available process models. Because of plant-model mismatch, model-based optimal inputs may be suboptimal or, worse, unfeasible for the plant. Modifier adaptation (MA) overcomes this obstacle by incorporating measurements in the optimization framework. However, the standard MA formulation requires that (1) the model satisfies adequacy conditions and (2) the model and the plant share the same degrees of freedom. In this article, three extensions of MA to problems where (2) does not hold are proposed. In particular, we consider the case of controlled plants for which the only a model of the open-loop plant is available. These extensions are shown to preserve the ability of MA to converge to the plant optimum despite disturbances and plant-model mismatch. The proposed methods are illustrated in simulation for the optimization of a CSTR.

Crosswind kite control – A benchmark problem for advanced control and dynamic optimization

This article presents a kite control and optimization problem intended as a benchmark problem for advanced control and optimization. We provide an entry point to this exciting renewable energy system for researchers in control and optimization methods looking for a realistic test bench, and/or a useful application case for their theory. The benchmark problem in this paper can be studied in simulation, and a complete Simulink model is provided to facilitate this. The simulated scenario, which reproduces many of the challenges presented by a real system, is based on experimental studies from the literature, industrial data and the first author’s own experience in experimental kite control. In par- ticular, an experimentally validated wind turbulence model is included, which subjects the kite to realistic disturbances. The benchmark problem is that of controlling a kite such that the average line tension is maximized. Two different models are provided: A more comprehensive one is used to simulate the ’plant’, while a simpler ’model’ is used to design and implement control and optimization strategies. This way, uncertainty is present in the form of plant-model mismatch. The outputs of the plant are corrupted by measurement noise. The maximum achievable average line tension for the plant is calculated, which should facilitate the performance comparison of different algorithms. A simple control strategy is implemented on the plant and found to be quite suboptimal, even if the free parameters of the algorithm are well tuned. An open question is whether or not more advanced control algorithms could do better.

Real-time optimization when plant and model have different sets of inputs

Abstract Model-based optimization is an increasingly popular way of determining the values of the degrees of freedom for a process. The drawback is that the available model is often inaccurate. An iterative set-point optimization method called “modifier adaptation” overcomes this obstacle by incorporating process measurements into the optimization framework. We extend this technique to optimization problems where the model inputs do not correspond to the plant inputs. Using the example of an incineration plant, we argue that this occurs in practice when a complex process cannot be fully modeled and the missing part encompasses additional degrees of freedom. This paper shows that the modifier-adaptation scheme can be modified accordingly. This extension makes modifier adaptation much more flexible and applicable, as a wider class of models can be used. The proposed method is illustrated through a simulated CSTR example.