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

Predictive Control of Autonomous Kites in Tow Test Experiments

In this paper we present a model-based control approach for autonomous flight of kites for wind power generation. Predictive models are considered to compensate for delay in the kite dynamics. We apply Model Predictive Control (MPC), with the objective of guiding the kite to follow a figure-of-eight trajectory, in the outer loop of a two level control cascade. The tracking capabilities of the inner-loop controller depend on the operating conditions and are assessed via a frequency domain robustness analysis. We take the limitations of the inner tracking controller into account by encoding them as optimisation constraints in the outer MPC. The method is validated on a kite system in tow test experiments.Comment: The paper has been accepted for publication in the IEEE Control Systems Letters and is subject to IEEE Control Systems Society copyright. Upon publication, the copy of record will be available at http://ieeexplore.ieee.or

On enforcing the necessary conditions of optimality under plant-model mismatch - What to measure and what to adapt?

Industrial processes are run with the aim of maximizing economic profit while simultaneously meeting process-critical constraints. To this end, model-based optimization can be performed to ensure optimal plant operations. Usually, inevitable model inaccuracies are dealt by collecting the plant measurements at the local operating conditions in order to adapt model parameters, followed by numerical re-optimization. This iterative two-step procedure often results in a sub-optimal solution, since the models are typically not designed for optimization. Modifier Adaptation (MA) is a Real-Time Optimization (RTO) technique that directly adds the affine-correction terms to the model. The affine corrections are parametrized in modifiers that are tailored to the optimization needs. This enables modifier adaptation to guarantee, upon convergence, matching the plant and the modified model's optimality conditions. However, computing the modifiers requires estimates of the plant gradients that are obtained via expensive plant experiments. The experimental cost can be reduced by relying more on the model of the considered plant. For example, Directional Modifier Adaptation (DMA) relies on offline-computed local parametric sensitivity analysis performed on the gradient of the Lagrangian function of the model resulting in reduced number of input directions that describe the gradient uncertainty in the model. Thereby, plant gradients are estimated only in a low-dimensional space of privileged input directions considerably reducing the experimental costs. However, local sensitivity analysis is often ineffective when the gradient of the model is considerably nonlinear in parameters. This thesis proposes an online procedure based on global sensitivity analysis for finding the most promising privileged directions that adequately compensates for the model deficiencies in predicting the plant optimality conditions. The discovered privileged directions are such that, upon parametric perturbations, the gradient varies a lot along the privileged directions and varies only a little along the remaining input directions. Consequently, the gradients of the model cost and constraints are corrected only along the privileged directions by adapting modifiers. The resulting methodology is named as Active Directional Modifier Adaptation (ADMA). Several simulation studies conducted show that the proposed approach reaches the near-optimality conditions at a considerably reduced experimental cost. In addition, this thesis attempts to establish a direct relation between the optimality conditions and the parameters of a given model. Model parameters are analyzed to discover mirror parameters that mimic the behavior of modifiers in influencing the optimality conditions. It is proposed to adapt mirror parameters instead of modifiers yielding the benefit of both, modifier adaptation in enforcing optimality conditions and of parameter adaptation in better noise handling and convergence. Moreover, it is investigated how to establish the synergies between privileged input directions with model parameters in order to reduce experimental efforts. The steady-state optimization of a simulated chemical process shows that the privileged directions and the selected parameters work together to reach near-optimal performance. Finally, the study on the power maximization of flying kites leads to the development of trust-region based ADMA method to better control the input step size

Real-Time Optimizing Control of an Experimental Crosswind Power Kite

The contribution of this article is to propose and experimentally validate an optimizing control strategy for power kites flying crosswind. The control strategy provides both path control (stability) and path optimization (efficiency). The path following part of the controller is capable of robustly following a reference path, despite significant time delays, 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 article focuses on experimental results

Modifier Adaptation for Real-Time Optimization - Methods and Applications

This paper presents an overview of the recent developments of modifier-adaptation schemes for real-time optimization of uncertain processes. These schemes have the ability to reach plant optimality upon convergence despite the presence of structural plant-model mismatch. Modifier Adaptation has its origins in the technique of Integrated System Optimization and Parameter Estimation, but differs in the definition of the modifiers and in the fact that no parameter estimation is required. This paper reviews the fundamentals of Modifier Adaptation and provides an overview of several variants and extensions. Furthermore, the paper discusses different methods for estimating the required gradients (or modifiers) from noisy measurements. We also give an overview of the application studies available in the literature. Finally, the paper briefly discusses open issues so as to promote future research in this area

Trajectory Optimization of a Tethered Underwater Kite

This dissertation addresses the challenge of optimizing the motion trajectory of a tethered marine hydrokinetic energy harvesting kite in order to maximize its average electric power output. The dissertation focuses specifically on the “pumping” kite configuration, where the kite is periodically reeled out from a floating base station at high tension, then reeled in at low tension. This work is motivated by the significant potential for sustainable electricity generation from marine currents such as the Gulf Stream. Tethered systems can increase their energy harvesting potential significantly through cross-current motion. Such motion increases apparent flow speed, which is valuable because the instantaneous maximum power that can be harvested is proportional to the cube of this apparent speed. This makes it possible for tethered systems to achieve potentially very attractive power densities and levelized costs of electricity compared to stationary turbines. However, this also necessitates the use of trajectory optimization and active control in order to eke out the maximum energy harvesting capabilities of these systems. The problem of optimizing the trajectories of these kites is highly non-linear and thus challenging to solve. In this dissertation we make key simplifications to both the modeling and the structure of the optimal solution which allows us to learn valuable insights in the nature of the power maximizing trajectory. We first do this analysis to maximize the average mechanical power of the kite, then we expand it to take into account system losses. Finally, we design and fabricate an experimental setup to both parametrize our model and validate our trajectories. In summary, the goal of this research is to furnish model-based algorithms for the online optimal flight control of a tethered marine hydrokinetic system. The intellectual merit of this work stems from the degree to which it will tackle the difficulty of solving this co-optimization problem taking into account overall system efficiency and the full range of possible system motion trajectories. From a broader societal perspective, this work represents a step towards experimentally validating the potential of pumped underwater kite systems to serve as renewable energy harvesters in promising environments such as the Gulf Stream

Feedback Control for Average Output Systems

In this work we propose new methods for the design of economic Nonlinear Model Predictive Control (NMPC) feedback schemes for Average Output Optimal Control Problems (AOCPs). AOCPs are Optimal Control Problems (OCPs) defined on infinite time horizons with averaging performance critera as objective functionals. Such problems arise frequently for continuously operating systems such as for example power plants. Due to the infinite time horizon and the resulting intrinsic nonuniqueness of solutions, the design of appropriate NMPC schemes for AOCPs is challenging. Often, the analysis of the closed-loop behavior of economic NMPC schemes depends on dissipativity conditions on the dynamical system and the associated performance criterion, which sometimes can be hard to check. The methods we develop are based on the observation that periodic solutions exhibit excellent approximation properties for AOCPs, which is exploited by splitting the time horizon and the objective functional of the NMPC subproblems into a transient and a periodic part. For the analysis of the closed-loop behavior of the resulting controller we develop new methods that essentially work by showing that the (appropriately defined) difference of two subsequent NMPC subproblem solutions vanishes asymptotically. Complementary to many other economic NMPC schemes, this approach is not based on dissipativity assumptions on the dynamical system and the associated performance criterion but rather on assumptions on existence of periodic orbits, controllability of the dynamical system, and uniqueness of the NMPC subproblem solutions itself. As a result, we can show that the economic performance of the closed-loop system is equal to the economic performance of the optimal periodic solutions. Furthermore, the approach is extended in two directions. First, we consider the general setting of a parameter dependent dynamical system where the parameter can be subject to change during operation. This parameter change can lead to a change in the optimal periodic behavior, in particular also to a change of the optimal period, which we take into account by including the period as an optimization variable in the NMPC subproblem. Second, we show that the approach can also be applied to systems with time-dependent periodic performance criteria. All the described methods are implemented within the MATLAB NMPC toolkit MLI and are applied to a number of demanding applications. The simulation results confirm that the generated closed-loop trajectories perform economically equally well as the optimal periodic trajectories

Application of aircraft's flight testing techniques to the aerodynamic characterization of power kites

This thesis has developed an experimental methodology for the flight testing and data analysis of power kites applied to Airborne Wind Energy Systems (AWES). In particular, the Estimation Before Modeling technique, a well-known method in the aerospace industry for the aerodynamic characterization of an aircraft using real flight data, has been adapted for tethered aircraft. The developed methodology has two main building blocks: (i) an experimental setup to record experimental data during the flight testing, and (ii) a Flight Path Reconstruction algorithm to estimate the state of the system from the experimental data. From them, the aerodynamic characteristics of two types of kites were investigated. The proposed experimental setup was designed to be low cost, portable and easily adaptable to both, rigid and semi-rigid kites. It is composed of an instrumented kite representative of the ones used in AWES, an instrumented control bar, a ground computer and a wind station. Whenever it was possible, commercial off the shelf components have been used, including low cost openhardware sensors based on the PixHawk platform. However, after the first flight tests were conducted and the obtained results were discussed, high precision sensors were also included. The Flight Path Reconstruction (FPR) algorithm for tethered aircraft is based on an Extended Kalman Filter (EKF). In addition to the standard set of estimated state variables (ie. Euler angles, position or ground speed), the algorithm also provides the aerodynamic torque and forces upon the kite as well as the tether tensions and wind velocity vector. The EBM technique, and the FPR algorithm have been used to identify the aerodynamic characteristics of both, four-line Leading Edge Inflatable (LEI) kites and two-line Rigid Frame Delta (RFD) kites. Quantitative and qualitative results have been obtained. Albeit both types of kites exhibited very high AoA during the flight, some significant differences were found. In particular, the estimated lift coefficient of the LEI kite showed a behavior identified with a post-stall condition, while the RFD showed a pre-stall behavior with a lower AoA and a positive relation between the lift coefficient and the kite AoA. The presented experimental methodology can be of great interest for AWE industry as it helps to improve modeling of tethered aircraft, leading to more accurate performance figures which may increase investors interest in the technology. Moreover, flight testing methodologies and experimental data analysis are of great interest for benchmarking AWES performances, contributing to de-risk their development process and providing better tools for AWE "best concept" identification. Finally, as a sub-product of the presented methodology, the FPR algorithm can be used as a validated state estimator of the tethered aircraft, which is a key element of a closed loop flight control system.Programa de Doctorado en Mecánica de Fluidos por la Universidad Carlos III de Madrid; la Universidad de Jaén; la Universidad de Zaragoza; la Universidad Nacional de Educación a Distancia; la Universidad Politécnica de Madrid y la Universidad Rovira i VirgiliPresidente: Marco Fontana.- Secretario: Manuel García-Villalba Navaridas.- Vocal: Félix Terroba Ramíre