Time filter

Source Type

Gros S.,Optimization in Engineering Center | Chachuat B.,Imperial College London
Wind Energy | Year: 2014

This paper describes an optimization-based approach to reducing extreme structural loads during rapid or emergency shutdown of multi-megawatt wind turbine generators. The load reduction problem is cast into an optimal control formulation, and a simple, low-order model is developed in order for this optimization problem to be tractable in reasonable time using state-of-the-art numerical methods. To handle the variations in wind speed and turbulence inherent to wind turbine operation as well as the presence of model mismatch, a real-time optimization strategy based on fast sensitivity updates is also considered, whose online computational burden is limited to the repeated solution of quadratic programs that are designed offline. The low-order model and both the open-loop and closed-loop optimal control strategies are validated against a high-fidelity model in the simulation environment Bladed™ for an industrial 3 MW wind turbine. Under favorable shutdown scenarios, i.e. when the wind turbine is operating properly and the actuators and sensors are not faulty, large reductions of the first compressive peak and subsequent compressive/tensile peaks of the tower load pattern are obtained at various above-rated wind speeds compared with normal pitch control shutdown. Extension to more challenging shutdown scenarios are also discussed. Copyright © 2013 John Wiley & Sons, Ltd. Copyright © 2013 John Wiley & Sons, Ltd.


Zanon M.,Optimization in Engineering Center | Gros S.,Optimization in Engineering Center | Andersson J.,Optimization in Engineering Center | Diehl M.,Optimization in Engineering Center
IEEE Transactions on Control Systems Technology | Year: 2013

The airborne wind energy (AWE) paradigm proposes to generate energy by flying a tethered airfoil across the wind flow at a high velocity. Although AWE enables flight in higher altitude and stronger wind layers, the extra drag generated by the tether motion imposes a significant limit to the overall system efficiency. To address this issue, two airfoils with a shared tether can reduce overall system drag. Although this technique may improve the efficiency of AWE systems, such improvement can only be achieved through properly balancing the system trajectories and parameters. This brief tackles that problem using optimal control. A generic procedure for modeling multiple-airfoil systems with equations of minimal complexity is proposed. A parametric study shows that at small and medium scales, dual-airfoil systems are significantly more efficient than single-airfoil systems, but they are less advantageous at very large scales. © 1993-2012 IEEE.


Savorgnan C.,Optimization in Engineering Center | Kozma A.,Optimization in Engineering Center | Andersson J.,Optimization in Engineering Center | Diehl M.,Optimization in Engineering Center
IFAC Proceedings Volumes (IFAC-PapersOnline) | Year: 2011

Distributed multiple shooting is a modification of the standard multiple shooting method which takes into account the structure of certain large-scale systems in order to obtain a better controller design exibility and high parallelizability. The aim of this paper is to extend the framework where distributed multiple shooting can be deployed and to propose a new solution method based on adjoint-based sequential quadratic programming. A numerical experiment shows that this can lead to considerable savings in computational time for the sensitivity generation. © 2011 IFAC.


Houska B.,Optimization in Engineering Center | Diehl M.,Optimization in Engineering Center
Mathematical Programming | Year: 2013

In this paper, we present a novel sequential convex bilevel programming algorithm for the numerical solution of structured nonlinear min-max problems which arise in the context of semi-infinite programming. Here, our main motivation are nonlinear inequality constrained robust optimization problems. In the first part of the paper, we propose a conservative approximation strategy for such nonlinear and non-convex robust optimization problems: under the assumption that an upper bound for the curvature of the inequality constraints with respect to the uncertainty is given, we show how to formulate a lower-level concave min-max problem which approximates the robust counterpart in a conservative way. This approximation turns out to be exact in some relevant special cases and can be proven to be less conservative than existing approximation techniques that are based on linearization with respect to the uncertainties. In the second part of the paper, we review existing theory on optimality conditions for nonlinear lower-level concave min-max problems which arise in the context of semi-infinite programming. Regarding the optimality conditions for the concave lower level maximization problems as a constraint of the upper level minimization problem, we end up with a structured mathematical program with complementarity constraints (MPCC). The special hierarchical structure of this MPCC can be exploited in a novel sequential convex bilevel programming algorithm. We discuss the surprisingly strong global and locally quadratic convergence properties of this method, which can in this form neither be obtained with existing SQP methods nor with interior point relaxation techniques for general MPCCs. Finally, we discuss the application fields and implementation details of the new method and demonstrate the performance with a numerical example. © 2012 Springer and Mathematical Optimization Society.


Sternberg J.,Catholic University of Leuven | Goit J.,Optimization in Engineering Center | Gros S.,Catholic University of Leuven | Meyers J.,Optimization in Engineering Center | Diehl M.,Catholic University of Leuven
IFAC Proceedings Volumes (IFAC-PapersOnline) | Year: 2012

Power-generating kite systems extract energy from the wind by periodically pulling a generator on the ground while flying fast in a crosswind direction. Kite systems are intrinsically unstable, and subject to atmospheric turbulences. As an alternative to closed-loop control, this paper investigates the open-loop stabilization and robustification of a kite system using techniques based on the solution of Lyapunov differential equation. A wind flow is computed as a solution to a time-dependent three dimensional Navier-Stokes equation. Open-loop stable trajectories for the power-generating kite system are computed based on the statistical properties of the wind field, and are robustified with respect to the system constraints. The stability and robustness of the resulting trajectories are assessed by simulating the system using the computed time- and space-dependent turbulent wind flow. © 2012 IFAC.


Houska B.,Optimization in Engineering Center | Diehl M.,Optimization in Engineering Center
Proceedings of the IEEE International Conference on Control Applications | Year: 2010

In this paper we formulate and solve optimal control problems for power generating kite systems. Here, the kite generates energy by periodically pulling a generator on the ground while flying fast in a crosswind direction. We are searching for an intrinsically open-loop stable trajectory such that the kite generates as much power as possible without needing feedback, while neither the kite nor the cable should touch the ground in the presence of wind turbulence. As the wind turbulences are unknown, robustness aspects need to be taken into account. The formulation of the associated optimal control problem makes use of periodic Lyapunov differential equations in order to guarantee local open-loop stability while robustness aspects are regarded in a linear approximation. The main result of this paper is that open-loop stable kite orbits exist and that open-loop stability only costs approximately 23% compared to the power-optimal unstable orbit. © 2010 IEEE.


Houska B.,Optimization in Engineering Center | Diehl M.,Optimization in Engineering Center
Proceedings of the IEEE International Symposium on Computer-Aided Control System Design | Year: 2010

In this paper, we discuss robust optimal control techniques for dynamic systems which are affine in the uncertainty. Here, the uncertainty is assumed to be time-dependent but bounded by an L-infinity norm. We are interested in finding a tight upper bound for the worst case excitation of the inequality state constraints requiring to solve a parameterized lower-level maximization problem. In this paper, we suggest to replace this lower level maximization problem by an equivalent minimization problem using a special version of modified Lyapunov equations. This new reformulation offers advantages for robust optimal control problems where the uncertainty is time-dependent, i.e. infinite dimensional, while the inequality state constraints need to be robustly regarded on the whole time horizon. © 2010 IEEE.


Gros S.,Optimization in Engineering Center | Ahmad H.,Optimization in Engineering Center | Geebelen K.,Optimization in Engineering Center | Swevers J.,Optimization in Engineering Center | Diehl M.,Optimization in Engineering Center
IFAC Proceedings Volumes (IFAC-PapersOnline) | Year: 2012

The Airborne Wind Energy paradigm proposes to generate energy by flying a tethered aircraft across the wind flow. Accurate models for tethered flight are essential for the control and optimization of airborne wind energy systems. This paper proposes an estimation of the aerodynamic roll damping of a tethered aircraft based on Inertial Measurement Unit data only, gathered at a high aircraft angular velocity. The resulting system dynamics are nonlinear and the estimation problem is non-convex. Because the aircraft is subject to disturbances, the perturbations are estimated alongside the uncertain parameters. In order to handle the unstable aircraft dynamics, a discretization of the model equations based on multiple-shooting is proposed. © 2012 IFAC.

Loading Optimization in Engineering Center collaborators
Loading Optimization in Engineering Center collaborators