Structured, Gain-Scheduled Control of Wind Turbines

Improvements in cost-effectiveness and reliability of wind turbines is a constant in the industry. This requires new knowledge and systematic methods for analyzing and designing the interaction of structural dynamics, aerodynamics, and controllers. This thesis presents novel methods and theoretical control developments, which contributes to the analysis and design of wind turbines in an integrated aeroservoelastic process. From a control point of view, a wind turbine is a challenging system since the wind, which is the energy source driving the machine, is a poorly known disturbance. Additionally, wind turbines inherently exhibit time-varying nonlinear dynamics along their nominal operating trajectory, motivating the use of advanced control techniques such as
gain-scheduling, to counteract performance degradation or even instability problems by continuously adapting to the dynamics of the plant. Robustness and fault-tolerance capabilities are also important properties, which should be considered in the design process. Novel gain-scheduling and robust control methods that adapt to variations in the operational conditions of the wind turbine are proposed under the linear parameter-varying (LPV) control framework. The modeling and design procedures allow gain-scheduling to compensate for plant non-linearities and reconfiguration of the controller in face of faults on sensors and actuators of the system. Stability and performance in closed-loop are measured in terms of induced L2-norm. The procedures are appealing to solve some of the practical wind turbine control problems because the controller structure can be chosen arbitrarily, and the resulting controllers are simple to implement online, requiring low data storage and simple math operations. The modeling procedures also allow the generation of reduced-order LPV models from high-fidelity aeroelastic tools. Structured controllers, simplicity in the implementation and aeroelastic codes are in line with the current industrial control practice. Simulation results illustrate the effectiveness of the
proposed methods. Tuning a model-based multivariable controller for wind turbines can be a tedious task. This often involves selecting weighting functions in a trial-and-error procedure. Multiobjective control via linear matrix inequalities (LMI) optimization is exploited to ease controller tuning. Regional pole constraints (D-stability) facilitate intuitive and physical specifications for vibration control, such as minimum damping and decay rate of aeroelastic modes. Moreover, the number of weighting functions and consequently the order
of the final controller is reduced. Inspired by this application, theoretical control developments are presented. New LMI conditions for some hard, structured control problems are proposed. Necessary and sufficient conditions for stability and quadratic performance of vector second-order systems are presented, as well as sufficient conditions for the synthesis of vector secondorder controllers. New sufficient conditions to the static output stabilization problem are also presented. A sufficient characterization is given to the H∞ and H2 model reduction problem. The passive plant design and simultaneous plant-controller design are characterized as sufficient LMI conditions. Due to the linear dependence of the proposed LMIs in the Lyapunov matrix, problem such as simultaneous stabilization, robust synthesis and LPV control can be treated naturally by defining the Lyapunov matrix as multiple or parameter-dependent. The effectiveness of the proposed conditions are verified by numerical experiments. Numerical examples also illustrate their application on wind turbine
control.