Robust, Gain-Scheduled Control of Wind Turbines

The control of wind turbines is a very challenging task becau se it requires multi-objective control that needs to take into account effects like structu ral fatigue, power production/quality, and slip in the generator. In this thesis, a nu mber of linear parameter varying (LPV) design methods are investigated for use with medium to large scale systems and a method has been found to provide a numerically reliable comp utation of the controller. The thesis begins with an introduction to the control of wind turbines and provides an overview of the different methods that have been applied. Th is introduction is followed by a general introduction to LPV systems and the base for the a vailable design methods. The application of the LPV framework to the control of nonlin ear systems requires a method for describing the system by a LPV model. For doing th is there are two main directions: Jacobian-based linearisation or quasi-LPV mo dels through a substitution of nonlinearities by parameters. In the latter method the sche duling parameter is a function of the state vector which can introduce conservatism. This i ssue is investigated in the thesis leading to a proposed procedure with focus on frozen p arameter dynamics. The numerics in the design algorithms is one of the key issues for getting the methods working for medium to large scale systems. For the associate d optimisation problem, a grid-based method has been found promising and it has been fo und that the choice of state space realisation plays a very important role and a sim ulation based method has been developed for choosing a proper realisation for contro ller design. For closed loop analysis a Gramian-based method has been found promising. The construction of the LPV controller can be very challengi ng from a numerical point of view. Several algorithms have been investigated an d a method based on a classical result fromH∞ control has been found superior from a numerical point of vie w. This method does not directly produce a parameterised contr oller and another method (which can calculate a parameterised controller) has been m odified to enhance numerical performance. The numerical performance of this modifie controller is still not as strong as the first method, which makes the choice of construc tion algorithm a trade-off between numerical performance and calculating a parameter is d controller. A graphical design tool has been developed on the basis of the numerical findings for conditioning of algorithms for the design of LPV control lers. This tool provides an easy user interface which makes it possible for non-experts to design LPV controllers without worrying about matrix inequalities, construction algorithms, etc. The designer only needs to enter the model, weighting functions, tolerat ed rate of variation and basis functions for the storage (Lyapunov) functions. Then the co ntroller can be designed automatically by pressing a few buttons. Large scale design problems can be very difficult to solve fro m a numerical point of view. For these systems the tool provides a number of numeric al tuning handles with

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