Chapter 5: Control of Variable-Speed Fixed-Pitch Wind Turbines Using Gain Scheduling Techniques

This chapter and the next are concerned with the setup and design of variable-speed wind turbine controllers. This one focuses on fixed-pitch WECS, whereas the following one deals with variable-pitch ones.

A wide variety of control tools have been employed for the design of wind turbine controllers. In particular, gain scheduling techniques are widespread used since they tackle the control of nonlinear systems with the tools of the well-known linear control theory. The term gain-scheduled controller is associated to a family of linear time-invariant (LTI) controllers and an algorithm that changes the controller applied to the plant as the operating point does.

In this book, the design of gain-scheduled controllers for wind turbines is framed in the context of linear parameter varying (LPV) systems. This recent reformulation of gain scheduling has become very popular, mainly because of its stability properties and the simplification of the scheduling design step. In the context of LPV systems, the design of the LTI controller family follows a procedure similar to the synthesis. In addition, the family of controllers and the scheduling algorithm are obtained in a single step. The design of an LPV gain-scheduled controller begins with the derivation of an LPV model for the nonlinear system. Then, the design objectives are stated in terms of bounds on the induced norm of certain input-output operators. This step resembles control. Once this design objectives are established, the gain-scheduled controller is obtained by means of an optimisation procedure with linear matrix inequalities (LMIs). This...