Gain-scheduled Linear Quadratic Control of Wind Turbines Operating at High Wind Speed

This paper addresses state estimation and linear quadratic (LQ) control of variable speed variable pitch wind turbines. On the basis of a nonlinear model of a wind turbine, a set of operating conditions is identified and a LQ controller is designed for each operating point. The controller gains are then interpolated linearly to get a control law for the entire operating envelope. The states and the gain-scheduling variable are not online available and an observer is designed. This is done in a modular approach in which a linear estimator is used to estimate the non-measured state variables and the unknown input, aerodynamic torque. From the estimated aerodynamic torque and rotor speed and measured pitch angle the scheduling variable effective wind speed is calculated by inverting the aerodynamic model. Simulation results are given that display good performance of the observers and comparisons with a controller designed by classical methods display the potential of the method.