Reducing LIDAR wind speed measurement error with optimal filtering

Recent research has shown the potential for reduction in wind turbine generator speed error and structural loads with the introduction of feedforward control using preview LIDAR measurements. Several sources of error exist in the estimation of the wind speeds that will interact with the turbine rotor, including LIDAR distortion and coherence loss due to wind evolution. If a feedforward controller is designed assuming perfect wind speed measurements, however, the error in the disturbance estimate may cause feedforward control to increase output errors. Here we derive the minimum mean square error feedforward controller for imperfect measurements using statistical descriptions of the wind. We show that the resulting controller is the ideal feedforward controller, assuming perfect measurements, in series with a Wiener prefilter to reduce the mean square error of the disturbance estimate. We derive the optimal filter in the frequency domain assuming infinite preview as well as the optimal filter in the time domain with preview time constraints. Examples illustrating the error reduction with optimal prefiltering are provided for simulated control and measurement scenarios.