Spectral Prediction of Pitch Rate Distribution for Actuator Duty Cycle and Rate Saturation Probability Estimation under Individual Pitch Control

Abstract. Pitch actuator usage under Individual Pitch Control is typically assessed a posteriori through computationally expensive aeroelastic simulations. This work proposes a spectral methodology to predict the pitch rate probability density function during linear control design stage, enabling the estimation of actuator duty cycle and rate saturation probability. The pitch rate is characterized as a Sine-on-Random process whose deterministic and stochastic parameters are estimated from operating point values, equivalent disturbance spectra and closed-loop transfer functions. Validation on the IEA 15 MW Reference Wind Turbine under turbulent inflow shows maximum errors of 0.79 % and 0.59 % for both indicators, respectively, providing an efficient methodology for designing linear controllers that explicitly account for actuator limitations, while reducing reliance on aeroelastic simulations.