Analysis of gain-scheduling implementation for the NREL 5-MW turbine blade pitch controller

Gain scheduling for the widely-used NREL 5-MW proportional-integral blade pitch controller can be implemented either by the original documented method (Integrate First): integrate the generator speed error before multiplying by the gain-scheduling correction factor, or the Multiply First method: multiply the generator speed error by the gain-scheduling correction factor, then integrate. The results of the Multiply First implementation are straightforward: the effective proportional and integral gains are simply the unscheduled gains multiplied by the value of the gain-scheduling function evaluated at the pitch operating point for the average wind speed. However, the original (Integrate First) implementation effectively reduces the proportional and integral gains significantly further than the Multiply First implementation, with the difference becoming more severe as wind speed increases. Integrating First results in effective gain reductions of 34% at 13 m/s and 41% at 18 m/s compared to Multiplying First. Further, this effective gain reduction disappears if the baseline pitch controller is augmented with a feedforward control signal whose average value is the pitch operating point. These effects are explained through analysis of a simplified version of the gain-scheduling feedback loop and verified through simulation. Simulation results also show that when effective gains are corrected to match each other, Integrating First improves performance compared to Multiplying First. This gain correction is not feasible for real-world implementation, but a simple change to the gain-scheduling function f(u) instead is feasible and is shown to have almost the same effect. Lifetime performance metrics for Integrating First with the new f(u) show a 4% reduction in tower base moment, a 2% reduction in blade root moment, a 4% reduction in RMS pitch rate, and a 10% reduction in RMS power error compared to Multiplying First.