Servo-Elastic Dynamics of a Hydraulic Actuator Pitching a Blade with Large Deflections

Abstract

This paper deals with the servo-elastic dynamics of a hydraulic pitch actuator acting on a largely bend wind turbine blade. The compressibility of the oil and flexibility of the hoses introduce a dynamic mode in the pitch bearing degree of freedom. This mode may obtain negative damping if the proportional gain on the actuator position error is defined too large relative to the viscous forces in the hydraulic system and the total rotational inertia of the pitch bearing degree of freedom. A simple expression for the stability limit of this proportional gain is derived for tuning the gain based on the Ziegler-Nichols method. Computed transfer functions from reference to actual pitch angles indicate that the actuator can be approximated as a low-pass filter with some appropriate limitations on pitching speed and acceleration. The structural blade model includes the geometrical coupling of edgewise bending and torsion for large flapwise deflections. This coupling is shown to introduce edgewise bending response for pitch reference oscillations around the natural frequency of the edgewise bending mode, in which frequency range the transfer function from reference to actual pitch angle cannot be modeled as a simple low-pass filter. The pitch bearing is assumed to be frictionless as a first approximation.