Exploring the limits in Individual Pitch Control S. Kanev and T. van Engelen

1. Exploring the limits in Individual Pitch ControlS. Kanev and T. van Engelen

2. Overview • Blade load reduction by individual pitch control (IPC) • Rotor balancing by IPC • Gain-scheduling • Dealing with actuator constraints (anti-windup) • Simulation results

3. IPC for blade load reduction • Pitch control algorithms: • collective pitch control for keeping rotor speed at rated • individual pitch control for load reduction: • Blade load reduction: usually flapping moments Mz are reduced around the 1p frequency, achieved by cyclic pitching. • Aerodynamic/mass unbalance: results in a static shaft load, can be counteracted by offsets on the blade pitch angles. • Starting point for IPC design: LPV model • Working point:

4. Coleman transform • For fixed p, above model is azimuth dependent => LTV model • Coleman transformation makes the model LTI simplifying controller design. non-rotating coordinates rotating coordinates

5. Basic IPC design • After Coleman transformation, model gets LTI for a given working point • 1p blade flap-wise loads (Mz) become static 0p rotor moments Mcm ! • Hence, integral action should be included in the IPC controller. • Tilt and yaw channels are almost decoupled at low frequencies, => SISO approach • FIPC includes series of band-stop filters around the 3p and 6p frequencies. Gains computed to achieve desired gain margin (e.g. 2) • To cover the whole working range, gain scheduling should be applied.

6. IPC controller implementation • Once the IPC is designed, the transformation matrices are added to the controller

7. Rotor balancing by IPC • Imperfections in the blades lead to aerodynamic and mass unbalance. • Unbalance results in static (0p) loading on the shaft, and 1p loading on the tilt and yaw moments at the yaw bearing. Aerodynamic unbalance can be represented by additional slowly varying terms to the flapping blade moments • It can be compensated by adding quasi-steady offsets to the blade pitch angles. • Possible measurements: • aerodyn. unbalance: blade root bending (0p), or shaft (0p), or rotor tilt/yaw moments (1p) • mass unbalance: either shaft (0p), or rotor tilt/yaw moments (1p) • Since with strain gauges 0p measurement is problematic, other alternatives are under investigation (tower top accelerations at 1p).

8. Rotor balancing IPC scheme • Assuming blade root moments measurement, the rotor unbalance compensation scheme is similar to the IPC scheme for blade load reduction: • Transformation: • At low frequencies, transformed system approximated as static, LTI, and diagonal. • Controller structure: Parameters chosen to get critically damped CL system with desired settling time (e.g. 50 sec).

9. Dealing with constraints • Blade pitch actuators have limits: • Ensuring these in the control algorithm especially important for controllers with integral term (such as both CPC and IPC). Otherwise windup can occur, which can lead even to instability. • Actuation freedom is distributed between CPC and IPC as follows: actuation freedom for CPC IPC can use remaining actuation freedom

10. Pitch limits in non-rotating coordinates • Total pitch angle reference for i-th blade: • Actuation freedom remaining for IPC: • Defining • The goal is to express the constraints • In terms of constraints on cm,2 and cm,3 (too technical, ref. paper). IPC term

11. Accel. limit Speed limit Pos. limit Anti-windup IPC implementation • To properly implement the constraints in the IPC controller, the integrator state should be driven by the constrained signal. The limiters can be implemented as follows:

12. Simulation model • Nonlinear simulation model used for validation of IPC methods: • TURBU structural dynamics model (156 states), consisting of 14 blade elements, 15 tower elements (each with 5 dof’s), 6 dof’s rotor shaft, 12 dof’s pitch actuators • Detailed aerodynamics module, incl. dynamic wake, oblique inflow modeling (Glauert) • Basic controller for rotor speed regulation and power control • IPC control for blade load reduction at 1p and rotor balancing, incl. actuator constraints (anti-windup implementation) • realistic blade effective wind speed signals, incl. deterministic (shear, tower shadow, wind gusts) and stochastic (turbulence) components. • Simulation at mean wind speed of 20 m/s, yaw misalignment of 10 degrees. • Aerodynamic unbalance modeled as blade pitch angle offsets of “-1”, “3” and “-2” deg.

13. Scenario 1: IPC for blade load reduction • Case 1: without IPC • Case 2: with IPC, no pitch limits • Case 3: with IPC, with pitch limits

14. Scenario 2: IPC for rotor balancing • Case 4: no rotor balancing IPC • Case 5: with rotor balancing

15. Scenario 3: IPC for blade load reduction and rotor balancing • Case 6: IPC for rotor balancing and blade load reduction, pitch limits included

16. Conclusions • IPC can be used for blade fatigue load reduction by mitigating the static tilt/yaw rotor moments, resulting in cyclic pitching around the 1p frequency • IPC can be used for compensation of rotor unbalance due to blade mass and aerodynamic imperfections. This can be achieved by mitigating the 0p shaft loads. • For rotor balancing IPC, either offset-free shaft/blade root bending moment measurements, or tower-top tilt/yaw moments measurements. • Gain scheduling is needed to cover the whole operating region of the turbine • IPC action significantly increases the pitch speeds and accelerations, requiring to properly deal with actuator constraints. The challenge here is to transform the original constraints into non-rotating coordinates.