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

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

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

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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

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Coleman transform

• For fixed p, above model is azimuth dependent gt
  LTV model
• Coleman transformation makes the model LTI
  simplifying controller design.

non-rotating coordinates
rotating coordinates
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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, gt 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.

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IPC controller implementation

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

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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).

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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).
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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
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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
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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
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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 dofs), 6 dofs rotor
  shaft, 12 dofs 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.

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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

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Scenario 2 IPC for rotor balancing

• Case 4 no rotor balancing IPC
• Case 5 with rotor balancing

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Scenario 3 IPC for blade load reduction and
rotor balancing

• Case 6 IPC for rotor balancing and blade load
  reduction, pitch limits included

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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.