NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

LIDAR Wind Speed 

Measurement Analysis and 

Feed-Forward Blade Pitch 

Control for Load Mitigation in 

Wind Turbines 

January 2010 — January 2011

F. Dunne, E. Simley, and L.Y. Pao 

University of Colorado

Boulder, Colorado

Subcontract Report

NREL/SR-5000-52098

October 2011
This publication received minimal editorial review at NREL.

NOTICE

This report was prepared as an account of work sponsored by an agency of the United States government. 

Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, 

express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of 

any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately 

owned rights. Reference herein to any specific commercial product, process, or service by trade name, 

trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, 

or favoring by the United States government or any agency thereof. The views and opinions of authors 

expressed herein do not necessarily state or reflect those of the United States government or any agency thereof.

Available electronically at http://www.osti.gov/bridge

Available for a processing fee to U.S. Department of Energy

and its contractors, in paper, from:

U.S. Department of Energy

Office of Scientific and Technical Information

P.O. Box 62

Oak Ridge, TN 37831-0062

phone: 865.576.8401

fax: 865.576.5728

email: mailto:reports@adonis.osti.gov

Available for sale to the public, in paper, from:

U.S. Department of Commerce

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22161

phone: 800.553.6847

fax: 703.605.6900

email: orders@ntis.fedworld.gov

online ordering: http://www.ntis.gov/help/ordermethods.aspx

Cover Photos: (left to right) PIX 16416, PIX 17423, PIX 16560, PIX 17613, PIX 17436, PIX 17721

Printed on paper containing at least 50% wastepaper, including 10% post consumer waste.
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

National Renewable Energy Laboratory

1617 Cole Boulevard

Golden, Colorado 80401

303-275-3000 • www.nrel.gov

Contract No. DE-AC36-08GO28308

LIDAR Wind Speed 

Measurement Analysis and 

Feed-Forward Blade Pitch 

Control for Load Mitigation in 

Wind Turbines 

January 2010 — January 2011

F. Dunne, E. Simley, and L.Y. Pao 

University of Colorado

Boulder, Colorado

NREL Technical Monitor: Alan D. Wright

Prepared under Subcontract No(s). XEE-9-99404-01

Subcontract Report

NREL/SR-5000-52098

October 2011
2 

Abstract

Light Detection and Ranging (LIDAR) systems are able to measure the speed of incoming wind 

before it interacts with a wind turbine rotor. These preview wind measurements can be used in 

feed-forward control systems designed to reduce turbine loads. However, the degree to which 

such preview-based control techniques can reduce loads by reacting to turbulence depends on 

how accurately the incoming wind field can be measured. The first half of this report examines 

the accuracy of different measurement scenarios that rely on coherent continuous-wave or pulsed 

Doppler LIDAR systems to determine their applicability to feed-forward control. In particular, 

the impacts of measurement range and angular offset from the wind direction are studied for 

various wind conditions. A realistic case involving a scanning LIDAR unit mounted in the 

spinner of a wind turbine is studied in depth with emphasis on choices for scan radius and 

preview distance. The effects of turbulence parameters on measurement accuracy are studied as 

well. Continuous-wave and pulsed LIDAR models based on typical commercially available units 

were used in the studies present in this report. 

The second half of this report discusses feed-forward control system designs that use preview 

wind measurements. Combined feedback/feed-forward blade pitch control is compared to 

industry standard feedback control when simulated in realistic turbulent above-rated winds. The 

feed-forward controllers are designed to reduce fatigue loads, increasing turbine lifetime and 

therefore reducing the cost of energy. Three feed-forward designs are studied: non-causal series 

expansion, Preview Control, and optimized FIR filter. The input to the feed-forward controller is 

a measurement of incoming wind speeds that could be provided by LIDAR. Non-causal series 

expansion and Preview Control methods reduce blade root loads but increase tower bending in 

simulation results. The optimized FIR filter reduces loads overall, keeps pitch rates low, and 

maintains rotor speed regulation and power capture, while using imperfect wind measurements 

provided by the spinning continuous-wave LIDAR model. 
3 

List of Acronyms, Abbreviations, and Nomenclature

b Collective blade pitch feed-forward command

d Measurement preview distance

Δp Length of range gate for a pulsed LIDAR 

Δr Full-width-at-half-maximum pulse width 

F Focal distance or feed-forward controller 

k Wind velocity wave number (m-1) 

o Output error

P Linearized model of wind turbine 

r Scan radius for spinning LIDAR

R Distance to center of range gate for a pulsed LIDAR

σu Standard deviation of u component of wind velocity 

θ LIDAR measurement angle

 Mean u wind speed

u* Friction velocity

UD

* Average friction velocity over rotor disk

φ Angle between laser and wind velocity vector 

ψ Angle in rotor plane 

ω Rotational rate of spinning LIDAR (RPM) 

AR Above rated wind speed

bcmd Collective blade pitch error 

CP Collective pitch

CW Continuous wave

DEL Damage equivalent load 

DOF Degree of freedom 

FAST Aeroelastic wind turbine simulator

IP Individual pitch

LIDAR Light detection and ranging 

LLJ Low level jet

MBC Multi-blade coordinate

Pobcmd Open-loop turbine transfer function from collective pitch error to output error

Pow Open-loop turbine transfer function from wind speed error to output error 

PI Proportional-integral 

RMS Root mean square 

TI Turbulence intensity

Tob Closed-loop transfer function from collective pitch feed-forward command to 

output error 

Tow Closed-loop transfer function from wind speed error to output error 
4 

Table of Contents

1 LIDAR Modeling Introduction ............................................................................................... 7

2 LIDAR Measurement Theory ................................................................................................. 8

2.1 Continuous Wave Range Weighting ............................................................................. 10

2.2 Measurement Geometry ................................................................................................ 12

2.3 Combined Range Weighting and Geometrical Errors .................................................. 13

2.4 Pulsed LIDAR Systems ................................................................................................ 15

3 LIDAR Simulation Results ................................................................................................... 17

3.1 Wind Conditions ........................................................................................................... 18

3.2 Impact of Turbulence on Measurement Errors ............................................................. 19

3.3 Hub Mounted Spinning LIDAR Analysis..................................................................... 22

4 LIDAR Modeling Conclusions and Future Work ................................................................. 27

5 Feed-Forward Control Introduction ...................................................................................... 30

6 Simulated Turbine and Turbulent Inflow ............................................................................. 31

6.1 5 MW Turbine Model and Baseline Control ................................................................ 31

6.2 Wind Fields ................................................................................................................... 32

7 Non-Causal Series Expansion ............................................................................................... 32

7.1 Design ........................................................................................................................... 32

7.2 Results ........................................................................................................................... 35

8 Preview Control .................................................................................................................... 36

8.1 Design ........................................................................................................................... 36

8.2 Results ........................................................................................................................... 38

9 Optimized FIR Filter ............................................................................................................. 43

9.1 Design ........................................................................................................................... 43

9.1.1 Cost Function .......................................................................................................... 45

9.1.2 Constraints .............................................................................................................. 45

9.1.3 Seeds ....................................................................................................................... 45

9.1.4 Creation Function.................................................................................................... 46

9.2 Results ........................................................................................................................... 46

10 Feed-Forward Control Conclusions ...................................................................................... 49

11 Overall Conclusions and Future Work ................................................................................. 49

12 References ............................................................................................................................. 50
5 

List of Figures

Figure 1. Block Diagram illustrating how LIDAR can be used in a combined 

feedforward/feedback control scenario ........................................................................................... 7

Figure 2. Coordinate system and measurement variables for LIDAR analysis. ............................. 9

Figure 3. Range weighting functions ............................................................................................ 11

Figure 4. Frequency response of range weighting functions. ....................................................... 11

Figure 5. The effects of measurement angle and range on measurement error ............................ 14

Figure 6. Illustration of range weighting and measurement angle errors. .................................... 15

Figure 7. Comparison of CW and pulsed LIDARs ....................................................................... 17

Figure 8. CW measurement error vs. turbulence intensity ........................................................... 20

Figure 9. CW measurement error vs. local friction velocity ......................................................... 21

Figure 10. Pulsed and CW Measurement errors vs. local friction velocity .................................. 22

Figure 11. Measurement error vs. preview distance for various scan radii .................................. 23

Figure 12. Minimum achievable errors and optimal preview distances vs. scan radius ............... 24

Figure 13. Friction velocity profiles. ............................................................................................ 25

Figure 14. Minimum achievable errors and optimal preview distances for all wind conditions .. 26

Figure 15. Measurement error vs. preview distance for CW and pulsed LIDARs. ...................... 27

Figure 16. Measurement error example with a coherent structure. .............................................. 29

Figure 17. Feedback Only Control ................................................................................................ 30

Figure 18. Combined Feedback/Feedforward Control ................................................................. 31

Figure 19. Linear plant model ....................................................................................................... 32

Figure 20. Combined Feedback/Feedforward Control ................................................................. 33

Figure 21. Non-Causal Series Expansion (NCSE) feedforward control ....................................... 35

Figure 22. A comparison of Damage Equivalent Loads (DELs) and nacelle RMS velocities, 

NCSE ............................................................................................................................................ 36

Figure 23. Preview Control pulse response for varying preview lengths ..................................... 38

Figure 24. Linear turbine model response comparing Preview Control to no Preview Control. . 39

Figure 25. Bode magnitude plot of linear turbine model with Preview Control. ......................... 40

Figure 26. Simulated nonlinear turbine model with Preview Control, step response. .................. 41

Figure 27. Simulated nonlinear turbine model with Preview Control, sine response. .................. 42

Figure 28. Time series comparing baseline collective pitch feedback control with and without 

Preview Control in wind field AR2_s1. ........................................................................................ 42

Figure 29. A comparison of Damage Equivalent Loads (DELs) and nacelle RMS velocities, 

Preview Control ............................................................................................................................ 43

Figure 30. Pulse responses ............................................................................................................ 44

Figure 31. Impulse response of the Optimized FIR filter ............................................................. 46

Figure 32. Bode magnitude plot of the Optimized FIR filter. ...................................................... 47

Figure 33. Damage equivalent loads, RMS nacelle accelerations, and RMS pitch rate of IP 

Baseline control without and with Optimized FIR feedforward, AR1-3 ...................................... 48

Figure 34. Damage equivalent loads, RMS nacelle accelerations, and RMS pitch rate of IP 

Baseline control without and with Optimized FIR feedforward, AR4-5 ...................................... 48
6 

List of Tables

Table 1. A Summary of the Great Plains Low Level Jet Wind Fields Used for Wind Speed 

Measurement Analysis. . ............................................................................................................... 18
7 

1 LIDAR Modeling Introduction

Wind speed measurements in front of a wind turbine can be used as part of feed-forward or 

preview-based controllers to help mitigate structural loads caused by turbulent wind conditions. 

Prior analyses have shown that improvements to turbine load performance can be achieved with 

knowledge of the incoming wind field [1,2,3]. A block diagram of such a control strategy is 

shown in Figure 1. Upstream wind is measured, providing an estimate of the wind speeds that 

will eventually reach the turbine. In reality, the turbulent structures in the wind will evolve 

between the time they are measured and when they reach the turbine, causing errors in the 

preview wind measurements [4]. This report focuses on the preview measurement stage, ignoring 

wind evolution. Thus, the authors’ model assumes the validity of Taylor's frozen turbulence 

hypothesis, which states that turbulent eddies tend to remain unchanged while advecting with the 

average wind velocity [5]. 

Figure 1. A block diagram illustrating how LIDAR can be used in a preview based combined feedforward/feedback control scenario. Although wind measured using LIDAR will evolve between 

preview measurement and contact with the turbine, wind evolution is not studied in this report. 

Although various optical and acoustical methods exist for measuring wind speeds, coherent 

Doppler LIDAR (light detection and ranging) provides the most accurate and versatile way to 

provide remote measurements [6]. The two main coherent LIDAR technologies that are currently 

available are continuous wave (CW) LIDAR and pulsed LIDAR. In this report, we provide an 

analysis of using both CW and pulsed LIDAR technologies to provide preview wind 

measurements, with an emphasis on CW. Aside from the technological merits of CW LIDAR, 

the recent application of fiber telecommunications technology to LIDAR instrumentation has 

made infrared, CW LIDAR an economical and eye-safe technology for measuring wind velocity 

in front of a turbine [6]. 

While some improvement can be gained by measuring wind speeds upwind of the hub location, 

it is much more advantageous to be able to measure the wind that will appear at each individual 

blade [7]. A commercially available CW LIDAR mounted in the spinner of a wind turbine has 

been successfully tested in the field, illustrating the ability of the technology to be applied to 

individual turbine control [8]. Therefore, we provide a detailed analysis of preview wind 

measurements at a variety of blade span positions using a spinning LIDAR mounted in the hub 

of a 5 MW turbine. Analyses are provided using separate CW and pulsed LIDAR models 
8 

developed for the National Renewable Energy Laboratory's (NREL's) FAST (Fatigue, 

Aerodynamics, Structures, and Turbulence) code [9]. The CW and pulsed models are based on 

commercially available LIDARs. The LIDAR measurement scenarios investigated involve 

NREL's reference 5 MW model [10] with turbulent wind inputs generated using NREL's 

TurbSim code [11,12]. 

The LIDAR modeling section of the report is organized as follows. Section 2 presents the 

principal equation used in the LIDAR measurement models, called the “range weighting 

function,” as well as the geometry of LIDAR measurements. The processes through which range 

weighting and measurement geometry cause measurement errors are discussed here. A 

subsection is then devoted to explaining the differences between CW and pulsed LIDARs and a 

derivation of the pulsed LIDAR range weighting function is provided. Section 3 describes the 

results from a simulation of the effects of wind turbulence parameters on wind speed 

measurement error. Section 3 also describes the investigation of a hub-mounted spinning LIDAR

scenario, with a focus on the optimal preview distances for wind speed measurements at given 

fractions of the rotor radius. Section 4 concludes the LIDAR modeling portion of the report and 

provides a discussion of plans for future research involving LIDAR and wind evolution 

modeling. 

2 LIDAR Measurement Theory

The analysis of LIDAR performance examined here uses the coordinate system shown in Figure 

2 (a). The ground referenced x, y, and z axes are defined such that -z is pointing in the direction 

of gravity and x is nominally pointing in the downwind direction. However, depending on the 

wind conditions being simulated, the x axis may not be aligned with the average wind direction. 

The wind speed vector is defined by u, v, and w components, where u is the streamwise 

component. Nominally, the u, v, and w axes are aligned with the x, y, and z axes, respectively, 

since the FAST simulations simply “march” the wind toward the turbine in the x direction. The 5 

MW model used for these LIDAR studies has a hub height of 90 meters and a rotor radius of 63 

meters.
9 

Figure 2. Coordinate system and measurement variables referred to in the discussions. (a) The x, 

y, z coordinate system along with the LIDAR measurement angle, θ, and the angle between the 

LIDAR beam and the wind speed vector, Φ. (b) Variables referred to in the analysis of a spinning 

LIDAR including preview distance, d, and scan radius, r. 

The LIDAR measurement model introduces two imperfections to wind speed measurements. 

Range weighting is the effect inherent to CW and pulsed LIDAR that applies a spatial filter 

along the laser beam, causing wind speeds at locations other than the focal distance to contribute 

to the measured value. The other primary source of error in wind speed measurements is due to 

estimating the u component of the wind velocity vector given a single line-of-sight measurement.

This is sometimes called the “cyclops dilemma.” Control systems utilizing preview wind speed 

measurements primarily focus on the component of the wind that is perpendicular to the rotor 

plane, nominally the u component. In our simulations, the mean streamwise wind direction is 

aligned with the x axis, so we are assuming that the rotor plane is always perpendicular to the x

axis. Therefore, our LIDAR measurements estimate the component of wind aligned with the x

axis, which will be treated as equivalent to the u component for the rest of the report. When the 

LIDAR is pointing in the x direction, there will be no geometrical measurement errors because 

the v and w components do not contribute to the detected radial velocity. If the laser is instead 

pointed in a direction other than along the x axis, unknown v and w components contribute to the 

measurement and an estimate of the u component must be formed. 

The errors due to measurement geometry are equivalent for CW and pulsed technologies, but 

effects due to range weighting are different. Whereas the range weighting function for CW 

LIDAR changes for every measurement range, it remains constant for all ranges with a pulsed 
10 

LIDAR. Therefore there are fewer variables to consider when analyzing pulsed LIDAR and the 

emphasis of this report is on CW LIDAR. 

2.1 Continuous Wave Range Weighting

CW LIDAR determines the radial wind speed at a specific location by focusing the laser beam at 

that location instead of relying on range gates and timing circuitry like a pulsed system. 

However, rather than only detecting the wind speed at the focal point, wind speed values along 

the entire laser beam are integrated according to a range weighting function W(R), inherent in the 

physics of a focused LIDAR system, to yield the detected value. Our model assumes that range 

weighting occurs only along an infinitely thin beam. The wind speed measurement due to range 

weighting at a focal distance F is determined by 

∫

∞

∞− = dRRWRvFvwgt r )()()( (2.1) 

where vr(R) is the radial velocity at a range R along the laser beam [13]. In the case when the 

effects of refractive turbulence on laser propagation are ignored, the range weighting function for 

a focal distance of F is given by 

2

2

2 1

)(

R

N

R

F

R R

K

RW





 



 −+

= (2.2) 

where RR is the Rayleigh range and KN is a normalizing constant so that 

.1)( ∫

∞

∞− dRRW = (2.3) 

The Rayleigh range is given by 

λ

π 2

a2 RR = (2.4) 

where λ is the laser wavelength and a2 is the e

-2 intensity radius of the Gaussian laser beam. The 

analyses in this study assume λ = 1.565 μm and a2 = 2.8 cm, which are characteristic of a 

commercially available CW Doppler LIDAR system. 

W(R) is presented in Figure 3 for several ranges that might be desired in wind preview control 

applications. Clearly, as the range of the measurement increases, the detected velocity contains 

increasingly significant contributions from a greater length along the beam. The spatial 

averaging effect of range weighting causes the LIDAR beam to low-pass filter the wind speeds it 

measures. As focal distance increases, the cut-off frequency of the equivalent filter decreases. 

Frequency responses for the range weighting functions shown in Figure 3 as well as those for 

focal distances of 200 and 250 meters are provided in Figure 4. In addition, Figure 4 shows the 

range weighting function for a commercially available pulsed LIDAR discussed in Section 2.4

and a typical wind spectrum used in this research. Note that typical focal distances for a CW

LIDAR are less than 200 meters.
11 

Figure 3. Normalized range weighting functions, W(R), for the CW LIDAR at a variety of focal 

distances, F. The range weighting functions spatially average the wind along the laser beam. As 

focal distance increases, spatial averaging along a greater length of the beam occurs.

Figure 4. The frequency responses of the normalized range weighting filters for a variety of focal 

distances along with the -3 dB bandwidths of the filters.

The -3 dB bandwidths of the CW LIDAR range weighting functions listed in Figure 4 are 

inversely related to the square of the focal distance through a simple formula based on 

observations. The -3 dB bandwidth is given by 

(2.5) 

where the factor of 87 is based on the specific LIDAR parameters used in this report. 
12 

Figure 4 can be used to determine the frequency responses of measurement error for various 

focal distances. The range weighting filters affect the magnitude of the measured wind but do not 

introduce any phase distortion. An implication of this is that the magnitude of measured wind as 

a function of spatial frequency is reduced by a factor of 

(2.6) 

where W(k) is the frequency response of the range weighting function, while the phase is 

unchanged. Using Eq. 2.6, the RMS measurement error as a function of frequency is found to be 

 (2.7) 

where U(k) is the frequency response of the u component of the wind. 

2.2 Measurement Geometry

A single LIDAR unit is capable of measuring only radial wind velocity, yet the wind velocity at 

a given location is a vector quantity consisting of u, v, and w components. Therefore, a single 

LIDAR cannot determine the entire wind vector quantity. Instead, the assumption that the 

measured radial wind speed is due to the u component alone with v = w = 0 is made, since ideally 

u >> v, w. When the LIDAR is pointing upwind at an angle θ off of the x axis, it is assumed that 

the angle φ, which is formed between the instantaneous wind vector and LIDAR beam, is equal 

to θ (although φ and θ will differ if the instantaneous wind direction is not aligned with the x

axis, as is almost always the case). The detected radial velocity (see Figure 2) is then given by

cos( ) φ 222

wvuvr ++= (2.8) 

and under the assumption that v = w = 0 (φ = θ), the estimate of u is

( ). cos ˆ θ

r v

u = (2.9) 

When the LIDAR is pointing nearly along the x axis, and θ is small, errors due to the LIDAR 

geometry will be small since the measured radial velocity will be dominated by the u component 

of wind speed. As θ increases, the radial velocity measured by the LIDAR will contain more 

contributions from the v and w components. For large angles off of the x axis where the u

component becomes close to orthogonal to the LIDAR direction, θ is close to π/2 and an 

approximation of the u estimate is

. 2/

2/ ˆ 222

θπ

φπ

−

− ++≈ wvuu (2.10) 

For large θ and φ, close to π/2, the u estimate is very sensitive to mismatches between θ and φ

and measurements will likely contain severe errors.
13 

An analysis of large angle errors has shown that for a variable u velocity, and a transverse wind 

speed component with fixed magnitude and uniformly distributed random 

direction in the yz plane, the RMS measurement error will be

(2.11) 

where θ is the measurement angle off of the x axis. Furthermore, for stochastic wind fields where 

the magnitude varies with time, the RMS error is given by 

(2.12) 

where αRMS is the RMS value of the transverse wind speed magnitude, or . The most 

revealing feature of this relationship is that in the absence of range weighting, measurement 

errors will scale with . 

2.3 Combined Range Weighting and Geometrical Errors

An analysis has been provided for range weighting errors and measurement angle errors 

separately, but in practice measurement errors are caused by a combination of the two sources. 

For very large θ, angular errors tend to dominate, while for moderate to small θ and large focal 

distances, range weighting dominates the overall error. Figure 5 (a) illustrates how measurement 

errors follow a trend for large θ as well as how range weighting will dominate overall CW 

measurement errors for small θ and great enough focal distances. The scenario used to generate 

the four curves in Figure 5 (a) is illustrated in Figure 5 (b). Each LIDAR is pointed at a different 

elevation, ΔZ , above the LIDAR unit, that does not vary with measurement angle. At any given 

measurement angle, the focal distance is then given by . Thus the curves representing 

large ΔZ have greater focal distances, and represent errors that are dominated by range 

weighting, at larger θ. Note that the chosen ΔZ represent 25%, 50%, 75%, and 100% blade span 

for the 5 MW turbine model investigated in this research. For larger θ (which correspond to 

smaller F for a constant ΔZ), measurement error follows the curve. Each solid curve in (a) 

begins a transition (at a different measurement angle) from predominantly representing angular 

errors to being dominated by range weighting errors. The ΔZ = 63 m curve diverges from 

at roughly 40° and F = 98 meters, the ΔZ = 47.25 m curve diverges at 33° and F = 86 meters, the 

ΔZ = 31.5 m curve diverges at 27° and F = 69 meters, and the ΔZ = 15.75 m curve diverges at 

20° and F = 46 meters.
14 

Figure 5. The combined effects of measurement angle and range weighting on overall 

measurement error for CW LIDAR. (a) Four curves showing RMS measurement error vs. 

measurement angle. The curves represent LIDAR measurements at four different fixed ΔZ values 

as a function of measurement angle θ. For each ΔZ, the focal distance F varies with measurement 

angle. The four different measurement scenarios are illustrated in (b). 

To graphically illustrate how range weighting and measurement angles affect CW wind speed 

measurements, Figure 6 compares actual u components of wind speed as well as the measured 

wind speeds for a variety of F and θ. For F = 10 and F = 25 meters, range weighting has little 

impact on detected wind while for larger F, the low-pass filtering effect of the measurement 

process can clearly be observed in Figure 6 (a). Figure 6 (b) illustrates the severity of wind speed 

errors for moderate to large θ. 
15 

Figure 6. Examples of (a) range weighting errors for a variety of F and (b) measurement angle 

errors for a variety of θ. The measurements in (b) involve focal distances less than 10 m, so all 

visible discrepancies from the true wind speed are solely due to geometrical errors.

For the analysis of a spinning LIDAR described in Section 3.3, another possible source of 

measurement error exists. The CW LIDAR being modeled provides a velocity sample at a rate of 

50 Hz. For a LIDAR that is pointed at some angle θ and spinning around the x axis, the focal 

point will travel along the circle being scanned while returns are being integrated to form a 

velocity estimate. This “blurring” effect could cause another source of spatial averaging error. 

The arc length that the focal point traverses during a sample period is equal to

(2.13) 

where ω is the rotational rate of the LIDAR and r is the scan radius as defined in Figure 2 (b). 

An investigation of this source of error showed that the blurring effect causes insignificant error

for ω less than 240 RPM. Since it is unlikely that a spinning LIDAR would scan at a rate higher 

than 240 RPM, we have ignored this source of error. It is possible that the resolution of the wind 

files used during simulation is not high enough to reveal the severity of the spatial averaging that 

would occur. Investigating the effect with higher resolution wind fields is an area of future work. 

2.4 Pulsed LIDAR Systems

Although pulsed LIDAR systems do not rely on focusing a laser at the range of interest as CW 

systems do, their spatial averaging can be similarly described by a range weighting function. 

Pulsed LIDARs emit a laser pulse and integrate the back-scattered light as the pulse travels 

through several "range gates." One drawback to using pulsed technology is that more time is 

required to integrate enough photons to provide a useful velocity estimate. The pulsed LIDAR 
16 

that the model is based on provides a sample once every second as opposed to 50 times per 

second with the CW LIDAR. 

The pulse shape for a pulsed system can usually be approximated by a Gaussian pulse, 

 (2.14) 

where R is the distance to the center of the range gate of interest and the e

-1 width of the pulse, rp,

is given by 

(2.15) 

where Δr is the full-width-at-half-maximum pulse width [14]. Returns are integrated as the 

Gaussian pulse travels through the range gate volume according to the range weighting function 

(2.16) 

where Δp is the size of the range gate. After integrating Eq. 2.16, in terms of the Erf function, the 

range weighting function for the range gate centered at a distance R away from the LIDAR is 

given by 

. (2.17) 

The pulsed LIDAR model in this report uses Δr = 30 m and Δp = 30 m. The first range gate is 

centered at a range of 35 meters and the last gate is centered at 275 meters, with range gates 

every 30 meters in between. 

Figure 7 (a) compares RMS measurement error for forward staring CW and pulsed LIDARs at 

the 9 range gates used in the pulsed LIDAR model. The amount of error for the pulsed LIDAR 

remains constant for all range gates since the range weighting function does not change, and the 

minor variations visible are due to simulation imperfections. For ranges below roughly 135 

meters the CW LIDAR measurements produce less error, and beyond 135 meters CW performs 

worse. Both technologies produce approximately the same amount of error at a range of 135 

meters. Figure 7 (b) compares the range weighting functions for the two technologies at a range 

of 135 meters. The Gaussian-like shape of the pulsed weighting function has more of its energy 

concentrated in a smaller area while the CW weighting function has significant “tails” that 

contribute to spatial averaging far away from the intended range. 
17 

Figure 7. A comparison of CW and pulsed LIDARs based on parameters from commercially 

available LIDARs. (a) A comparison of RMS errors for a forward-pointing LIDAR configuration 

using the AR1 wind condition at ranges corresponding to range gates of a pulsed LIDAR. (b) A 

comparison of the pulsed range weighting function and the CW range weighting function at F = 

135 meters.

The frequency response of the pulsed LIDAR range weighting function is provided in Figure 4

along with the CW frequency responses. Clearly the difference in the shape of the pulsed range 

weighting function results in a different spectral shape. If the range weighting functions are 

being described as low-pass filters, then the pulsed LIDAR filter has a much sharper transition 

between the pass band and the stop band and is therefore closer to an ideal low-pass filter.

3 LIDAR Simulation Results

Simulations were performed in FAST to assess the performance of CW and pulsed LIDARs in 

realistic preview measurement scenarios. All wind fields used were generated for use with a 5 
18 

MW turbine model with a hub height of 90 meters. RMS wind speed measurement errors were 

analyzed for a forward-pointing LIDAR (θ = 0) at the hub location to assess the effects of range 

weighting alone for a variety of wind conditions. Ideal preview control systems might include 

LIDAR units mounted in the blades, so that preview measurements can be made in front of 

outboard sections of the blades, avoiding geometrical measurement errors. However, since a 

more economical and realistic method involves placing a single scanning LIDAR angled off of 

the x axis in the spinner of a turbine, spinning LIDAR performance was analyzed for different 

blade span positions and preview distances.

3.1 Wind Conditions

In order to test the performance of CW LIDAR in realistic wind environments, simulations were 

run using a variety of wind files generated with the Great Plains low level jet (LLJ) spectral 

model in TurbSim, characteristic of wind observed near Lamar, Colorado [12,2]. A library of 

wind files consisting of below rated (mean u component of wind speed = 9 m/s), rated ( = 

11.4 m/s), and above rated ( = 13 m/s) conditions with various stability and friction velocity 

values was used for the simulations. A total of 31 wind fields, each 630 seconds in length were 

stochastically generated for each of the five varieties of wind conditions available at the three 

mean wind speeds. The wind files are sampled at 20 samples/second and contain 31 by 31 points 

in the yz plane. A summary of the library of wind files used is provided in Table 1. Although 

coherent structures have been generated to be superimposed over some of the wind files, the 

results in this section do not include coherent structures. Uhub indicates the reference streamwise 

wind speed, RiTL indicates the turbine layer gradient Richardson number, and αD indicates the 

wind shear power law exponent. UD

*

 is the average friction velocity, defined in Eq. (3.1), of 

wind at the hub, top of the rotor, and bottom of the rotor. , , and are the mean 

turbulence intensities of the u, v, and w components of wind speed, defined in Eq. (3.2), 

respectively. For the wind scenarios that do not have power law wind shears, jet height indicates 

the height of the center of the jet, which is at hub height for the 5 MW model. 

Table 1. A Summary of the Great Plains Low Level Jet Wind Fields Used for Wind Speed Measurement 

Analysis 
19 

3.2 Impact of Turbulence on Measurement Errors

It is important to be able to judge the fidelity of wind speed measurements in a variety of wind 

conditions to determine when preview measurements will be reliable enough for use in control 

systems. RMS measurement error over an entire 10-minute wind field is used as a metric to 

compare LIDAR performance in this section. The amount of measurement error is not directly 

related to the mean wind speed of a wind field but rather to the turbulence parameters. For a 

forward pointing LIDAR at hub height, the wind shear profile will not affect wind speed errors 

either. Parameters that will likely impact range weighting errors are the Richardson number, 

defining vertical stability, the turbulence intensity (TI), and the local friction velocity, in m/s, 

defined as 

(3.1) 

where and . Because range weighting acts as a filter on the wind field, 

another approach is to study the impact of range weighting for a variety of spectral shapes of the 

wind. In this research, this was not possible since all LLJ wind spectra, once normalized by some 

value, have roughly the same spectral shape.

The turbulence intensities of the three wind components, given by 

(3.2)

where σu, σv, and σw are the standard deviations of the u, v, and w wind speed components, 

respectively, are common ways of describing wind conditions [3] and are also easy to measure. 

The turbulence intensity value most commonly used to describe wind conditions is TIu. Since it 

is actually the standard deviation of the wind that causes measurement errors rather than the 

turbulence intensity, the variable analyzed here is TIu multiplied by the mean wind speed, or just 

the standard deviation of the u component, σu. Results showing the CW RMS errors between true 

wind speeds at the hub location and wind passed through range weighting filters are shown in 

Figure 8 as functions of σu. 

Results for all 31 seeds for each of the 15 wind conditions are provided for a total of 465 wind 

conditions due to the fact that the various stochastic realizations of the 15 basic wind types have 

varying amounts of TI. While the results show that there is a general trend between σu and RMS 

error, it is clear that all seeds within one basic wind type produce roughly the same amount of 

error regardless of σu. At a focal distance of 200 meters, it appears that σu plays more of a role in 

determining RMS error. A possible reason for this is that at F = 200 m, the range weighting filter 

has a very low cutoff frequency of 0.0022 m-1. Only turbulent features with wavelengths on the 

order of 450 meters or above are able to pass through the filter and it is likely that a TI value 

captures the low frequency fluctuations very well. 
20 

Figure 8. RMS wind speed measurement errors for a LIDAR pointed along the -x axis at hub height 

for various focal distances as functions of standard deviation of the u component of wind speed. 

Results are shown for all 465 wind files generated for use with the 5 MW model. 

Rather than treating standard deviation of wind speed as a reliable variable for estimating 

measurement error, a variable common to all of the realizations of a basic wind type is desired. 

Local friction velocity, or u*

, is a good figure for judging measurement errors because all seeds 

of a main wind type have the same local u*

 values for the LLJ spectral model analyzed here. In 

fact, local u* values control the scaling of the velocity spectra in the LLJ model.1 In addition, u

* 

has been shown to be a good indicator of the number of high-loading events on a turbine [15,16] 

and may therefore be a useful value for analyzing the performance of a controller based on wind 

preview measurements. Results of RMS errors between true and measured wind for CW LIDAR 

are included in Figure 9 as functions of local u*

 at hub height. It is important to note that the 

friction velocity referred to in this analysis is the local u* at hub height rather than the average 

friction velocity over the entire rotor disk, UD

*

, shown in Table 1. Clearly, local u* provides a 

much better indicator of forward-looking LIDAR performance, especially for the 25, 50, and 100 

meter focal distances. When the LIDAR is focused at a distance of 200 meters, local u* is still a 

reasonably good indicator of RMS error, but there tends to be more variation within a basic wind 

type. This is consistent with the results in Figure 8 that reveal an increasing dependence on σu for 

errors at greater focal distances.

 

1 While the LLJ spectra scale with u*

, other spectral models such as the IEC models scale with σu. 
21 

Figure 9. RMS wind speed measurement errors for a LIDAR pointed along the -x axis at hub height 

for various focal distances as functions of the local friction velocity u*

. Results are shown for all 

465 wind files generated for use with the 5 MW model. 

Pulsed LIDAR errors as a function of wind condition need to be analyzed for only one range, 

since the range weighting function does not change with measurement distance. Figure 10 shows 

pulsed LIDAR RMS error as a function of u* and compares the trend with the CW results. The 

pulsed RMS errors are almost identical to the CW errors for a focal distance of 135 meters, as 

predicted in Figure 7. Pulsed and CW LIDARs focused at 135 meters provide the same amount 

of error as a function of u*

 for a constant spectral shape of the wind. However, it is likely that 

overall RMS error for a pulsed LIDAR would be equivalent to CW error at some other focal 

distance for different spectral shapes of the wind due to the different shapes of the frequency 

responses for the pulsed and CW range weighting functions. For example, if the wind's spectrum 

was contained at frequencies very close to DC, the CW LIDAR focused at 135 meters would 

filter the wind more than the pulsed LIDAR, as seen in Figure 4, and would cause more 

measurement error. In this case, a CW LIDAR focused at a shorter distance than 135 meters 

would result in the same measurement error as the pulsed LIDAR. 
22 

Figure 10. RMS wind speed measurement errors for a LIDAR pointed along the -x axis at hub 

height for pulsed LIDAR and CW LIDAR at various focal distances as functions of the local friction 

velocity u*

. 

3.3 Hub Mounted Spinning LIDAR Analysis

By mounting a LIDAR in the spinner of a wind turbine, the LIDAR can be offset at an angle θ

and focused at a distance F so that measurements will be made at a radius r and a preview 

distance d in front of the turbine [see Figure 2 (b)]. In addition to the rotational rate of the turbine

rotor, which may be too slow for the measurement rate desired, an additional rotational rate can 

be introduced. Since this method has been successfully tested on a 2.5 MW turbine [8], it is 

reasonable to assume that a likely measurement technique for a preview control implementation 

will involve a spinning LIDAR. 

Observations based on the results in Figure 5 encouraged the study of “optimal” preview 

distances using CW LIDAR for specific scan radii, r, and wind conditions. For pulsed LIDAR 

there is no notion of an optimal preview distance yet, since error decreases monotonically with 

preview distance. The optimal preview distance is defined here as the distance for a given r that 

provides the lowest RMS measurement error while using a LIDAR mounted at the hub location. 

Although wind evolution would cause even more error between the measured wind speed and the 

wind speed that reaches the rotor, Taylor's frozen turbulence hypothesis is assumed here, 

meaning that the optimal preview distance is judged based on measurement errors alone. In this 

report, RMS errors for a given r are calculated by averaging wind speed measurements at rotor 

angles ψ = 0, 90, 180, and 270 degrees [see Figure 2(b)], the angles where measurements lie on 

wind field grid points for the chosen scan radii. We found that by modeling wind measurements 

on the TurbSim grid points, wind speeds more indicative of the intended turbulence conditions 

could be acquired. Measurement errors are shown as functions of preview distance for 14 
23 

different blade span radii in Figure 11 for the AR1 and AR3 wind conditions. The 14 radii 

analyzed correspond to the 14 sample locations along the y and z axes in the TurbSim file that 

are less than or equal to blade span. The AR1 wind type is the most turbulent of all wind types 

analyzed here, while AR3 represents relatively calm conditions. Figure 12 summarizes the 

minimum errors detected and the corresponding preview distances for the 14 blade span 

positions analyzed in Figure 11. 

Figure 11. RMS measurement error as a function of preview distance for various scan radii, 

assuming a spinning LIDAR mounted in the spinner of a wind turbine. The optimal (minimum RMS 

error) preview points are plotted for each scan radii. (a) Results for the high turbulence AR1 wind 

type. (b) Results for the relatively calm AR3 wind condition. 
24 

Figure 12. Optimal (minimum RMS error) measurement errors and preview distances 

corresponding to Figure 11 as functions of scan radius, r. 

The optimal measurement distance can be roughly described as the point at which both 

geometrical errors and range weighting errors are low. For shorter distances measurement angle 

errors will cause error to increase, and for greater distances the low-pass filtering effect of range 

weighting will cause more significant error. The results of Figure 11 show that the optimal 

measurement distance is a strong function of r. As r increases, the optimal preview distance is 

greater because of the large measurement angle required to focus at a radius r. In addition, for 

the calmer wind condition, AR3, optimal preview distances tend to be closer to the turbine than 

for the AR1 case. In Figure 11 (a), one can see that for very large preview distances, all error 

curves tend to converge, because range weighting dominates over the low angular errors caused 

by very small θ. 

Results for AR3 in Figure 11 (b) reveal a very interesting phenomenon. At great enough preview 

distances, measurements at smaller scan radii produce errors that are greater than those resulting 

from larger radii. This is a counterintuitive result because for a given preview distance larger 

scan radii should produce greater measurement errors, since θ is greater and the measurement 

angle errors have more of an impact. However, by observing how local u* varies with height, 

some insight into this phenomenon can be gained. In Section 3.2, we found u* to be a good 

indicator of the amount of measurement error that can be expected. Normalized profiles of u* for 

AR1 through AR5 are shown in Figure 13. The ratio of u* at 50% blade span above hub height to 

u*

 at hub height, for example, is 0.62 for AR3, while it is 0.83 for AR1. This means that 

measurements at 50% blade span will be far less corrupted by turbulence compared to 

measurements at hub height for AR3 than they would be for AR1. Beyond a certain preview 

distance, for AR3, the decrease in range weighting error due to lower turbulence causes overall 

error to be lower for larger scan radii, even though the measurement angles are slightly greater. 

For AR1, the ratio between turbulence levels at hub height and larger blade radii is not great 

enough to counteract the increase in error due to greater measurement angles, θ. Therefore, the 

curves representing measurement error for small scan radii, r, in Figure 11 (a) do not eventually 

intersect and become greater than the curves corresponding to larger r, as they do in Figure 11

(b).
25 

Figure 13. Height profiles of u* for AR1 through AR5. All profiles have been normalized to their 

maximum value of u*

. 

Previous LIDAR-based preview control studies have required knowledge of wind speeds 

concentrated heavily between 60% to 80% rotor radius [3] and at 75% rotor radius [1,2] because 

of maximum power extraction at these spans. To reflect the interest in wind speed measurements 

at these spans, simulations were performed for all 15 wind types for a scan radius of 75% blade 

span along with 50% and 100% blade span for comparison. Results from these simulations are 

included in Figure 14, which displays the average minimum measurement error achieved for 

each wind condition along with the preview distance at which the minimum error was measured. 

Minimum achievable RMS error is clearly a much stronger function of wind condition than 

optimal preview distance. For the high-interest 75% blade span scan radius, typical optimal 

preview distances for a variety of wind conditions are between 110 and 150 meters. 
26 

Figure 14. Minimum RMS measurement errors and corresponding optimal preview distances for 

measurements using a spinning LIDAR located at the hub of a wind turbine for scan radii of 

53.7%, 76.7%, and 99.7% blade span (33.83 m, 48.33 m, and 62.83 m, respectively). The scanned 

radii correspond to the grid points closest to 50%, 75%, and 100% blade span containing wind 

speed samples in the TurbSim files.

In order to assess how pulsed LIDAR measurements would perform compared to CW, error as a 

function of preview distance is shown for the AR1 wind category for pulsed and CW LIDARs in 

Figure 15 for 50%, 75%, and 100% blade span. There are three regions in the plot worth noting. 

The first region is for very short preview distances where errors are high but pulsed 

measurements perform slightly better than CW measurements. The second region is for moderate 

preview distances. Here, CW LIDAR performs better because its range weighting function filters 

out less wind energy than the pulsed weighting function. The third region is for large preview 

distances. In this region, pulsed LIDARs produce less error because the CW range weighting 

functions have become wide enough to filter out more wind components than the pulsed 

weighting functions. The second and third regions are expected. It is the first region that contains 

counterintuitive results. 
27 

One would expect CW to perform better in the first region because of the relatively short focal 

distances and therefore insignificant range weighting. However, at these close preview distances, 

the main source of error is the wind component in the yz plane (see the Appendix), and this 

source is reduced slightly more with wider range weighting functions. The estimate of the 

desired u component of wind assumes that v and w are zero and a wide weighting function will 

spatially average these components more than a narrow weighting function. Since v and w are 

zero mean, by averaging the wind speed vectors over a wider area, they will be reduced more 

and will cause the u estimate to contain more accurate assumptions. For short distances, the 

wider pulsed weighting function is reducing the contributions from v and w enough to produce 

slightly lower overall errors than the CW LIDAR. 

Figure 15. RMS measurement error as a function of preview distance for the high-turbulence AR1 

wind type. Results are shown for CW and Pulsed LIDAR.

It is worth noting that the results shown in Figure 15 were generated assuming the measurement 

range of the pulsed LIDAR could be continuously varied and that the sample rate was as high as 

that of the CW LIDAR. In reality, the slower sampling rates of pulsed LIDARs may make them 

undesirable for spinning LIDAR applications due to the spatial averaging that occurs as the 

LIDAR measurement point moves along an arc while returns are integrated (see Eq. 2.13).

4 LIDAR Modeling Conclusions and Future Work

This section of the report has provided an analysis of the application of continuous-wave (CW) 

and pulsed Doppler LIDARs to preview wind measurements on a wind turbine. The analysis has 

specifically focused on the two main sources of error during LIDAR measurement, including 

range weighting and geometrical errors, and the measurement scenarios where each source is 

dominant. Figure 5 and Figure 6 suggest that measurement angles greater than 45 degrees should 

be used with caution because of the large errors introduced by the relatively strong v and w

components of radial velocity. The local friction velocity, u*, was shown through simulation to 

provide a good indication of the amount of wind speed measurement error due to range 
28 

weighting. An analysis of a realistic hub mounted spinning CW LIDAR measurement scenario 

for a 5 MW turbine was made, with results revealing the preview distances that one might expect 

to provide the minimum RMS error for specific scan radii. Initial results for wind preview based 

feed-forward controllers utilizing the CW LIDAR model developed in this study are documented 

later in this report and in Dunne et al. [17] and Laks et al. [18].

On-going work involving CW LIDAR modeling includes investigating random LIDAR errors 

due to optical and electronic noise. Measurement noise likely varies with turbulence conditions 

and a model of noise is desirable in a future LIDAR model. A thorough analysis of 

measurements of coherent structures, such as Kelvin-Helmholtz billows, in the wind fields is 

needed. Studies have shown that coherent structures cause severe turbine loads [15], and it is a 

goal of wind preview-based controllers to mitigate the loads caused by coherent structures. 

Therefore, it is essential to determine the fidelity that LIDAR measurements of coherent 

structures can achieve.

Initial results have illustrated the problems that can be caused by coherent turbulence events and 

an example of the large measurement errors that can be caused is provided in Figure 16. Figure 

16 (a) shows the turbulent wind field in the xz plane (y = 0), without the mean u component of 13 

m/s, from the AR4 wind type with a superimposed coherent structure. The measurement scenario 

used to assess the measurement errors is shown as well. A LIDAR is focused at hub height at a 

range of 100 meters and an angle of 30°. Figure 16 (b) shows the measurement errors 

corresponding to the x measurement locations at hub height in (a). It can be seen that the 

coherent structure introduces very strong positive w wind components around hub height that last 

for about 200 meters in the x direction. Due to the measurement geometry these coherent positive 

w components cause a lower line-of-sight velocity to be measured by the LIDAR. The result is 

that the measured and estimated u value is much lower than the actual u component, with a peak 

underestimation of 2.5 m/s. 
29 

Figure 16. An example of a coherent structure causing severe wind measurement error. (a) The 

wind field, with the mean u wind speed of 13 m/s subtracted, in the xz plane containing a 

superimposed coherent structure. (b) Wind speed measurement errors caused by a CW LIDAR 

measuring the wind field in (a) at hub height at an angle of 30° with a focal distance of 100 meters.

As shown in Figure 1, wind evolution presents another source of wind preview uncertainty that 

was not discussed in this work. Future efforts in wind evolution modeling and simulation are 

required to fully assess the effectiveness of LIDAR wind preview measurements for control 

applications. An implication of the studies in this report is that it may be impractical for a 

LIDAR unit based in the spinner of a wind turbine to provide accurate wind preview 

measurements at large scanning radii close to the turbine. To avoid measurement errors due to 

geometry, one possibility is to measure the wind farther away from the turbine and delay the 

measurements before they are input to a controller if the controller requires very short preview 

times [1]. We anticipate that with the addition of wind evolution modeling, optimal preview 

distances such as those shown in Figure 12 and Figure 14 will no longer be valid because wind 

evolution will cause shorter preview distances to be favored, since wind evolves more over 

greater distances. As a result, it may be difficult to provide highly accurate preview 

measurements to a controller using a hub mounted spinning LIDAR. More simulations using 
30 

LIDAR and wind evolution models are required to fully understand the capabilities of LIDARbased wind preview measurements.

5 Feed-Forward Control Introduction

Current commercial wind turbine control algorithms are feedback only, as shown in Figure 17. 

Blade pitch is often controlled by a simple proportional-integral (PI) based collective blade pitch 

controller, which receives its input signal from the error in generator speed. Recent work

[19,20,21,22] has verified that more advanced feedback controllers can reduce structural fatigue 

loads. These advanced controllers typically employ individual pitch control and may be based on 

signals from strain gauges and position encoders in addition to generator speed. 

LIDAR can be used to remotely measure wind speed. Recent improvements in LIDAR size, cost, 

and reliability have made it realistic to obtain accurate wind speed measurements upstream of the 

turbine [8]. When wind speed measurements are available, it is possible to use this additional 

information through disturbance feed-forward control. This feed-forward control can be 

combined with either standard or advanced feedback control, as shown in Figure 18. The use of 

these wind speed measurements to reduce turbine fatigue loads is an area that is being actively 

researched [1,2,3,6,7]. 

In this study, a feed-forward controller is added on to a standard feedback controller, and the 

results are compared to the standard feedback controller alone. A previous study [2] investigated 

the same configuration, but with different feed-forward control designs: model-inverse and 

shaped compensators. The best of these previous designs, with perfect wind measurements, 

resulted in blade root and tower fore-aft load reductions between 5% and 15%, but slightly 

increased tower side-to-side motion. 

Figure 17. Feedback only control 
31 

Figure 18. Combined feedback/feed-forward control 

6 Simulated Turbine and Turbulent Inflow

6.1 5 MW Turbine Model and Baseline Control

All simulations are performed using a full non-linear turbine model provided by the FAST [9] 

software code developed at NREL. The particular model used in FAST is the NREL 5 MW 

reference turbine [10]. All available degrees of freedom (DOFs) except teeter are turned on in 

simulations. The baseline collective pitch controller is a gain-scheduled PI control [10]. 

An individual pitch feedback-only controller was also designed [19] for use as another baseline 

controller for comparison with individual pitch feed-forward controllers. In addition to generator 

speed, its inputs are the three out-of-plane blade root bending moments, and the rotor azimuth, 

which is used for the multi-blade coordinate (MBC) transformation [23]. The horizontal and 

vertical components are controlled with PI controllers, and the collective component is 

controlled with the same PI feedback control as the baseline collective pitch controller.

For all simulations, a 2nd-order pitch actuator model has been added to the 5 MW turbine model, 

with a natural frequency of 1 Hz and a damping ratio of 0.7. After FAST is used to find a 

linearized model of the turbine, this pitch actuator model is also added on to the linear model. 

FAST linearization is performed with a constant torque, while actual Region 3 operation has a 

varying torque to maintain rated power. Therefore the linear model is also modified to account 

for this varying torque by augmenting it with a generator speed-to-torque feedback linearized at 

the operating point. This overall model, shown as P in Figure 19, is then used for design. 
32 

Figure 19. Linear plant model used for control design. The linear turbine model from FAST is 

augmented with an actuator model and linearized torque feedback.

6.2 Wind Fields

The wind fields used in simulation are described by rows AR1, AR2, and AR3 from Table 1. 

These turbulent fields all have a 13 m/s mean hub-height wind speed and are representative of 

the Great Plains region. The first 99 sec of each 630 second simulation are discarded before 

calculating any performance measures to allow initial transients to settle out. Two of the 

realizations in particular, AR2_s1 and AR2_s13 (seed 1 and seed 13 of subpopulation AR2) will 

be referred to later in this report. 

7 Non-Causal Series Expansion

7.1 Design

Non-causal series expansion is a model-inverse method not tested in the previous study [2]. A 

first step in designing a linear model-inverse feed-forward controller is obtaining a linear model 

of the turbine (P). In this study, the turbine is linearized with five degrees of freedom turned on: 

first flapwise blade mode (for each of the 3 blades), drivetrain rotational-flexibility, and 

generator. This is performed using the linearization capability of FAST [9] to create a state-space 

model of the turbine based on perturbations from a particular operating point. 

From the state-space model, two transfer functions are extracted: maps collective blade 

pitch error bcmd to the error o in some output to be regulated; Pow maps deviation from nominal 

wind speed w to the output error o. Then a linearized version of the baseline feedback control is 

connected to this state-space model of the turbine, resulting in two closed-loop transfer 

functions: Tob maps collective blade pitch feed-forward input b to the error o in some output to 

be regulated. Tow maps deviation from nominal wind speed w to the output error o. 

A feed-forward controller is shown as F in Figure 20. A linear model-inverse feed-forward

approach uses F to cancel the effect of w on o. Therefore, as can be seen in Figure 20, 
33 

Figure 20. Combined feedback/feed-forward control, labeled to illustrate a linear model-inverse 

feed-forward approach 

In the special case when o=ofb (e.g., when the output of interest is generator speed error, the 

same output used in the collective-pitch feedback loop), it turns out that the closed-loop transfer 

functions Tob and Tow each differ from their corresponding open-loop transfer functions in the 

same way, so that F = – Tob

-1Tow = – 

-1Pow, and it doesn't matter whether the open-loop or 

closed-loop transfer functions are used. However, when o ≠ ofb, it is important to use the closedloop transfer functions when determining F. 

Ideally, the feed-forward controller would be set equal to F as above. However, in this case the 

resulting F is unstable because Tob contains non-minimum phase zeros. Therefore a stable modelinverse approximation is used instead. 

In the previous study [2], three different model-inverse techniques [24,25,26,27] were 

investigated: nonminimum-phase zero ignore (NPZ-Ignore), zero-phase-error tracking control 

(ZPETC), and zero-magnitude-error tracking control (ZMETC). These worked well when 

controlling a linear plant model, but performed worse than the baseline controller alone when 

simulated in FAST with the full nonlinear wind turbine dynamics. This study investigates a 

different model-inverse approximation method: non-causal series expansion (NCSE) [28,29]. 

NPZ-Ignore is actually a zeroth-order NCSE, but this study addresses higher orders of NCSE. 

This type of inversion requires the most preview time and should theoretically provide a better 

approximate inverse than the NPZ-Ignore, ZPETC, and ZMETC methods.

The NCSE method results in a stable approximate model-inverse by using a Taylor series 

approximation. For example, if the desired F contains an unstable pole a, then we replace 

with which is stable, but non-causal. For each term included 

in the approximation, an additional sample of preview is required. 

Other improvements were also made in addition to changing the approximate inversion method. 

The three previous model-inverse controllers [2] were designed to regulate the generator speed 

output, with the hope that they would also reduce structural loads. This NCSE control is instead 

directly designed to regulate the blade root bending moment output. The previous controllers 

were based on a model linearized about an operating point of 18 m/s wind speed and were gain 

scheduled, while this NCSE control is linearized at 13 m/s to better match simulation conditions 
34 

and is not gain scheduled. Low-pass filtering was also treated differently; the original design had 

one low-pass filter on the linear feed-forward controller, and a different low-pass filter on its 

gain-scheduling multiplier. The new design has no gain-scheduling multiplier, but instead has 

two parts described below, each with a different low-pass filter. Finally, the wind speed 

measurement used by the feed-forward control in previous simulations was an average of five 

points taken at the hub and outer edges of the rotor plane. In this study, it is an average of three 

points, one at 75% span of each blade, since accounting for tip losses, the blades are most 

sensitive to wind speed around this span location [3]. 

The NCSE control was first tested on the linear model for three varying parameters: 

approximation series order, sample rate used in conversion to discrete time, and number of DOFs 

turned on in linearization. Greater approximation series orders, sample rates, and number of 

DOFs were expected to improve performance, but they also increased the occurrence of 

numerical problems. We attempted to compare these different design options using the norm 

from wind speed error to root bending moment error, but numerical problems with Matlab's [30] 

 function appeared with higher orders of approximation. Careful choice of system 

representation in Simulink was also required to avoid numerical problems, with the feed-forward

controller split into a transfer function portion and a zero-pole-gain portion. The following 

choices were made in the design: approximation order = 199, 80 Hz sample rate, and 5 DOFs in 

linearization. This resulted in a 2.5 sec preview time (200 samples: 199 from the approximation 

order plus 1 because the 5 DOF model had 1 non-minimum phase zero [28]).

This NCSE feed-forward control does not need to operate at very low frequencies, because the 

focus is more about minimizing fluctuations in root moment, and less about the steady-state 

value. On the other hand, steady-state rotor speed is very important. Therefore the overall feedforward control is the sum of a high-pass filtered NCSE control and a low-pass filtered rotor 

speed control, as shown in Figure 21. Both filters have a 3 dB point at 10-2 Hz, since wind begins 

to affect rotor speed relatively less than root bending moment above this frequency. The wind 

speed input to the rotor speed feed-forward control signal (upper path in Figure 21) can also be 

delayed compared to the NCSE feed-forward control signal (lower path in Figure 21), since only 

the NCSE control was designed to have a 2.5 second preview. The rotor speed control uses a 

simple lookup table, with values based on testing of the non-linear turbine model at various 

operating points over a range of wind speeds from 11.4 to 25 m/s to find the required steady-state 

blade pitch at each operating point such that rated rotor speed is maintained. The feedback 

controller is still working to control rotor speed as well.
35 

Figure 21. Feed-forward control combining rotor speed regulation at low frequencies (upper path) 

and NCSE root bending moment reduction at higher frequencies (lower path). The linearization 

operating point is at 13 m/s wind speed and 0.1141 rad (6.537 degrees) blade pitch.

7.2 Results

The non-causal series expansion controller was simulated in both individual pitch and collective 

pitch form. In the individual pitch version, there are three copies of the feed-forward controller, 

one controlling each blade. Three perfect point wind speed measurements are taken, 2.5 seconds 

ahead of each blade at 75% span, and these are fed into their respective feed-forward controllers. 

This individual pitch feed-forward control is then added on to the individual pitch baseline 

feedback controller. Results shown here are for the individual pitch version simulated in wind 

field AR2_s1; the collective pitch version had similar results.

Structural loading measures include RMS nacelle velocities and damage equivalent loads (DELs) 

of blade and tower bending moments. DELs are calculated using code from NREL based on a 

rainflow counting algorithm [31] also used in the NREL code CRUNCH and the Sandia code 

LIFE2, with a Wohler curve exponent of 10, typical for composite material. 

Figure 22 shows that the NCSE controller does reduce blade root bending loads as designed, but 

also causes unacceptable increases in RMS nacelle velocity. Various other configurations of the 

NCSE control were also simulated considering different low-pass and high-pass filters, different 

preview lengths to each path of the controller, only one or the other path of the controller, etc. 

However, no configuration produced results that were clearly better overall than the individual 

pitch baseline feedback controller. Simulations were done in wind field AR2_s1, using perfect 

point wind measurements. Peak pitch rates were 0.81, 2.63, 7.23, 7.96, and 2.60 degrees/sec, 

respectively, for the five methods whose results are summarized in Figure 22. All controllers 

produced an average power of 5000.0 kW. Based on the plotted performance measures, the 

combined shaped feed-forward IP compensator augmented to the baseline IP feedback controller 

[2] remains the best overall controller, even compared with the new NCSE feed-forward 

compensators augmented to the baseline IP feedback controller. 
36 

Figure 22. A comparison of damage equivalent loads (DELs) and nacelle RMS velocities for the 

baseline collective pitch (CP) feedback-only controller, the baseline individual pitch (IP) feedbackonly controller, the non-causal series expansion (NCSE) individual pitch (IP) feed-forward 

controller augmented to the baseline IP feedback controller, the same NCSE controller without the 

lowpass (LP) filtered rotor speed control path, and the shaped IP feed-forward compensator with 

5s preview and IP feedback (best of previous work [2]). All results are normalized to the Baseline 

IP results.

8 Preview Control

Preview Control [32] is a method that incorporates a preview of the wind speed disturbance and 

includes a cost function that allows explicit minimization of rotor speed error, loads, and pitch 

rate.

8.1 Design

The particular version of Preview Control used in this study is one that is designed to be added to 

a predetermined feedback controller, which in this case is the baseline collective-pitch PI 

controller. Given a linear turbine model, predetermined feedback PI gains, weights for the cost 

function, and the desired number of preview samples, Preview Control allows researchers to 

solve for a feed-forward controller that minimizes the cost, given a step change in disturbance 

(wind speed). 

Initially, Preview Controllers were designed to minimize only rotor speed error and pitch rate. 

On both the linear model and in nonlinear simulation, these designs reduced blade root loads in 

addition to rotor speed error, but increased tower fore-aft motion compared to the baseline 

controller. Therefore, the procedure was modified so that the rate of change of nacelle fore-aft 

velocity could be included in the cost function: the weighting matrix used (on the right side of 

equation 17 in the solution in [32]) is changed from the originally intended
37 

to

where Q is a matrix, weighting the error e in the no outputs (just generator speed in this 

case), and Ws is an matrix, weighting the rate of change of the n plant states x. This 

changes the cost function from

to

where R is a weighting on actuator rate (pitch rate in this case).

The initial design was based on a 5 DOF turbine model (generator, drive train torsion, and first 

blade flap for each of the 3 blades), linearized about a wind speed of 13 m/s, and augmented with 

the actuator model and torque control feedback. The revised design instead has all DOFs 

(including tower bending) included in the linear model. The baseline PI feedback control is gain 

scheduled, so the gains at the 13 m/s linearization point were used: Kp = 9.68e-4 and Ki = 4.15e4. The weights chosen were: Q=1 (generator speed error), R=104 (pitch rate), and Ws = 105

CTC

(tower sway) where C is a row vector that returns the fore-aft nacelle velocity when multiplied 

by the column vector of plant states. The number of preview samples chosen was 396, requiring 

4.95 seconds of wind preview (very close to the “Shaped 5s” controller, which actually has 4.96 

seconds of preview). 

Figure 23 shows the pulse response for the Preview Controller with varying preview lengths. 

These pulse responses show what the pitch angle command would be for a discrete unit impulse 

in wind speed at time 0. If the pulse responses of two linear controllers are the same, then the 

controllers are the same. Pulse responses that are non-zero before time 0 require preview 

measurements. In the initial design, additional preview does not have much effect beyond about 

2 seconds of preview. This can be seen in Figure 23 because the blue, green, and red lines all 

overlap and match each other very closely. (The pulse response is 0 at any time where it is not 

shown.) But when the design is revised to include tower sway, additional preview continues to 

have an effect up until about 30 seconds of preview. However, a preview length of 4.95 seconds 

was chosen instead. Thirty seconds was deemed too large because the longer the preview time, 

the farther ahead of the turbine the LIDAR must be focused, increasing errors due to wind 

evolution and spatial averaging by the LIDAR [33]. However, focusing too close to the turbine 

can also cause errors, as discussed in the first part of this report. If the LIDAR is mounted on the 

turbine hub or nacelle, and scanning ahead of the turbine around a circle with a radius equal to 
38 

75 % of the rotor radius, its angle θ relative to an axis pointing into the wind will increase as the 

LIDAR measurement is taken closer to the turbine. The LIDAR measures wind speed in its lineof-sight direction, and wind speed is estimated in the downwind direction, assuming the nondownwind components of wind speed are zero. In practice, since the non-downwind components 

of wind speed are not always zero, errors increase as this angle θ increases. For the 5 MW 

turbine considered and wind measurements of 75 % span, a LIDAR angle of 30 degrees 

corresponds to 82 meters ahead of the turbine, which gives a preview time of 3.3 to 7.2 seconds 

in the rated-to-cut-out range of 11.4 m/s to 25 m/s. The chosen preview length of 4.95 seconds 

falls in this range.

Figure 23. Preview Control pulse responses for varying preview lengths (shown in different 

colors) for (a) the initial 5 DOF design and (b) the revised design with tower sway included in the 

cost function. The blue line in (b) is the final design used.

8.2 Results

Figure 24 and Figure 25 show that the preview controller works as designed on the linear model, 

reducing the effect of wind disturbance on rotor speed error as well as blade and tower loads. 

Additional testing on the linear model also demonstrates that the Preview Controller is still 

beneficial with a 1/8 second error (delay or advance from the designed 4.95 seconds) in preview 

time, and that performance degrades to worse than baseline control alone when errors in preview 

time become greater than 1/2 second. 
39 

Figure 24. Linear turbine model response to a step change in wind speed hitting the turbine at 

4.95 seconds, comparing Preview Control to no Preview Control. 
40 

Figure 25. Bode magnitude plot of linear turbine model showing that Preview Control improves 

rejection of wind speed disturbances. This shows reduced generator speed error, increased blade 

pitching, and reduced blade root moment and fore-aft nacelle velocity.

In simulation, the Preview Controller was implemented in collective pitch form, with wind 

speeds measured 4.95 seconds ahead of the three blades at 75% span and averaged together for 

the feed-forward control input. When simulated in simple uniform wind fields, Figure 26 and 

Figure 27 show that the Preview Controller is still working to reduce the rotor speed error as well 

as blade and tower loads on the nonlinear turbine model, although there is some loss in 

performance. However, when simulated in a turbulent wind field, tower fore-aft motion is worse 

with Preview Control, as shown in Figure 28 and Figure 29. Initial investigations of IP Preview 

Control produced similar results to the CP Preview Control shown, and IP Preview Control may 

be investigated further in the future. 
41 

Figure 26. Simulated nonlinear turbine model response to a step change (from 13 m/s to 14 m/s) in 

uniform wind speed hitting the turbine at 200 seconds, comparing Preview Control to no Preview 

Control. 
42 

Figure 27. Simulated nonlinear turbine model response to a sinusoidal uniform wind speed with a 

period of 5 seconds, comparing Preview Control to no Preview Control. 

Figure 28. Time series comparing baseline collective pitch feedback control with and without 

Preview Control in wind field AR2_s1. The lowest plot shows increased tower motion with Preview 

Control. 
43 

Figure 29. A comparison of damage equivalent loads (DELs) and nacelle RMS velocities for the 

baseline collective pitch (CP) controller and the CP 4.95 second Preview Controller in wind field 

AR2_s1. Peak pitch rates were 0.81 and 4.60 degrees/second, respectively. Both controllers 

produced an average power of 5000.0 kW. Results are normalized to the Baseline CP results.

9 Optimized FIR Filter

9.1 Design

Many of the previously mentioned feed-forward designs can be represented as finite impulse 

response (FIR) filters with discrete-time transfer functions with all poles at zero. Given an input 

of a unit pulse in wind speed, the FIR filter is described by its finite output sequence. For 

example, the pulse responses of the controllers described above are shown in Figure 30. In this 

figure, the amplitudes have been scaled for this comparison so that all controllers have the same 

DC gain, because different controllers were originally designed at different operating points and 

therefore different DC gains. Time 0 is when the wind pulse hits the turbine. The Shaped 10/3s 

feed-forward controller [2] has a pulse response that begins and ends 10/3s before and after time 

0. Similarly, the Shaped 5s begins and ends 5s before and after time 0. The NCSE controller 

response, although it looks very small everywhere except near time 0, actually begins 2.5s before 

0 and continues indefinitely. The Preview Controller response begins 4.95 seconds before 0, and 

ends at 0. 
44 

Figure 30. Pulse responses of various feed-forward controllers from previous and current studies

(right plot is a zoom-in of the left plot). 

For the optimized FIR filter, a sample time of 0.0125 seconds and a total response length of 10 

seconds were chosen. Its input is wind speed with a preview time of 5 seconds. This filter is 

therefore characterized by a sequence of 800 pitch command gain values, which all need to be 

optimized. The optimized FIR filter was found using a genetic algorithm [34], which simulates 

thousands of random possible FIR filters, converging on combinations of those with the best 

simulation results. Performance was based on fatigue load reduction (blade and tower damage 

equivalent loads and nacelle accelerations), RMS pitch rate, peak rotor speed, and average power 

achieved in a simulation of the nonlinear turbine, with all DOFs, in above rated wind conditions. 

Wind field AR2_s13 from the previous study [2] was used for these simulations because it was 

shown that it produced the highest blade root loads out of all AR wind fields. 

This genetic algorithm optimization approach is advantageous because it optimizes the controller 

directly on the nonlinear turbine model in a turbulent wind field, with LIDAR errors modeled, 

whereas feed-forward controllers designed based on a linearized turbine model with uniform 

wind fields often perform poorly in nonlinear turbulent simulations. The algorithm was seeded 

with the best of previous feed-forward designs, ensuring that results will be at least as good as 

previous designs on wind field AR2_s13. 

The optimization was performed using the Genetic Algorithm function of the Matlab 

Optimization Toolbox [30]. To reduce the number of variables that need to be optimized by the 

algorithm, the FIR sequence is down sampled to 81 points instead of 800, with heaviest sampling 

near 5 sec (since there will be a 5 sec preview time, this corresponds to time 0 in Figure 30, 

where the most detail is required). For simulation, the full sequence of values was interpolated. 

After interpolation, the DC gain of the FIR filter is scaled to 1. This scaled FIR filter is then 

placed in series with a lookup table that converts from steady-state wind speed values to the 

corresponding steady-state blade pitch values.

Three copies of this feed-forward controller are then implemented, one controlling each blade. 

Three wind speed measurements are taken, 5 seconds ahead of each blade at 75 % span, and fed 
45 

into their respective feed-forward controllers, giving us individual pitch control. This feedforward control is then added on to the individual pitch baseline feedback controller. 

While the previous controllers used wind speed measurements that were perfect point 

measurements, here wind speed measurements that incorporate a CW LIDAR model [33] are 

used. It includes spatial averaging, which is significant at the preview distance that is used (5 sec 

13 m/s = 65 m). We also assume three hub-mounted LIDARs spinning at a cone angle θ of 

about 35 degrees. A LIDAR can only measure wind speed in its line-of-sight direction, which is 

at a 35-degree angle from the horizontal downwind direction in this model. Thus, the wind speed 

in the horizontal downwind direction can only be estimated. To make this estimate, it is assumed 

that the vertical and crosswind wind speed components are zero. Therefore, by using the LIDAR 

model, measurement angle errors are included as well as spatial averaging errors in the wind 

speed measurements.

9.1.1 Cost Function

The genetic algorithm attempts to find the filter with the minimum cost. This cost is calculated as 

the sum of the following eight performance measures, after each has been normalized by the 

corresponding value for an individual pitch baseline simulation: DELs on blade root, tower-top 

fore-aft, tower-base fore-aft, and shaft; RMS values of nacelle acceleration in the x, y, and z

directions; and RMS pitch rate. This sum is then divided by 8, so that a cost < 1 represents better 

performance than IP baseline, and a cost > 1 is worse. Further, if rotor speed and power 

requirements are not met, the cost is increased sharply, as shown in the following pseudocode: 

if PeakRotorSpeed > 13 (rpm), then cost = cost ∙( 1 + (PeakRotorSpeed - 13) ∙10)

if AveragePower < 4999.9 (kW), then cost = cost ∙( 1 + (5000 - AveragePower) ∙10)

9.1.2 Constraints

To reduce the amount of time required for the algorithm to run, the set of possible filters to 

evaluate was reduced to those most likely to produce good results. First, the slope of the impulse 

response was constrained to be no more than 0.0002 rad/sample, because based on experience 

from initial tests, FIR filters with large impulse-response slopes returned high costs. For 

example, the Preview Controller returned a higher cost than the baseline individual-pitch 

controller when evaluated with the cost function described above. If no limit is placed on slope, 

the individual FIR filters that the algorithm creates all tend to have very high slope. Second, the 

algorithm requires an initial range, so the values of the impulse response were limited to between 

-0.01 and 0.01 radians, since the well-performing shaped controller impulse responses fell within 

this range. Both of these constraints are imposed before the DC gain is scaled to 1. 

9.1.3 Seeds

The genetic algorithm was seeded with the following FIR filters: Shaped 10/3 second and 

Shaped 5 second. These shaped compensators had the best results in previous work [2]. The 

NCSE and Preview Controllers were not used as seeds. The NCSE controller has an infinite 

impulse response. While it could be approximated as an FIR filter, its impulse response is 

significant out to 100 seconds, and begins to cause computer memory problems if stored in FIR 

form at this length. The Preview Controller impulse response contains steep changes in pitch that 

do not meet the slope constraints indicated above. 
46 

9.1.4 Creation Function

The genetic algorithm begins by creating a random initial population of individual FIR filters to 

evaluate. Starting with this initial population, the best (lowest cost) individuals in each 

generation are used as “parents” for the next generation, where they are randomly mutated and 

combined with each other. We chose to begin with an initial population size of 1000. Because we 

already had 2 seeds, this left 998 individuals that needed to be created before running the genetic 

algorithm. The Matlab Optimization Toolbox comes with a creation function, but using this 

creation function with our chosen constraints resulted in 998 individuals that looked almost 

exactly the same. Therefore we created a custom creation function to create individuals more 

randomly. These more adequately spanned the space of possible impulse responses. This custom 

creation function was based on the Matlab function . This is a linear programming 

function that outputs the vector x that minimizes f T

x, subject to constraints, where the vector f is 

an input. To create each of the 998 individuals, we ran using an input f that was 

randomly generated, and used the output x as a new individual. The result was that each 

individual x was random and also met our chosen constraints. 

9.2 Results

On wind field AR2_s13, the lowest cost for a FIR filter returned by the genetic algorithm was 

0.924. This is the result of about four weeks of simulation time. This cost represents an overall 

load reduction of about 8% compared to IP baseline. Figure 31 and Figure 32 show the impulse 

response and Bode magnitude plot of this best performing FIR filter. In the impulse response, the 

general shape of the Shaped 5 second feed-forward controller can still be seen, along with 

additional spikes. The Bode magnitude plot shows that the feed-forward gain decreases with 

frequency, and has already decreased significantly at the fairly low frequency of 0.1 Hz. 

Figure 31. Impulse response of the Optimized FIR filter. Its cost on wind field AR2_s13 is 0.924. 
47 

Figure 32. Bode magnitude plot of the Optimized FIR filter. Its cost on wind field AR2_s13 is 0.924. 

Optimized FIR filter results should be at least as good as the best feed-forward controllers so far, 

since these were used to seed the optimization algorithm. However, error in wind speed 

measurement is also being introduced through a CW LIDAR model, so overall load reduction is 

not as high as before. For comparison, the Shaped 5 second controller seed returned a cost of 

0.99. 

The best controller on wind field AR2_s13 (shown in Figure 31 and Figure 32) was also tested 

on all of wind fields AR1 through AR3 and compared to the IP baseline controller alone. On 15 

of these 93 wind fields, running the IP baseline controller alone results in an average power of 

below 4999.9 kW. Therefore, it no longer makes sense in the cost function to penalize the feedforward controller for power below 4999.9 kW. With this part of the cost removed, the average 

cost for the optimized feed-forward controller over AR1 through AR3 is 0.945. None of the runs 

resulted in any rotor speed above 13 rpm, so the cost is based solely on structural loading and 

pitch actuation and represents an average of 5.5% load reduction. The average power over all 

wind fields was 5000 kW, both with and without the optimized FIR feed-forward controller. 

Figure 33 shows how the 5.5% average cost reduction is broken down among the eight different 

measures.
48 

Figure 33. Damage equivalent loads, RMS nacelle accelerations, and RMS pitch rate of IP baseline 

control without and with optimized FIR feed-forward (using 5 second preview from three rotating 

LIDAR wind measurements). Values are shown relative to IP baseline alone, and are averaged 

over 93 wind fields (AR1, AR2, AR3). The optimized FIR's overall cost of 0.945 is the average of its 

eight bars.

This optimized FIR filter was also tested on wind fields AR4 and AR5 from Table 1. These wind 

fields include coherent structures. Results are shown in Figure 34. When results are averaged 

over all of AR1 through AR5, loads are reduced by 5%. 

Figure 34. Damage equivalent loads, RMS nacelle accelerations, and RMS pitch rate of IP baseline 

control without and with optimized FIR feed-forward (using 5 second preview from three rotating 

LIDAR wind measurements). Values are shown relative to IP Baseline alone, and are averaged 

over 62 wind fields (AR4, AR5). The optimized FIR's overall cost of 0.961 is the average of its eight 

bars. 
49 

10 Feed-Forward Control Conclusions

Three feed-forward blade pitch control designs have been investigated and evaluated: non-causal 

series expansion, Preview Control, and optimized FIR filter. The non-causal series expansion 

controllers reduce blade loads, but increase tower sway, and are overall not an improvement over 

baseline individual pitch control. NCSE and other model-inverse methods are designed to reduce 

the effect of wind disturbances on only one choice of output. However, it is advantageous to 

control several outputs, including rotor speed, blade bending, and tower sway. In addition, 

model-inverse design methods result in feed-forward controllers with high gain at high 

frequencies, and also do not account for actuator limits, and so the pitch command reaches the 8 

degree/second rate limit when using NCSE control and other model-inverse methods tried. For 

these reasons, Preview Control was investigated, which minimizes a cost that can include 

multiple outputs and actuator effort. 

Preview Control was able to reduce both blade and tower loads on the linear model as well as in 

simple uniform wind field simulations. However, when simulated in turbulent wind conditions, 

like the NCSE control, Preview Control increased tower sway and was not an overall 

improvement over baseline control. 

There are nonlinear approaches to model-inverse control [35], and possibly also to Preview 

Control, but since linear controllers have implementation and analysis conveniences, we 

investigated the optimized FIR filter as another linear control design. The optimized FIR filter 

was designed directly on the nonlinear turbine model in turbulent wind conditions with LIDAR 

errors modeled. It reduced loads on different parts of the turbine by varying amounts, with an 

average 5% load reduction overall, while maintaining rated power and rotor speed and without 

significantly increasing pitch rate.

11 Overall Conclusions and Future Work

This study focused on the use of a hub-mounted LIDAR for feed-forward wind turbine controls. 

The two major sources of LIDAR measurement error studied were spatial averaging and 

measurement angle error. On the 5 MW turbine model with a hub-mounted spinning CW 

LIDAR, when measuring wind speeds at 75% span, the minimum RMS error occurred between 

about 100 and 150 meters ahead of the turbine, depending on the local friction velocity of the 

wind. Once wind evolution error is also included, it is expected that this optimal measurement 

distance will decrease. Therefore, using a preview distance of 65 meters, various feed-forward

blade pitch controllers were designed to reduce turbine loads. The best simulation results were 

from the optimized FIR controller. When this individual pitch feed-forward controller was added 

to a baseline individual pitch feedback controller, the average load reduction over a set of eight 

different turbine components was 5%, compared to individual pitch feedback alone. Future 

investigations will study random LIDAR noise errors, measurements in coherent structures, wind 

evolution, and methods for smoothly turning on and off the feed-forward controller so that it is 

operational only when LIDAR measurements are “accurate enough”. 
50 

12 References 

1. Laks, J., Pao, L., Wright, A., Kelley, N., and Jonkman, B., “Blade pitch control with 

preview wind measurements,” in Proc. 48th AIAA Aerospace Sciences Meeting, 

Orlando, FL, AIAA-2010-251, Jan. 2010.

2. Dunne, F., Pao, L., Wright, A., Jonkman, B., and Kelley, N., “Combining standard 

feedback controllers with feedforward blade pitch control for load mitigation in wind 

turbines,” in Proc. 48th AIAA Aerospace Sciences Meeting, Orlando, FL, AIAA-2010-

250, Jan. 2010. 

3. Schlipf, D., and Kühn, M., “Prospects of a collective pitch control by means of predictive 

disturbance compensation assisted by wind speed measurements,” in Proc. German Wind 

Energy Conference (DEWEK), Bremen, Germany, Nov. 2008. 

4. Schlipf, D., Trabucchi, D., Bischoff, O., Hofsäß, M., Mann, J., Mikkelsen, T., 

Rettenmeier, A., Trujillo, J., and Kühn, M., “Testing of frozen turbulence hypothesis for 

wind turbine applications with a scanning LIDAR system,” in Proc. International

Symposium for the Advancement of Boundary Layer Remote Sensing, Paris, France, Jun. 

2010. 

5. Taylor, G., “The spectrum of turbulence,” in Proceedings of the Royal Society of 

London, 1938. 

6. Harris, M., Hand, M., and Wright, A., “LIDAR for turbine control,” National Renewable 

Energy Laboratory, NREL/TP-500-39154, Golden, CO, Tech. Rep., Jan. 2006. 

7. Laks, J., Pao, L., and Wright, A., “Combined feedforward/feedback control of wind 

turbines to reduce blade flap bending moments,” in Proc. 47th AIAA Aerospace Sciences 

Meeting, Orlando, FL, AIAA-2009-687, Jan. 2009. 

8. Mikkelsen, T., Hansen, K., Angelou, N., Sjöholm, M., Harris, M., Hadley, P., Scullion, 

R., Ellis, G., and Vives, G., “LIDAR wind speed measurements from a rotating spinner,” 

in Proc. European Wind Energy Conference, Warsaw, Poland, Apr. 2010. 

9. Jonkman, J., and Buhl, M., “FAST User's Guide,” National Renewable Energy 

Laboratory, NREL/EL-500-38230, Golden, CO, Tech. Rep., 2005. 

10. Jonkman, J., Butterfield, S., Musial, W., and Scott, G., “Definition of a 5-MW reference 

wind turbine for offshore system development,” National Renewable Energy Laboratory, 

NREL/TP-500-38060, Golden, CO, Tech. Rep., 2009. 

11. Kelley, N., and Jonkman, B., “Overview of the TurbSim stochastic inflow turbulence 

simulator,” National Renewable Energy Laboratory, NREL/TP-500-39796, Golden, CO, 

Tech. Rep., 2007. 

12. Jonkman, B., “TurbSim user's guide: Version 1.50,” National Renewable Energy 

Laboratory, NREL/TP-500-46198, Golden, CO, Tech. Rep., 2009. 
51 

13. Frehlich, R., and Kavaya, M., “Coherent laser performance for general atmospheric 

refractive turbulence,” Applied Optics, vol. 30, no. 36, pp. 5325–5352, Dec. 1991. 

14. Frehlich, R., Meillier, Y., Jensen, M., Balsley, B., and Sharman, R., “Measurements of 

Boundary Layer Profiles in an Urban Environment,” Applied Meteorology and 

Climatology, vol. 45, no. 6, pp. 821-837, June 2006. 

15. Kelley, N., Osgood, R., Bialasiewicz, J., and Jakubowski, A., “Using wavelet analysis to 

assess turbulence/rotor interactions,” Wind Energy, vol. 3, pp. 121–134, 2000. 

16. Kelley, N., “The identification of inflow fluid dynamics parameters that can be used to 

scale fatigue loading spectra of wind turbine spectral components,” National Renewable 

Energy Laboratory, NREL/TP-442-6008, Golden, CO, Tech. Rep., 1993. 

17. Dunne, F., Pao, L, Wright, A., Jonkman, B., Kelley, N., and Simley, E., “Adding 

feedforward blade pitch control for load mitigation in wind turbines: Non-causal series 

expansion, preview control, and optimized FIR filter methods,” in Proc. 49th AIAA 

Aerospace Sciences Meeting, Orlando, FL, Jan. 2011. 

18. Laks, J, Pao, L., Simley, E., Wright, A., Kelley, N. , and Jonkman, B.,“Model predictive 

control using preview measurements from LIDAR,” in Proc. 49th AIAA Aerospace 

Sciences Meeting, Orlando, FL, Jan. 2011. 

19. Bossanyi, E. A., “Individual Blade Pitch Control for Load Reduction,” Wind Energy, vol. 

6, pp. 119–128, 2003. 

20. Stol, K. and Fingersh, L., “Wind Turbine Field Testing of State-Space Control Designs,” 

NREL/SR-500-35061, NREL Report, National Renewable Energy Laboratory, Golden, 

CO, 2004. 

21. Wright, A., Fleming, P., and van Wingerden, J., “Refinements and Tests of an Advanced 

Controller to Mitigate Fatigue Loads in the Controls Advanced Research Turbine,” Proc. 

49th AIAA Aerospace Sciences Meeting, Orlando, FL, Jan. 2011. 

22. Stol, K., Zhao, W., and Wright, A., “Individual Blade Pitch Control for the Controls 

Advanced Research Turbine (CART),” ASME J. Solar Energy Engineering, vol. 128, no. 

4, pp. 498–505, Nov. 2006. 

23. Bir, G., “Multi-blade Coordinate Transformation and its Application to Wind Turbine 

Analysis,” Proceedings AIAA/ASME Wind Energy Symposium, Reno, NV, Jan. 2008. 

24. Butterworth, J., Pao, L., and Abramovitch, D., “The Effect of Nonminimum-Phase Zero 

Locations on the Performance of Feedforward Model-Inverse Control Techniques in 

Discrete-Time Systems,” Proc. American Control Conference, Seattle, WA, 2008, pp. 

2696–2702. 

25. Tomizuka, M., “Zero Phase Error Tracking Algorithm for Digital Control,” ASME J. 

Dyn. Sys., Meas. & Ctrl., vol. 109, pp. 65–68, Mar. 1987. 
52 

26. Wen, J. T. and Potsaid, B., “An Experimental Study of a High Performance Motion 

Control System,” Proc. American Control Conference, June 2004, p. 5158–5163. 

27. Potsaid, B., Wen, J. T., Unrath, M., Watt, D., and Alpay, M., “High Performance Motion 

Tracking Control for Electronic Manufacturing,” ASME J. Dyn. Sys., Meas., & Ctrl, vol. 

129, pp. 767–776, Nov. 2007. 

28. Rigney, B. P., Pao, L. Y., and Lawrence, D. A., “Nonminimum Phase Dynamic Inversion 

for Settle Time Applications,” IEEE Trans. Control Systems Technology, vol. 17, no. 5, 

pp. 989–1005, Sept. 2009. 

29. Widrow, B. and Walach, E., Adaptive Inverse Control - a Signal Processing Approach, 

Wiley, Hoboken, NJ, 2008. 

30. Matlab, Simulation and Model-Design Software Package, The MathWorks, Inc., Natick, 

MA.

31. Downing, S. D. and Socie, D. F., “Simple Rainflow Counting Algorithms,” International 

J. Fatigue, vol. 4, no. 1, pp. 31–40, Jan. 1982. 

32. Tomizuka, M. and Fung, D., “Design of Digital Feedforward/Preview Controllers for 

Processes with Predetermined Feedback Controllers,” ASME J. Dyn. Sys., Meas. & Ctrl., 

vol. 102, pp. 218–225, Dec. 1980. 

33. Simley, E., Pao, L. Y., Frehlich, R., Jonkman, B., and Kelley, N., “Analysis of Wind 

Speed Measurements using Coherent LIDAR for Wind Preview Control,” Proc. AIAA 

Aerospace Sciences Meeting, Orlando, FL, Jan. 2011. 

34. Goldberg, D. E., Genetic Algorithms in Search Optimization and Machine Learning, 

Addison Wesley, 1989. 

35. Devasia, S., Paden, B., and Chen, D., “Nonlinear Inversion-Based Regulation,” IEEE 

Transactions on Automatic Control, vol. 41, no. 7, pp. 930–942, Jul. 1996. 
53 

Appendix: Derivation of Measurement Error Sensitivity to 

Measurement Angle

Without loss of generality, consider a LIDAR measurement of wind velocity where the LIDAR

is located at the origin [see Figure 2 (a)] and the measurement point is contained in the xz plane 

with y = 0, upwind from the LIDAR. Consider the wind to have a positive u component, aligned 

with the x direction, which will be referred to as U. The wind velocity vector has a transverse 

component in the yz plane with magnitude and uniformly distributed random 

angle, ψ, in the yz plane. If the LIDAR measures this wind velocity with a measurement angle θ, 

the detected radial velocity is given by

(0.1) 

The estimate of the u component, using Eq. (2.9), is given by 

(0.2) 

and therefore the measurement error, , is 

(0.3) 

When many wind speed measurements are made, the RMS measurement error is calculated as

(0.4) 

Since θ is constant and ψ and α are independent random variables, Eq. (0.4) becomes

(0.5) 

Finally, since the RMS value of is , the RMS measurement error is given by

(0.6) 

where αRMS is the RMS magnitude of the transverse wind component.