A national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

National Renewable Energy Laboratory 

Innovation for Our Energy Future 

Influence of Control on the Pitch 

Damping of a Floating Wind 

Turbine 

J.M. Jonkman

Presented at the 2008 ASME Wind Energy Symposium 

Reno, Nevada 

January 7–10, 2008 

Conference Paper 

NREL/CP-500-42589 

March 2008 

NREL is operated by Midwest Research Institute ● Battelle Contract No. DE-AC36-99-GO10337 
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Influence of Control on the Pitch Damping 

of a Floating Wind Turbine*

Jason M. Jonkman†

National Renewable Energy Laboratory (NREL), Golden, Colorado, 80401-3393 

This paper presents the influence of conventional wind turbine blade-pitch control 

actions on the pitch damping of a wind turbine supported by an offshore floating barge with 

catenary moorings. There was a concern that the drop in steady-state wind turbine rotor 

thrust with wind speed above rated would lead to negative damping of the barge-pitch mode 

and contribute to the large system-pitch motions. It is demonstrated that neither the 

addition of a control loop through feedback of tower-top acceleration nor the modification to 

pitch-to-stall rotor-speed regulation satisfactorily improved the barge-pitch response. The 

latter modification helped conclude, however, that the actual barge-pitch damping was 

considerably greater than that implied by the steady-state rotor thrust response, but that it 

was still beneficial to increase the damping as much as possible. Detuning the gains in the 

baseline blade-pitch-to-feather controller helped, but still did not entirely resolve the bargepitch-motion problem. 

Nomenclature 

ARadiation = added inertia (added mass) associated with hydrodynamic radiation in pitch 

Aξ = amplitude of the platform-pitch oscillation 

BRadiation = damping associated with hydrodynamic radiation in pitch 

BViscous = damping associated with hydrodynamic viscous drag in pitch 

CHydrostatic = hydrostatic restoring in pitch 

CLines = linearized hydrostatic restoring in pitch from all mooring lines 

Cx = effective damping in the equation of motion for the platform pitch in terms of the translation of the 

hub 

IMass = pitch inertia associated with wind turbine and barge mass 

KPx = proportional gain in the tower-feedback control loop 

Kx = effective stiffness in the equation of motion for the platform pitch in terms of the translation of the 

hub 

LHH = hub height 

Mx = effective mass in the equation of motion for the platform pitch in terms of the translation of the hub 

T = aerodynamic rotor thrust 

T0 = aerodynamic rotor thrust at a linearization point 

V = rotor-disk-averaged wind speed 

x = translational displacement of the hub 

&x = translational velocity of the hub 

&&x = translational acceleration of the hub 

Δ x ζ = effective increase in the platform-pitch damping ratio 

Δθ = small perturbation of the blade-pitch angles about their operating point 

 

*

 Employees of the Midwest Research Institute under Contract No. DE-AC36-99GO10337 with the U.S. Dept. of 

Energy have authored this work. The United States Government retains, and the publisher, by accepting the article 

for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, 

worldwide license to publish or reproduce the published form of this work, or allow others to do so, for the United 

States Government purposes. 

†

 Senior Engineer I, National Wind Technology Center (NWTC), 1617 Cole Boulevard, AIAA Professional 

Member. 

1
Δθ& = blade-pitch rate 

ζx = damping ratio of the response associated with the equation of motion for the platform pitch in terms of 

the translation of the hub 

ζφ = damping ratio of the response associated with the equation of motion for the PI-controlled rotor-speed 

error 

θ = full-span rotor-collective blade-pitch angle 

ξ = platform-pitch angle (rotational displacement) 

ξ

& = platform-pitch rotational velocity 

ξ

&& = platform-pitch rotational acceleration 

ωxn = natural frequency of the response associated with the equation of motion of the platform pitch in 

terms of the translation of the hub 

ωφn = natural frequency of the response associated with the equation of motion for the PI-controlled rotorspeed error 

I. Introduction 

N previous work,1 Buhl and I performed a preliminary, but integrated, loads analysis for the National Renewable 

Energy Laboratory (NREL) 5-MW baseline wind turbine2

 mounted both on land and offshore on the floating ITI 

Energy barge,3

 which has slack, catenary moorings (see for an illustration of the offshore concept). By 

comparing the responses of the land- and sea-based systems, we were able to quantify the impact brought about by 

the dynamic couplings between the turbine and floating barge in the presence of combined wind and wave loading. 

I 

Figure 1

We used a simulation tool that can model the fully coupled time-domain aero-hydro-servo-elastic response of 

offshore floating wind turbines to run the loads analysis. I developed this capability by leveraging the 

computational methodologies and analysis tools of the onshore wind turbine and offshore oil and gas (O&G) 

industries. The onshore wind-industry-accepted aero-servo-elastic turbine simulation capability of FAST (Fatigue, 

Aerodynamics, Structures, and Turbulence)4

 with AeroDyn5,6 has been interfaced with the external hydrodynamic 

wave-body interaction program WAMIT® (Wave Analysis at the Massachusetts Institute of Technology),7

 which is 

commonly employed in the offshore O&G industry. I established the interfaces among these simulation capabilities 

by developing modules for treating time-domain hydrodynamics (HydroDyn) and quasi-static mooring system 

responses. summarizes the modules and their interfaces. References 8 and 9 explain the theoretical 

framework and limitations of the recently 

developed hydrodynamic and mooring system 

modules in detail. In addition, Ref. 

Figure 2

9 presents a 

model-to-model verification of these modules and 

of the fully coupled simulation tool. 

To summarize the loads-analysis results 

presented in Ref. 1, the pitching motion of the 

barge brings about load excursions in the 

supported wind turbine that exceed those 

experienced by the turbine when it is installed on 

land. The load excursions are worse in the tower 

than in the blades because of the increased effect 

of inertia from the barge-pitch motion. To arrive 

at a technically feasible concept, the design will 

have to be modified, except possibly at the most 

sheltered of sites. Two forms of design 

modifications are possible. First, the turbine, 

especially the tower, could be strengthened to 

enable it to withstand the increased loading. 

However, this approach may not be cost-effective 

even though the wind turbine in an offshore 

floating system represents a smaller fraction of the 

total installed cost than in an onshore system. 

Second, design alterations may be able to improve Figure 1. Illustration of the NREL 5-MW wind turbine on 

the ITI Energy barge. 

2
the response of the floating system to diminish the increases in loading. 

Figure 2. Interfacing modules to achieve fully coupled aero-hydro-servo-elastic simulation. 

One possible approach to improving the response of the floating system is to incorporate design features that will 

increase damping to stabilize the barge-pitch motion. Damping can be tailored through passive design features and 

active control. The NREL 5-MW baseline wind turbine I developed and used in the land- and sea-based loads 

analyses relied on a conventional variable-speed, variable blade-pitch-to-feather control system. The generator 

torque is computed as a tabulated function of the filtered generator speed, incorporating five control regions: 1 

(start-up), 11⁄2 (transition), 2 (optimal power capture), 21⁄2 (transition), and 3 (constant power). In Region 3, the fullspan rotor-collective blade-pitch-angle commands are computed using gain-scheduled proportional-integral (PI) 

control of the rotor speed.2

 A consequence of conventional pitch-to-feather control of wind turbines, though, is that 

steady-state rotor thrust is reduced with increasing wind speed above rated as shown in Figure 3. As pointed out by 

Nielsen, Hanson, and Skaare,10 “this effect may introduce negative damping in the system that may lead to large 

resonant motions of [a] floating wind turbine.” As the loads-analysis results of Ref. 1 demonstrated, it is important 

that the damping of the barge-pitch mode be positive and kept as large as possible. 

Section III addresses the influence of conventional wind turbine control methodologies to the pitch damping of 

the floating wind turbine system analyzed in Ref. 1. In this work, my aim was to modify the baseline control system 

of the NREL 5-MW turbine to improve the pitch damping of the ITI Energy barge. Moreover, I wanted to make 

these improvements by using conventional wind turbine control techniques to establish a modified baseline with 

0

200

400

600

800

1,000

3 5 7 9 11 13 15 17 19 21 23 25

Wind Speed, m/s

Rotor Thrust, kN

Region 11⁄2 2 21⁄2 3

Figure 3. Steady-state rotor thrust as a function of wind speed for the NREL 5-MW baseline wind turbine. 

3
which I could compare more advanced or unconventional control scenarios. Even though I performed this work 

specifically for the NREL baseline wind turbine and the ITI Energy barge, the analysis process is valid for other 

concepts in which floating platforms support wind turbines controlled by blade pitch. Section IV qualitatively 

discusses other potential methods for improving the damping performance with wind turbine control. 

First, however, it is important to describe the barge-pitch damping problem in more detail. Section II presents 

more details and a quantification of the problem. 

II. Overview of the Platform-Pitch-Damping Problem 

The barge-pitch damping problem can be analyzed by considering the rigid-body platform-pitch mode as a single 

degree of freedom (DOF). The equation of motion for this simple model is 

( )( ) IMass Radiation + + + + += A BB C C ξ ξ Radiation Viscous ( Hydrostatic Lines HH ) && & ξ L T , (1) 

where ξ is the platform-pitch angle (i.e., rotational displacement), ξ

& is the platform-pitch rotational velocity, ξ&& is 

the platform-pitch rotational acceleration, IMass is the pitch inertia associated with wind turbine and barge mass, 

ARadiation is the added inertia (added mass) associated with hydrodynamic radiation in pitch, BRadiation is the damping 

associated with hydrodynamic radiation in pitch, BViscous is the linearized damping associated with hydrodynamic 

viscous drag in pitch, CHydrostatic is the hydrostatic restoring in pitch, CLines is the linearized hydrostatic restoring in 

pitch from all mooring lines, T is the aerodynamic rotor thrust, and LHH is the hub height (i.e., rotor-thrust moment 

arm). 

Though not directly evident from Eq. (1), the aerodynamic rotor thrust also contributes to the platform-pitch 

damping. To consider its effect, it is convenient to state the equation of motion in terms of the translational motion 

of the hub instead of the pitching motion of the platform. For small pitch angles, the translational displacement of 

the hub, x, is linearly related to the platform-pitch angle by 

HH x L = ξ . (2) 

The aerodynamic rotor thrust depends on wind speed, rotor speed, and blade-pitch angle. To be clear, its 

dependence on the wind speed is actually a dependence on the relative wind speed at the hub because the hub can 

move in this simple model of the platform-pitch mode. If the hub translation varies slowly, the wake of the rotor 

will respond to changes in hub speed just as it does to changes in wind speed. Considering variations in 

aerodynamic rotor thrust with hub speed only, a first-order Taylor series expansion gives 

0

T TT x

V

∂ = − ∂ & , (3) 

where T0 is the aerodynamic rotor thrust at a linearization point and V is the rotor-disk-averaged wind speed. 

The negative sign appears in Eq. (3) because, from Figure 1, positive platform-pitch angles correspond to 

downwind translational displacements of the hub, which reduces the relative wind speed. By combining Eqs. (1)

through (3) and simplifying, the equation of motion of the platform-pitch mode stated in terms of the translational 

motion of the hub becomes 

xx x

Mass Radiation Radiation Viscous Hydrostatic Lines

22 2 0

HH HH HH

MC K

IA B B T C C x x LL L V

⎛ ⎞⎛ ⎞⎛ ⎞ + + ∂ +

⎜ ⎟⎜ ⎟⎜ ⎟ + ++

∂ ⎝ ⎠⎝ ⎠⎝ ⎠

&& &

1442443 14444244443 144424443

x = T . (4) 

One can see that the isolated rigid-body platform-pitch DOF will respond as a second-order system with the 

natural frequency, ωxn, and damping ratio, ζx, equal to 

x

xn

x

K

M

ω = (5) 

4
and 

x

x

x x 2 KM ζ = C . (6) 

Most of the terms in the effective mass, damping, and stiffness coefficients in Eq. (4) are easy to quantify. In 

particular, the terms related to the effective mass and stiffness, including the added inertia (added mass) in pitch and 

the linearized pitch restoring of the mooring system, are easily computed from a linearization analysis in FAST with 

HydroDyn. This linearization analysis resulted in a platform-pitch natural frequency for the ITI Energy barge with 

the NREL 5-MW baseline wind turbine of ωxn = 0.5420 rad/s = 0.0863 Hz.‡

Two terms in Eq. (4), the damping associated with hydrodynamic radiation in pitch, BRadiation, and the thrust 

sensitivity to wind speed, ∂ ∂ T V , are more difficult to quantify. The former is problematic because the 

hydrodynamic wave-radiation loads in the true linear hydrodynamic-loading expressions are actually described by a 

convolution integral, which is used to capture the wave-radiation memory effect.8

 This convolution term is not 

convenient in this analysis or in the design of modern control systems. For use in controls engineering, for instance, 

Ref. 11 describes a method of converting the convolution term to state-space form by adding “radiation memory 

states.” To avoid this complication in this analysis, however, I neglected the memory effect and approximated 

BRadiation as the amount of linear radiation damping at the platform-pitch natural frequency, ωxn. This choice is 

consistent with the linear time-domain representation of the frequency-domain problem that is described in Ref. 8. 

The thrust sensitivity to wind speed, ∂ ∂ T V , can be computed in multiple ways. One way would be to estimate 

this sensitivity (at each wind speed) as the slope of the steady-state thrust versus wind-speed response presented in 

Figure 3. (Because the aerodynamic rotor thrust depends on wind speed, among other factors, the thrust sensitivity 

to wind speed depends on wind speed as well.) This way of computing the thrust sensitivity to wind speed 

characterizes the sensitivity of an ideal closed-loop blade-pitch speed-regulation system. I say “ideal” because a real 

blade-pitch control system responds to rotor-speed error (not variations in wind speed) and because the steady-state 

rotor speed is constant with wind speed throughout Region 3 where the rotor-speed control system functions.2

A second way of estimating the thrust sensitivity to wind speed would be to perform a linearization analysis in 

FAST with AeroDyn. FAST with AeroDyn could be used to compute ∂T V∂ at each of a number of given, steady, 

and uniform wind speeds and at the associated rotor speeds and blade-pitch angles from the steady-state response. 

This would be accomplished by perturbing the wind speed at each operating point and measuring the variation in the 

resulting aerodynamic thrust. (Within FAST, the central-difference-perturbation numerical technique is used to 

compute the partial derivative.) This way of computing the thrust sensitivity to wind speed characterizes the 

sensitivity of an open-loop system because the blade-pitch angle is not varied with the perturbations in wind speed. 

I calculated ∂ ∂ T V using both methods. Using these thrust sensitivities to wind speed and other properties of 

the ITI Energy barge with the NREL 5-MW baseline wind turbine, I estimated the barge-pitch damping ratios 

according to Eq. (6). presents these ratios. I found the slope of the steady-state thrust versus wind-speed 

response in the ideal closed-loop method from the central-difference approximation of the derivative using the two 

wind speeds on either side of each given wind speed. This is why I did not estimate the barge-pitch damping ratios 

at the cut-in and cut-out wind speeds. The barge-pitch damping ratio is largest in magnitude and changes sign at the 

rated wind speed of 11.4 m/s for the ideal closed-loop method, just like the thrust sensitivity to wind speed. Just 

above rated, the damping ratio is less than −10%. Near the cut-out wind speed of 25 m/s, the positive-valued 

hydrodynamic-radiation and viscous damping exceed the magnitude of the negative-valued aerodynamic damping, 

Figure 4

 

‡

 This frequency falls in the range of typical sea states, which have peak spectral periods in the range of 5 to 20 s 

(see Ref. 1) corresponding to frequencies in the range of 0.05 to 0.2 Hz (i.e., 0.314 to 1.257 rad/s). The barge will 

tend to oscillate at the excitation frequency of the incident waves, but the motions will be most severe when the 

wave-excitation frequency is at or near the barge’s natural frequency. If the barge were to oscillate at its natural 

frequency with a pitch amplitude of Aξ, the amplitude of the hub translational velocity would be HH xn A Lξ ω and the 

amplitude of the hub translational acceleration would be 2

HH xn A Lξ ω . For Aξ = 5o, this translates into hub velocity and 

acceleration amplitudes of about 4.26 m/s and 2.31 m/s2

 = 0.24 g’s, respectively; for Aξ = 10o, this translates into hub 

velocity and acceleration amplitudes of about 8.51 m/s and 4.61 m/s2

 = 0.47 g’s, respectively. At these amplitudes, 

the wind turbine control system will continuously switch between below- and above-rated control regions, except at 

the very lowest and highest mean hub-height wind speeds. 

5
so the barge-pitch damping ratio becomes slightly positive again. In the open-loop method, the thrust sensitivity and 

barge-pitch damping ratio increase with wind speed below rated and remain flat and positive above rated. 

Consequently, the barge-pitch damping ratio remains positive across all wind speeds in the open-loop method. With 

real blade-pitch-control speed regulation above rated, the actual damping ratio is difficult to quantify with this 

simple model, but will fall somewhere between the bounds imposed by the open- and ideal closed-loop results. 

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

3 5 7 9 11 13 15 17 19 21 23 25

Wind Speed, m/s

Barge-Pitch Damping Ratio, -

Open-Loop

Ideal Closed-Loop

Figure 4. Pitch-to-feather barge-pitch damping ratios. 

III. Influence of Conventional Wind Turbine Control Methodologies 

To improve the barge-pitch damping, I modified the baseline control system with a number of conventional wind 

turbine control methodologies. These included (A) adding a second blade-pitch control loop through feedback of 

tower-top acceleration, (B) changing from variable blade-pitch-to-feather to variable blade-pitch-to-stall speedcontrol regulation, and (C) detuning the gains in the variable blade-pitch-to-feather rotor-speed controller. I 

developed and tested (through simulation) each approach independently. The rationale behind each approach and 

the main findings are presented in Sections III.A, III.B, and III.C, respectively. 

A. Feedback of Tower-Top Acceleration 

The conventional approach to improving the tower fore-aft damping in land-based wind turbines is to append the 

conventional blade-pitch controller for rotor-speed regulation with an additional blade-pitch control loop, which 

uses a tower-top acceleration measurement.12 Naturally, the same technique could be applied to modify the 

platform-pitch damping of an offshore floating wind turbine. The intent of the new control loop would be to 

augment the aerodynamic rotor thrust with adjustments to the blade-pitch angle based on the tower-top acceleration 

measurement. To see the effect of blade-pitch angle on the platform-pitch damping, consider variations in the 

aerodynamic thrust with full-span rotor-collective blade-pitch angles, θ, in addition to hub speed, as was accounted 

for in Eq. (3): 

0

T T TT x

V

θ

θ

∂ ∂ = − +Δ

∂ ∂ & . (7) 

6
In Eq. (7), is a small perturbation of the blade-pitch angles about their operating point. If the blade-pitch 

rate in the tower-feedback (TFB) control loop is proportional to a tower-top acceleration measurement through a 

gain KPx, then: 

Δθ

KPx Δθ = x & && (8a) 

or 

t

Px Px

0

Δθ = = K xdt K x ∫

&& & . (8b) 

By combining Eqs. (8b) and (7) with the equations presented in Section II and simplifying, the addition of a TFB 

control loop modifies the effective damping coefficient from Eq. (4) and becomes 

Radiation Viscous

x 2

HH

New Term

B B T C

L V Px

T K

θ

+ ∂ ∂

= + − ∂ 1424∂

3

. (9) 

The effective mass and stiffness coefficients from Eq. (4) are left unchanged by the addition of the TFB control 

loop. 

In an active blade-pitch-to-feather wind turbine, the thrust sensitivity to rotor-collective blade pitch, ∂T ∂θ , is 

negative-valued from cut-in to cut-out so damping is increased with a positive control gain. Once the thrust 

sensitivity to rotor-collective blade pitch is known and a control gain is chosen, the effective increase in platformpitch damping ratio, Δ x ζ , according to the given model is 

Px

x

x x

K T

2 KM Δζ θ

⎛ ∂ = − ⎜ ⎞

⎟ ⎝ ⎠ ∂ . (10) 

Alternatively, a proper control gain can be chosen specifically from any desired increase in platform-pitch 

damping according to the given model. Just like the thrust sensitivity to wind speed, though, the thrust sensitivity to 

rotor-collective blade-pitch angle depends on the wind speed, rotor speed, and blade-pitch angle. Consequently, one 

cannot achieve a constant increase in damping ratio across control regions without gain-scheduling. The gainscheduling law for the TFB control system will not, however, be as simple as the law used in the blade-pitch rotorspeed-regulation controller, because the thrust sensitivity to blade pitch is not linearly related to the blade-pitch 

angle. I calculated the thrust sensitivity to blade pitch from a linearization analysis in FAST with AeroDyn. 

In the middle of Region 3 (18 m/s), a modest 0.05 increase in effective damping ratio requires a control gain of 

KPx = 0.007556 rad/(m/s) and a large 0.5 increase in effective damping ratio requires a control gain of KPx = 0.07556 

rad/(m/s). Naturally, the larger the control gain, the larger the blade-pitch-rate requirement. Conversely, to limit the 

blade-pitch rate, one has to minimize the effective increase in damping ratio. From the footnote on page 2, bargepitch amplitudes in the range of Aξ = 5 to 10o can result in hub-acceleration amplitudes ranging from 2.31 to 4.61 

m/s2

. In the middle of Region 3, according to the given model, damping these motions using the TFB control loop 

developed previously will require blade-pitch-rate amplitudes in the range of Δθ

& = 1.0 to 2.0o/s for the modest 0.05 

increase in effective damping ratio and = 10.0 to 20.0o/s for the large 0.5 increase in effective damping ratio. 

Consequently, only moderately large increases in effective damping ratio are achievable with the given blade-pitchrate limit of 8o/s (from Ref. 

Δθ&

2). 

I incorporated the TFB control loop into my FAST with AeroDyn and HydroDyn simulations through a simple 

modification of the baseline control system. As implemented, I found the TFB blade-pitch angle commands by 

measuring the tower-top fore-aft acceleration, integrating to find the tower-top fore-aft velocity, and then 

multiplying by the control gain. This blade-pitch-angle command was then added to the blade-pitch-angle command 

from the rotor-speed controller, which had already been saturated for the angle and rate limits. Said another way, I 

did not saturate the TFB control system commands. 

7
For the NREL 5-MW wind turbine mounted atop the ITI Energy barge, I tested the system response at a variety 

of wind and wave conditions with both the modest and high TFB gains. shows a response with the high 

KPx = 0.07556 rad/(m/s) TFB gain for a simulation with stochastic winds with a mean hub-height wind speed of 18 

m/s and irregular waves with a significant wave height of 3.673 m and a peak spectral period of 13.376 s. (These 

waves have the expected value of the significant wave height and the median value of the peak spectral period 

conditioned on the mean hub-height wind speed at the chosen reference site; see Ref. 

Figure 5

Figure 5

Figure 5

gure 5

1.) The system response with 

the unmodified (baseline) control system is shown for comparison in . I ran the simulations with all 

appropriate and available DOFs enabled, as applied in the loads analysis and described in Ref. 1, but without 

considering the rotor-mass imbalance or the increased blade structural-damping ratio. In , the ordinates 

“GenPwr,” “GenSpeed,” “BlPitch1,” and “PtfmPitch” correspond to the instantaneous electrical output of the 

generator, generator (high-speed shaft) rotational speed, pitch angle of the reference blade (Blade 1), and platformpitch angle, respectively. 

It may seem surprising at first that the results do not show a large improvement in the damping of the barge-pitch 

motion (“PtfmPitch”). The exacerbated excursions in generator speed and electrical output are more prominent. 

These results can be understood by thinking about the problem in more detail than is provided in the simple model. 

The relative wind speed is highest when the system is pitching into the wind (i.e., from maximum to minimum 

barge-pitch angles). This causes the rotor-speed control system to pitch the blades to feather (more positive) to shed 

power and regulate speed while the TFB damping control system pitches the blades to stall (more negative) to 

increase thrust and introduce damping. The reverse is true when the turbine is pitching with the wind. In this case, 

the relative wind speed is lowest when the system pitches downwind, causing the rotor-speed control system to pitch 

the blades to stall while the TFB damping control system commands pitching to feather. Said another way, the two 

blade-pitch control systems are at odds and fight with each other in this situation. This can be seen by the bladepitch angle responses of Fi , where in many instances, the pitch-angle commands in the baseline control system 

move in the opposite direction to the pitch-angle commands in the combined baseline and TFB control system. 

Similar results (not shown) are obtained with the more modest KPx = 0.007556 rad/(m/s) TFB gain. Here, the 

generator speed and power excursions are not as badly exacerbated, but there is also less improvement in the 

damping of the barge-pitch motion. 

The simple model I describe in this section is routinely applied in the design of TFB damping control algorithms 

0

2,000

4,000

6,000

8,000

Time (sec)

GenPwr, kW

Baseline Baseline+TFB

0

500

1,000

1,500

2,000

Time (sec)

GenSpeed, rpm

-40

-20

0

20

40

Time (sec)

BlPitch1, o

-10

-5

0

5

10

0 50 100 150 200 250 300

Simulation Time, s

PtfmPitch, o

Figure 5. System response with and without a tower-feedback control loop. 

8
for land-based wind turbines. But, because the amplitude of the overall tower motion is less in land-based turbines, 

the problem with generator speed and power excursions is less of an issue. Instead, the control system designer for 

land-based wind turbines must make a basic trade-off between improved tower damping and increased generator 

speed and power excursions. For the floating system considered in this work, however, the severity of the tower-top 

motions induced by the barge’s movement with surface waves renders the conventional TFB damping control 

system ineffective. 

B. Active Pitch-to-Stall Speed-Control Regulation 

As described in Section I, the problem to be addressed is that the reduction in steady-state rotor thrust with 

increasing wind speed in Region 3, which occurs as a result of variable blade-pitch-to-feather speed-control 

regulation, may introduce negative damping in the platform-pitch mode. This implies that variable blade-pitch-tostall speed-control regulation may damp the barge-pitch motions more effectively because drag (and hence thrust) 

increase as power is shed (to regulate speed) in increasing relative winds in wind turbines controlled by an active 

pitch-to-stall system. Although variable blade-pitch-to-stall speed-control regulation has been shown to work 

effectively in simulation, it has not been widely pursued in the wind industry because of the “uncertainty that 

remains in the theoretical understanding of stalled rotor aerodynamics” as pointed out by Bossanyi.12 In spite of this 

uncertainty, I tested the effects of active pitch-to-stall speed-control regulation for the floating wind barge concept. 

Before pursuing the design of the pitch-to-stall controller, I decided to smooth the airfoil-data coefficients (as 

presented in Ref. 2) near stall to eliminate the existing fluctuations that could have led to numerical problems in the 

blade-element / momentum (BEM) aerodynamic-induction solution algorithm. I modified the airfoils by manually 

manipulating the lift coefficients. 

Once the airfoil data were corrected, I redeveloped the full-span rotor-collective blade-pitch controller according 

to the same procedure I used to arrive at the blade-pitch-to-feather speed-control gains (see Ref. 2). The blade-pitch 

angles that produce the rated mechanical power are negative- and double-valued over the wind-speed range of 

Region 3, first decreasing, then increasing, with increasing wind speed. By being double-valued, it is impossible to 

use the same gain-scheduling law I implemented in the active pitch-to-feather controller. But because, the variation 

in blade-pitch sensitivity across Region 3 is less pronounced, gain scheduling is less of a requirement. Instead, I 

chose constant gains. These gains are smaller in magnitude than the pitch-to-feather gains at rated because the 

blade-pitch sensitivity—or control authority—is higher in pitch-to-stall operation. I incorporated the blade-pitch-tostall speed-regulation controller into my FAST with AeroDyn and HydroDyn simulations through a simple 

modification of the baseline control system. 

As in Section III.A, I tested the system response of the NREL 5-MW wind turbine mounted atop the ITI Energy 

barge with this new control system at a variety of wind and wave conditions. compares the active pitch-tofeather and active pitch-to-stall system responses for the simulation with the same wind and wave conditions applied 

to the simulations presented in (i.e., an 18-m/s stochastic wind, a 3.673-m significant wave height, and a 

13.376-s peak spectral period). Again, I ran the simulations with all appropriate and available DOFs enabled, but 

without considering the rotor-mass imbalance or the increased blade structural-damping ratio. 

Figure 6

Figure 6

Figure 5

As shown in , active blade-pitch-to-stall control regulates generator speed—and hence electrical 

power—very well. It performs even better than the baseline active blade-pitch-to-feather controller. It does not, 

however, dampen the barge-pitch motions as intended. In fact, the barge-pitch motions are exaggerated in 

comparison to the response using the baseline active pitch-to-feather controller. This seemingly contradictory result 

can be understood by examining the barge-pitch damping ratios resulting from the active pitch-to-stall control. As 

for the pitch-to-feather system, the thrust sensitivity to wind speed ( ∂T V∂ ) can be found by using the open-loop 

and ideal closed-loop methods, and both methods can be used to estimate the barge-pitch damping ratios. The 

results of these calculations are presented in . Figure 7

In , the barge-pitch damping ratios associated with the pitch-to-stall system are plotted along with the Figure 7

original values presented in for the pitch-to-feather system. Because the two systems are identical below 

rated wind speed, so are the barge-pitch damping ratios. Above rated wind speed, however, the pitch-to-stall ratios 

diverge from the pitch-to-feather ratios. Unlike the pitch-to-feather values, the barge-pitch damping ratio remains 

positive-valued across control regions for the ideal closed-loop pitch-to-stall method because the thrust sensitivity to 

wind speed remains positive-valued. In the pitch-to-stall system slightly above rated, the open- and ideal closedloop bounds imposed by the barge-pitch damping ratios converge toward each other and remain at or near 2.5% 

across the remainder of Region 3. 

Figure 4

As I mentioned at the end of Section II, with real blade-pitch-control speed regulation above rated wind speed, 

the actual damping ratio will lie somewhere between the bounds imposed by the open- and ideal closed-loop results. 

This implies that the real blade-pitch-to-stall controller, regardless of its gains, will give the system a slightly stable 

9
barge-pitch damping ratio near 2.5% across Region 3, starting just above rated. Moreover, because the barge-pitch 

motions for the pitch-to-stall system are larger than those for the pitch-to-feather system in the time histories 

presented in , I can conclude that the real blade-pitch-to-feather speed controller actually has an effective 

damping ratio higher than 2.5% (at least for the conditions considered). In other words, the real pitch-to-feather 

barge-pitch damping ratio is actually much greater than that predicted by the ideal closed-loop results. It is still, 

however, beneficial to increase the damping as much as possible. 

0

2,000

4,000

6,000

8,000

Time (sec)

GenPwr, kW

Baseline (Pitch-to-Feather) Pitch-to-Stall

0

500

1,000

1,500

2,000

Time (sec)

GenSpeed, rpm

-30

-15

0

15

30

Time (sec)

BlPitch1, o

-20

-10

0

10

20

0 50 100 150 200 250 300

Simulation Time, s

PtfmPitch, o

Figure 6. Comparison of pitch-to-feather and pitch-to-stall system responses. 

Figure 6

One possibility for increasing the barge-pitch damping through active pitch-to-stall control is to tailor the airfoildata coefficients so that rotor thrust increases more with wind speed in Region 3 than what resulted with the existing 

airfoils. Experimental data from NREL’s Phase VI Unsteady Aerodynamics Experiment (UAE),13 which tested a 

passive stall-regulated wind turbine in the National Full-Scale Aerodynamics Complex at the National Aeronautics 

and Space Administration (NASA) Ames Research Center, showed a nearly steady increase in rotor thrust with wind 

speed from cut-in to cut-out. This would translate into a nearly constant steady-state thrust sensitivity to wind 

speed, ∂ ∂ T V , across all wind speeds for the UAE wind turbine. If the NREL 5-MW wind turbine were modified 

to behave comparably (e.g., to make its thrust sensitivity to wind speed in Region 3 similar to that seen in Region 2), 

the ideal closed-loop barge-pitch damping ratio would increase to about 15% in Region 3. This is slightly higher 

damping than the open-loop damping ratio achieved with active pitch-to-feather control. To achieve the necessary 

augmentation in rotor thrust, however, the existing airfoils will need to be modified and the rotor will need to be 

redesigned. Both tasks are beyond the scope of this work. I also suspect that it would be quite difficult to achieve 

damping ratios much above 15% through rotor-thrust augmentation and active pitch-to-stall speed regulation, even 

though a higher amount of damping is desirable. 

One might also think that combining the controller developed in this section with the TFB control loop 

developed in Section III.A would be another way to improve the barge-pitch damping through active pitch-to-stall 

speed-regulation control. But unfortunately, a pitch-to-stall control system cannot be combined with a classic TFB 

control loop for two reasons. First, the thrust sensitivity to rotor-collective blade pitch changes sign midway through 

Region 3, implying that the TFB control gain would also have to change sign midway through Region 3. Otherwise, 

the TFB control loop would actually act to reduce the effective platform-pitch damping in certain operating regions. 

Second, the magnitude of the thrust sensitivity to blade pitch is much smaller with pitch-to-stall control than with 

10
pitch-to-feather control. This implies that one could not achieve any significant increase in platform-pitch damping 

without very large control gains and resulting blade-pitch-rate requirements. 

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

3 5 7 9 11 13 15 17 19 21 23 2

Wind Speed, m/s

Barge-Pitch Damping Ratio, -

5

Pitch-to-Feather - Open-Loop

Pitch-to-Feather - Ideal Closed-Loop

Pitch-to-Stall - Open-Loop

Pitch-to-Stall - Ideal Closed-Loop

Figure 7. Pitch-to-feather and -stall barge-pitch damping ratios. 

C. Detuning the Gains in the Pitch-to-Feather Controller 

Neither the addition of the TFB control loop presented in Section III.A nor the modification to pitch-to-stall 

rotor-speed regulation presented in Section III.B gave satisfactorily improved the barge-pitch response. This section 

describes one more approach I took to improve the platform-pitch damping of the ITI Energy wind barge concept 

through conventional wind turbine control methods. 

This control strategy was the simplest modification I made to the baseline control system developed in Ref. 2, 

involving only a reduction of gains in the active blade-pitch-to-feather controller. The basic premise behind this 

control strategy is the understanding that reducing the gains in the rotor-speed controller will cause the floating wind 

turbine system to behave less like the results for the ideal closed-loop pitch-to-feather method, and more like the 

results for the open-loop control method. Because of knowledge about barge-pitch damping ratios acquired from 

Figure 4 or , this end result is important. Figure 7

As in the isolated rigid-body platform-pitch response, the idealized PI-based rotor-speed controller responds as a 

second-order system with a natural frequency, ωφn, and damping ratio, ζφ.

2

 To maintain a reasonable relationship 

between the proportional and integral gains in the rotor-speed control system, I reduced the gains by choosing a 

smaller controller-response natural frequency (ωφn). I preserved the recommended controller damping ratio (ζφ = 0.6 

to 0.7). The recommended value found in Ref. 14, and the value selected for the baseline control system,2

 of ωφn = 

0.6 rad/s is slightly above the barge-pitch natural frequency of ωxn = 0.5420 rad/s (see Section II). This relationship 

between frequencies has the potential to introduce negative damping of the barge-pitch mode. Larsen and Hanson15

found that the smallest controller-response natural frequency must be lower than the smallest critical supportstructure natural frequency to ensure that the support structure motions of an offshore floating wind turbine with 

active pitch-to-feather control remain positively damped. 

Reducing ωxn by one-third will ensure that the controller-response natural frequency is lower than the bargepitch natural frequency and also lower than wave-excitation frequency of all but the most severe sea states. Using 

the properties for the NREL 5-MW wind turbine, I used ωφn = 0.4 rad/s and ζφ = 0.7 to derive the reduced (detuned) 

gains. As in the baseline control system,2

 I used the upper limit of the recommended damping ratio range (ζφ = 0.7) 

11
to compensate for neglecting negative damping from the generator-torque controller in the determination of the 

proportional gain. 

As in Sections III.A and III.B, I tested the system response of the NREL 5-MW wind turbine mounted atop the 

ITI Energy barge with this new control system. Figure 8 compares the system responses with the detuned and 

original (baseline) blade-pitch-to-feather gains for a simulation with the same wind and wave conditions used in the 

simulations presented in and (i.e., an 18-m/s stochastic wind, a 3.673-m significant wave height, 

and a 13.376-s peak spectral period). As before, I ran the simulations with all appropriate and available DOFs 

enabled, but without considering the rotor-mass imbalance or the increased blade structural-damping ratio. 

Figure 5 Figure 6

As shown in Figure 8, the detuned blade-pitch control system is marginally effective at reducing the barge-pitch 

motions. Furthermore, it attains this positive performance without negatively affecting the generator speed and 

power excursions. As a matter of fact, the generator speed and power excursions have actually been diminished. 

And all of this has been accomplished with a reduction in blade-pitch duty cycle! 

There is an upper bound, though, to the amount of improvement in the barge-pitch damping that is attainable 

with a basic detuning of the blade-pitch control system gains. That upper bound is simply the amount of damping 

shown in Fi or for the open-loop pitch-to-feather control system, or roughly 13% in Region 3. gure 4 Figure 7

In addition, one cannot expect that further and further reductions in the blade-pitch controller gains will continue 

to improve the damping of the barge-pitch motions without eventually exacerbating the excursions in the system 

response. This is because the rotor-speed error is unstable in the open-loop (uncontrolled) scenario in Region 3. 

(The rotor-speed error response is negatively damped if all blade-pitch control gains are zero.) To confirm this 

behavior, I reran simulations with detuned blade-pitch control gains derived from varying values of ωφn, from 0.1 to 

0.5 rad/s in steps of 0.1 rad/s. As expected, with ωφn = 0.1 or 0.2 rad/s the system responses (not shown) exhibited 

much higher excursions in barge-pitch, generator speed, and electrical power output. With ωφn = 0.5 rad/s and ωφn = 

0.3 rad/s, I obtained responses (not shown) very similar to the system responses obtained for gains derived with ωφn

= 0.4 rad/s. (The barge-pitch damping from the simulation with ωφn = 0.4 rad/s was slightly better than the damping 

with ωφn = 0.3 or 0.5 rad/s.) 

0

2,000

4,000

6,000

8,000

Time (sec)

GenPwr, kW

Baseline Detuned Gains

0

500

1,000

1,500

2,000

Time (sec)

GenSpeed, rpm

0

6

12

18

24

Time (sec)

BlPitch1, o

-10

-5

0

5

10

0 50 100 150 200 250 300

Simulation Time, s

PtfmPitch, o

Figure 8. System responses with and without detuned blade-pitch control gains. 

12
IV. Other Ways to Improve the Pitch Damping with Turbine Control 

As demonstrated in Section III, conventional wind turbine control methodologies are limited in what they can do 

to improve the platform-pitch motions while limiting rotor-speed excursions of the ITI Energy wind barge concept. 

A number of other unconventional methods are also worth considering. Because a quantitative consideration of 

each method is beyond the scope of this work, I leave these considerations for future work. But this section 

highlights some of the possibilities. 

I. Edwards of ITI Energy proposed one idea for an unconventional wind turbine control system. Edwards 

suggested that part of the problem with the barge-pitch damping in Region 3 might be that the generator is already 

operating at full (rated) power, so that there is no “head room” for absorbing more power as the barge pitches into 

the wind as a result of wave excitation. This implies that it might be better to regulate to some “below-rated” power 

level across all (even high) wind speeds to leave room for absorbing more power. This would, perhaps, permit the 

wind turbine rotor to capture not only wind power, but some wave power as well. Assessing this control strategy 

would require a study that examines the trade-off between improving the damping of the barge and reducing the 

capacity factor of the wind turbine. 

Another unconventional wind turbine control strategy, proposed by Dr. R. Thresher of NREL, would be to use 

nacelle-yaw actuation, instead of blade-pitch actuation, to regulate the rotor speed of the turbine. This strategy 

could eliminate the problems from the drop in steady-state rotor thrust with increasing wind speed above rated 

resulting from blade-pitch-to-feather control. One would, however, have to determine whether the gyroscopic 

moments induced by the required yaw rates would have undesirable consequences. 

A simple, but unconventional, modification to the control strategy would be to change Region 3 from a constant 

generator power to a constant generator-torque control region. With this change, the generator-torque controller 

would not introduce negative damping in the rotor-speed response (which must be compensated by the blade-pitch 

controller), and so, might reduce the rotor-speed excursions. Larson and Hanson15 demonstrated the effectiveness of 

this modification for one offshore floating wind turbine concept. This change, however, would not improve the 

barge-pitch damping. 

Conventional wind turbine control methodologies rely on the independent development and concatenation of 

multiple single-input, single-output (SISO) proportional-integral-derivative-based (PID-based) control loops that use 

the conventional turbine actuators of blade pitch, generator torque, and nacelle yaw (and, as required, shaft brakes 

and other actuators). Naturally, modern control theories, such as disturbance-accommodating control (DAC),16 offer 

the potential to bring about improved performance. Previous controls studies by Stol,17 Hand,18 and Wright19 have 

demonstrated the applicability of combining a state estimator, a wind-disturbance estimator, and full-state feedback 

using DAC to develop multiple-input, multiple-output (MIMO) state-space-based control systems for mitigating 

dynamic loads and stabilizing flexible modes of land-based wind turbines without compromising energy capture. 

But these studies have not yet been extended to offshore floating wind turbines. 

Through MIMO state-space-based control, it may be possible to enhance rotor-speed regulation and platformpitch damping through unified control of the generator torque and blade-pitch angles. For example, because rotorspeed regulation requires a blade-pitch command that is opposite of the one required to add damping to the bargepitch motion (see Section III.A), it might be possible to develop a combined generator-torque and blade-pitch 

controller to address both objectives simultaneously. The generator-torque commands may be able to mitigate the 

rotor-speed excursions while the blade-pitch commands attempt to augment aerodynamic rotor thrust to dampen the 

platform-pitch motion. When used in conjunction with off-axis flow through nacelle-yaw actuation, it may also be 

possible to introduce platform-roll damping through the blade-pitch commands (and thrust augmentation). 

Rotor-collective blade-pitch control can be used to adapt rotor thrust, which induces a moment on the floating 

platform through the hub-height moment arm, but independent blade-pitch control may also be useful. For example, 

independent blade-pitch control can be used to introduce pitching moments within the rotor itself through 

asymmetric aerodynamic loading of the rotor. If developed properly, it may be possible to use such a moment to 

counteract the hydrodynamic pitching loads on the platform brought about by surface waves. 

Reference 1 discusses other design alterations, beyond wind turbine control, that may be applied to improve the 

response of the floating wind barge system. 

V. Conclusion 

In this paper, I presented the influence of conventional wind turbine blade-pitch control actions on the pitch 

damping of the NREL 5-MW baseline wind turbine mounted atop the ITI Energy barge. I was concerned that the 

drop in steady-state wind turbine rotor thrust with wind speed above rated would lead to negative damping of the 

barge-pitch mode and contribute to the large system-pitch motions. 

13
I demonstrated that neither the addition of a control loop through feedback of tower-top acceleration nor the 

modification to pitch-to-stall rotor-speed regulation satisfactorily improved the barge-pitch response. The latter 

modification helped me conclude, however, that the actual barge-pitch damping was considerably greater than that 

implied by the steady-state rotor thrust response, but that it was still beneficial to increase the damping as much as 

possible. I also showed that detuning the gains in the baseline blade-pitch-to-feather controller helped, but still did 

not entirely resolve the barge-pitch-motion problem. 

Acknowledgments 

I would like to thank everyone who helped with this work, including Ian Edwards of ITI Energy for sponsoring 

the loads-analysis activities and Professor Nigel Barltrop and Willem Vijfhuizen of the Universities of Glasgow and 

Strathclyde for developing the ITI Energy barge and mooring system concept. Thank you also to Torben Larsen of 

Risø National Laboratory and the Technical University of Denmark for introducing me to the importance of the role 

that a variable blade-pitch-to-feather control system can play in offshore floating wind turbines and to Lee Jay 

Fingersh and Dr. Alan Wright for their guidance and advice in my controls-development activities. I also thank my 

Ph.D. committee at the University of Colorado at Boulder for evaluating this project and Rene Howard, Stefanie 

Woodward, and Bonnie Jonkman of NREL for editing this paper to make it much more readable. 

This work was performed at NREL in support of the U.S. Department of Energy under contract number DEAC36-99-GO10337 and in support of a Cooperative Research and Development Agreement (CRD-06-178) with ITI 

Energy. 

References 1

Jonkman, J. M. and Buhl, M. L., Jr., “Loads Analysis of a Floating Offshore Wind Turbine Using Fully Coupled 

Simulation,” WINDPOWER 2007 Conference and Exhibition, Los Angeles, California, 3–6 June 2007 [CD-ROM], Washington, 

D.C.: American Wind Energy Association, June 2007, NREL/CP-500-41714, Golden, CO: National Renewable Energy 

Laboratory. 2

Jonkman, J., Butterfield, S., Musial, W., and Scott, G., Definition of a 5-MW Reference Wind Turbine for Offshore System 

Development, NREL/TP-500-38060, Golden, CO: National Renewable Energy Laboratory, February 2007 (to be published). 3

Vijfhuizen, W. J. M. J, Design of a Wind and Wave Power Barge, M.S. Dissertation, Department of Naval Architecture and 

Mechanical Engineering, Universities of Glasgow and Strathclyde, Glasgow, Scotland, September 2006. 4

Jonkman, J. M. and Buhl, M. L., Jr., FAST User’s Guide, NREL/EL-500-29798, Golden, CO: National Renewable Energy 

Laboratory, October 2004. 5

Laino, D. J. and Hansen, A. C., User’s Guide to the Wind Turbine Dynamics Aerodynamics Computer Software AeroDyn, 

Salt Lake City, UT: Windward Engineering LLC, Prepared for the National Renewable Energy Laboratory under Subcontract 

No. TCX-9-29209-01, December 2002. 6

Moriarty, P. J. and Hansen, A. C., AeroDyn Theory Manual, NREL/EL-500-36881, Golden, CO: National Renewable 

Energy Laboratory, December 2005. 7

Lee, C. H. and Newman, J. N., WAMIT® User Manual, Versions 6.3, 6.3PC, 6.3S, 6.3S-PC, WAMIT, Inc., Chestnut Hill, 

MA, USA, 2006. 8

Jonkman, J. M. and Sclavounos, P. D., “Development of Fully Coupled Aeroelastic and Hydrodynamic Models for Offshore 

Wind Turbines,” 44th AIAA Aerospace Sciences Meeting and Exhibit, 9–12 January 2006, Reno, NV, AIAA Meeting Papers on 

Disc [CD-ROM], Reston, VA: American Institute of Aeronautics and Astronautics, January 2006, AIAA-2006-995, NREL/CP500-39066, Golden, CO: National Renewable Energy Laboratory. 9

Jonkman, J. M. and Buhl, M. L., Jr., “Development and Verification of a Fully Coupled Simulator for Offshore Wind 

Turbines,” 45th AIAA Aerospace Sciences Meeting and Exhibit, 8–11 January 2007, Reno, NV, AIAA Meeting Papers on Disc

[CD-ROM], Reston, VA: American Institute of Aeronautics and Astronautics, January 2007, AIAA-2007-212, NREL/CP-500-

40979, Golden, CO: National Renewable Energy Laboratory. 10Nielsen, F. G., Hanson, T. D., and Skaare, B., “Integrated Dynamic Analysis of Floating Offshore Wind Turbines,” 

Proceedings of OMAE2006 25th International Conference on Offshore Mechanics and Arctic Engineering, 4–9 June 2006, 

Hamburg, Germany [CD-ROM], Houston, TX: The American Society of Mechanical Engineers (ASME International) Ocean, 

Offshore and Arctic Engineering (OOAE) Division, June 2006, OMAE2006-92291. 11Kristiansen, E., Hjulstad, Å., and Egeland, O., “State-Space Representation of Radiation Forces in Time-Domain Vessel 

Motions,” Ocean Engineering, Vol. 32, 2005, pp. 2195–2216. 12Bossanyi, E. A., “Wind Turbine Control for Load Reduction,” Wind Energy, Vol. 6, No. 3, June 2003, pp. 229–244. 13Hand, M. M., Simms, D. A., Fingersh, L. J., Jager, D. W., Cotrell, J. R., Schreck, S., and Larwood, S. M., Unsteady 

Aerodynamics Experiment Phase VI: Wind Tunnel Test Configurations and Available Data Campaigns, NREL/TP-500-29955, 

Golden, CO: National Renewable Energy Laboratory, December 2001. 14Hansen, M. H., Hansen, A., Larsen, T. J., Фye, S., Sørensen, and Fuglsang, P., Control Design for a Pitch-Regulated, 

Variable-Speed Wind Turbine, Risø-R-1500(EN), Roskilde, Denmark: Risø National Laboratory, January 2005. 

14
15Larsen, T. J. and Hanson, T. D., “A Method to Avoid Negative Damped Low Frequent Tower Vibrations for a Floating, 

Pitch Controlled Wind Turbine,” Journal of Physics: Conference Series, The Second Conference on The Science of Making 

Torque From Wind, Copenhagen, Denmark, 28–31 August 2007, [online journal], Vol. 75, 2007, 012073, URL: 

http://www.iop.org/EJ/article/1742-6596/75/1/012073/jpconf7_75_012073.pdf?request-id=SpEuhRBu3BG0xV3r2wi7Kg, [cited 

28 August 2007]. 16Johnson, C. D., “Theory of Disturbance Accommodating Controllers,” Advances in Control and Dynamic Systems, Vol. 12, 

1976. 17Stol, K. A., Dynamics Modeling and Periodic Control of Horizontal-Axis Wind Turbines, Ph.D. Dissertation, Department of 

Aerospace Engineering Sciences, University of Colorado, Boulder, CO, USA, 2001. 18Hand, M. M., Mitigation of Wind Turbine/Vortex Interaction Using Disturbance Accommodating Control, Ph.D. 

Dissertation, Department of Mechanical Engineering, University of Colorado, Boulder, CO, USA, December 2003, NREL/TP500-35172, Golden, CO: National Renewable Energy Laboratory. 19Wright, A. D., Modern Control Design for Flexible Wind Turbines, Ph.D. Dissertation, Department of Aerospace 

Engineering Sciences, University of Colorado, Boulder, CO, USA, July 2004, NREL/TP-500-35816, Golden, CO: National 

Renewable Energy Laboratory. 

15
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Influence of Control on the Pitch Damping of a Floating Wind 

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This paper presents the influence of conventional wind turbine blade-pitch control actions on the pitch damping of a 

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