research article wind and wave disturbances compensation...

Research ArticleWind and Wave Disturbances Compensation to FloatingOffshore Wind Turbine Using Improved Individual PitchControl Based on Fuzzy Control Strategy

Feng Yang1 Qing-wang Song1 Lei Wang2 Shan Zuo3 and Sheng-shan Li1

1 School of Automation Engineering University of Electronic Science and Technology of China Chengdu 611731 China2 School of Automation Chongqing University Chongqing 400044 China3 School of Energy Science and Engineering University of Electronic Science and Technology of China Chengdu 611731 China

Correspondence should be addressed to Lei Wang leiwang08cqueducn

Received 23 January 2014 Revised 17 February 2014 Accepted 17 February 2014 Published 30 March 2014

Academic Editor Hui Zhang

Copyright copy 2014 Feng Yang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Due to the rich and high quality of offshore wind resources floating offshore wind turbine (FOWT) arouses the attentions of manyresearchers But on a floating platform the wave and wind induced loads can significantly affect power regulation and vibration ofthe structure Therefore reducing these loads becomes a challenging part of the design of the floating system To better alleviatethese fatigue loads a control system making compensations to these disturbances is proposed In this paper an individual pitchcontrol (IPC) system integrated with disturbance accommodating control (DAC) and model prediction control (MPC) throughfuzzy control is developed to alleviate the fatigue loads DAC is mainly used to mitigate the effects of wind disturbance and MPCcounteracts the effects of wave on the structure The new individual pitch controller is tested on the NREL offshore 5MW windturbine mounted on a barge with a spread-mooring system running in FAST operating above-rated condition Compared to theoriginal baseline collective pitch control (CPC) (Jonkman et al 2007) the IPC system shows a better performance in reducingfatigue loads and is robust to complex wind and wave disturbances as well

1 Introduction

Wind has been proved to be the most promising renewableenergy resource during the last few decades Compared toonshore wind turbines floating offshore wind turbines havemore potential to become a large contributor to society due tothe rich and high quality of offshore wind resource Howeveroffshore wind brings new problems to floating offshorewind turbines including additional wave loading unstableplatform and ice problems The above problems aggravatethe unbalanced fatigue loads of the structure Thereforereducing these fatigue loads becomes an extremely importantbut challenging part of the design of the floating system

Currently variable speed variable pitch wind turbines[1] simply use collective pitch control with PID controllerto limit the excess of wind power above rated wind speedneglecting the uneven loads distributed in the structure

However aerodynamic forces and wave influence on thestructure are different Hence the wind turbine and platformendure unbalanced loads all the way [2] IPC which hasexcellent performance in wind turbine control can be usedto alleviate the wind turbine fatigue loads caused mainly bywind and waves [3]

In the last few years some related works have been doneto explore the way to reduce these fatigue loads NationalRenewable Energy Laboratory (NREL) provides us with avariety of wind turbine models to test various kinds ofimportant features using FAST Jonkman has done a widerange of research work on the floating offshore wind turbineswith a baseline controller Bossanyi [4] introduced the IPCconception and reduced fatigue loads around one time therotational frequency (1p) The IPC used in [5 6] are basedon two separate single input single output (SISO) systemsUsing Coleman transformation the 1p variables of the blade

Hindawi Publishing CorporationAbstract and Applied AnalysisVolume 2014 Article ID 968384 10 pageshttpdxdoiorg1011552014968384

2 Abstract and Applied Analysis

loads can be transformed into stationary variables like rotortilt and yaw moments The SISO systems use PI controllersto reduce the tilt and yaw moments However FOWTis a strongly coupled nonlinear time-varying system withcomplex disturbances and obviously SISO cannot accountfor these disturbances This can be improved by 119867

infincontrol

in [7ndash10] sliding mode in [11 12] optimal control in [13 14]or linear quadratic Gaussian control (LQG) [15 16]The LQGcontroller consists of a linear model of the wind turbine anda state estimator used to estimate the states of themodel fromknown turbine variables byKalmanfilter A control lawwhichcanminimize the quadratic cost function of the wind turbinesates was used to make the control This method successfullybrings about a significant loads reduction but has no effect onthe fatigue loads of the stationary parts

Another way to deal with the strong disturbance isdisturbance-accommodating controllers implemented byNamik and Stol [17] on Spar-Buoyfloatingwind turbineDACcontroller consisted of a state regulation term with full statefeedback controllers and a disturbance estimator is used tolower the influence of persistent disturbances like turbulencewind on the wind turbine Compared to the original baselinecontroller designed by Jonkman theDAC reduces tower fore-aft and side-side bending fatigue loads greatly But the dis-turbance estimator in DAC did not consider much influenceof the wave To study the impact of wave on wind turbineBae and Kim [18] investigated the wave-load effect on 5 MWmonocolumn TLP-type FOWT The sum-frequency waveloading is applied in both coupled and uncoupled conditionthe results show that there exist complicated coupling effectsamong wind turbine variables and wave condition should befully considered when designing the FOWT

It is notable that the above method cannot bring allthe disturbances into consideration Wind as well as waveshould be fully considered In this paper a new individualpitch control based on combined DAC and MPC usingfuzzy control is proposed DAC can deal with persistentdisturbances like wind but ignore the wave who is a typeof periodic disturbance MPC can reduce the structuraloscillation and decrease the fatigue loads caused by incidentwaves through tracking the state trajectory of the undisturbedreference model So the new individual pitch control strategythat combines the two methods through fuzzy control canbetter deal with wind and wave disturbances

Section 2 introduces the configuration of the floatingoffshore wind turbine Section 3 gives a brief introduction tothe disturbances such as wind and wave Section 4 focuseson the design of the new controller First give a detailedintroduction to theDACandMPC and then a new individualpitch controller combined with DAC and MPC comes intobeing through fuzzy control In Section 5 the new individualpitch controller is tested and proved to be effective for thefatigue loads reduction

2 Wind Turbine Configurations

The wind turbine used in this paper is a model called ldquoNRELoffshore 5-MW baseline wind turbinerdquo from NREL This

is a realistic model of a three-bladed upwind 5-MW windturbine mounted on a barge with a spread-mooring systemdeveloped at MIT through a contract with NREL [19] Thegross properties of the wind turbine are given in Table 1 andthe platform properties are given in Table 2

3 Disturbance Loads Modeling

Wind turbine is not a static structure Due to rotatingrotor turbulent wind complex wave conditions huge slendercomponents and complex design the structural vibrationswhich can significantly contribute to dynamic fatigue loadingof the structure are introduced to the system Among all thefactors cause fatigue loads of wind turbine wave and windshould be first taken into consideration

31 Wind Loads Wind turbine components exposed in windcondition will cause movement because of aerodynamicsbetween wind flow and wind turbine structure That is thereason wind turbine can be used to generate electricity Windshear and tower shadowwill introduce additional disturbanceto the wind turbine systemWindmodel is important to loadsdefinition as well as design of the wind turbine and platformsystem The accuracy of wind parameters affects the designof wind turbine system significantly The wind load can bemodeled by formulas based on lift theory [20]

119865wind =1

2120588air]wind119878119862119911

]wind = ]mean + ]ws + ]ts + ]wk(1)

where 119865wind is the wind forces on blade 120588air is air density119878 is the blade surface area and ]wind is the wind speedwhich consists of mean wind speed ]mean the wind shearcomponent ]ws the tower shadow component ]ts and farwake component of one preceding wind turbine ]wk Windshear and the tower shadow which lead to significant vibra-tion of the structure were specified in [21]

32 Wave Loads In addition to wind condition wave force isalso a main contributor to loads on the structure The waveforce can be calculated based on Airyrsquos linear theory wherethe horizontal and vertical wave velocity are introduced in[22]

119865wave =1

2120588water119862119863119863 |119906| 119906 + 120588water119862119868

1205871198632

4119886119909

119906 =120596ℎ

2

cos 119896119910sin 119896119889

cos (119896119909 minus 120596119905)

(2)

where 119865wave is the wave force on platform 120588water is waterdensity 119862

119863and 119862

119868are the drag and inertia coefficients

respectively 119863 is the diameter of the structural member 119906

which is the horizontal velocity of water and 119886119909is the water-

particle acceleration which can be obtained by means of 119886119909asymp

120597119906120597119905 The first part of this formula can be described as thedrag term who is proportional to the square of the watervelocity Another part is referred to the inertial term It isproportional to the water acceleration

Abstract and Applied Analysis 3

Table 1 NREL 5MWwind turbine model properties

Properties ValueRating 5MWRotor orientation configuration Upwind 3 blades

Control Variable speed collectivepitch

Drivetrain Multiple-stage gearboxRotor hub diameter 126m 3mHub height 90mCut-in rated cut-out wind speed 3ms 114ms 25msCut-in rated rotor speed 69 rpm 121 rpmRated tip speed 80msOverhang shaft tilt precone 5m 5∘ 25∘

Rotor mass 110000 kgNacelle mass 240000 kgTower mass 347460 kgCoordinate location of overall CM (minus02m 00m 640m)Using the data from NREL

Table 2 NREL 5MW platform properties

Properties ValueDiameter height 36m 95mDraft freeboard 5m 45mWater displacement 5089m3

Mass including ballast 4519150 kgCM location below SWL 388238mRoll inertia about CM 390147000 kgsdotm2

Pitch inertia about CM 390147000 kgsdotm2

Yaw inertia about CM 750866000 kgsdotm2

Anchor (water) depth 200mLine diameter 0127mLine mass density 1160 kgmLine extensional stiffness 1500000000NUsing the data from NREL

4 Controller Design

This section describes the new individual pitch controlbased on disturbance accommodating control with wave dis-turbance compensation component using model predictivecontrol method Furthermore a cooperation strategy usingfuzzy control was introduced to actively alleviate the fatigueloads caused by wave and wind disturbances

41 IPCwithDAC Disturbance accommodating control [23]which is a kind of feedforward control is an effective methodto reduce the influence caused by persistent disturbances likewind In this section the use of DAC on floating offshorewind turbine is introduced where the wind condition wasconsidered into the DAC system Since variables relatedto disturbances are assumed to be unavailable straightwaya disturbance estimator designed through variables whichcan directly be measured was employed To design the IPC

controller first a generic linearized state-space mode shouldbe described as

= 119860119909 + 119861119906 + 119861119889119906119889 (3)

119910 = 119862119909 + 119863119906 + 119863119889119906119889 (4)

where 119860 is the state matrix 119861 is the actuator gain matrix119861119889is the disturbance gain matrix 119862 is the measurements

to the states 119863 is the measurements to the control inputs119863119889is the measurements to the disturbance inputs 119909 relates

to the state variable vector 119910 relates to the system outputvector 119906 relates to the actuators vector and 119906

119889relates to

disturbance inputs vector In order to minimize the effectscaused by disturbances such as wind and platform persistentdisturbances should be first modeled by (5) and (6) where 119911 isthe disturbance states vector and 119866 and 119876 are assumed to beknown but with unknown initial conditions [24]The naturesof the assumed model can be determined by the matrices 119866

and 119876

119906119889= 119866119911 (5)

= 119876119911 (6)

The feedback control law that can deal with the effectsof disturbances on wind turbine is given by (7) where 119870

is the state feedback controller gain matrix and 119866119889is the

disturbance reduction gain matrix

119906 = minus119870119909 + 119866119889119911 (7)

Equation (8) can be derived from (3) (5) and (7) whichclearly shows that in order to cancel the effects of persistentdisturbances (9) must hold true

= (119860 minus 119861119870) 119909 + (119861119866119889+ 119861119889119866) 119911 (8)

119861119866119889+ 119861119889119866 = 0 (9)

A disturbance state estimator can be designed by a newstate vector120596which consists of turbine states and disturbancestatesThrough (3) to (6) a new a state-spacemodel is createdand given by

= 119860120596 + 119861119906

119910 = 119862120596 + 119863119906

(10)

where 119860 = [119860 119861119889119866

0 119876] 119861 = [

119861

0] and 119862 = [119862 119863

119889119866] The state

estimator dynamics are given by (11) and (12) where 119870119890is

the state estimator gain matrix The symbol indicates anestimate as follows

120596 = 119860 + 119861119906 + 119870119890(119910 minus 119910) (11)

119910 = 119862 + 119863119906 (12)

119890 = 120596 minus = 119860 (120596 minus ) minus 119870119890119862 (120596 minus ) = (119860 minus 119870

119890119862) 119890 (13)

Therefore if the pair (119860 119862) is observable then the aug-mented vector 120596 can be fully estimated [25]


Controller

Tc(120595)

Δulowast

ud

u

y

z

++

+

+

minus

minus

Δx

xTminus1

c(120595)

Ts(120595)Disturbance

Estimator

Nonlinear windturbine model

Saturation

minusKnrxnr + Gdnr z

Δulowast

nr

Δunr

Δu

Δxnr

uop

xop

nrΔxnr nr

(Anr minus KenrCnr )nr + E(120595)V

Figure 1 DAC implemented for OFWT

Finally multiblade coordinate transformation (MBC) isused to deal with the periodic nature of the wind turbineTheDAC law in the nonrotating frame and the time-invariantDACgainmatrix are given by (14) and (15) respectivelyMBCtransformation matrices 119879

119888(120595) 119879

119904(120595) and 119879

0(120595) transform

the corresponding input vectors to the nonrotating frameof reference The nr symbol indicates nonrotating framevariables

119906nr = minus119870nr119909nr + 119866119889nr (14)

119866119889nr = minus119861

+

nr119861119889nr119866 (15)

The DAC law transformed into the mixed frame of referenceis described as

119906 = minus119879119888(120595)119870nr119879

minus1

119904(120595) 119909 + 119879

119888(120595)119866

119889nr (16)

The disturbance estimator for the MBC transformed systemcan be expressed in

120596nr = (119860nr minus 119870119890nr119862nr) nr + 119861nr119879

minus1

119888(120595) 119906

+ 119870119890nr119879minus1

0(120595) 119910

= (119860nr minus 119870119890nr119862nr) nr

+ [119861nr119879minus1

119888(120595) 119870

119890nr119879minus1

0(120595)] [

119906

119910]

= (119860nr minus 119870119890nr119862nr) nr + 119864 (120595)119881

(17)

The block diagram of DAC controller for FOWT is shown inFigure 1

42 Wave Disturbance Compensation to the DAC The IPCcontroller based on DAC takes the persistent disturbancelike wind into consideration but ignoring the wave who isa type of periodic disturbance In order to overcome theimpact brought about by the wave a compensation moduleis introduced and added to the DAC system This periodicdisturbance compensation module based on MPCmethod isadded to the DAC system through fuzzy control

421 Wave Disturbance Compensation Using MPC

(A) Model Predictive Controller In this paper to reducethe structural vibration caused by incident wave MPC wasutilized Model predictive control is a closed-loop optimiza-tion model-based control strategy The core of the algorithmis as follows a dynamic model can predict the futureonline repeated optimization and the model error feedbackcorrection The main idea of this method is that the bladesrsquopitch is controlled by a model predictive controller basedon a reference model without periodic disturbance fromincident waves Then the state trajectory of the undisturbedsystem which can be used as a reference to the real systemis produced by the reference model The model predictivecontrol will reduce the structural oscillation and decrease thefatigue loads caused by incident waves through tracking thestate trajectory of the undisturbed reference model

Assume that the model of the wave disturbance includedOFWT open-loop system is given in

119909 (119896 + 1) = 119860120596119909 (119896) + 119861

120596119906 (119896)

119910 (119896) = 119862120596119909 (119896)

(18)

where 119860120596 119861120596 and 119862

120596are state matrix actuator gain matrix

and measurements to the states of the disturbance includedsystem respectively

Whenwave disturbance is removed in the state vector theopen-loop model of the undisturbed plant is given by

119909119903(119896 + 1) = 119860

119903119909119903(119896) + 119861

119903119906119888(119896)

119910119903(119896) = 119862

119903119909119903(119896)

(19)

where 119860119903 119861119903 and 119862


and measurements to the states of the undisturbed systemrespectively And the controller for the undisturbed plant isdescribed by

119909119888(119896 + 1) = 119860

119888119909119888(119896) + 119861

119888119910119903(119896) + 119864

119888119903 (119896)

119906119888(119896) = 119862

119888119909119888(119896) + 119863

119888119910119903(119896) + 119865

119888119903 (119896)

(20)

where 119903 is the reference signal Variables with subscript 119888 arecontrol parameters Assume that119883 and119880 are states and input


variables Then design of the model predictive controllerbecomes the following optimization problem at each step

min119906(119896)119906(119896+119879minus1)

119879

sum

119896=1198960

1003817100381710038171003817119909(119896) minus 119909119903(119896)

1003817100381710038171003817

2

119876+ 119906(119896)

2

119877

st

119909 (1198960) = 1199090

119909119903(1198960) = 1199091199030

119909 (119896 + 1) = 119860120596119909 (119896) + 119861

120596119906 (119896)

119910 (119896) = 119862120596119909 (119896)

119909119903(119896 + 1) = 119860

119903119909119903(119896) + 119861

119903119906119888(119896)

119910119903(119896) = 119862

119903119909119903(119896)

119909119888(119896 + 1) = 119860

119888119909119888(119896) + 119861

119888119910119903(119896) + 119864

119888119903 (119896)

119906119888(119896) = 119862

119888119909119888(119896) + 119863

119888119910119903(119896) + 119865

119888119903 (119896)

119909 (119896) isin 119883

119906 (119896) isin 119880

119896 = 1198960 119896

0+ 119879

(21)

At each iteration step the first value of input sequence119906(119896)is applied to the control systemThis process will repeat untilan optimal solution is foundThe initial states of the referencemodel can be seen as the initial states of the optimizationproblem The states of the reference model are updated ateach iteration step through a state estimator designed byextended Kalman filter The nonlinear system is linearized ateach sample time around the current state so the matrices ofthe model at current state can be updated as well

(B) State Estimator Since not all the variables used in themodel are directly available especially for the states relatedto disturbances like wind and wave a state estimator needto be designed by available measurements Here an extendedKalman filter is employed to estimate the unmeasured statesas described in above system Kalman filter is a recursive filterof high efficiency which can estimate the state of the dynamicsystem from a series of measurement with incomplete noiseBased on the wind turbine system model and disturbancemodel described in (1) and (2) an extended Kalman filteris implemented to estimate the unavailable states caused bydisturbances especially periodic disturbance like wave Formore detailed description of the estimator please refer to[26 27]

(C) Reference Model The Baseline control model imple-mented by Jonkman on the OFWT (5MW) used to studythe performance of the barge floating platform over ratedspeed condition [28] is selected to be the reference model toresemble the dynamics of the closed-loop system of a floatingwind turbine The control law of baseline control is given in(22) where 120579angle relates to the commanded pitch angle 119896

119901

and 119896119894are the proportional and integral gain respectivelyThe

detailed parameters of baselinemodel controller are shown inTable 3

120579angle (119905) = 119896119901119890 (119905) + 119896

119894int

119905

0

119890 (120591) 119889120591 (22)

MPC Nonlinearwind

turbine model

u(k)

r(k)

y(k)

x(k)A B

Referencemodel

Stateestimator

Figure 2 Wave disturbance using MPC

Table 3 Baseline pitch controller properties

Properties ValueRated power 5296610MWRated torque 4309355NsdotmProportional gain 001882681Integral gain 0008068634Minimum blade pitch 0∘

Maximum blade pitch 90∘

Maximum absolute blade pitch rate 8∘sUsing the data from NREL

The control strategy is shown in Figure 2 which consistsof three modules a model predictive controller which canreduce the disturbance introduced by wave a state estimatorwho can estimate the states that cannot be measured directlyand a reference model which can provide a reference withoutdisturbance to the real disturbed system

422 Cooperation Strategy Using Fuzzy Control In thispaper Section 41 introduced the IPC based on DAC whotakes the persistent disturbance like wind into considerationbut ignoring the wave who is a type of periodic disturbanceThis means that DAC controller can effectively deal with thewind disturbance but wave disturbance And Section 421describes a method to overcome influence caused by thewave disturbance on FOWT using model predictive controlIn order to reduce or cancel the effect of both wind andwave disturbances on FOWT the model predictive controlcomponent is added to the DAC system by fuzzy logicmethod based on the wind and wave loads on the FOWTsystem The overall control strategy of FOWT is shown inFigure 3

Fuzzy control which is widely used in complex systemslike [10 29] is a type of intelligent control based on fuzzy settheory fuzzy linguistic variables and fuzzy logic inferenceThe design process of a fuzzy controller generally consistsof input and output variables definitions fuzzification stagerule base design and defuzzification stage Here the inputs


Controller

DisturbanceEstimator

Fuzzy controlRule base

Fuzzification Fuzzy logic Defuzzification

MPC

DAC

Model predictive control

Coefficients

++

+

+

+ ++

Δulowast

Tc(120595)

u

ud

y

Δu

Saturation

minus

minus


Δx

x

z

Tminus1

c(120595)

Ts(120595)

CDAC CDAC

Δulowast

nr

Δunr


uop

nrx

op

Δxnr


Δxnr nr

Figure 3 Block diagram of the overall control scheme

Externalconditions Applied loads Wind turbine

Control system

Windinflow

Aerodyna-mics

Aerodyna-mics

Rotordynamics

Drivetraindynamics

Powergeneration

TurbSim

Nacelle dynamics

Tower dynamics

Platform dynamics

Mooring dynamics

Wave andcurrents

Hydrodyn-amics

Hydrodyn-amics FAST and ADAMS

Figure 4 Offshore FAST structure (from NREL)

are wave force 119865wave and wind force 119865wind and the outputs are119862DAC (DAC coefficient) and 119862MPC (MPC coefficient) In thefuzzification stage inputs119865wave119865wind and outputs119862DAC119862MPCare represented by the fuzzy setmembership 119868

1 11986821198621 and119862

2

respectively1198681= NL

1198941NS1198941ZE1198941

sdot PS1198941PL1198941

1198682= NL

1198942NS1198942ZE1198942

sdot PS1198942PL1198942

1198621= PSS

1199001PS1199001PM1199001

sdot PL1199001PLL1199001

1198622= PSS

1199002PS1199002PM1199002

sdot PL1199002PLL1199002

(23)


Table 4 Rule table of 1198621

1198621

NL1198942

NS1198942

ZE1198942

PS1198942

PL1198942

NL1198941

PM1199001

PS1199001

PS1199001

PSS1199001

PSS1199001

NS1198941

PL1199001

PM1199001

PS1199001

PSS1199001

PSS1199001

ZE1198941

PL1199001

PL1199001

PM1199001

PS1199001

PSS1199001

PS1198941

PLL1199001

PLL1199001

PLL1199001

PM1199001

PS1199001

PL1198941

PLL1199001

PLL1199001

PLL1199001

PL1199001

PM1199001


1198622

NL1198942

NS1198942

ZE1198942

PS1198942

PL1198942

NL1198941

PM1199002

PL1199002

PL1199002

PLL1199002

PLL1199002

NS1198941

PS1199002

PM1199002

PL1199002

PLL1199002

PLL1199002

ZE1198941

PS1199002

PS1199002

PM1199002

PL1199002

PLL1199002

PS1198941

PSS1199002

PSS1199002

PS1199002

PM1199002

PL1199002

PL1198941

PSS1199002

PSS1199002

PSS1199002

PS1199002

PM1199002

where ldquoNSrdquo ldquoNLrdquo ldquoZErdquo ldquoPSrdquo and ldquoPLrdquo are entitled negativesmall negative large zero positive small and positive largerespectively ldquoPSSrdquo ldquoPSSrdquo ldquoPMrdquo ldquoPLrdquo and ldquoPLLrdquo are entitledpositive very small positive small positive small mediumpositive large and positive very large respectively

Themost important part of designing the fuzzy controlleris to design the rule base It stores the expert knowledgewhichgoverns the behavior of the fuzzy controller The control ruledescribed by the input variables 119865wave (wave force) 119865wind(wind force) and output variables 119862DAC and 119862MPC is givenIf 119865wave is 119868

1and 119865wind is 119868

2 then 119862DAC is 119862

1and 119862

2is 119862DAC

Since thewinddisturbance has larger influence on the FOWTthe value of 119862

1will increase or 119862

1will decrease Similarly

when wave disturbance increases the value of 1198622will follow

the same law The detailed rule tables are shown in Tables 4and 5

5 Simulation and Results

To test the performance of the method proposed in thispaper the new individual pitch control based on combinedDAC and MPC using fuzzy control is implemented in FASTwhere the controller of the wind turbine is implemented in aDynamic Link Library (DLL) file called ldquoDISCONDLLrdquoTheFAST (Fatigue Aerodynamics Structures and Turbulence)code is a comprehensive aeroelastic simulator capable ofpredicting both the extreme and fatigue loads of two- andthree-bladed horizontal-axis wind turbines (HAWTs) Theoffshore FAST structure is shown in Figure 4

As a comparison ldquoNREL offshore 5-MW baseline windturbinerdquomodel whose detailed control parameter is describedin Table 3 is also run in FAST Both models operate aboverated wind speed (114ms) with complex wave conditionsFigure 5 shows the wind condition with average 15msturbulence wind speed and wave condition

The three blades can be controlled separately based ondifferent loads distributed on each blade due to the new indi-vidual pitch controller Figure 6 show that the three bladespitch angle changing individually with different wind and

0 20 40 60 80 100

0

5

10

15

20

25

Time (s)

Win

d an

d w

ave (

ms

)

WindWave

minus5

Figure 5 Wave and wind conditions

0 20 40 60 80 1000

10

20

30

Time (s)

Pitc

h an

gle (

deg)

Blade1Blade2Blade3

Figure 6 Pitch angles of three blades

0 20 40 60 80 1000

2000

4000

6000

Time (s)

Pow

er (k

W)

IPCCPC

Figure 7 Power output

wave conditions In order to analyze the performance of thisnew controller several parameters can reflect that the windturbine fatigue loads are selected Tower fore-aft momentcan refers to fatigue loads distributed on the tower andout-of-plane bending moment in-plane bending momentflapwise moment and edgewise moment represent the bladeroot loads Figures 8 9 10 11 and 12 show a significantloads reduction in both tower and blades compared to thebaseline control due to the well design of wind and wavedisturbance controller To further illustrate the effect of new


0 20 3010 40 50 60 70 80 90 100

0

2

3

Time (s)

IPCCPC

minus1

Tow

er fo

re-a

m

omen

t (Nmiddotm

)

1

times105

Figure 8 Tower fore-aft bending moment

0 20 40 60 80 100

0

1

2

3

4

Time (s)

IPCCPC

minus1

Out

-of-p

lane

ben

ding

mom

ent (

Nmiddotm

)

3010 50 70 90

times104

Figure 9 Out-of-plane bending moment

0 20 40 60 80 100

0

05

1

15

Time (s)

IPCCPC

minus1

minus05

In-p

lane

ben

ding

mom

ent (

Nmiddotm

)

3010 50 70 90

times104

Figure 10 In-plane bending moment

individual controller on fatigue loads reduction a summaryof simulation data is shown in Figure 13 where fatigue loadsdecrease by about 20 to 40 Figures 8 9 and 11 showthat the magnitude becomes smaller with average declinesalso In addition to reducing the fatigue load the controllercan ensure stable power output (Figure 7) as well as showingexcellent robustness of the new pitch controller Simulationresults show that the new individual pitch controller is welldesigned and is highly effective to fatigue loads reduction

0 20 40 60 80 100

0

1

2

3

4

Time (s)

IPCCPC

minus1Flap

wise

mom

ent (

Nmiddotm

)

3010 50 70 90

times104

Figure 11 Flapwise moment

0 20 40 60 80 100

0

05

1

Time (s)

IPCCPC

minus1

minus05Ed

gew

ise m

omen

t (Nmiddotm

)

times104

3010 50 70 90

Figure 12 Edgewise moment

Tower fore-aft bending

moment

Out-of-plane bending

moment

In-planebendingmoment

Flapwisemoment

Edgewisemoment

1

08

06

04

02

0

CPCIPC

Figure 13 Fatigue loads comparison between CPC and IPC

6 Conclusions

In this paper a new individual pitch control is proposed toreduce the fatigue loads caused by wind and wave distur-bancesThe new controller consists of three modules DAC isa component aimed to eliminate the wind disturbancesMPCis a part who can remove the influence of wave disturbanceon the wind turbine and fuzzy control is used to combine thetwo algorithms tomake cooperation work Simulation results


show that the new individual pitch controller shows excellentrobustness to turbulence wind and complex wave conditionsIn summary compared to the baseline pitch controllerthe new individual controller has a better performance inreducing fatigue loads caused by wind and wave disturbancesand therefore is more suitable for FOWT

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National HighTechnology Research and Development Program of China(SS2012AA052302) Fundamental Research Funds for theCentral Universities (ZYGX2012J093) and National NaturalScience Foundation of China (51205046)

References

[1] L Wang S Zuo Y D Song and Z Zhou ldquoVariable torquecontrol of offshore wind turbine on spar floating platform usingadvanced RBF neural networkrdquo Abstract and Applied Analysisvol 2014 Article ID 903493 2014

[2] X Yao X Wang Z Xing Y Liu and J Liu ldquoIndividual pitchcontrol for variable speed turbine blade load mitigationrdquo inProceedings of the IEEE International Conference on Sustain-able Energy Technologies (ICSET rsquo08) pp 769ndash772 SingaporeNovember 2008

[3] E Muhando T Senjyu E Omine T Funabashi and K Chul-Hwan ldquoFunctional modeling for intelligent controller designforMW-class variable speed wecs with independent blade pitchregulationrdquo in Proceedings of the IEEE 2nd International Powerand Energy Conference (PECon rsquo08) pp 413ndash418 Johor BahruMalaysia December 2008

[4] E A Bossanyi ldquoIndividual blade pitch control for load reduc-tionrdquoWind Energy vol 6 no 2 pp 119ndash128 2003

[5] M Jelavic V Petrovic and N Peric ldquoEstimation based individ-ual pitch control of wind turbinerdquoAutomatika vol 51 no 2 pp181ndash192 2010

[6] M Jelavic V Petrovic and N Peric ldquoIndividual pitch controlof wind turbine based on loads estimationrdquo in Proceedings of the34thAnnual Conference of the IEEE Industrial Electronics Society(IECON rsquo08) pp 228ndash234 Orlando Fla USA November 2008

[7] H Zhang J Wang and Y Shi ldquoRobust 119867infin

sliding-modecontrol for Markovian jump systems subject to intermittentobservations and partially known transition probabilitiesrdquo Sys-tems amp Control Letters vol 62 no 12 pp 1114ndash1124 2013

[8] H-R KarimiM Zapateiro andN Luo ldquoRobustmixed1198672119867infin

delayed state feedback control of uncertain neutral systemswithtime-varying delaysrdquo Asian Journal of Control vol 10 no 5 pp569ndash580 2008

[9] H Zhang Y Shi and M Liu ldquoHinfin

step tracking control fornetworked discrete-time nonlinear systems with integral andpredictive actionsrdquo IEEE Transactions on Industrial Informaticsvol 9 no 1 pp 337ndash345 2013

[10] H Zhang Y Shi and B Mu ldquoOptimal 119867infin-based linear-

quadratic regulator tracking control for discrete-time Takagi-Sugeno fuzzy systemswith preview actionsrdquo Journal of Dynamic

Systems Measurement and Control vol 135 no 4 Article ID044501 5 pages 2013

[11] I Munteanu S Bacha A I Bratcu J Guiraud and D RoyeldquoEnergy-reliability optimization of wind energy conversionsystems by sliding mode controlrdquo IEEE Transactions on EnergyConversion vol 23 no 3 pp 975ndash985 2008

[12] Z Zhang W Wang L Li et al ldquoRobust sliding mode guidanceand control for soft landing on small bodiesrdquo Journal of theFranklin Institute vol 349 no 2 pp 493ndash509 2012

[13] F D Kanellos and N D Hatziargyriou ldquoOptimal control ofvariable speed wind turbines in islanded mode of operationrdquoIEEE Transactions on Energy Conversion vol 25 no 4 pp 1142ndash1151 2010

[14] Z Shuai H Zhang J Wang J Li and M Ouyang ldquoLat-eral motion control for four-wheel-independent-drive electricvehicles using optimal torque allocation and dynamic messagepriority schedulingrdquo Control Engineering Practice vol 24 pp55ndash66 2014

[15] Z Xing L Chen H Sun and Z Wang ldquoStrategies study ofindividual variable pitch controlrdquo Proceedings of the ChineseSociety of Electrical Engineering vol 31 no 26 pp 131ndash138 2011

[16] L Wang B Wang Y D Song et al ldquoFatigue loads alleviation offloating offshore wind turbine using individual pitch controlrdquoAdvances in Vibration Engineering vol 12 no 4 pp 377ndash3902013

[17] H Namik andK Stol ldquoIndividual blade pitch control of floatingoffshore wind turbinesrdquo Wind Energy vol 13 no 1 pp 74ndash852010

[18] Y H Bae and M H Kim ldquoRotor-floater-tether coupleddynamics including second-order sum-frequency wave loadsfor a mono-column-TLP-type FOWT (floating offshore windturbine)rdquo Ocean Engineering vol 61 pp 109ndash122 2013

[19] E N Wayman Coupled dynamics and economic analysis offloating wind turbine systems [MS dissertation] DepartmentofMechanical EngineeringMassachusetts Institute of Technol-ogy Cambridge Mass USA 2006

[20] D Chen K Huang V Bretel and L Hou ldquoComparison ofstructural properties between monopile and tripod offshorewind-turbine support structuresrdquoAdvances inMechanical Engi-neering vol 2013 Article ID 175684 9 pages 2013

[21] D S Dolan and P Lehn ldquoSimulation model of wind turbine 3ptorque oscillations due to wind shear and tower shadowrdquo IEEETransactions on Energy Conversion vol 21 no 3 pp 717ndash7242006

[22] DNV ldquoDesign of offshore wind turbine structuresrdquo OffshoreStandard DNV-OS-J101 Det Norske Veritas Oslo Norway2010

[23] S Zuo Y D Song L Wang and Q-W Song ldquoComputationallyinexpensive approach for pitch control of offshore wind turbineon barge floating platformrdquo The Scientific World Journal vol2013 Article ID 357849 9 pages 2013

[24] M J Balas Y J Lee and L Kendall ldquoDisturbance tracking con-trol theory with application to horizontal axis wind turbinesrdquoin Proceedings of the ASME Wind Energy Symposium pp 95ndash99 Reno Nev USA January 1998

[25] GHHostetter C J Savant andR T StefaniDesign of FeedbackControl Systems Saunders College Publishing New York NYUSA 2nd edition 1989

[26] T Knudsen T Bak andM Soltani ldquoPredictionmodels for windspeed at turbine locations in a wind farmrdquoWind Energy vol 14no 7 pp 877ndash894 2011


[27] P Shi E-K Boukas and R K Agarwal ldquoKalman filtering forcontinuous-time uncertain systems with Markovian jumpingparametersrdquo IEEE Transactions on Automatic Control vol 44no 8 pp 1592ndash1597 1999

[28] J M Jonkman S Butterfield W Musial and G Scott ldquoDefi-nition of a 5-MW reference wind turbine for offshore systemdevelopmentrdquo Tech Rep TP-500-38060 National RenewableEnergy Laboratory 2007

[29] H Zhang Y Shi and J Wang ldquoOn energy-to-peak filtering fornonuniformly sampled nonlinear systems a Markovian jumpsystem approachrdquo IEEE Transactions on Fuzzy Systems vol 22no 1 pp 212ndash222 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


loads can be transformed into stationary variables like rotortilt and yaw moments The SISO systems use PI controllersto reduce the tilt and yaw moments However FOWTis a strongly coupled nonlinear time-varying system withcomplex disturbances and obviously SISO cannot accountfor these disturbances This can be improved by 119867

infincontrol

in [7ndash10] sliding mode in [11 12] optimal control in [13 14]or linear quadratic Gaussian control (LQG) [15 16]The LQGcontroller consists of a linear model of the wind turbine anda state estimator used to estimate the states of themodel fromknown turbine variables byKalmanfilter A control lawwhichcanminimize the quadratic cost function of the wind turbinesates was used to make the control This method successfullybrings about a significant loads reduction but has no effect onthe fatigue loads of the stationary parts

Another way to deal with the strong disturbance isdisturbance-accommodating controllers implemented byNamik and Stol [17] on Spar-Buoyfloatingwind turbineDACcontroller consisted of a state regulation term with full statefeedback controllers and a disturbance estimator is used tolower the influence of persistent disturbances like turbulencewind on the wind turbine Compared to the original baselinecontroller designed by Jonkman theDAC reduces tower fore-aft and side-side bending fatigue loads greatly But the dis-turbance estimator in DAC did not consider much influenceof the wave To study the impact of wave on wind turbineBae and Kim [18] investigated the wave-load effect on 5 MWmonocolumn TLP-type FOWT The sum-frequency waveloading is applied in both coupled and uncoupled conditionthe results show that there exist complicated coupling effectsamong wind turbine variables and wave condition should befully considered when designing the FOWT

It is notable that the above method cannot bring allthe disturbances into consideration Wind as well as waveshould be fully considered In this paper a new individualpitch control based on combined DAC and MPC usingfuzzy control is proposed DAC can deal with persistentdisturbances like wind but ignore the wave who is a typeof periodic disturbance MPC can reduce the structuraloscillation and decrease the fatigue loads caused by incidentwaves through tracking the state trajectory of the undisturbedreference model So the new individual pitch control strategythat combines the two methods through fuzzy control canbetter deal with wind and wave disturbances

Section 2 introduces the configuration of the floatingoffshore wind turbine Section 3 gives a brief introduction tothe disturbances such as wind and wave Section 4 focuseson the design of the new controller First give a detailedintroduction to theDACandMPC and then a new individualpitch controller combined with DAC and MPC comes intobeing through fuzzy control In Section 5 the new individualpitch controller is tested and proved to be effective for thefatigue loads reduction

2 Wind Turbine Configurations

The wind turbine used in this paper is a model called ldquoNRELoffshore 5-MW baseline wind turbinerdquo from NREL This

is a realistic model of a three-bladed upwind 5-MW windturbine mounted on a barge with a spread-mooring systemdeveloped at MIT through a contract with NREL [19] Thegross properties of the wind turbine are given in Table 1 andthe platform properties are given in Table 2

3 Disturbance Loads Modeling

Wind turbine is not a static structure Due to rotatingrotor turbulent wind complex wave conditions huge slendercomponents and complex design the structural vibrationswhich can significantly contribute to dynamic fatigue loadingof the structure are introduced to the system Among all thefactors cause fatigue loads of wind turbine wave and windshould be first taken into consideration

31 Wind Loads Wind turbine components exposed in windcondition will cause movement because of aerodynamicsbetween wind flow and wind turbine structure That is thereason wind turbine can be used to generate electricity Windshear and tower shadowwill introduce additional disturbanceto the wind turbine systemWindmodel is important to loadsdefinition as well as design of the wind turbine and platformsystem The accuracy of wind parameters affects the designof wind turbine system significantly The wind load can bemodeled by formulas based on lift theory [20]

119865wind =1

2120588air]wind119878119862119911

]wind = ]mean + ]ws + ]ts + ]wk(1)

where 119865wind is the wind forces on blade 120588air is air density119878 is the blade surface area and ]wind is the wind speedwhich consists of mean wind speed ]mean the wind shearcomponent ]ws the tower shadow component ]ts and farwake component of one preceding wind turbine ]wk Windshear and the tower shadow which lead to significant vibra-tion of the structure were specified in [21]

32 Wave Loads In addition to wind condition wave force isalso a main contributor to loads on the structure The waveforce can be calculated based on Airyrsquos linear theory wherethe horizontal and vertical wave velocity are introduced in[22]

119865wave =1

2120588water119862119863119863 |119906| 119906 + 120588water119862119868

1205871198632

4119886119909

119906 =120596ℎ

2

cos 119896119910sin 119896119889

cos (119896119909 minus 120596119905)

(2)

where 119865wave is the wave force on platform 120588water is waterdensity 119862

119863and 119862

119868are the drag and inertia coefficients

respectively 119863 is the diameter of the structural member 119906

which is the horizontal velocity of water and 119886119909is the water-

particle acceleration which can be obtained by means of 119886119909asymp

120597119906120597119905 The first part of this formula can be described as thedrag term who is proportional to the square of the watervelocity Another part is referred to the inertial term It isproportional to the water acceleration













4 Controller Design




= 119860119909 + 119861119906 + 119861119889119906119889 (3)

119910 = 119862119909 + 119863119906 + 119863119889119906119889 (4)




119889relates to


and 119876

119906119889= 119866119911 (5)

= 119876119911 (6)




119906 = minus119870119909 + 119866119889119911 (7)


= (119860 minus 119861119870) 119909 + (119861119866119889+ 119861119889119866) 119911 (8)

119861119866119889+ 119861119889119866 = 0 (9)


= 119860120596 + 119861119906

119910 = 119862120596 + 119863119906

(10)

where 119860 = [119860 119861119889119866

0 119876] 119861 = [

119861

0] and 119862 = [119862 119863

119889119866] The state



120596 = 119860 + 119861119906 + 119870119890(119910 minus 119910) (11)

119910 = 119862 + 119863119906 (12)


119890119862) 119890 (13)



Controller

Tc(120595)

Δulowast

ud

u

y

z

++

+

+

minus

minus

Δx

xTminus1

c(120595)


Estimator


Saturation


Δulowast

nr

Δunr

Δu

Δxnr

uop

xop

nrΔxnr nr




119888(120595) 119879

119904(120595) and 119879

0(120595) transform


119906nr = minus119870nr119909nr + 119866119889nr (14)

119866119889nr = minus119861

+

nr119861119889nr119866 (15)


119906 = minus119879119888(120595)119870nr119879

minus1

119904(120595) 119909 + 119879

119888(120595)119866

119889nr (16)



minus1

119888(120595) 119906

+ 119870119890nr119879minus1

0(120595) 119910

= (119860nr minus 119870119890nr119862nr) nr

+ [119861nr119879minus1

119888(120595) 119870

119890nr119879minus1

0(120595)] [

119906

119910]

= (119860nr minus 119870119890nr119862nr) nr + 119864 (120595)119881

(17)






119909 (119896 + 1) = 119860120596119909 (119896) + 119861

120596119906 (119896)

119910 (119896) = 119862120596119909 (119896)

(18)

where 119860120596 119861120596 and 119862




119909119903(119896 + 1) = 119860

119903119909119903(119896) + 119861

119903119906119888(119896)

119910119903(119896) = 119862

119903119909119903(119896)

(19)

where 119860119903 119861119903 and 119862



119909119888(119896 + 1) = 119860

119888119909119888(119896) + 119861

119888119910119903(119896) + 119864

119888119903 (119896)

119906119888(119896) = 119862

119888119909119888(119896) + 119863

119888119910119903(119896) + 119865

119888119903 (119896)

(20)




min119906(119896)119906(119896+119879minus1)

119879

sum

119896=1198960

1003817100381710038171003817119909(119896) minus 119909119903(119896)

1003817100381710038171003817

2

119876+ 119906(119896)

2

119877

st

119909 (1198960) = 1199090

119909119903(1198960) = 1199091199030

119909 (119896 + 1) = 119860120596119909 (119896) + 119861

120596119906 (119896)

119910 (119896) = 119862120596119909 (119896)

119909119903(119896 + 1) = 119860

119903119909119903(119896) + 119861

119903119906119888(119896)

119910119903(119896) = 119862

119903119909119903(119896)

119909119888(119896 + 1) = 119860

119888119909119888(119896) + 119861

119888119910119903(119896) + 119864

119888119903 (119896)

119906119888(119896) = 119862

119888119909119888(119896) + 119863

119888119910119903(119896) + 119865

119888119903 (119896)

119909 (119896) isin 119883

119906 (119896) isin 119880

119896 = 1198960 119896

0+ 119879

(21)




119901



120579angle (119905) = 119896119901119890 (119905) + 119896

119894int

119905

0

119890 (120591) 119889120591 (22)

MPC Nonlinearwind

turbine model

u(k)

r(k)

y(k)

x(k)A B

Referencemodel

Stateestimator










Controller




MPC

DAC


Coefficients

++

+

+

+ ++

Δulowast

Tc(120595)

u

ud

y

Δu

Saturation

minus

minus


Δx

x

z

Tminus1

c(120595)

Ts(120595)

CDAC CDAC

Δulowast

nr

Δunr


uop

nrx

op

Δxnr


Δxnr nr



Control system

Windinflow

Aerodyna-mics

Aerodyna-mics

Rotordynamics

Drivetraindynamics

Powergeneration

TurbSim

Nacelle dynamics

Tower dynamics

Platform dynamics

Mooring dynamics

Wave andcurrents

Hydrodyn-amics




1 11986821198621 and119862

2


1198941NS1198941ZE1198941

sdot PS1198941PL1198941

1198682= NL

1198942NS1198942ZE1198942

sdot PS1198942PL1198942

1198621= PSS

1199001PS1199001PM1199001

sdot PL1199001PLL1199001

1198622= PSS

1199002PS1199002PM1199002

sdot PL1199002PLL1199002

(23)



1198621

NL1198942

NS1198942

ZE1198942

PS1198942

PL1198942

NL1198941

PM1199001

PS1199001

PS1199001

PSS1199001

PSS1199001

NS1198941

PL1199001

PM1199001

PS1199001

PSS1199001

PSS1199001

ZE1198941

PL1199001

PL1199001

PM1199001

PS1199001

PSS1199001

PS1198941

PLL1199001

PLL1199001

PLL1199001

PM1199001

PS1199001

PL1198941

PLL1199001

PLL1199001

PLL1199001

PL1199001

PM1199001


1198622

NL1198942

NS1198942

ZE1198942

PS1198942

PL1198942

NL1198941

PM1199002

PL1199002

PL1199002

PLL1199002

PLL1199002

NS1198941

PS1199002

PM1199002

PL1199002

PLL1199002

PLL1199002

ZE1198941

PS1199002

PS1199002

PM1199002

PL1199002

PLL1199002

PS1198941

PSS1199002

PSS1199002

PS1199002

PM1199002

PL1199002

PL1198941

PSS1199002

PSS1199002

PSS1199002

PS1199002

PM1199002



1and 119865wind is 119868

2 then 119862DAC is 119862

1and 119862

2is 119862DAC










0 20 40 60 80 100

0

5

10

15

20

25

Time (s)

Win

d an

d w

ave (

ms

)

WindWave

minus5


0 20 40 60 80 1000

10

20

30

Time (s)

Pitc

h an

gle (

deg)

Blade1Blade2Blade3


0 20 40 60 80 1000

2000

4000

6000

Time (s)

Pow

er (k

W)

IPCCPC




0 20 3010 40 50 60 70 80 90 100

0

2

3

Time (s)

IPCCPC

minus1

Tow

er fo

re-a

m

omen

t (Nmiddotm

)

1

times105


0 20 40 60 80 100

0

1

2

3

4

Time (s)

IPCCPC

minus1

Out

-of-p

lane

ben

ding

mom

ent (

Nmiddotm

)

3010 50 70 90

times104


0 20 40 60 80 100

0

05

1

15

Time (s)

IPCCPC

minus1

minus05

In-p

lane

ben

ding

mom

ent (

Nmiddotm

)

3010 50 70 90

times104



0 20 40 60 80 100

0

1

2

3

4

Time (s)

IPCCPC

minus1Flap

wise

mom

ent (

Nmiddotm

)

3010 50 70 90

times104


0 20 40 60 80 100

0

05

1

Time (s)

IPCCPC

minus1

minus05Ed

gew

ise m

omen

t (Nmiddotm

)

times104

3010 50 70 90



moment


moment


Flapwisemoment

Edgewisemoment

1

08

06

04

02

0

CPCIPC


6 Conclusions






Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





















4 Controller Design




= 119860119909 + 119861119906 + 119861119889119906119889 (3)

119910 = 119862119909 + 119863119906 + 119863119889119906119889 (4)




119889relates to


and 119876

119906119889= 119866119911 (5)

= 119876119911 (6)




119906 = minus119870119909 + 119866119889119911 (7)


= (119860 minus 119861119870) 119909 + (119861119866119889+ 119861119889119866) 119911 (8)

119861119866119889+ 119861119889119866 = 0 (9)


= 119860120596 + 119861119906

119910 = 119862120596 + 119863119906

(10)

where 119860 = [119860 119861119889119866

0 119876] 119861 = [

119861

0] and 119862 = [119862 119863

119889119866] The state



120596 = 119860 + 119861119906 + 119870119890(119910 minus 119910) (11)

119910 = 119862 + 119863119906 (12)


119890119862) 119890 (13)



Controller

Tc(120595)

Δulowast

ud

u

y

z

++

+

+

minus

minus

Δx

xTminus1

c(120595)


Estimator


Saturation


Δulowast

nr

Δunr

Δu

Δxnr

uop

xop

nrΔxnr nr




119888(120595) 119879

119904(120595) and 119879

0(120595) transform


119906nr = minus119870nr119909nr + 119866119889nr (14)

119866119889nr = minus119861

+

nr119861119889nr119866 (15)


119906 = minus119879119888(120595)119870nr119879

minus1

119904(120595) 119909 + 119879

119888(120595)119866

119889nr (16)



minus1

119888(120595) 119906

+ 119870119890nr119879minus1

0(120595) 119910

= (119860nr minus 119870119890nr119862nr) nr

+ [119861nr119879minus1

119888(120595) 119870

119890nr119879minus1

0(120595)] [

119906

119910]

= (119860nr minus 119870119890nr119862nr) nr + 119864 (120595)119881

(17)






119909 (119896 + 1) = 119860120596119909 (119896) + 119861

120596119906 (119896)

119910 (119896) = 119862120596119909 (119896)

(18)

where 119860120596 119861120596 and 119862




119909119903(119896 + 1) = 119860

119903119909119903(119896) + 119861

119903119906119888(119896)

119910119903(119896) = 119862

119903119909119903(119896)

(19)

where 119860119903 119861119903 and 119862



119909119888(119896 + 1) = 119860

119888119909119888(119896) + 119861

119888119910119903(119896) + 119864

119888119903 (119896)

119906119888(119896) = 119862

119888119909119888(119896) + 119863

119888119910119903(119896) + 119865

119888119903 (119896)

(20)




min119906(119896)119906(119896+119879minus1)

119879

sum

119896=1198960

1003817100381710038171003817119909(119896) minus 119909119903(119896)

1003817100381710038171003817

2

119876+ 119906(119896)

2

119877

st

119909 (1198960) = 1199090

119909119903(1198960) = 1199091199030

119909 (119896 + 1) = 119860120596119909 (119896) + 119861

120596119906 (119896)

119910 (119896) = 119862120596119909 (119896)

119909119903(119896 + 1) = 119860

119903119909119903(119896) + 119861

119903119906119888(119896)

119910119903(119896) = 119862

119903119909119903(119896)

119909119888(119896 + 1) = 119860

119888119909119888(119896) + 119861

119888119910119903(119896) + 119864

119888119903 (119896)

119906119888(119896) = 119862

119888119909119888(119896) + 119863

119888119910119903(119896) + 119865

119888119903 (119896)

119909 (119896) isin 119883

119906 (119896) isin 119880

119896 = 1198960 119896

0+ 119879

(21)




119901



120579angle (119905) = 119896119901119890 (119905) + 119896

119894int

119905

0

119890 (120591) 119889120591 (22)

MPC Nonlinearwind

turbine model

u(k)

r(k)

y(k)

x(k)A B

Referencemodel

Stateestimator










Controller




MPC

DAC


Coefficients

++

+

+

+ ++

Δulowast

Tc(120595)

u

ud

y

Δu

Saturation

minus

minus


Δx

x

z

Tminus1

c(120595)

Ts(120595)

CDAC CDAC

Δulowast

nr

Δunr


uop

nrx

op

Δxnr


Δxnr nr



Control system

Windinflow

Aerodyna-mics

Aerodyna-mics

Rotordynamics

Drivetraindynamics

Powergeneration

TurbSim

Nacelle dynamics

Tower dynamics

Platform dynamics

Mooring dynamics

Wave andcurrents

Hydrodyn-amics




1 11986821198621 and119862

2


1198941NS1198941ZE1198941

sdot PS1198941PL1198941

1198682= NL

1198942NS1198942ZE1198942

sdot PS1198942PL1198942

1198621= PSS

1199001PS1199001PM1199001

sdot PL1199001PLL1199001

1198622= PSS

1199002PS1199002PM1199002

sdot PL1199002PLL1199002

(23)



1198621

NL1198942

NS1198942

ZE1198942

PS1198942

PL1198942

NL1198941

PM1199001

PS1199001

PS1199001

PSS1199001

PSS1199001

NS1198941

PL1199001

PM1199001

PS1199001

PSS1199001

PSS1199001

ZE1198941

PL1199001

PL1199001

PM1199001

PS1199001

PSS1199001

PS1198941

PLL1199001

PLL1199001

PLL1199001

PM1199001

PS1199001

PL1198941

PLL1199001

PLL1199001

PLL1199001

PL1199001

PM1199001


1198622

NL1198942

NS1198942

ZE1198942

PS1198942

PL1198942

NL1198941

PM1199002

PL1199002

PL1199002

PLL1199002

PLL1199002

NS1198941

PS1199002

PM1199002

PL1199002

PLL1199002

PLL1199002

ZE1198941

PS1199002

PS1199002

PM1199002

PL1199002

PLL1199002

PS1198941

PSS1199002

PSS1199002

PS1199002

PM1199002

PL1199002

PL1198941

PSS1199002

PSS1199002

PSS1199002

PS1199002

PM1199002



1and 119865wind is 119868

2 then 119862DAC is 119862

1and 119862

2is 119862DAC










0 20 40 60 80 100

0

5

10

15

20

25

Time (s)

Win

d an

d w

ave (

ms

)

WindWave

minus5


0 20 40 60 80 1000

10

20

30

Time (s)

Pitc

h an

gle (

deg)

Blade1Blade2Blade3


0 20 40 60 80 1000

2000

4000

6000

Time (s)

Pow

er (k

W)

IPCCPC




0 20 3010 40 50 60 70 80 90 100

0

2

3

Time (s)

IPCCPC

minus1

Tow

er fo

re-a

m

omen

t (Nmiddotm

)

1

times105


0 20 40 60 80 100

0

1

2

3

4

Time (s)

IPCCPC

minus1

Out

-of-p

lane

ben

ding

mom

ent (

Nmiddotm

)

3010 50 70 90

times104


0 20 40 60 80 100

0

05

1

15

Time (s)

IPCCPC

minus1

minus05

In-p

lane

ben

ding

mom

ent (

Nmiddotm

)

3010 50 70 90

times104



0 20 40 60 80 100

0

1

2

3

4

Time (s)

IPCCPC

minus1Flap

wise

mom

ent (

Nmiddotm

)

3010 50 70 90

times104


0 20 40 60 80 100

0

05

1

Time (s)

IPCCPC

minus1

minus05Ed

gew

ise m

omen

t (Nmiddotm

)

times104

3010 50 70 90



moment


moment


Flapwisemoment

Edgewisemoment

1

08

06

04

02

0

CPCIPC


6 Conclusions






Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Controller

Tc(120595)

Δulowast

ud

u

y

z

++

+

+

minus

minus

Δx

xTminus1

c(120595)


Estimator


Saturation


Δulowast

nr

Δunr

Δu

Δxnr

uop

xop

nrΔxnr nr




119888(120595) 119879

119904(120595) and 119879

0(120595) transform


119906nr = minus119870nr119909nr + 119866119889nr (14)

119866119889nr = minus119861

+

nr119861119889nr119866 (15)


119906 = minus119879119888(120595)119870nr119879

minus1

119904(120595) 119909 + 119879

119888(120595)119866

119889nr (16)



minus1

119888(120595) 119906

+ 119870119890nr119879minus1

0(120595) 119910

= (119860nr minus 119870119890nr119862nr) nr

+ [119861nr119879minus1

119888(120595) 119870

119890nr119879minus1

0(120595)] [

119906

119910]

= (119860nr minus 119870119890nr119862nr) nr + 119864 (120595)119881

(17)






119909 (119896 + 1) = 119860120596119909 (119896) + 119861

120596119906 (119896)

119910 (119896) = 119862120596119909 (119896)

(18)

where 119860120596 119861120596 and 119862




119909119903(119896 + 1) = 119860

119903119909119903(119896) + 119861

119903119906119888(119896)

119910119903(119896) = 119862

119903119909119903(119896)

(19)

where 119860119903 119861119903 and 119862



119909119888(119896 + 1) = 119860

119888119909119888(119896) + 119861

119888119910119903(119896) + 119864

119888119903 (119896)

119906119888(119896) = 119862

119888119909119888(119896) + 119863

119888119910119903(119896) + 119865

119888119903 (119896)

(20)




min119906(119896)119906(119896+119879minus1)

119879

sum

119896=1198960

1003817100381710038171003817119909(119896) minus 119909119903(119896)

1003817100381710038171003817

2

119876+ 119906(119896)

2

119877

st

119909 (1198960) = 1199090

119909119903(1198960) = 1199091199030

119909 (119896 + 1) = 119860120596119909 (119896) + 119861

120596119906 (119896)

119910 (119896) = 119862120596119909 (119896)

119909119903(119896 + 1) = 119860

119903119909119903(119896) + 119861

119903119906119888(119896)

119910119903(119896) = 119862

119903119909119903(119896)

119909119888(119896 + 1) = 119860

119888119909119888(119896) + 119861

119888119910119903(119896) + 119864

119888119903 (119896)

119906119888(119896) = 119862

119888119909119888(119896) + 119863

119888119910119903(119896) + 119865

119888119903 (119896)

119909 (119896) isin 119883

119906 (119896) isin 119880

119896 = 1198960 119896

0+ 119879

(21)




119901



120579angle (119905) = 119896119901119890 (119905) + 119896

119894int

119905

0

119890 (120591) 119889120591 (22)

MPC Nonlinearwind

turbine model

u(k)

r(k)

y(k)

x(k)A B

Referencemodel

Stateestimator










Controller




MPC

DAC


Coefficients

++

+

+

+ ++

Δulowast

Tc(120595)

u

ud

y

Δu

Saturation

minus

minus


Δx

x

z

Tminus1

c(120595)

Ts(120595)

CDAC CDAC

Δulowast

nr

Δunr


uop

nrx

op

Δxnr


Δxnr nr



Control system

Windinflow

Aerodyna-mics

Aerodyna-mics

Rotordynamics

Drivetraindynamics

Powergeneration

TurbSim

Nacelle dynamics

Tower dynamics

Platform dynamics

Mooring dynamics

Wave andcurrents

Hydrodyn-amics




1 11986821198621 and119862

2


1198941NS1198941ZE1198941

sdot PS1198941PL1198941

1198682= NL

1198942NS1198942ZE1198942

sdot PS1198942PL1198942

1198621= PSS

1199001PS1199001PM1199001

sdot PL1199001PLL1199001

1198622= PSS

1199002PS1199002PM1199002

sdot PL1199002PLL1199002

(23)



1198621

NL1198942

NS1198942

ZE1198942

PS1198942

PL1198942

NL1198941

PM1199001

PS1199001

PS1199001

PSS1199001

PSS1199001

NS1198941

PL1199001

PM1199001

PS1199001

PSS1199001

PSS1199001

ZE1198941

PL1199001

PL1199001

PM1199001

PS1199001

PSS1199001

PS1198941

PLL1199001

PLL1199001

PLL1199001

PM1199001

PS1199001

PL1198941

PLL1199001

PLL1199001

PLL1199001

PL1199001

PM1199001


1198622

NL1198942

NS1198942

ZE1198942

PS1198942

PL1198942

NL1198941

PM1199002

PL1199002

PL1199002

PLL1199002

PLL1199002

NS1198941

PS1199002

PM1199002

PL1199002

PLL1199002

PLL1199002

ZE1198941

PS1199002

PS1199002

PM1199002

PL1199002

PLL1199002

PS1198941

PSS1199002

PSS1199002

PS1199002

PM1199002

PL1199002

PL1198941

PSS1199002

PSS1199002

PSS1199002

PS1199002

PM1199002



1and 119865wind is 119868

2 then 119862DAC is 119862

1and 119862

2is 119862DAC










0 20 40 60 80 100

0

5

10

15

20

25

Time (s)

Win

d an

d w

ave (

ms

)

WindWave

minus5


0 20 40 60 80 1000

10

20

30

Time (s)

Pitc

h an

gle (

deg)

Blade1Blade2Blade3


0 20 40 60 80 1000

2000

4000

6000

Time (s)

Pow

er (k

W)

IPCCPC




0 20 3010 40 50 60 70 80 90 100

0

2

3

Time (s)

IPCCPC

minus1

Tow

er fo

re-a

m

omen

t (Nmiddotm

)

1

times105


0 20 40 60 80 100

0

1

2

3

4

Time (s)

IPCCPC

minus1

Out

-of-p

lane

ben

ding

mom

ent (

Nmiddotm

)

3010 50 70 90

times104


0 20 40 60 80 100

0

05

1

15

Time (s)

IPCCPC

minus1

minus05

In-p

lane

ben

ding

mom

ent (

Nmiddotm

)

3010 50 70 90

times104



0 20 40 60 80 100

0

1

2

3

4

Time (s)

IPCCPC

minus1Flap

wise

mom

ent (

Nmiddotm

)

3010 50 70 90

times104


0 20 40 60 80 100

0

05

1

Time (s)

IPCCPC

minus1

minus05Ed

gew

ise m

omen

t (Nmiddotm

)

times104

3010 50 70 90



moment


moment


Flapwisemoment

Edgewisemoment

1

08

06

04

02

0

CPCIPC


6 Conclusions






Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











min119906(119896)119906(119896+119879minus1)

119879

sum

119896=1198960

1003817100381710038171003817119909(119896) minus 119909119903(119896)

1003817100381710038171003817

2

119876+ 119906(119896)

2

119877

st

119909 (1198960) = 1199090

119909119903(1198960) = 1199091199030

119909 (119896 + 1) = 119860120596119909 (119896) + 119861

120596119906 (119896)

119910 (119896) = 119862120596119909 (119896)

119909119903(119896 + 1) = 119860

119903119909119903(119896) + 119861

119903119906119888(119896)

119910119903(119896) = 119862

119903119909119903(119896)

119909119888(119896 + 1) = 119860

119888119909119888(119896) + 119861

119888119910119903(119896) + 119864

119888119903 (119896)

119906119888(119896) = 119862

119888119909119888(119896) + 119863

119888119910119903(119896) + 119865

119888119903 (119896)

119909 (119896) isin 119883

119906 (119896) isin 119880

119896 = 1198960 119896

0+ 119879

(21)




119901



120579angle (119905) = 119896119901119890 (119905) + 119896

119894int

119905

0

119890 (120591) 119889120591 (22)

MPC Nonlinearwind

turbine model

u(k)

r(k)

y(k)

x(k)A B

Referencemodel

Stateestimator










Controller




MPC

DAC


Coefficients

++

+

+

+ ++

Δulowast

Tc(120595)

u

ud

y

Δu

Saturation

minus

minus


Δx

x

z

Tminus1

c(120595)

Ts(120595)

CDAC CDAC

Δulowast

nr

Δunr


uop

nrx

op

Δxnr


Δxnr nr



Control system

Windinflow

Aerodyna-mics

Aerodyna-mics

Rotordynamics

Drivetraindynamics

Powergeneration

TurbSim

Nacelle dynamics

Tower dynamics

Platform dynamics

Mooring dynamics

Wave andcurrents

Hydrodyn-amics




1 11986821198621 and119862

2


1198941NS1198941ZE1198941

sdot PS1198941PL1198941

1198682= NL

1198942NS1198942ZE1198942

sdot PS1198942PL1198942

1198621= PSS

1199001PS1199001PM1199001

sdot PL1199001PLL1199001

1198622= PSS

1199002PS1199002PM1199002

sdot PL1199002PLL1199002

(23)



1198621

NL1198942

NS1198942

ZE1198942

PS1198942

PL1198942

NL1198941

PM1199001

PS1199001

PS1199001

PSS1199001

PSS1199001

NS1198941

PL1199001

PM1199001

PS1199001

PSS1199001

PSS1199001

ZE1198941

PL1199001

PL1199001

PM1199001

PS1199001

PSS1199001

PS1198941

PLL1199001

PLL1199001

PLL1199001

PM1199001

PS1199001

PL1198941

PLL1199001

PLL1199001

PLL1199001

PL1199001

PM1199001


1198622

NL1198942

NS1198942

ZE1198942

PS1198942

PL1198942

NL1198941

PM1199002

PL1199002

PL1199002

PLL1199002

PLL1199002

NS1198941

PS1199002

PM1199002

PL1199002

PLL1199002

PLL1199002

ZE1198941

PS1199002

PS1199002

PM1199002

PL1199002

PLL1199002

PS1198941

PSS1199002

PSS1199002

PS1199002

PM1199002

PL1199002

PL1198941

PSS1199002

PSS1199002

PSS1199002

PS1199002

PM1199002



1and 119865wind is 119868

2 then 119862DAC is 119862

1and 119862

2is 119862DAC










0 20 40 60 80 100

0

5

10

15

20

25

Time (s)

Win

d an

d w

ave (

ms

)

WindWave

minus5


0 20 40 60 80 1000

10

20

30

Time (s)

Pitc

h an

gle (

deg)

Blade1Blade2Blade3


0 20 40 60 80 1000

2000

4000

6000

Time (s)

Pow

er (k

W)

IPCCPC




0 20 3010 40 50 60 70 80 90 100

0

2

3

Time (s)

IPCCPC

minus1

Tow

er fo

re-a

m

omen

t (Nmiddotm

)

1

times105


0 20 40 60 80 100

0

1

2

3

4

Time (s)

IPCCPC

minus1

Out

-of-p

lane

ben

ding

mom

ent (

Nmiddotm

)

3010 50 70 90

times104


0 20 40 60 80 100

0

05

1

15

Time (s)

IPCCPC

minus1

minus05

In-p

lane

ben

ding

mom

ent (

Nmiddotm

)

3010 50 70 90

times104



0 20 40 60 80 100

0

1

2

3

4

Time (s)

IPCCPC

minus1Flap

wise

mom

ent (

Nmiddotm

)

3010 50 70 90

times104


0 20 40 60 80 100

0

05

1

Time (s)

IPCCPC

minus1

minus05Ed

gew

ise m

omen

t (Nmiddotm

)

times104

3010 50 70 90



moment


moment


Flapwisemoment

Edgewisemoment

1

08

06

04

02

0

CPCIPC


6 Conclusions






Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Controller




MPC

DAC


Coefficients

++

+

+

+ ++

Δulowast

Tc(120595)

u

ud

y

Δu

Saturation

minus

minus


Δx

x

z

Tminus1

c(120595)

Ts(120595)

CDAC CDAC

Δulowast

nr

Δunr


uop

nrx

op

Δxnr


Δxnr nr



Control system

Windinflow

Aerodyna-mics

Aerodyna-mics

Rotordynamics

Drivetraindynamics

Powergeneration

TurbSim

Nacelle dynamics

Tower dynamics

Platform dynamics

Mooring dynamics

Wave andcurrents

Hydrodyn-amics




1 11986821198621 and119862

2


1198941NS1198941ZE1198941

sdot PS1198941PL1198941

1198682= NL

1198942NS1198942ZE1198942

sdot PS1198942PL1198942

1198621= PSS

1199001PS1199001PM1199001

sdot PL1199001PLL1199001

1198622= PSS

1199002PS1199002PM1199002

sdot PL1199002PLL1199002

(23)



1198621

NL1198942

NS1198942

ZE1198942

PS1198942

PL1198942

NL1198941

PM1199001

PS1199001

PS1199001

PSS1199001

PSS1199001

NS1198941

PL1199001

PM1199001

PS1199001

PSS1199001

PSS1199001

ZE1198941

PL1199001

PL1199001

PM1199001

PS1199001

PSS1199001

PS1198941

PLL1199001

PLL1199001

PLL1199001

PM1199001

PS1199001

PL1198941

PLL1199001

PLL1199001

PLL1199001

PL1199001

PM1199001


1198622

NL1198942

NS1198942

ZE1198942

PS1198942

PL1198942

NL1198941

PM1199002

PL1199002

PL1199002

PLL1199002

PLL1199002

NS1198941

PS1199002

PM1199002

PL1199002

PLL1199002

PLL1199002

ZE1198941

PS1199002

PS1199002

PM1199002

PL1199002

PLL1199002

PS1198941

PSS1199002

PSS1199002

PS1199002

PM1199002

PL1199002

PL1198941

PSS1199002

PSS1199002

PSS1199002

PS1199002

PM1199002



1and 119865wind is 119868

2 then 119862DAC is 119862

1and 119862

2is 119862DAC










0 20 40 60 80 100

0

5

10

15

20

25

Time (s)

Win

d an

d w

ave (

ms

)

WindWave

minus5


0 20 40 60 80 1000

10

20

30

Time (s)

Pitc

h an

gle (

deg)

Blade1Blade2Blade3


0 20 40 60 80 1000

2000

4000

6000

Time (s)

Pow

er (k

W)

IPCCPC




0 20 3010 40 50 60 70 80 90 100

0

2

3

Time (s)

IPCCPC

minus1

Tow

er fo

re-a

m

omen

t (Nmiddotm

)

1

times105


0 20 40 60 80 100

0

1

2

3

4

Time (s)

IPCCPC

minus1

Out

-of-p

lane

ben

ding

mom

ent (

Nmiddotm

)

3010 50 70 90

times104


0 20 40 60 80 100

0

05

1

15

Time (s)

IPCCPC

minus1

minus05

In-p

lane

ben

ding

mom

ent (

Nmiddotm

)

3010 50 70 90

times104



0 20 40 60 80 100

0

1

2

3

4

Time (s)

IPCCPC

minus1Flap

wise

mom

ent (

Nmiddotm

)

3010 50 70 90

times104


0 20 40 60 80 100

0

05

1

Time (s)

IPCCPC

minus1

minus05Ed

gew

ise m

omen

t (Nmiddotm

)

times104

3010 50 70 90



moment


moment


Flapwisemoment

Edgewisemoment

1

08

06

04

02

0

CPCIPC


6 Conclusions






Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











1198621

NL1198942

NS1198942

ZE1198942

PS1198942

PL1198942

NL1198941

PM1199001

PS1199001

PS1199001

PSS1199001

PSS1199001

NS1198941

PL1199001

PM1199001

PS1199001

PSS1199001

PSS1199001

ZE1198941

PL1199001

PL1199001

PM1199001

PS1199001

PSS1199001

PS1198941

PLL1199001

PLL1199001

PLL1199001

PM1199001

PS1199001

PL1198941

PLL1199001

PLL1199001

PLL1199001

PL1199001

PM1199001


1198622

NL1198942

NS1198942

ZE1198942

PS1198942

PL1198942

NL1198941

PM1199002

PL1199002

PL1199002

PLL1199002

PLL1199002

NS1198941

PS1199002

PM1199002

PL1199002

PLL1199002

PLL1199002

ZE1198941

PS1199002

PS1199002

PM1199002

PL1199002

PLL1199002

PS1198941

PSS1199002

PSS1199002

PS1199002

PM1199002

PL1199002

PL1198941

PSS1199002

PSS1199002

PSS1199002

PS1199002

PM1199002



1and 119865wind is 119868

2 then 119862DAC is 119862

1and 119862

2is 119862DAC










0 20 40 60 80 100

0

5

10

15

20

25

Time (s)

Win

d an

d w

ave (

ms

)

WindWave

minus5


0 20 40 60 80 1000

10

20

30

Time (s)

Pitc

h an

gle (

deg)

Blade1Blade2Blade3


0 20 40 60 80 1000

2000

4000

6000

Time (s)

Pow

er (k

W)

IPCCPC




0 20 3010 40 50 60 70 80 90 100

0

2

3

Time (s)

IPCCPC

minus1

Tow

er fo

re-a

m

omen

t (Nmiddotm

)

1

times105


0 20 40 60 80 100

0

1

2

3

4

Time (s)

IPCCPC

minus1

Out

-of-p

lane

ben

ding

mom

ent (

Nmiddotm

)

3010 50 70 90

times104


0 20 40 60 80 100

0

05

1

15

Time (s)

IPCCPC

minus1

minus05

In-p

lane

ben

ding

mom

ent (

Nmiddotm

)

3010 50 70 90

times104



0 20 40 60 80 100

0

1

2

3

4

Time (s)

IPCCPC

minus1Flap

wise

mom

ent (

Nmiddotm

)

3010 50 70 90

times104


0 20 40 60 80 100

0

05

1

Time (s)

IPCCPC

minus1

minus05Ed

gew

ise m

omen

t (Nmiddotm

)

times104

3010 50 70 90



moment


moment


Flapwisemoment

Edgewisemoment

1

08

06

04

02

0

CPCIPC


6 Conclusions






Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 20 3010 40 50 60 70 80 90 100

0

2

3

Time (s)

IPCCPC

minus1

Tow

er fo

re-a

m

omen

t (Nmiddotm

)

1

times105


0 20 40 60 80 100

0

1

2

3

4

Time (s)

IPCCPC

minus1

Out

-of-p

lane

ben

ding

mom

ent (

Nmiddotm

)

3010 50 70 90

times104


0 20 40 60 80 100

0

05

1

15

Time (s)

IPCCPC

minus1

minus05

In-p

lane

ben

ding

mom

ent (

Nmiddotm

)

3010 50 70 90

times104



0 20 40 60 80 100

0

1

2

3

4

Time (s)

IPCCPC

minus1Flap

wise

mom

ent (

Nmiddotm

)

3010 50 70 90

times104


0 20 40 60 80 100

0

05

1

Time (s)

IPCCPC

minus1

minus05Ed

gew

ise m

omen

t (Nmiddotm

)

times104

3010 50 70 90



moment


moment


Flapwisemoment

Edgewisemoment

1

08

06

04

02

0

CPCIPC


6 Conclusions






Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article wind and wave disturbances compensation...

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