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Robust fault estimation of a blade pitch and drivetrain system in windturbine model

Hamideh Sedigh Ziyabari, S., Aliyari Shoorehdeli, M., & Karimirad, M. (2020). Robust fault estimation of a bladepitch and drivetrain system in wind turbine model. Journal of Vibration and Control.https://doi.org/10.1177/1077546320926274

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https://doi.org/10.1177/1077546320926274https://pure.qub.ac.uk/en/publications/robust-fault-estimation-of-a-blade-pitch-and-drivetrain-system-in-wind-turbine-model(3fa5fb32-1c0b-4e5b-a8c0-ccdb0986c159).html

Robust fault estimation of a blade pitchand drivetrain system in wind turbinemodel

Journal TitleXX(X):1–15c©The Author(s) 2016

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S.Hamideh Sedigh Ziyabari1 and Mahdi Aliyari Shoorehdeli2 and Madjid Karimirad 3

AbstractIn this paper, a novel robust fault estimation scheme to ensure efficient and reliable operation of Wind Turbines(WTs) has been presented. WTs are complex systems with large flexible structures that work under very turbulentand unpredictable environmental conditions for a variable electrical grid. The proposed observer-based estimationscheme consists of a set of possible faults affecting the dynamics, sensors, and actuators of WTs. First, the pitchand drivetrain system faults occur simultaneously with process and sensor disturbances that are called unknowninput signals. Second, through a series of coordinate transformations, the faulty subsystem is decoupled from therest of the system. The first subsystem is affected by unknown inputs and the second one is affected by faults. AReduced-order Unknown Input Observer (RUIO) is designed to reconstruct states accurately while a Reduced-orderSliding Mode Observer (RSMO) is designed for the second subsystem such that it is robust against unknown inputsand faults. Moreover, the RUIO guarantees the asymptotic stability of the error dynamics using the Lyapunov theorymethod and completely removing unknown inputs; on the other hand, RSMO is designed to reconstruct faults forthe faulty subsystem accurately. Until now, authors only focused on an unknown input signal in the dynamics of thesystem, especially in non-linear systems. The estimated fault will be adequate to accommodate the control loop, andsufficient conditions are developed to guarantee the stability of the state estimation error. In the next step, to figure theeffectiveness of the proposed approach, a WT benchmark system model is considered with faults and unknown inputsscenarios. The simulation results will be used to validate the robustness of proposed algorithms under noise conditions,and the results show that the algorithm could classify faults robustly.

KeywordsRobust fault estimation, Pitch and drivetrain fault, Reduced-order unknown input observer, Reduced-order sliding modeobserver, Orthogonal transformation, Wind turbine

Introduction

Nowadays renewable energies play a more sufficient rolein power generation in the world. Energy production basedon combustion of fossil fuels, such as coal or oil, hasled to increasing temperature and greenhouse gasses. Windturbines (WTs) have to compete with many other energysources, and it is essential that they should be cost-effective,convenient and reliable. WTs are exposed to extremelyvariable and harsh conditions such as severe winds, lighting,arctic cold, hail, and snow; further, they need to meetdifferent loads and produce stable energy. Marquez et al.(2012) explained for a 20-year old turbine, the operation,and maintenance costs of 750Kw turbines might be around25− 30% of the overall power generation cost or around75− 90% of the investment cost.

High mechanical stress on WTs because of extremelyvariable operating conditions and continuously changing,leads to more maintenance. Mainly, for WTs are locatedoffshore. As a result, different approaches on fault diagnosisand control of WTs using a realistic WT benchmark Odgaardet al. (2009) and FAST (NREL) Jonkman et al. (2005)have been highlighted by different researchers in academiaWang et al. (2019); Witczak et al. (2016); Gao et al. (2016).The purpose of WT Fault Detection and Isolation (FDI)systems is to detect and locate degradation and failures

in the operation of WT components as early as possibleso that maintenance operations can be performed in duetime. Therefore, the number of costly corrective maintenanceactions can be reduced and consequently, the loss ofwind power production due to maintenance operations isminimized. Most of the FDI algorithms for WTs werebased on some form of signal analysis approach Qiao andLu (2015). The signals used for fault diagnosis for WTs,mainly include vibration, acoustic emission (AE), strain,torque, temperature, lubrication oil parameters, electricaland supervisory control and data acquisition (SCADA)system signals. The signal processing approaches for faultdiagnosis used typically includes classical time-domainanalysis methods like statistical analysis Marquez et al.

1Research Laboratory for Fault Detection and Identification (FDI)Faculty of Electrical Engineering, K. N. Toosi University of Technology,Tehran, Iran2Faculty of Electrical Engineering Department of MechatronicsEngineering, K. N. Toosi University of Technology, Tehran, Iran3 School of Natural and Built Environment, Queen’s University Belfast,Northern Ireland, United Kingdom

Corresponding author:Mahdi Aliyari Shoorehdeli, Department of Mechatronics Engineering, K.N. Toosi University of Technology, Tehran, IranEmail: [email protected]

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2 Journal Title XX(X)

(2012), classical frequency analysis methods like FastFourier Transform (FFT) Zhang et al. (2012), classicaltime-frequency analysis methods like wavelet transformHuang et al. (2008) and artificial intelligence (AI) methodsSchlechtingen and Santos (2011). The fault mode andlocation can then be identified by a classification technique,like artificial neural networks (ANNs), support vectormachines (SVMs) Laouti et al. (2011). Signal-basedapproaches such as neural networks and experts systemsSahin et al. (2012) are more suitable for information-poorsystems. Compared with the signal processing methodsfor fault diagnosis for WTs, the model-based methodsdo not need high-resolution signals. The low-resolution,low-sampling-rate SCADA signals of a WT can be usedeffectively by model-based fault diagnosis. This is effectivein installing additional sensors and data acquisition hardwareto obtain high-resolution signals. In addition, the complexand costly computations in the signal-based methods toextract fault features from signals are unneeded in themodel-based methods. The most commonly used approachesinclude Observer-based Chen et al. (2011), Parity spaceGhaniee and Shoorehdeli (2011) and Parameter estimation-based Yin et al. (2012). In general, the parity space andparameter-based approaches are unsuitable for non-linearsystems and will be unconsidered in this paper. The observer-based technique has received much attention to design a faultdetection filter and is the base of this paper.

Model-based fault detection and isolation (FDI) is basedon a residual signal that is generated by using themathematical model of the system. In these methods,the objective is commonly obtained by comparing thesystem’s measurements with the corresponding signals of itsmathematical model. The difference between these signalscalled residuals is sensitive to any unknown input signalsand faults. Since Model-based fault diagnosis methods havereceived a high sensitivity to corresponding mathematicalmodels, it completely requires precise mathematical modelswhich are not easy to derive. Any difference between thesystem and its models such as uncertainties, complexities,and unknown inputs cause seriously misleading alarms offaults; therefore, this problem has motivated to robust faultdiagnosis schemes and many related studies have been doneby other researchers Chen and Patton (2012); Nazir et al.(2017). Over the recent decades, many schemes have beenachieved for FDI of non-linear systems with disturbance andfault together Lan and Patton (2017). On the other hand, itis challenging for a FDI scheme to provide the exact faultinformation, e.g. fault magnitude and shape. Compared withFDI strategies, fault identification or estimation techniquecan provide accurate fault information and it is able toreact to the system in an Active Fault Tolerant Control(AFTC) and real-time decision Zhang and Jiang (2008);Azizi et al. (2019). Chen et al. (2011); Wei et al. (2010)proposed model-based FDI schemes employing a diagnosticobserver for the pitch system and drivetrain faults on thebenchmark model. Fault detection and isolation have beensupported. Malik and Mishra (2015) a diagnostic techniquefor imbalance fault identification based on a probabilisticneural network was presented. Mathematical and statisticaloperations are performed on the measurements in signalprocessing fault diagnosis. Fault detection and isolation

scheme in Dong and Verhaegen (2011) is a data-drivenmethod to overcome the difficulty of modelling. Ghaneet al. (2016); Feng and Liang (2014) demonstrated statisticalchange detection for a gearbox model of a wind turbineusing frequency analysis. Fault detection, isolation, andaccommodation to detect faults of the blade pitch systemshave been considered in Cho et al. (2018). In this paper, toestimate the blade pitch angle, a Kalman filter is designedand a fault isolation scheme is proposed that could determinethe fault type, location, magnitude. After that, the fault-tolerant controller with a virtual sensor and shut-downmode controls WT to avoid unexpected external loadshas been designed. Liu et al. (2017) focuses on robustfault estimation and tolerant control for T-S fuzzy model.A certain class of actuator and sensor faults consideredgenerating an augmented system. Observability and somerestricted conditions are limitations of this design. Simaniand Castaldi (2019) proposed a non-linear relationshipbetween measurements and faults of the offshore WT modelwith neural networks and fuzzy inference. It has beenshown that due to the increased number of data in FWTs,implementing deep learning algorithms could be effectivein the analysis of the operating condition. Fu et al. (2019)proposed a convolutional neural network (CNN) to analysethe temperature data of gearbox bearing. Moreover, inanother research, Wu et al. (2019) designed fault diagnosiswith noisy measurements by denoising autoencoder (DAE)and Wang et al. (2016) proposed a deep autoencoder as anindicator of impending blade breakages. Data based methodsneed more sensors to analyse vibration, temperature, andother condition monitoring signals. Although the windturbine industry has the interest to exploit effective conditionmonitoring methods, these methods suffer from high cost andcomplexity.

Fault estimation as one of the most important model-basedfault diagnosis problems, which can also be perceived asthe estimation of an unknown input has been done. In theliterature, some of these fault estimation strategies usuallyattention, namely: system augmentation, especially the statevector by the new states Gao et al. (2016); Raoufi (2010),unbiased minimum-variance input and state estimationGillijns and De Moor (2007), adaptive observers Azmiand Khosrowjerdi (2016); Guo et al. (2015), sliding modeobservers Tan and Edwards (2003), high gain observersVeluvolu et al. (2011), Hinf approach Raoufi et al. (2010)and unknown input observers Saoudi et al. (2015); Raoufiet al. (2010). The last two decades have witnessed enormousgrowth in fault diagnosis and to extend the previousapproaches to non-linear systems. For robust fault estimationin non-linear systems, the observer-based approaches havegained many interest Raoufi and Marquezz (2010); Raoufiet al. (2010); Progovac et al. (2014); Guo et al. (2015).It should be emphasized that accurate fault estimation is asignificant challenge for the non-linear system particularlyin the presence of disturbances Mellucci et al. (2017) anddefinite faults Witczak (2014). Current solutions to robustfault estimation in a non-linear system are inadequate aswell because there is not a distinct solution for non-linearobservers Hassan (2002). In spite of its shortcomings, thesemethods have been widely employed to different kind of non-linear systems. In Witczak et al. (2016); Raoufi et al. (2010)

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Lipschitz systems are considered that is a familiar form ofuniform continuity for non-linear functions.

Disturbance attenuation by using optimization methodsis generally more than using disturbance decompositiontechniques. In contrast, disturbance decomposition can betterrelieve the adverse effects from the disturbances Witczaket al. (2016); Raoufi et al. (2010); Guo et al. (2015).A recent review of the literature on this area foundthat unknown input observers could completely attenuateunknown inputs like disturbances Raoufi and Marquezz(2010); Saoudi et al. (2015); Aldeen and Sharma (2008).In Raoufi and Marquezz (2010), both actuator and sensorfault simultaneously considers and augmented system isformed of a descriptor system. Although descriptor systemshave been shown as conventional systems; it is difficultto solve their numerical problems, especially in industrialsystems. Sliding mode observers (SMO) are robust againstuncertainties and disturbance Edwards and Spurgeon (1998).SMO has been widely applied as an effective method tocompensate for the uncertainty component in non-linearsystems Yan and Edwards (2007). Indeed, it will be capableof preserving the error dynamics on a sliding surface inspite of the existence of uncertainty or fault. Furthermore,the exact estimation will exist and the equivalent outputerror signal that it is injected to observer structure willachieve an unwanted signal. In the fault estimation scheme,an unwanted signal is a fault and the equivalent outputerror signal will reach this after some transient time. Raoufiet al. (2010) a H disturbance attenuation level proposed bythe sliding mode observer design using LMIs optimization.The main contribution of this paper is using UIO forexact state estimation since UIO can exactly remove thedramatic effect of unknown inputs. Moreover, the equivalentoutput error signal in sliding mode structure will attainthe unwanted signal. Ke Zhang and Cocquempot (2016)proposed a less conservative UIO design method by usinga finite frequency range technique instead of an entire-frequency method. In Valibeygi et al. (2016) estimation ofsensor faults in non-linear systems in the presence of processdisturbance was considered. The unknown input observerfor Lipschitz systems was applied for the fault diagnosisin Witczak et al. (2016). Ziyabari and Shoorehdeli (2017a)proposed a scheme that includes both component and sensorfault with the non-linear system that transferred to non-linear T-S model to generate a residual signal. Moreover,Ziyabari and Shoorehdeli (2018) have designed the faultestimation scheme for the component fault. In addition,both studies have considered unknown inputs signals in adynamic equation. Moreover, in Ziyabari and Shoorehdeli(2017b), the component fault was considered with theunknown input signal in state and output equations, but itwas not included sensor and component fault estimationsimultaneously. The essential contribution of this paper isa robust state and actuator fault estimator design proceduretogether. Two sources of uncertainty, unknown input, andexogenous external disturbance are present.

This paper is focused on the issue of robust faultestimation for a disrupted Wind Turbines (WT) subjectto component and sensor faults and unknown inputssimultaneously via two reduced-order unknown input andsliding mode observers. It should also be pointed out

that the proposed description of non-linearity is Lipschitzconstraint. In this paper, the orthogonal transform hasbeen improved, and the procedure for the component andsensor fault has been modified. This novelty does notlead to an increase the computation and there is not anyrestriction on time profile of faults, but faults should be normbounded. This paper is motivated by the development ofthe Ziyabari and Shoorehdeli (2017b, 2018) by reformingthe strategy of fault estimation to have disturbance inthe measurements as well. The main contributions thatare worth emphasizing are summarized in the followingtwo aspects: (a) Through a coordinate transformation, theoriginal system is decomposed into two separate subsystems.The first subsystem is affected only by faults and is freefrom unknown inputs; the second subsystem is affected byunknown inputs; (b) A UIO design is suggested to robustlyestimate states to reconstruct faults in SMO. In addition,the analysis of the observers is formulated in terms of aseries of LMIs that can be conveniently solved using LMIoptimization technique such that a systematic calculation forobserver gain matrices can be readily obtained using MatlabLMI toolbox. The effectiveness of the proposed method isdemonstrated through its application to numerical simulationand compared to Ziyabari and Shoorehdeli (2017a). Itwill be indicated that these results clearly recommend theproposed approach for the purpose of AFTC. In contrastto the present works, the main contributions of this paperlie in the following aspects: (1) Robust fault estimationwith two estimation mechanisms for unknown inputs indynamic and measurement signals is designed; (2) Tomake a streamlined unknown input sliding mode observer,it is proved that the proposed controller guarantees thatthe closed-loop is asymptotically stable in the presence offaults and disturbances. (3) All possible faults (actuator,component, sensor) may happen in a real non-linear MIMOsystem simultaneously.

The rest of this paper is arranged as follows: First,provides a review of WT systems. The benchmark model andWTs faults and disturbances are presented to introduce theessential concepts of the system under study. Next sectionintroduces the main ideas of the fault estimation scheme.First, reduced unknown input and sliding mode observers,second, fault estimation from previous observers has beendone. Finally, with simulating the proposed scheme on WTbenchmark system model, its ability for the industrial systemhas been demonstrated. A conclusion completes the paper.

Wind turbine system description

The WT considered in this paper was proposed in thebenchmark described in Odgaard et al. (2009) that is a three-blade horizontal-axis turbine with a full converter coupling.The closed-loop system comprises five subsystems: aerody-namics, blade and pitch system, drivetrain, generator unit,controller and Figure 1 represents the relations between thesesubsystems faults and disturbance. The variables of WT aredefined in Table 1.

Exact descriptions of the sub-blocks, the mathematicalmodels and the numerical values of the different parametersare given in the following sections.



Figure 1. Interconnection of sub-models describing the characteristics of the wind turbine in Odgaard et al. (2009) benchmark.

Table 1. Wind model variables used in the benchmark modelOdgaard et al. (2009)

Symbol Descriptionνω wind speed on the turbineTω torque from wind on the bladesTr rotor torqueωr rotational speed of the rotorTg generator torqueωg rotational speed of the generatorβi,r reference to the pitch positionβi the pitch position iFP fault in the pitch systemFDT fault in the drivetrain systemτg,r reference to generator torquePr power reference to the wind turbinePg power produced by the generator

Wind turbine model

The wind on the turbine blades forces the wind turbine rotorto spin around. Then, a rotating shaft converts the kineticwind energy into mechanical energy. A generator, coupled toa converter, performs the conversion from mechanical energyto electrical energy. The system is operated by the windspeed that affects the aerodynamic properties of the windturbine, together with the pitch angles of the blades and thespeed of the rotor. An aerodynamic torque is transferred fromthe rotor to the generator through the drivetrain. Finally, thegenerator and converter provide electric power.

Aerodynamic model: A wind model that describesstochastic wind behaviour (speed variation and lateral effectsof wind) is presented in Odgaard et al. (2009). It consistsof the mean wind, a stochastic part, wind shear and towershadow. The torque acting on the blades are modelled byaerodynamic Tr(t). This model is a combination of the

aerodynamic model and the wind and pitch model.

Tr(t) =∑3i=1

ρπR3Cq(λ(t), βi(t))ν2w,i(t)

6(1)

where ρ is the air density, R is the radius of the blades,νw is the wind speed and Cq is the torque coefficient (themapping used in this paper is in Odgaard et al. (2009)). Thisparameter characterizes the efficiency of the energy transferfrom wind energy to mechanical energy, and it depends onthe tip speed ratio λ and the pitch angle β. This model forsmall differences between the pitch angles is valid.

Pitch system model: The hydraulic pitch system ismodelled as a second-order system between the measuredpitch angle βi and its reference βi,r:

β̈i = −2ζiωn,iβ̇i − ω2n,iβi + ω2n,iβi,r (2)

ωn,i is the natural frequency and ζi is damping ratio withi = 1, 2, 3. This is an individual blade pitch and the pitchangles βi, i = 1, 2, 3 are measured. βi is available for thewind turbine control system and for FDI and FTC schemes.

DriveTrain Model: The drivetrain model is an intercon-nection of a low-speed and a high-speed shaft by a transmis-sion that has a gear ratio Ng and an efficiency ηdt, combinedwith a torsion stiffness Kdt, and a torsion damping Bdt. Thedrivetrain transfers torque from the rotor to the generator. Itincludes a gearbox that increases the rotational speed fromthe low-speed rotor side to the high-speed generator side.Thus, the drivetrain can be described by the following threedifferential equations:

Jrω̇r = −(Bdt +Br)ωr +BdtNg

ωg −Kdtθδ + Tr (3)

Jgω̇g =ηdtBdtNg

ωr +(ηdtBdtN2g

+Bg

)ωg+

ηdtKdtNg

θδ − Tg(4)

θ̇δ = ωr −ωgNg

(5)


5

where Jr and Jg low-speed shaft and high-speed shaftinertia, Br and Bg friction coefficients, ωr is the rotorspeed, ωg is the generator speed, θδ is the torsion angle ofthe drivetrain, Tr is the aerodynamic torque and Tg is thegenerator torque. Both the rotor speed ωr and the generatorspeed ωg are measured.

Generator model: The generator torque Tg is controlledby the reference Tg,r. The dynamics are approximated by afirst-order model:

Ṫg = −Tgτg

+Tg,rτg

(6)

where τg is the time parameter of the generator subsystem.The power produced by the generator is given by:

Pg = −ηgωgTg (7)

and ηg is the efficiency of the generator and ωg is thegenerator speed measurement. The values of the systemparameters used in this paper have been extracted from Table2.

Table 2. System parameters values

R = 57.5 ρ = 1.225ωn,1 = 11.11 ωn,2 = 5.73 ωn,3 = 3.42ζ0 = 0.6 ζ2 = 0.45 ζ3 = 0.9Bdt = 775.49 Br = 7.11 Bg = 45.6Ng = 95 Kdt = 2.7e9 ηdt = 0.97Jg = 390 Jr = 55e6τg = 0.02 ηg = 0.98

Finally, the general profile parameters of the wind turbineare presented in Table 3.

Table 3. General profile of wind turbine used in the benchmarkmodel Odgaard et al. (2009)

Parameter valueWind regime stochastic windRotor orientation Clockwise rotation -UpwindType of wind turbine horizontal-axisRated Power 4.8 MWRated wind speed 12.5 m/sNumber of blades 3Converter coupling fullRated wind speed 12.5 m/sCut in wind speed 3m/sCut out wind speed 25 m/s

Fault scenariosIn this paper, sensor, actuator, and process faults in differentparts of WT have been covered. Some of the faults are veryserious and must be detected in a fast and safe condition. Therest is less critical, and the controller can accommodate thesefaults while staying in operation.

First, fault in the pitch position measurements is commonsensor faults. The origin of these faults will be eitherelectrical or mechanical and can result in either a fixed valueor a changed gain factor on the measurements. The controller

handles the pitch positions based on measurements, if it isnot handled correctly, these faults will influence the system’sperformance.

Second, the deviations in rotor and generator speedmeasurements denote faults. Both the rotor and generatorspeed measurements are done using encoders and bothelectrical and mechanical failures are possible, which resultin either a fixed value or a changed gain factor on themeasurements. In case of a fixed value fault, the output ofthe encoder is not updated with new values. The gain factorfault is introduced when the encoder reads more marks onthe rotating part than actually present, which can happenas dirt or other false alarm on the rotating part. Converterfaults as a sample of actuator fault are denoted as an offsetor in changing dynamics of the converter. This fault can beinternal to the converter or because of electronics or an off-set on the converter torque estimate.

Third, The pitch hydraulic system has the possibilityof faults on all three blades. It can result in changingdynamics due to either a drop in pressure in the hydraulicsupply system or high air content in the oil. The formerrepresents faults like leakage in the hose, a blocked pumpor similar others. There will always be some air contentin the hydraulic oil used, the content level will vary, andit is not possible to control it well. Air is much morecompressible than oil, so it alters the dynamics of thehydraulic actuator. Where the friction coefficient in themodel changes slowly with time, the system fault will appear.This change will result in two correlated fault signals: ωrand ωg . These changes evolve slowly in reality; however, itis expected to be extremely demanding in the benchmarksimulator from a computational point of view to simulatesuch a fault realistically evolving over for months or evenyears. Consequently, in this benchmark model Odgaard et al.(2009), this fault is represented by a small change of thefriction coefficient within a few seconds. The main pointis that the change in the drivetrain friction is considerablyslower than the system dynamics and the system sample rate.Typically, faults in wind turbine gearboxes are found usingcondition monitoring methods relying on additional sensorsthat measure accelerations and noise levels on the gearbox. Itwould be more cost-efficient if such faults could be detectedand isolated using standard measurement in the wind turbinecontrol system. A fault occurring in the pitch system caninfluence the closed-loop control system and the dynamics ofa wind turbine. Faults of the blade pitch system are mainlycategorized by the pitch sensor and actuator fault. The pitchsensor fault occurs by dust on encoder disc, miss-adjustmentof the blade pitch bearing, beyond the acceptable range oftemperature and humidity or improper calibration. Thesecauses can result in the unbalanced rotation of the rotor fromthe sensor bias and fixed outputs from last measurements.

In this paper, the pitch system and in the drivetrainare considered for illustrating the proposed fault estimationapproach. Combining results of the previous equation (2),together with sensor and actuator faults and disturbances, inthe following set of the first-order differential equations

ẋps = Apsxps +Bpsups + Ecfa(t) + Edd(t)yps = Cpsxps + Fdd(t) + Fcfa(t)

(8)



where

xps =[β̈1 β̇1 β̈2 β̇2 β̈3 β̇3

]Tups = [β1,r β2,r β3,r]

T

Api =[

−2ζiωn,i −ω2n,i1 0

], Aps =

[Ap1 0 00 Ap2 00 0 Ap3

]Bpi =

[1

0

], Bps =

[Bp1 0 00 Bp2 0

0 0 Bp3

]

Cpi = [ 0 ω2n,i ] , Cps =

[Cp1 0 0

0 Cp2 00 0 Cp3

](9)

for i = 1, 2, 3 and the fault in the drivetrain consists ofactuator and sensors with disturbances. Similarly to the pitchsystem case:

ẋdt = Adtxdt +Bdtudt + Ecfa(t) + Edd(t)ydt = Cpsxdt + Fdd(t) + Fcfa(t)

(10)

where

xdt = [ωr ωg θδ]T, udt = [Tr Tg]

T

Adt =

−Bdt+BrJr

BdtNgJr

−KdtJr

ηdtBdtNgJg

(ηdtBdtN2g

+Bg

)Jg

ηdtKdtNgJg

1 − 1Ng 0

Bdt =

1Jr 00 − 1Jg0 0

, Cps = 1 0 00 1 0

0 0 1

(11)

d(t) and fa(t) are disturbance and fault for each subsystemand Ec, Fc and Fd are corresponding fault and disturbancedistribution matrices with appropriate dimensions.

System transformationConsider the following non-linear system:

ẋ(t) = Ax(t) +Bu(t) +Gf(x, u) + Edd(t) + Ecfa(t)y(t) = Cx(t) + Fdd(t) + Fcfa(t)

(12)where x ∈ Rn, u ∈ Rnu and y ∈ Rny are the state vector,the input vector and the output vector, respectively; theknown non-linear function f(x, u) is Lipschitz with respectto x uniformly for u ∈ U ( U is an admissible control set)with positive Lipschitz constant γ0

‖f(x1, u)− f(x2, u)‖ ≤ γ0‖x1 − x2‖ (13)

and Ec and Fc are distribution matrices of component faultfc ∈ Rnc and fc(t) is norm bounded with positive constantsγ1 as follows :

‖fa(t)‖ ≤ γ1 (14)

d(t) ∈ Rnd contains the uncertainty and disturbance, in thegeneral case, it is commonly called unknown input signal.The number of measurements is more than the number offaults occur in the system (nc < ny) and this assumptioncan be overcome by using more than one observer, eachobserver for a subset of the faults that satisfy this assumption.A,B,G,Ed, Ec, C, Fd and Fc are real constant knownmatrices of appropriate dimensions.

Lemma 1. For any matrices X and Y with appropriatedimensions, the following property holds for any positivescalar � Alessandri (2004):

XTY + Y TX ≤ �XTX + �−1Y TY (15)

Lemma 2. There exists a coordinate system in which the set(Ed, Ec, Fd, Fc) has the following structure:([

ed0(n−nd)×nd

],

[0nd×ncec

][

fd0(ny−nd)×nd

],

[0nd×ncfc

]) (16)where ed ∈ Rnd×nd , ec ∈ R(n−nd)×nc , fd ∈ Rnd×nd , fc ∈R(ny−nc)×nd and ed, fd should be full rank matrices.

Proof:Without loss of generality, it can be assumed that there

exists a QR transformation T0 such that:

T0Ed =

[ed0

](17)

where ed ∈ Rnd×nd . By using T0, matrix Ec has beenfollowing partitions:

T0Ec =

[e1ec

](18)

Now, introduce a non-singular transformation T1 as

T1 =

[Ind −e1e−1c0(n−nd)×nd In−nd

](19)

then

T1T0Ed =

[ed0

], T1T0Ec =

[0ec

](20)

Also, it can be assumed that there exists a QR transformationS0 such that:

S0Fd =

[fd0

](21)

where fd ∈ Rnd×nd . By using S0, matrix Fc has beenfollowing partitions:

T0Fc =

[f1fc

](22)

Now, introduce a non-singular transformation S1 as

S1 =

[Ind −f1f−1c

0(ny−nd)×nd I(ny−nd)

](23)

then

S1S0Fd =

[fd0

], S1S0Fc =

[0fc

](24)

Now S1S0CT−10 T−11 partitions as

S1S0CT−10 T

−11 =

[c1 c2c3 c4

](25)

TAT−1 =

[a1 a2a3 a4

](26)


7

Then T = T1T0, S = S1S0.Lipschitz systems are a very fundamental class and many

non-linearities are locally Lipschitz. Also, Lipschitz non-linear systems have received much attention in a differentclass of non-linear systems Valibeygi et al. (2016); Azmi andKhosrowjerdi (2016); Witczak et al. (2016) Trigonometricnon-linearities are a suitable example for Lipschitz non-linear that are common in robotics and non-linearities thatare square or cubic. Relation (14) is not a conservativecondition for fault estimation design because of havingbounded signals to measure for fault diagnosis system is ahealthy condition.

Robust fault estimation architectureIn this section, a robust fault estimation scheme will beintroduced using the structure characteristics shown in thesection ”System transformation.” Without loss of generality,the transformations are introduced in Lemma (2) as keyto address the problem of robust fault estimation designwhich are x̄ := [xT1 , x

T2 ]T = Tx, ȳ := [yT1 , y

T2 ]T = Sy, the

original system (12) can be rewritten

ẋ1 = a1x1 + a2x2 + b1u+ g1f(T−1x̄, u) + edd(t)

ẋ2 = a3x1 + a4x2 + b2u+ g2f(T−1x̄, u) + ecfa(t)

y1 = c1x1 + c2x2 + fdd(t)y2 = c3x1 + c4x2 + fcfa(t)

(27)where x1 ∈ Rnd , x2 ∈ Rn−nd are partitioned transformedstate of the original system (12). g1, b1 and g2, b2 are thefirst nd and the last n− nd components of transformed G,Brespectively. ed, ec, c1, c2, c3 and c4 are defined from Lemma(2). Thus, the faulty state space and output equations havebeen decoupled from the fault-free state space and outputequations. Given the above preliminaries and assumptions,the objective of the subsequent part of this paper is toprovide a reduced-order unknown input estimation strategyto attenuate unknown inputs and another RUIO to attenuatefaults separately for the class of non-linear systems (12).The main advantage of the proposed approach is the factthat apart from estimating the sensor and component faultsimultaneously, it is able to decouple the effect of unknowninputs in measurements and dynamics of the system withinRUIOs.

Reduced unknown input observerIn this section, a theorem to design RUIO for the fault-freeand faulty part of system (27) is separately proposed. Thefault-free part will be rewritten as:

ẋ1 = a1x1 + b̄1ū1 + g1f(T−1x̄, u) + edd(t)

y1 = c1x1 + d̄1ū1 + fdd(t),(28)

where ū1 = [xT2 uT ]T , b̄1 = [a2, b1] d̄1 = [c2, 0] and the

RUIO is inferred as follows:

ż1 = H1z1 + J1ū2 +W1(y1 − d̄1ū) +Q1g1f(T−1 ˆ̄x, u)x̂1 = z1 −R1(y1 − d̄1ū)

(29)where H1, J1, W1, Q1 and R1 for i = 1, . . . , r are constantmatrices with appropriate dimensions defined as:

H1 = Q1a1 −K1c1, J1 = Q1b̄1,Q1ed −K1fd = 0, R1fd = 0.

(30)

Also, the faulty part is rewritten as follow:

ẋ2 = a4x2 + b̄2ū2 + g2f(T−1x̄, u) + ecfa(t)

y2 = c4x2 + d̄2ū2 + fcfa(t),(31)

where ū2 = [xT1 uT ]T , b̄2 = [a3, b2] d̄2 = [c3, 0] and the UIO

is inferred as follows:

ż2 = H2z2 + J2ū2 +W2(y2 − d̄2ū) +Q2g2f(T−1 ˆ̄x, u)x̂2 = z2 −R2(y2 − d̄2ū)

(32)where H2, J2, W2, Q2 and R2 are constant matrices withappropriate dimensions defined as:

H2 = Q2a4 −K2c4, J2 = Q2b̄2,Q2ec −K2fc = 0, R2fc = 0.

(33)

And K1, R1 and K2, R2 are independent variables andProposition (1) will choose them. z1 ∈


Let us consider the Lyapunov function V (e1(t)) =eT1 (t)P1e1(t) , the derivative of the Lyapunov function isgiven by

V̇ (e1(t)) = eT1 (H

iT

1 P1 + P1H1)e2 + 2eT1 P1Q1g1f̃

(39)Using the Lemma (1) and Lipschitz constrain (13),

V̇ (e1(t)) ≤ eT1 (HiT

1 P1 + P1H + �P1QiT

1 Q1P1+�−1γ20I)e1

(40)

Stability condition for the estimation error yields to that thetime derivative of the Lyapunov function should be negativedefine.

HiT

1 P1 + P1H1 + �P1QT1Q1P1 + �

−1γ20I < −α. (41)

By replacing H1 and Q1, then using the variable changeR̄ = P1R1 and K̄1 = P1K1, the last inequality (41) can bewritten as:

((P1 + R̄c1)− K̄1c1)T + (P1 + R̄c1)− K̄1c1+�P1Q1g1g

T1 Q

T1 P1 + �

−1γ20I(42)

Inequality (42) is given by using the Schur complementrelation. Thus LMI (34) with parameters of (35) concludes.Since V̇ in (41), a exponential function for upper bound ofe1(t) exists as

‖e1(t)‖ ≤M‖e1(0)‖exp(−αt

2) (43)

where a choice is M =√

λmax(P1)λmin(P1)

; as a result, there exits a

dynamic system for upper bound of M‖e1(0)‖exp(−αt2 )

ẇ(t) = −12αw(t) (44)

then, it is easy to see that ‖e1(t)‖ ≤ w(t),∀t ≥ 0.A similar proof can be obtained for relations (31)-(33) for

the fault free subsystem.

Reduced sliding mode observerIt is assumed that UIOs have been designed, a proposition todesign SMO for faulty part of system (27) to estimate faultis proposed and the faulty part is (31). The RSMO is inferredas follows:

˙̂x2 = a4x̂2 + b̄2ū2 + g2f(T−1 ˆ̄x, u) +N(ˆ̄x2 − x̂2)

+ν(x̂, ˆ̄x)ŷ2 = c4x̂2 + d2ū2,

(45)where ˆ̄x2 is estimated x̂2 from RUIO (32), N is constantmatrix with appropriate dimensions and the gain functionν(.) is defined by

ν(x̂, ˆ̄x) := k(.)ˆ̄x2 − x̂2‖ˆ̄x2 − x̂2‖

(46)

where k(.) is a positive scalar function to be determined anda sliding surface

S = {t ∈ R+ : s(t) = 0|s(t) = ˆ̄x2 − x̂2} (47)

is considered and x̂2 has affected by only fault signal; there-fore, sufficient condition for guaranteeing the asymptoticconvergence of fault estimation error and output estimationerror system is described by the following Proposition.

Proposition 2. Given the non-linear system (31) withLipschitz constant γ0, consider RSMO structure (45)-(46).The observer error dynamics is asymptotically stable suchthat N for i = 1, . . . , r and a positive-definite symmetricmatrix P3 exist such that the following conditions hold:

a4P3 + P3aT4 − N̄ − N̄T < 0 (48)

with N = P−12 N̄ and to derive the sliding surface (47) infinite time and remains on it if k(.) in (46) is chosen to satisfy

k(.) ≥ (‖a3‖+ ‖g2‖γ0)w(t) + ‖ec‖γ1 + η (49)

Proof. Let e3 = ˆ̄x2 − x̂2. Then from (45) and (32), thestate estimation error is described by

ė3 = (a4 −N)e3 − a3e1 + g2f̃ + ecfa(t)− ν (50)

let V (e3) = eT3 P3e3; therefore, the time derivative of Valong the trajectories of the system (50) is given by

V̇ (e3) = eT3 ((a4 −N)P3 + P3(a4 −N)T )e3+

2eT3 P3(a3e1 + g2f̃ + ecfa(t)− ν)(51)

since by design symmetric negative definite first part of (51)

(a4 −N)P3 + P3(a4 −N)T < 0 (52)

first condition (48) is concluded. By applying (13), (14) and(44) in (51)

V̇ ≤ 2‖e3‖λmax(P3)((‖a3‖+ ‖g2‖γ0)w(t)+‖ec‖γ1 − ν

(53)

thus second condition (49) is concluded.

Fault estimation schemeIt is assumed that the UIO and SMO are given, have beendesigned. In this part, the estimation of fault by using theSMO’s output and output information is done. Basically thefollowing theory is the result of two prior Propositions.

Theorem 1. Consider subsystem (31) exists and assumethat the LMIs (34)-(48) are solvable and k(.) is chosen tosatisfy (49),

f̂a(t) = k(.)e−1c

ˆ̄x2 − x̂2‖ˆ̄x2 − x̂2‖+ σ1exp{−σ2t}

(54)

Proof. In finite time the error dynamics (50) will be takenplace on surface (47) and ė3 = e3 = 0; therefore, during thesliding motion, the error dynamics for e3 is given by

0 = −a3e1 + g2f̃ + ecfa(t)− ν (55)

− a3e1 + g1f̃ + ecfa(t) = ν (56)

where ν denotes discontinuous signal (46) must take onthe average νeq , the equivalent output error injection signalEdwards and Spurgeon (1998) to preserve the sliding motion.From Lipschitz constrain (13) and upper bound (44),

‖ − a3e1 + g2f̃‖ ≤ (‖a3‖+ γ0)‖e1‖ → 0(t→ 0) (57)


9

Figure 2. Suggested robust fault estimation scheme for Windturbine with its interconnections.

thus estimation of fault f̂a(t) is recovered by the equivalentoutput error injection signal νeq .

νeq ' k(.)ˆ̄x2 − x̂2

‖ˆ̄x2 − x̂2‖+ σ1exp{−σ2t}(58)

where σ1 and σ2 are both positive constants such that

f̂a(t) ' k(.)e−1cˆ̄x2 − x̂2

‖ˆ̄x2 − x̂2‖+ σ1exp{−σ2t}(59)

Hence the proof completes.Each element of νeq corresponds to the same fault,

therefore we have accurate fault estimation. First set of RUIOcan remove all disturbances or uncertainties and second setRSMO estimates exact fault; therefore, the estimated faultcan be used for fault accommodation control. In the Figure2 to make it clear the proposed fault estimation scheme, itssubsystems and the signalling configuration has been shown.Figure 1 next to Figure 2 shows a complete layout of faults,disturbances in wind turbine and the robust fault diagnosisscheme.

The disadvantage of the proposed approach may be offlinecomputation and apply the result to real-life experiments;but, it will be an advantage when a real-time case isconsidered for less computational volume.

Case study: Wind turbineIn this section, simulation results of the proposed faultestimation scheme for the WT are presented. Simulations ofthe WT subjected to a stochastic wind speed under fault inpitch and drivetrain subsystems are conducted with respectto the fault-free case. The results prove the performance ofthe fault estimation technique under different fault scenarios.Wind speed time series with a mean speed of 12m/s,and over 44000(sec) of simulation time is illustrated inFigure (3) with the wind elevation and four different windspeeds at hub height and three speeds at the three-blade tips,respectively, shown in Figure (4). In the following section,to test normal condition, performance and effectiveness ofthe controller presented. The wind profile is applied to thewind turbine without any sensor and actuator faults anddisturbances. Then, in fault scenario sections, faults in thedrivetrain and pitch subsystems are considered and the timeincrement is chosen 0.01(sec).

0 0.5 1 1.5 2 2.5 3

x 104

4

6

8

10

12

14

16

18

20

time (s)

win

d m

/s

Figure 3. Wind speed time series with a mean speed of12m/s.

0 500 1000 1500 2000 2500 3000 3500 4000 45000

5

10

15

20

25

time (s)

win

d s

pe

ed

m/s

Wind speed at hub

Wind speed at the blade 1



Figure 4. Wind speed time series at the hub (blue solid line),blade 1 (green dashed line), 2 (magenta asterisk) and 3 (cyanpoint) for WT.

Fault-free case

In this section, the wind turbine works in two specificregions of the graph are shown in Figure 5. In zone 1,the wind turbine will be awaiting higher wind speeds 0 -3m/s. In zone 2, the generated power of the wind turbinewill be optimized and in zone 3, the wind turbine will becontrolled to keep a constant power generation. In zone4, the wind turbine will be parked, preventing damagedue to the high wind speed. Zone 2 is denoted the poweroptimization and zone 3 is denoted power reference and theseare corresponded to control modes 1 and 2. In this paper,a simple control scheme Odgaard et al. (2009) has beenused and the focus is on the fault estimation of the windturbine. Figure 6 shows the control procedure for power andpitch-regulated wind turbine algorithm. In Figure 6, ωnomand ωδ are the nominal generator speed and small offsetsubtracted from the nominal generator speed (to avoid thecontrol modes are switching all the time). In both controlmodes, the generator torque reference and the pitch referenceTg,r and βr are the control parameters and the same referenceis for all three pitch systems.



Figure 5. Illustration of the reference power curve for the windturbine depending on the wind speed.

The controller starts

in mode 1

Condition

monitoring

Yes

Shutdown

No

Yes

The controller switches

from mode 1 to 2

No

Yes

Without control mode

switches

No

The controller switches

from mode 2 to 1

Figure 6. Control procedure for a wind turbine.

In control mode 1, The optimal value of λ is denotedλopt is the optimum point in the torque coefficient Cp. Thisoptimal value is achieved by setting the pitch reference tozero βr = 0 and the reference torque to the converter Tg,r asfollows:

Tg,r = Kopt

(ωgNg

)2(60)

whereKopt =

1

2ρAR3

Cpmaxλopt3

(61)

with ρ the air density,A the area swept by the turbine blades,and Cpmax the maximum value of the torque coefficient.

In control mode 2, the pitch system using a PI controllertrying to keep ωg at ωnom has been controlled.

β̇r = Kpe+Ki

∫e (62)

where e = ωg - ωnom. In this case, the converter reference isused to suppress fast disturbances by

Tg,r =Pr

ηgcωg(63)

The used controller parameters can be found in Table 4.

Table 4. Controller parameters used in the benchmark modelOdgaard et al. (2009)

ωnom = 162rad/s Kopt = 1.2171ωδ = 15rad/s Ki = 1Pr = 4.8× 106W Kp = 4

A series of simulation results are presented to investigatethe performance of the standard condition of the closed-loopsystem. Rotor and generator speed simulation responses areshown in Figure 7 for drivetrain and pitch positions in Figure8 are shown for pitch subsystems. Figure 9 presents generatortorque time series and its reference. Figure 10 presentspower generated from the generator subsystem and powergenerated reference is 4.8MW . The operating conditions arenormal, and the system has been capable to meet its controlobjectives, the pitch angels and the generator torque. This isabsolutely seen in the Figures 8 , 9.

0 500 1000 1500 2000 2500 3000 3500 4000 45000.5

1

1.5

2

roto

r sp

ee

d (

rpm

)

0 500 1000 1500 2000 2500 3000 3500 4000 450050

100

150

200

ge

ne

rato

r sp

ee

d (

rpm

)

time (s)

ωg

ωr

ωg

Figure 7. Rotor speed (blue dashed line) and generator speed(green solid line) time series for drivetrain subsystem.

Fault scenario 1: faults in the drivetrainsubsystemIn this section the effectiveness of the proposed faultestimation design is demonstrated by applying it to a wind


11

0 500 1000 1500 2000 2500 3000 3500 4000 45000

0.5

1

1.5

2

2.5

3

3.5x 10

4

time (s)

ge

ne

rato

r to

rqu

e

Tg,r

Tg

Figure 8. Generator torque reference (blue solid line) andgenerated by generator and converter subsystem (greendot-dashed line) time series.

Figure 9. The pitch position (blue dashed line, black asteriskand magenta point) and its reference (green solid line) for blade1,2 and 3.

0 500 1000 1500 2000 2500 3000 3500 4000 45000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

6

time (s)

po

we

r p

rod

uce

d b

y t

he

ge

ne

rato

r

Pg

Pr

Figure 10. The power generated from the generator (greendashed line) and power refer to the wind turbine (blue solid line).

turbine benchmark Odgaard et al. (2009). The generatorand rotor speed is simulated with a constant and ramp bias

fault during 200s− 400s, 1200s− 1400s, 2200s− 2400sand 3200s− 3400s. Step or ramp signals are the usual testsignal that has used in this paper as the system is capableof responding and estimating different types of fault with theabrupt or incipient profile. The proposed method in this paperis not dependent to signal domain or time occurrence. Thesimulation results are shown in Figures 11-14.

0 200 400 600 800 1000−5

−4

−3

−2

−1

0

1

2

3

4

5

time (s)d

rive

tra

in

fau

lt a

nd

its

estim

atio

ns

fdtDisdtf̂dt

Figure 11. The drivetrain fault (blue solid line), disturbance(green dashed line) and fault estimated (magenta dot line) f̂ in0s− 1000s.

1000 1200 1400 1600 1800 2000−1

0

1

2

3

4

5

time (s)

drive

tra

in

fau

lt a

nd

its

estim

atio

ns

fdtDisdtf̂dt


where it can be seen that the estimated faults follows thereal fault signals closely whether or not a disturbance hasoccurred. Distribution matrices are:

Ed =

100

, Ec = 01

0

, Fd = 11

0

, Fc = 01

0

(64)

and transformation matrices:

T =

1 0 00 1 00 0 1

S = −1.4142 0 0−0.7071 0.7071 0

0 0 1

(65)



2000 2200 2400 2600 2800 3000−1

−0.5

0

0.5

1

1.5

2

time (s)

drive

tra

in

fau

lt a

nd

its

estim

atio

ns

fdtDisdtf̂dt



The observer parameters are designed as follows:RUIO: The RUIOs are proposed to disturbance and faults

rejection separately. The observer parameters are selected asfollow:

H1 =[−.9715

]J1 =

[0 −48.9135 0 0

]W1 =

[−0.6845

]R1 =

[0.0026

](66)

H2 =

[−.0408 0.001510 −1.7169

]J2 =

[0.0042 0 −0.00260 0 0

]W2 =

[1.4152 7.0685e40 0

]R2 =

[0.0001 0.00420 −1

](67)

RSMO: The RSMO scheme is designed to generateestimated faults in the pitch subsystem. The observer

parameters are selected as follow:

N =

[0.9600 7e4−0.0105 2

]k(.) =

[2]

(68)

The estimated fault is shown in Figures 11 - 14 in differentduration, from which it is straightforward to determinewhether there is a fault or not and also the severity of thefault. From the simulation results, there is an exact faultestimation by using the RUIO and RSMO scheme. Thereis different shape and domain for disturbance and faultsignal, but the fault estimator could detect the fault andreject disturbance as early as possible. The high precisionin tracking fault signals occurred at different operating timesof the system indicates the effectiveness of the system. Infault signals with an abrupt change, the estimated signalhas overshoot in their transient responses (Figure 11). Butin incipient fault signals, there is no trace of overshoot(Figure 14). Although overshoot in transient response couldnot affect the estimator and it has followed the changes inthe fault signals. The rapid reaction in this scheme shown inall figures will be effective for starting each FTC scheme.Another scenario that the fault and disturbance occurred indifferent duration is carried out in the following section.

Fault scenario 2: faults in the pitch subsystem

Faults in the pitch system influence the structural dynamicsof the WT. Distribution matrices are:

Ed =

001000

, Ec =

100010

, Fd = 00

1

, Fc = 11

0

(69)

and transformation matrices:

T =

0 0 −1 0 0 00 1 0 0 0 0−1 0 0 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

S =

0 0 −10 1 0−1 0 0

(70)

Faults in actuators and sensors can be estimated effectivelyby RSMO. More information about observers schemes arelisted as:

RUIO:

H1 =[−5.1570

]J1 =

[0 0 32.8329 0 0 −1

]W1 =

[1.0083

]R1 =

[0.0016

] (71)


13

H2 =

−123.5012 −1.0006 −58.0869246.7908 −13.3325 99.74300 0 −0.6481−19.3941 −0.1557 12.6707−115.8723 0.0606 −55.1028

0 00 00 0

−6.1560 −11.69641 0

J2 =

0 00 −10 00 −10 0

W2 =

0 −1.00110 1.00050 00 −0.15920 −0.9380

R2 =

0 00 0−0.0305 00 −0.00130 0.0005

(72)

RSMO:

N =

0.1 −1 0 0 0123.4321 −13.1320 0 0 00 0 0.3 0 0

0 0 0 −5.656 −11.69640 0 0 1 0.15

k(.) =

[20]

(73)The pitch subsystem fault scenarios are presented in termsof pitch angle variations in Figures 15-16. It is easy toknow whether or not a fault has occurred from the providedestimation results. For example in Figure 15, it is clearthat a pitch sensor fault occurred during 200− 400 hasbeen estimated by the proposed fault estimation schemecarefully. Moreover, the estimated signal is not affected bythe disturbance during 500− 700. The estimation of the faultsignal f̂a defined according to (54), is shown in Figures 15-16. With the estimated fault signal, RSMO is carried out withthe strategy presented in ”Fault estimation scheme” section.

Faults in actuators and sensors can be detected effectivelyby the fault estimator scheme. Figure 15 shows the effects ofa fault and disturbance in control mode. The fault has beenestimated, and the disturbance has been rejected accurately.Figures 15 - 16 show effects the incipient fault in controlmode 2. The results show that faults will be estimatedaccurately, and it is not dependent on the operating point ofthe wind turbine. This section and previous section providesome comparative results with respect to fault estimationscheme with a fault in the process and measurementwith disturbance in the process and measurement of awind turbine model. It was assumed that the processunder investigation could be non-linear and its availablemeasurements were usually not absolutely reliable, due tothe wind speed uncertain nature. The simulation results are

2000 2200 2400 2600 2800 3000−1

−0.5

0

0.5

1

1.5

2

time (s)

pitch

po

sitio

n f

au

lt a

nd

its

estim

atio

ns

fpsDisps

f̂ps

Figure 15. The pitch position fault (blue solid line), disturbance(green dashed line) and fault estimated (magenta dot line) f̂ in2000s− 3000s.

3000 3200 3400 3600 3800 4000 4200 4400−5

−4

−3

−2

−1

0

1

2

3

4

5

time (s)

pitch

po

sitio

n f

au

lt a

nd

its

estim

atio

ns

fpsDisps

f̂ps

Figure 16. The pitch position fault (blue solid line), disturbance(green dashed line) and fault estimated (magenta dot line) f̂ in3000s− 4400s.

completely accurate for estimated fault and without anydelay time that is shown in Figures 15 - 16 and also in Figures11 - 14.

Conclusion and Future workThe wind power generation systems have great potential toovercome the environmental problem of reducing carbonemissions. WTs are complex that depends on many factorson the cost associated with maintenance thus it is importantto continue operating in the presence of faults, minimizingdowntime and maximizing productivity. Each WT iscompletely different with foundation properties as well asenvironmental conditions like wind turbulence and waves.This paper has presented on a benchmark onshore version ofa large WT for the simulations and analyzed to examine thedesign of the fault estimation scheme. At first, faults in pitchand drivetrain systems and disturbances in dynamic modeland measurements are considered. Then, with proposedorthogonal transformations, faulty subsystems are separatedfrom the rest of the system. Two reduced order unknown



input and sliding mode observers designed to estimate sensorand actuators faults. Finally, sensor and actuators correctedwith estimated faults. The novelty is the strategy is notdepended to the current controller, but the result will beeffective on the quality of the closed-loop system. Thisconcept can also be applied in the different type of WTswith a variety of control methodologies where describes thecomplexity of the system, reference trajectories, memorycapabilities and other different design factors. This strategycan be easily implemented in practice because of low datastorage and off-line systematic mathematical operations.This method can easily expand to non-linear modelling ofthe physical systems. The system behaviours in simulationsin healthy and faulty conditions are acceptable or closetogether. The proposed fault estimation scheme detects in ashort time the shape and magnitude of the faults. This featureis a novelty for development of other fault tolerant schemesfor WTs itself. The new scheme tracked the fault signalin the presence of any disturbance and rejected it totally,but SMO scheme could not achieve this. To compare oldmethodology, the effectiveness of this scheme is completelyis shown by simulation results. Indeed, a robust scheme isproposed in order to be sensitive to a fault and insensitiveto the disturbance or any unknown input signals. Themost significant contribution of this article is to proposea novel and powerful scheme to remove disturbance inmeasurements and estimate sensor and component faults.The state observer, obtained via a Lyapunov function, andall the procedure is formulated by LMIs. The results ofthe application of these observers to sample models showsatisfactory identification properties in the existence ofoutput and input disturbances. We remark that the resultingstrategies in this paper can be easily implemented in the real-time plant.

Some highlighted issue during the development of thispaper has been detected that could be investigated in futurework. The first is a different type of WTs structures,especially types of floating can be used to analyze thedifferent environmental factors that belong to the systems.The second is the different types of faults. In this paper,faults in two subsystems of a WT were considered, but thereare many sources of faults in present and also the future.The third is fault accommodation that has some limitation incompensation of process faults. Although the proposed faultestimation can conquer all types of faults, the control strategyfor fault accommodation is not suitable for component typesof faults.

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IntroductionWind turbine system descriptionWind turbine modelFault scenariosSystem transformation

Robust fault estimation architectureReduced unknown input observerReduced sliding mode observerFault estimation scheme

Case study: Wind turbine Fault-free caseFault scenario 1: faults in the drivetrain subsystemFault scenario 2: faults in the pitch subsystem

Conclusion and Future work

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