Tushar JAIN,Joseph J.YAM′E,Dominique SAUTER

1.Aalto University School of Chemical Technology,P.O.Box 16100,FI-00076 Aalto,Finland;

2.Centre de Recherche en Automatique de Nancy,Universit′e de Lorraine,54506 Vandoeuvre-l`es-Nancy,France

A novel trajectory-based online controller design approach to fault accommodation in NREL's 5MW wind turbine systems

Tushar JAIN1?,Joseph J.YAM′E2,Dominique SAUTER2

1.Aalto University School of Chemical Technology,P.O.Box 16100,FI-00076 Aalto,Finland;

2.Centre de Recherche en Automatique de Nancy,Universit′e de Lorraine,54506 Vandoeuvre-l`es-Nancy,France

This paper presents a real-time mechanism to tolerate faults occurring in a wind turbine(WT)system.This system is composed of a FAST coded simulator designed by the U.S.National Renewable Energy Laboratory.The demonstrated mechanism lies under the taxonomy of active fault-tolerant control(FTC)systems,namely online redesign based approach.In the proposed approach,we do not use anya prioriinformation about the model of the turbine in real-time.In fact,we use online measurements generated by the WT.Based on the given control specifications,and the observed measurement an occurred fault is accommodated by reconfiguring the online controller such that the WT generates rated power even under faulty conditions.Second,no explicit fault diagnosis(FD)module is used in this approach.As a result,issues of model uncertainty,false alarms,etc.associated with an integrated FD and controller reconfiguration approach to FTC systems are not experienced here.

Fault-tolerant control;Behavioral theory;Wind turbines;Online controller redesign

1 Introduction

Renewable sources of energy are always considered to be on the priority level of energy policies.Seeing to an enormous increase in world population,and to a large-scale utilization of polluting sources of energy,wind power is recognized as one of the valuable nonpolluting renewable sources of energy.In view of this,today many variable speed wind turbines are installed offshore,which contribute to a larger part of world's power production[1].

Various control schemes are designed for wind turbine(WT)systems to deliver the performance specifications[2].It becomes a point of major concern,whenever unknown malfunctions,termed as 'fault',appear in actuators,sensors or other system components.As a matter of consequence,an effectively designed con-ventional control scheme may result in an unsatisfactory performance,or even instability.The control of systems under such scenarios in real-time is known as active fault-tolerant control(AFTC).Generally,an AFTC system is composed of two cascaded working modules,namely fault diagnosis(FD),and controller reconfiguration(CR)[3].The former module is used to detect,isolate,and identify occurred faults,while the latter module reconfigures controller based on a precisely obtained FD information so that the system can still deliver the specified performance.One of the biggest challenges in this cascaded structure is to handle effectively the model uncertainties appearing during FD operation,which can lead to 'false alarms'.In addition,a strong dynamical interaction between the FD module and the CR module imposes some difficulties considering the real-time constraints[4].

In recent years,a significant amount of work has been done that deal mainly in diagnosing a fault,see[5]and the references therein.Within the aforesaid FD-CR integrated AFTC systems,a robust linear parameter-varying FTC is carried out in[6],the use of a fuzzy FTC approach addressing sensor faults is demonstrated in[7],and an adaptive sliding-mode FTC approach is discussed in[8].The worth noting point is that neither FD nor FTC has been demonstrated on the benchmark model considered in this paper apart from the author's earlier work[9].We use the benchmark model of WT designed by the U.S.National Renewable Energy Laboratory's(NREL)National Wind Turbine Center[10],which will be presented in the next section.

Stating precisely,apart from the aforementioned contribution within the paper,the other contribution is to present a measurement-based solution to deal with a problem of controlling the system subjected to unknown faults,where no mathematical model of the WT is used in real-time.In addition,any explicit FD module that extracts in online the information about the system to diagnose a fault is not used.Instead,whenever a fault occurs in the system,the controller is reconfigured online solely based on the real-time measurements generated by the NREL's WT guaranteeing the fault accommodation.This approach lies under the broad classification of AFTC systems,namely the online redesign based approach.We develop a novel measurement-based faulttolerant control mechanism by acquiring the mathematical framework of behavioral system theory[11].In this framework,the interconnection of two dynamical systems via system variables plays the central role.

2 Benchmark model description

The benchmark model is a variable-speed,3-blade horizontal axis wind turbine with a full converter.The basic functionality includes a two-step energy conversion.The first step is to convert the wind energy into mechanical energy,where the wind turns the turbine blades around.In the second step,the mechanical energy is converted to electrical energy by a generator fully coupled to a converter.

2.1 Dynamics of the system

The system is composed of various sub-systems,namely blade&pitch system(BPS),drive train(DT),and generator&converter(GC).The BPS model is the combination of an aerodynamic model,and a pitch model.The latter model is treated as an actuator within the system and will be discussed later together with other actuators.The aerodynamic properties of the wind turbine are affected by the pitch angles of the blades β(t),the speed of the rotor ωr(t),and the wind speedvw(t).This aerodynamic torqueTais applied to the rotor and is expressed by

2.2 Actuator model

In this benchmark WT model,three actuators for the pitch,generator,and yaw systems are modeled and implemented externally,i.e.,apart from the embedded FAST Simulink code.In this paper,we mainly concentrate on the other two actuators but the yaw system.Actually,the yaw actuator model and the associated yaw controller,which is conceived as an overall yaw mechanism is used to orient the wind-turbine upright to the wind direction.The FAST implementing nonlinear WT model requires a yaw angular velocity and yaw angular position as one of the inputs.At all time,it is assumed that a yawing system exists,which keep the wind direction perpendicular to the rotor plane.

The hydraulic pitch system consists of three identical pitch actuators,which is modeled as a differential equation between the pitch angle β and its reference βr.In principle,it is a piston servo-system which can be expressed by a second-order differential system[10]:

where ζ and ωndenotes the damping factor and the naturalfrequency,respectively.The differential equation(2)is associated with each of the three pitch actuators.

In the GC system,the converter loads the generator producing the electric power with a certain torque.The dynamics of the converter can be approximated by a first-order differential system[10],which is given by

whereTgandTg,rrepresents the generated torque and the reference generated torque,respectively,with a constant model parameter αgc=50.The power produced by the generatorPgis given bywhere ηgand ωgdenotes the efficiency of the generator and the generator speed,respectively.

2.3 Fault scenario

Various types of faults are addressed in the literature[10].However,in this paper,we consider a fault that causes an abrupt power drop in the hydraulic pressure.This power drop fault affects the dynamics of the pitch system by changing the parameters,ζ and ωnfrom their nominal or healthy-mode values ζnand ωn,nto their values in faulty-mode ζfand ωn,f.The faulty dynamics of the pitch system can be described by the following second-order differential system:

where

with Θf(t) ∈ [0,1]representing the various operating modes of the WT.

2.4 Fault-tolerant control objectives

The WT principally operates inside four regions or control-zones depending on the speed of windvw(t).In this paper,we consider the wind speed at a mean value of 17m/s,where the control objective is to design controllers such that the generated powerPg(t)can track the rated powerPratedaround its mean value of 5MW.Nevertheless,under the fault occurrence,satisfying the above requirement can no longer be guaranteed.Consequently,the fault-tolerant control objective is to design a real-time controller reconfiguration mechanism such that the aforementioned control requirement on the WT can be fulfilled.In addition,suppressing large transients during accommodating an occurring fault is another requirement from the practical implementation point of view.

3 Real-time fault accommodation

We view a dynamical system as an exclusion law that indicates which trajectories are admissible for the system.A trajectory is a vector-valued functions:T→S,that take its values in the signal space S where T?R is the time axis,S?Rswithsdenoting the dimension ofs(t).The behavior of such systems can be expressed by the set of solutions of a system of linear,constant-coefficient differential equations.The system is defined by a linear differential equation

3.1 Feedback interconnection of dynamical systems

The concept of interconnection plays the central role in modeling and control of system within the behavioral framework.By an interconnected system,we mean a system that consists of interacting subsystems.Here,we deal within the special type of interconnection,termed as the feedback interconnection as illustrated in Fig.1.Let P∈Lw+cdenotes the full behavior of the plant anddenotes the behavior of the controller,wherewithw=col(r,y)andc=col(e,u),whose values lies in the signal space S having the dimension

Fig.1 Feedback interconnection:shaded behavior indicates that no a priori information is available in real-time.

Acquiring the behavioral point of view,we can now define the trajectory-based dynamical system for the plant and the controller byand ΣC=(T,S,C),respectively,where T?R,S?Rr+y+e+u,P?ST,and their behaviors in the following way.

where

withbeing co-prime polynomials,and 0.,andI.representing the zero matrix,and the identity matrix of suitable dimension.From the input/output point of view,yis considered as the output of the plant anduas the input.With this partition of inputs and outputs,together with[12,Definition 3.3.1],evidentlydefines a proper rational matrix withIn a similar way,the behavior of the controlleris given by

where

withbeing co-prime polynomials,andrepresenting a proper rational matrix withDc(ξ)≠ 0.In this controller configuration,uis the output of the controller,andeis the input.Whenever the above two system interconnects,the controller imposes some restrictions on the behavior of the plant.The imposed restrictions on P by C yields the full controlled behavior,which is given by

Generally,the interest lies in controlling the behavior of the manifest variables in the controlled system.The controlled behavior in terms of the manifest variables in the full interconnected system,defined in(9),can be obtained by using the elimination theorem[12,Theorem 6.2.6],which is then given by

3.2 Effects of fault

The real-time notion of controlling a faulty system is that the operating plant must achieve the control objectives at anytime,i.e.,regardless of any occurrence of a fault.In this respect,we can single out a subset of plants' behavior as desirable.We call it the desired behavior,denoted by D,which is provided by an effective failure mode and effective analysis(FMEA).Indeed,this analysis procedure is a mandatory prerequisite to study fail-safe systems[3].FMEA's objective is to forecast systematically how fault effects on elements relate to faults at inputs,or outputs within the elements,and what reactions should be imposed on the system whenever certain faults appear.We termed this phase as the analysis&development(AD)phase that aims at providing a complete coverage of possible occurring faults into the system as well as the achievable or implementable desired behavior.An approach to perform this analysis procedure is presented in[13].The desired behavior D will,indeed,be defined in terms of the manifest variables,which is given by

where

withas the co-prime polynomials,andrepresenting a set of proper rational matrices withDy(ξ)≠ 0.

The International Federation of Automatic Control(IFAC)Safe Process(Supervision and Safety of Technical Processes)Technical Committee defines a fault as an unpermitted deviation of at least one characteristic property or parameter of the system from the acceptable/usual/standard condition.With the above consideration,we define a fault as follows[14].

Definition 1(Occurred faults) A fault is said to be occurred into the system whenever

The real-time FTC problem we are dealing with can now be posed in the following way.Given a vector space of time dependent signals ST,and the desired behavior D,the problem is to 'synthesize' an appropriate controller C,without using any mathematical model of the plant in real-time,which have the suitable control actions such that the controlled behavior K satisfy the desired behavior D at anytime.

3.3 Design and implementation of real-time FTC mechanism

The implementability of the desired behavior plays a key role in an online design of the controller.Otherwise,if the desired behavior is not achievable or not implementable,then no controller exists that can guarantee the fault tolerance in the sense that the faulty system satisfy the specified performance as it was satisfied in the fault-free operating mode.Roughly speaking,the faults for which the desired behavior is not implementable can be termed as 'intolerable faults'.To support the implementability of D,we posit the 'Willems' Theorem'[15].

Theorem 1(Willems' theorem)Let P be a behavior of the plant,and let D be a desired behavior.Then,the following statements are equivalent:

1)D is achievable or implementable with respect to the plant.

2)There exists a controller C that implements D.

3)N?D?Pw,where Pwis the manifest plant behavior and N is the hidden plant behavior,defined by

Based on the above implementability theorem,van der Schaft[16]gives a 'general behavioral description' of the existing controller,irrespective of any particular control configuration,that can implement the desired behavior.

Theorem 2Let P be a behavior of the plant,and let D be the implementable desired behavior.Then,the controller,defined as

implements the desired behavior D.

The controller defined in Theorem 2 is termed as the canonical controller.Basically,this controller is constructed by the interconnection of the plant(with reversed terminal)and the desired behavior.For determining the kernel representation of the above controller C,we will now use the implementability theorem.From the first inclusion of Theorem1,i.e.,N?D,there exists a polynomial matrix,sayL(ξ)such that

where D=ker(D(ξ)),and N=ker(R(ξ)).The full behavior of the plant is given by the following kernel representationR(ξ)w=M(ξ)c.Pre-multiplying the last differential equation byL(ξ),we obtainL(ξ)R(ξ)w=L(ξ)M(ξ)c.From the above,it follows thatD(ξ)w=L(ξ)R(ξ)w=0.This yields the kernel representation of the canonical controller,which is given by

From the above,clearly the controller is constructed for general systems without imposing any realizability requirements.This issue is of utmost practical importance for a possible implementation of the controller in the closed-loop.Theoretically,in[17,Theorem 16],the so-called regularity of interconnection is imposed for the design of the canonical controller.By construction,the control configuration considered in this paper guarantees that whatever be the controller,it will always make the so-called regular interconnection with the plant.In addition,giving a closer look at the kernel representa-tion of the controller given in(12),it includes the plant's embedded knowledge within theM(ξ)matrix,which has to be available in real-time while synthesizing an online controller.As we mentioned before,we do not have any mathematical model of the plant in real-time,i.e.,R(ξ)andM(ξ)matrices are not available during the controller reconfiguration process,therefore,we cannot use the above equation to compute the controller's polynomials.

The main result of this section is given in the following proposition where we directly compute the controller polynomials using the real-time measurements observed from the plant.First,we define the 'filtered' plant signals,denoted by(ˉu,ˉy),which are given as

together with polynomialsDr(ξ),Dy(ξ)considering to take the form as,where

Proposition 1Given a vector space of time dependent signals(TXS),the implementable desired behavior D,for any closed-loop controller C if an unknown fault occurs into the system then the following statements are equivalent:

1)The system is a real-time fault-tolerant control system.

Proof1)?2):Since the desired behavior D is implementable,from Theorem 1 it follows that there exists a controller C that implements D.Therefore,we now only required to synthesize the kernel representation of that controller C without using anya prioriinformation of the plant's model to guarantee the fault tolerance.For the considered feedback configuration,substitute the explicit kernel representation of D and N into(11),which gives

In the sequel,the dimension of the identity and zero matrix will be avoided whenever it is clear from context.

The matrixR(ξ)can be factored as

Putting(16)in(15),we obtain

For the brevity of explanation,we shall omit the indeterminate ξ wherever it is clear from the text.Since the matrixDp(ξ)is invertible,so we can write the last equation in the following form:

Owing to the considered form of the desired behavior,we can further simplified the last equation

Assign the RHP of the last equation toL′(ξ).From(12),it follows that

Accordingly,the kernel representation of the controller(still in terms of plant's parameters)can be written as

Writing it explicitly,we have

Pre-multiply the last equation byand rearranging it yields

From the structure of the feedback configuration,we have the relationThus,the last equation can be written as

Pre-multiplying the above equation by the polynomialNc(ξ)yields

Note that the solution sets(e,y)of(18)will contain those of(17).Using the expression,and from the above,we can write

2)?1):The proof of this implication is trivial,which can be obtained by substituting the filtered plant signals(13)in the kernel representation of the controller C(8).

One of the deep consequences of the above proposition is that the observed signalsis independent of any particular setting in the feedback configuration,i.e.,one can collect these signals with any arbitrary controller working in the closed-loop.Therefore,the controller synthesized in the above manner is a pure 'data-driven online controller',i.e.,a controller which is directly synthesized without a mathematical model of the plant but solely on the basis of the desired behavior and the any experimental input/output data produced by the plant.In this way,we can use the signalˉw,which amounts to the measurements of the physical plant signals col(u,y),to design an online controller 'which-when' makes an interconnection with the plant subject to faults yields the desired behavior.Interestingly,solving equation(14)is a continuous-time system identification problem,which can be solved using various methods listed in the literature[18].Note that on fixing(or if we know)the degree of controller's polynomials at the outset,the controller synthesized using the tools borrowed from the system identification community becomes an approximated controller that implements the desired behavior.

4 Simulations

The model described in Section 2 has just been discussed to show how the dynamics of the WT system evolves.However,we do not use any of this knowledge to demonstrate the proposed real-time fault-tolerant control mechanism.The two control inputs to the wind turbine are the generated torqueTg,r,and the blade pitch angle βr.Since,we are working in Zone-3,the control objective is to track the generator power at its rated value of 5MW.As suggested in[10],the main control scheme is developed in the torque control and the pitch controls from the industry standpoint.FAST also requires a yaw angular velocity and a yaw angular position as inputs.Here no yaw system is installed within the benchmark model since the direction of the wind is considered to be perpendicular to the blades.The torque controller is a nonlinear controller which depends on the wind speed,and the pitch controller is a PI(proportional+integral)controller.In the proposed fault-tolerant controller design,the control objective can be achieved by reconfiguring only the PI pitch controller,described by

where

The nonlinear torque controller,embedded within the benchmark model,will not be reconfigured.With this consideration,the closed-loop system can be viewed as a single-input single-output system.The structural description of the online redesign based fault-tolerant wind turbine control is shown in Fig.2.

In the AD phase,the parameter space Θ(t) ∈ [0,1]was gridded with a 0.1 step yielding eleven points.For testing the proposed FTC scheme,we will focus on two significant faulty dynamics given by the grid values of Θ(t) ∈ {0,0.9}.The AD phase also provides the implementable desired behavior D covering the parameter space Θ(t).To collect the filtered signals,we only need the polynomialsDrandDyof the desired behavior.These polynomials are given asDr(ξ)=49,and a filtered measurement set is observed during every interval of length τ=10s.

Fig.2 Block diagram of the Simulink-based WT FTC system.

The experimental setup considers the wind profile with aerodynamics around the mean speed of 17m/s,which is illustrated Fig.3,together with fault scenarios as discussed in Section 2.3,where the parametric values of the pitch system are taken as ζn=0.6,ωn,n=11.11,ζf=0.1,ωn,f=1.

An experiment is run with an initial value of pitch actuator parameters as ωn(Θ(t)=0),ζ(Θ(t)=0).The parameters of the initial controller operating in the closedloop are computed as

A pressure power drop fault appears within the WT system at time 80s,which changes the value of pitch parameters to ωn(0.9),ζ(0.9).Based on the theory developed in previous sections,a new controller is determined at interval of lengthnXτ,n=1,2,....Thus,a controller C0.9is then computed online and switched into the closed-loop at time 90s.The computed parameters of C0.9are given by

The generated power by the WT system is shown in Fig.4.

Fig.4 Closed-loop signals of fault-tolerant WT system.

It has been shown here that without any fault-tolerant strategy,the dynamics of the system oscillates that might damage some internal components of the Wind Turbine.However,with the proposed real-time faulttolerant strategy,the behavior of the system satisfies the desired behavior at anytime.

Indeed,the online synthesized controller is introduced in the closed-loop through a one-time switch.From the practical implementation point of view,avoiding the appearance of large transients during the switching of controllers is of utmost importance.These unpermitted transients due to an instant switching deteriorates the system performance.To tackle with this issue,we have used the approach proposed in[19,Section 4]that takes care of these undesirable transients appearing during the fault accommodation.In that approach,a real-time smooth interconnection between the unknown plant and the controller is guaranteed using the mathematical framework of behavioral theory.The main idea behind the smooth interconnection is that the 'state'(in the sense of state-space equation)of the new controller is reset whenever it is switched into the closed-loop.Clearly,the effect of real-time smooth interconnection can be visualized in the illustrated figure.

5 Conclusions

In this paper,we have demonstrated a successful implementation of a AFTC system to deal with occurring faults in the NREL's 5MW Wind Turbine benchmark model such that the generator can produce the rated power.The novelty of the demonstrated FTC mechanism lies in its trajectory-based viewpoint derived from the behavioral theory.The fault accommodation delay is the time taken by an FTC algorithm to accommodate a fault from the time it appears in the system.In the traditional integrated FD-FA approach to AFTC systems,a significant amount of time is utilized during the FD operation,and later the controller reconfiguration is initiated.No doubt the primary aim of any FTC system is to accommodate the fault as soon as possible.It has been shown here that an occurring fault is accommodated without using an explicit FD module.Clearly,the aforementioned prevailing issues with an integrated-FD FTC mechanism are not experienced here.The fault accommodation process only considers the real-time trajectories generated by the wind turbine.As a consequence,the fault accommodation delay in the proposed approach is smaller than the delay as experienced in the traditional FTC architecture.

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18 October 2012;revised 14 August 2013;accepted 26 August 2013

DOI10.1007/s11768-014-2234-z

?Corresponding author.

E-mail:tushar.jain@aalto.fi.Tel.:+358-50-4382296;fax:+358-94-7023854.

?2014 South China University of Technology,Academy of Mathematics and Systems Science,CAS,and Springer-Verlag Berlin Heidelberg

Tushar JAINwas born in Meerut,India.He received his B.Tech degree with Honours in Electronics and Telecommunication Engineering in 2007,M.Tech degree in Electronics and Communication Engineering with specialization in system modelling and control from the Indian Institute of Technology(IIT),Roorkee,India,in 2009,and Ph.D.degree in Automatique et traitement du signal with specialization in dependability and system diagnosis from the University of Lorraine(ex.Henri Poincar′e University,a.k.a.Nancy 1),France,in 2012.His research interests include fault tolerant control and fault diagnosis,control in behavioural setting,supervisory control,and bio-inspired optimization.E-mail:tushar.jain@aalto.fi.

received his Ph.D.degreein Applied Sciences with the Highest Distinction from the University Libre de Bruxelles(ULB),Brussels,Belgium,in 2001.He previously graduated from Ecole Polytechnique of the ULB in Electrical and Mechanical Engineering with the title of 'Ing′enieur Civil' and received also the B.E.degree in Automatic Control.He was a research associate in the Control Engineering and Systems Analysis Department of the ULB,Brussels from 2000 to 2005.In September 2005,he joined the University of Lorraine,Nancy,France,as an associate professor in Control Engineering and Computer Science.During the past several years,his educational and research activities have focused on different subjects in systems theory and advanced control engineering with special interests in dual adaptive control of stochastic systems,mathematical control theory with an emphasis on sampled-data control and infinite-dimensional discrete-time systems,and the analytical aspects of fuzzy control.His recent research interest has been mainly concentrated on fault diagnosis/fault tolerant control and networked control systems.He is a member of the Institute of Electrical and Electronics Engineers(IEEE),the American Mathematical Society(AMS),the American Society for Engineering Education(ASEE)and a senior member of the American Institute of Aeronautics and Astronautics(AIAA).E-mail:joseph.yame@univ-lorraine.fr.

Dominique SAUTERreceived his Ph.D.degree(1991)from the University Henri Poincar′e,Nancy,France.Since 1993,he is a full professor at the University(now University of Lorraine),where he teaches Automatic Control.He has been the head of the Electrical Engineering Department during 4 years and Vice-Dean of the Faculty of Sciences and Technology.He is a member of the Research Center In Automatic Control of Nancy(CRAN)associated to the French National Center For Scientific Research(CNRS).At CRAN,he is co-leader of the research Department on Control Identification and Diagnosis including 40 permanent researchers.His current research interests are focused on model-based fault diagnosis and fault tolerant control with emphasis on networked control systems.The results of his research works are published in over 60 articles in journals and book contributions and 150 conference papers.Dr.Sauter is currently serving as an associate editor for the Journal of Applied Mathematics and Computer Science and senior editor for the Journal of Intelligent&Robotic Systems.Dr.Sauter is a member of SafeProcess Technical Committee of the International Federation of Automatic Control(IFAC).He has also been appointed by the IEEE Control System Society to the position of general chair for the organisation of the IEEE Multi-Conference on System and Control 2014(IEEE MSC'14).E-mail:dominique.sauter@univ-lorraine.fr.