Bi Ying,Xie Changchuan,An Chao,Yang Chao

School of Aeronautic Science and Engineering,Beihang University,Beijing 100083,China

Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control

Bi Ying,Xie Changchuan*,An Chao,Yang Chao

School of Aeronautic Science and Engineering,Beihang University,Beijing 100083,China

Active control;Aeroelastic wing;Gust load alleviation;Gust response;Piezoelectric actuators;Wind tunnel test

An active control technique utilizing piezoelectric actuators to alleviate gust-response loads of a large-aspect-ratio flexible wing is investigated.Piezoelectric materials have been extensively used for active vibration control of engineering structures.In this paper,piezoelectric materials further attempt to suppress the vibration of the aeroelastic wing caused by gust.The motion equation of the flexible wing with piezoelectric patches is obtained by Hamilton’s principle with the modal approach,and then numerical gust responses are analyzed,based on which a gust load alleviation(GLA)control system is proposed.The gust load alleviation system employs classic propor tional-integral-derivative(PID)controllers which treat piezoelectric patches as control actuators and acceleration as the feedback signal.By a numerical method,the control mechanism that piezoelectric actuators can be used to alleviate gust-response loads is also analyzed qualitatively.Furthermore,through low-speed wind tunnel tests,the effectiveness of the gust load alleviation active control technology is validated.The test results agree well with the numerical results.Test results show that at a certain frequency range,the control scheme can effectively alleviate thezandxwingtip accelerations and the root bending moment of the wing to a certain extent.The control system gives satisfying gust load alleviation efficacy with the reduction rate being generally over 20%.

1.Introduction

High-altitude long-endurance unmanned aerialvehicles(HALE UAVs)and large transport aircraft are increasingly used for the military and civil aviation industry in recent years.In order to satisfy the requirement of long endurance,largeaspect-ratio wings are commonly used because of their high lift-drag ratio and low structural weight,for example,the Global Hawk,the Helios,and the Sensorcraft with a flying wing configuration.The structures of aircraft(especially the slenderwings)always have noticeable structural flexibility making gust load the main design boundary in aircraft design1;therefore,gust response analysis,load alleviation,and vibration suppression have become research focuses for such aircraft.

Plenty of research works have been carried out on the gust analysis problems of large-aspect-ratio wings.Among them,Su and Cesnik2investigated gust response coupling with flight dynamics of a flexible flying wing.They studied the effects of flexibility,loading distribution,and gust disturbance and found that finite gust disturbances could bring the flying wing to a strong unstable divergence response.Khodaparast et al.3,4developed an approach to rapidly predict the worst case gust loads for aircraft,which could signi ficantly reduce the amount of time and computational effort required to determine the worst case gust loads for aircraft.In comparison to gust analysis methods,there have been more studies in the literature addressing gust load alleviation(GLA)control problems.According to McLean’s work5,using active control will reduce acceleration at particular aircraft stations and airframe loads and improve flying qualities while an aircraft is disturbed by gust.Several control methods have shown a positive effect on reducing gust-response loads.Dillsaver et al.6,7performed linear-quadratic-Gaussian(LQG)gust load alleviation control for a rigid-elastic coupling flexible aircraft to reduce wing deflection by 47%,and also analyzed gust response sensitivity characteristics with stiffness variation for open-and closedloop systems.Tang et al.8studied gust response of largeaspect-ratio flexible wings using analytical and experimental methods and showed that the structural analysis method which was based on a nonlinear beam theory combined with the ONERA aerodynamic model had reasonable accuracy.Frost et al.9applied optimal control allocation techniques on a nonlinear simulation of a generic transport aircraft to alleviate gust loads.Cook et al.10conducted robust gust load alleviation control and stability analysis of a flexible wing.They compared closed-loop responses with open-loop dynamics for both linearized and nonlinear systems to discrete gust distributions and showed that the robust controller could give a good performance in different cases.Haghighat and Liu11completed gust load alleviation of flexible aircraft adopting a model prediction technique and demonstrated the load alleviation effectiveness of the controller for an aircraft encountering discrete and continuous atmospheric disturbances.Wang et al.12employed static output feedback to reduce the wingtip deflections of a solar-powered flexible UAV by 33%.

However,most current works in gust load alleviation control of high-aspect-ratio flexible aircraft focus on various modern control techniques to minimize vertical acceleration and conventionalaerodynamic controlsurfaces are always employed as actuating devices.Under certain circumstances,flexible aircraft exhibit large root bending moments which could shorten the strength and fatigue life of the structure signi ficantly.Hence,gust load alleviation control which can accomplish multi-objectivealleviation including reducing accelerations and root bending moments for flexible aircraft is needed.In addition,there has been little research in different sorts of control actuating methods.A conventional control surface has its own limitations such as limited deflection angles and low frequency band,besides they are mainly used in flight stability and maneuver load control,so there is not enough space for the limits of control authority applied on gust load alleviation.Exploration of new control actuation techniques is one key research aspect in this paper.

Exploration of intelligent materials as beneficial effects on aircraft structures and flight control has been one of the major tasks followed by researchers during the last forty years.Moreover,piezoelectric materials have shown a great application value in aeroelastic control because of their low weight,fast responsibility,simple driving device,high energy efficiency,and flexible distribution.Ehlers and Weisshaar13,14studied wing surface divergence control using piezoelectric actuators.Khot et al.15,16employed piezoelectric actuators in changing the wing surface shape to control flight attitude.Integrated structure and strength design with respect to piezoelectric actuators used in HALE UAVs were first presented by Cesnik and Brown.17Scott18and Hajela19et al.validated the feasibility and validity of wing surface active control by means of piezoelectric actuators.The earliest wind tunnel tests taking advantage ofpiezoelectric actuators to suppress flutterwas completed by Heeg.20Crawley et al.21,22made use of piezoelectric actuators to synthesize a flutter suppression control law and optimize actuators positions,and performed a wind tunnel test.Active buffet suppression of the F/A-18 vertical tail was also accomplished using piezoelectric actuators by Lazarus et al.23Chen et al.24,25utilized piezoelectric materials to perform single-input-single-output(SISO)and multi-inputmulti-output(MIMO)flutter suppression wind tunnel tests.Hui et al.26studied wing surface thermal flutter suppression with distributed piezoelectric actuators.Nam et al.27designed an active aeroelastic wing(AAW)with piezoelectric materials and implemented gust load alleviation with respect to a numerical model.By installing a piezoelectric tab on the aileron trailing edge,Heinze and Karpel28alleviated gust response and performed wind tunnel test validation.Except for the traditional linear condition,Tsushima and Su29tried to install piezoelectric actuators on a numerical nonlinear beam model to achieve gust response alleviation.However,it is very important to notice that using piezoelectric materials as the control method is mainly applied to flutter or buffet suppression and flight attitude control,but with regard to gust load alleviation,the application is still rare.Meanwhile,the more important advantage for applying piezoelectric control to alleviate gustresponse loads is that it will not contend with a flight control system for the limits of control authority.

Above all,most research for gust load alleviation has mainly focused on utilizing different modern control methods to alleviate vertical acceleration by deflecting conventional control surfaces to verify the effectiveness of a certain control technique,but the loading moment is always out of consideration.On the other hand,the application of intelligent materials in flight control has spread primarily on flutter or buffet suppression,which has not taken root in gust load alleviation.Hence,there comes to the idea that exploring piezoelectric intelligent materials to alleviate gust loads including both accelerations and bending moments.In this paper,a method for the gust load alleviation of a high-aspect-ratio flexible wing adopting piezoelectric control is presented,which considers piezoelectric actuators characteristics,unsteady aerodynamics,and feedback control.Moreover,a wing model has been manufactured to carry out gust response and gust load alleviation analysis.Finally,by a wind tunnel test,the method presented in this paper about gust load alleviation with piezoelectric control is validated.The following sections of the paper will describe all the numerical activities that have been performed to realize piezoelectric control and gust load alleviation,as well as the experimental activities with extensive wind tunnel test data.

2.Mathematical modeling

In this section,aiming at a large-aspect-ratio flexible wing with piezoelectric actuators,a structural model will be established by a mathematical method firstly,then the aerodynamic force acting on it will be discussed,and at last,these two structural and aerodynamic models will be connected together to form a synthesized state-space model which is convenient for gust load alleviation control law design and time-domain simulation.

2.1.Structural modeling

In this study,the large-aspect-ratio flexible wing is modeled as a cantilever beam.Fig.1 illustrates the schematic diagram of the whole cantilever wing with a piezoelectric patch system.

For the base cantilever beam,the relationship between the strain and the displacement is written as

where εyis the strain along thezaxis andwis the transverse displacement of the beam.The stress-strain relationship is given by

where σyis the stress andEis the elastic modulus of the material.

The polarization direction of the piezoelectric material is in thezaxis.An outer voltage is applied across the piezoelectric layer thickness.The constitutive equations of the piezoelectric patch are written as

where σpyis the stress,e31is the piezoelectric constant,λ33is the dielectric constant,Dzis the electric displacement,Ez=V0/his the electric intensity along thezdirection,30–33V0is the external applied voltage,andhis the thickness of the piezoelectric layer.

The motion equation of the beam with the piezoelectric patch system will be derived from Hamilton’s principle,which is written as34,35

wheret1andt2are the integration time limits,δ(·)indicates the first variation,TandUare the total kinetic energy and total potential energy of the beam with the piezoelectric patch system,respectively,andWis the work done by external loads.The formulations ofT,U,andWare shown below in detail.

The total kinetic energy of the whole system consists of two parts which are the kinetic energy of the base beam and the kinetic energy of the piezoelectric patch,so the total kinetic energy can be written as

where ρsand ρpare the mass densities of the base beam and piezoelectric patch,respectively,VsandVpare the volumes of the beam and piezoelectric patch,respectively,and the dot denotes the differentiation with respect to the time.

The total potential energy of the whole system consists of three parts including the strain energies of the base beam and the piezoelectric patch and the electric potential energy of the piezoelectric patch,so the total potential energy can be given by

The external work acting on the system is caused by the unsteady aerodynamics which is induced by the structural vibration and the atmospheric gust.The virtual work can be shown as

whereqsandqgrepresent the aerodynamic load components per unit area along thezdirection induced by the structural vibration and the gust,respectively,andAis the surface area of the beam.

The modal approach is applied here to establish the structural dynamics equation,which assumes that the structural displacement vector is a linear combination of some lowfrequency normal modes of the structure.That is,

where Φ(x，y)is the structural mode shapes and q(t)is the generalized coordinate.

Substituting Eqs.(1)–(3)and(8)into Eqs.(5)–(7),the kinetic energy,potentialenergy,and virtualwork are expressed in terms of the normal modes and the generalized coordinate as

where Mmand Kmare the modal mass and stiffness matrices of the whole cantilever beam with the piezoelectric patch system,respectively,KsφandK0are the electromechanical coupling matrix and the piezoelectric capacitance of the piezoelectric patch,respectively,and Psand Pgare the force matrices of the base beam concerning the structural vibration and the atmospheric gust,respectively.

Substituting Eqs.(9)–(11)into Eq.(4)and performing the variation operation in terms of q,then pre-multiplying the equation above with ΦTyields the dynamic motion equation of the whole beam with the piezoelectric patch system as follows:where the left side coefficient matrices M,C,and K are the generalized mass,damping,and stiffness matrices of the whole system.It is obvious that the structural damping effect is excluded in the previous analysis for simplicity,but it can be easily included.Anything on the right side of the equation represents the generalized forces applied on the structure.Fqand Fgare the generalized unsteady aerodynamic forces induced by the structural vibration and the atmospheric gust,respectively,and^B=-ΦTKsφis the generalized driving matrix of the piezoelectric patch.In this study,the generalized matrices M,C,and K as well as the mode shapes Φ derived from the structural finite element method and the dynamic analysis can be easily carried out in common commercial software such as MSC NASTRAN.

Eq.(12)is called the actuator equation which characterizes the piezoelectric actuator driven under the external applied voltageV0.It relates the external applied voltage to the structural deformation.Time-domain aeroservoelasticity(ASE)models for dynamic response analysis and response alleviation control will be established based on Eq.(12).

2.2.Aerodynamic modeling

Unsteady aerodynamics is modeled using the subsonic double lattice method(DLM).36Unsteady aerodynamic forces excited by structure vibration and atmospheric gust in the frequency domain under the generalized coordinate system are given by

where 1/2ρV2represents the dynamic pressure,ρ is the air density,Vis the flight speed,Qqand Qgare the aerodynamic influence coefficient matrices with respect to the structural and gust modes,respectively,which are complex functions of reduced frequency,andwgdenotes the gust velocity.

In order to express the motion equation in a state-space form,the frequency-domain unsteady aerodynamics should be described in time domain.The time-domain aerodynamics can be obtained with Karpel’s minimum-state ration function approximation37

To facilitate time-domain formulation,an augmenting aerodynamic state vector is defined by its Laplace transform as follows:

Its Laplace inverse transform is given below:

Substituting Eq.(14)and Eq.(15)into Eq.(13)and completing the Laplace inverse transform lead to the timedomain aerodynamics

2.3.Synthesized modeling

Synthesized modeling of the flexible wing with piezoelectric control completes the connection between structural modeling and aerodynamicmodeling.Substituting Eq.(17)into Eq.(12),the time-domain aeroelastic equation of the whole system can be expressed as

By connecting Eqs.(16),(18),and(19),the ASE state-space model of the flexible wing bonded with a piezoelectric patch is obtained as follows

Eq.(20)will be used to study the aeroelastic dynamic response and gust-response loads alleviation characteristics of the flexible wing with piezoelectric control by an acceleration feedback method.It is particularly worth mentioning that although the structural modeling above only employs one piezoelectric patch,the process applies to multiple piezoelectric patches as well,in which case,the external applied voltage scalarV0turns into the voltage vector V0.

3.Active control strategy

Based on the state-space model established above,the control law to alleviate gust loads can be designed in time domain.In this section,the control architecture used in this study will be introduced first,on account of which,the control parameters optimization method will be put forward as the next step.

3.1.Control architecture

The gust load alleviation control law is based on a feedback loop as shown in Fig.2.Two pairs of piezoelectric patches are bonded at the wing:one pair lies at the root of the wing spar with a piece on the top and bottom surfaces,respectively,and the other pair lying at the middle of the wing spar is the same.Piezoelectric patches can be activated by appropriate external control voltages to obtain active damping and active mass.The acceleration measured at the wingtip is fed back to the piezoelectric actuators as control voltages with a propor tional-integral-derivative(PID)control algorithm.The control loop contains two same routes which have the same control algorithm to gain two sets of control voltages applying on the piezoelectric patches placed at the root and the middle separately.It is seen that on each route,thezwingtip acceleration passes through a first-order low-pass filter which improves the quality of the sensor signal and then is sent to a PID controller to obtain an external control voltage used for activating piezoelectric patches to alleviate gust-response loads.To avoid excessively high working voltage puncturing piezoelectric patches,signal limiter blocks after the PID controllers have been introduced in the feedback loop.The piezoelectric actuator voltages are limited to±750 V.

whereV0(s)is the Laplace transformation of the piezoelectric patches control voltagesV0(t),kpandkiare the feedback control gains of proportion and integration coefficient in the PI controllers,and subscripts‘1’and ‘2’denote the root and middle piezoelectric patches control routes,respectively.

Time-domain control voltages can now be calculated by performing inverse Laplace transformation,so the control voltages exerted to the piezoelectric actuators can be expressed in terms of the acceleration and velocity at the wingtip as

Substituting Eq.(23)into Eq.(12),the following equation of motion with active mass and active damping is obtained

where Mpand Cpare the active mass and damping matrices due to the piezoelectric patches and are expressed as

It is seen from Eq.(24)that the acceleration feedback control strategy provides the active mass and active damping to the wing.By changing the control gainskpandki,the active mass Mpand the active damping Cpare added to the structure making the structural natural frequency and vibration modes change.Therefore,the structural aeroelasticity will also be changed.In the following sections,it will be observed that the active mass and active damping can alleviate the gustresponse loads of the cantilever flexible wing.

3.2.Control parameters optimization

In general,the control parameters for gust-response loads alleviation are settled in the aircraft control system.The aircraft encounters the atmospheric gust of different frequencies in flight,and ideally,the control parameters settled are expected to alleviate various gust-response loads.However,regardless of what type of controller is and what the control parameters are,the control law designed is only sensitive to the gust disturbance in certain frequency range or some frequency points.Accordingly,in terms of the control system,the effectiveness evaluation criterion of gust load alleviation in a specified frequency band should be put forward.In this study,2.0–6.5 Hz gust disturbance is under consideration.

In aircraft design and simulation,the gust is commonly modeled as a stationary,random,Gaussian process.There are two widely used models,both of which are based on power spectral density(PSD):the Dryden model and the von Karman model.PSD is a frequency-domain function reflecting the signal power distribution along with a frequency change,that is to say,gust characteristics can be described from the viewpoint of energy.Fig.3 illustrates the classical Dryden PSD in 2.0–6.5 Hz,from which it can be seen that the major energy of gust concentrates in the low-frequency range,and with the frequency increasing,the power declines rapidly.Based on this,this paper presents a calculation method evaluating the gust load alleviation level in a specified frequency range,i.e.,

where εGAis the gust load alleviation evaluation indicator,while εjis the reduction rate at the frequency pointjand τjis the weighting coefficient derived from the Dryden PSD,which are given as

whereRopenandRclosedare the peak values of the gust responses when the gust load alleviation control system is open and closed,respectively,p(j)is the PSD at the frequency pointj,andlis the sum of all the frequency points considered.

Based on the gust load alleviation evaluation indicator εGA,the effectiveness evaluation criterion of gust load alleviation in a specified frequency range can be completely described as

In this study,the optimized control parameterskpandkiare chosen from specified intervals to satisfy the effectiveness evaluation criterion.

4.Numerical studies

In Sections 2 and 3,the mathematical modeling and control law design processes for the flexible large-aspect-ratio wing with piezoelectric actuators to alleviate gust loads have been described thoroughly.Here,a numerical analysis will be carried out according to the theoretical methods above.Both an open-loop gust responses analysis and closed-loop gust load alleviation effects will be presented.

4.1.Model description

The semi-span flexible wing model which is used during the numerical analysis and wind tunnel test is shown in Figs.4 and 5.The design parameters of the large-aspect-ratio flexible wing are given in Table 1.

A single spar with a gradually varied ‘+’cross-section is chosen for the stiffness simulation of the wing.The spar made of aluminum alloy is located on the 40%chord line of the wing.The density of the material is 2790.0 kg/m3,the modulus is 70 GPa,and the Poisson ratio is 0.3.The wing shape is simulated by 11 wing sections made of balsa wood and shrinkable film.Each section is attached to the wing spar with a single point.Enough clearance is left between each section to make sure that no stiffness will be added to the wing spar by the external shell.Table 2 shows the detailed parameters of‘+’cross-section belonging to each wing section.

An accelerometer is assembled near the wingtip of the model to measure the transverse and vertical accelerations,and strain sensors are mounted at the root of the wing spar to measure the bending moment.In order to study the active control scheme with piezoelectric actuators,two pairs of piezoelectric patches are mounted on the wing spar,one being fixed at the root and the other in the middle.Fig.4 shows the layout of these sensors and piezoelectric actuators,and the detailed information of the piezoelectric patches is given in Table 3.

In order to obtain the gust responses of the wing model through theoretical computation,an aeroelastic analysis model of the wing is established.The structural finite element model(FEM)depicted in Fig.6 uses the beam element and the lumped mass element for the stiffness and mass simulations,where the piezoelectric patches are also modeled within beam elements.Depending on the finite element model,the structure dynamic analysis with clamped boundary conditions is carried out and the main modal analysis results are presented in Table 4.In order to figure out the safe range of flow velocity,flutter analysis for the FEM is conducted beforehand.Fig.7 shows the aerodynamic model of the wing used to compute the unsteady aerodynamics.The result shows that the flutter speed of this model is 48 m/s,the flutter frequency is about 18 Hz,and the associated modes are the first bending mode and the first torsional mode.Accordingly,it is safe to simulate and test at a flow velocity range of 15–32 m/s.

Table 1 Design parameters of flexible wing model.

Table 2 Parameters of‘+ ’cross-sections along spar.

Table 3 Parameters of piezoelectric patches.

Table 4 Main modal parameters of wing.

4.2.Open-loop results

Open-loop gust response is defined as the response of the wing while the gust load alleviation control system is opened.The simulated flow velocity range is 15–32 m/s,and the gust frequency range is 2.0–6.5 Hz.The wing model is forced to vibrate under the disturbance of sinusoidal gust.Open-loop gust response results at different flow velocities and gust frequencies are depicted in Fig.8.Fig.8(a)and(b)represent thezwingtip acceleration and the root bending moment,respectively.It can be seen that with the flow velocity increasing,thezwingtip acceleration has its peak value with frequency changed from 3.5 to 5.0 Hz.The gust loads of the root bending moment are excited by the first bending mode of the wing,which is for the reason that the root bending moment is more obvious at a frequency of 2.0–3.5 Hz than that of 4.0–6.5 Hz,and the first bending mode of the wing happens around a frequency of 3.3 Hz.

4.3.Closed-loop results

Based on the previous studies of active control strategy elaborated in Section 3,the closed-loop numerical simulation of this wing model under gust disturbance is carried out.According to the gust load alleviation effectiveness evaluation criterion which has been put forward in Section 3.2,the optimized control parameters should be picked up from a design space to meet the requirements of both thezwingtip acceleration and the root bending moment to be alleviated at least 20%.

The design space of control gains isS=S(-0.02≤kp≤ 0，-6.5≤ki≤ 0),which means that the main parameters of interestkpandkiare varied from-0.02 to 0 and-6.5 to 0,respectively,and the satisfactory gains will be chosen in those ranges.In order to simplify,the control parameterskpandkiin one route of the control loop are respectively equal to the counterparts in the other one.The close-loop results are calculated while the flow velocity is 15 m/s and the range of the sinusoidal gust frequency is 2.0–6.5 Hz.In the specified design space,the reduction rates of thezwingtip acceleration and the root bending moment are shown in Fig.9.Here,the reduction rate is calculated by Eq.(26).

According to Fig.9,the optimized parameters range is-0.02≤kp≤0 along with-6.5≤ki≤-4.5.In this range,any control gains combination satisfies the effectiveness evaluation criterion of gust load alleviation,i.e.,it can alleviate both thezwingtip acceleration and the root bending moment above 20%.Furthermore,it is observed that these two objectives can be alleviated respectively 31.02%and 25.43%at most.

4.4.Control mechanism analysis

In general,gust-response loads can be alleviated following the stages below:the motion state of the wing is first detected via an accelerometer,piezoelectric patches are then activated according to the control laws,the external control voltages are generated to drive the piezoelectric actuators,and finally a direct control moment is produced to alleviate the gustresponse loads.

In detail,by means of the numerical analysis aiming at thezwingtip acceleration and some applied moments acting on the wing while the gust load alleviation system is opened and closed,the control mechanism that piezoelectric actuators can be used to alleviate gust-response loads is analyzed qualitatively.Figs.10–12 show the dynamic response processes of thezwingtip acceleration,direct control moments produced by piezoelectric actuators,and the inertia moment,aerodynamic moment,and root bending moment exerting at the wing root,respectively,when the control system begins to work.From the comparison between Figs.10 and 11,it can be seen that at the very start,once the accelerometer feels the movement tendency of thezwingtip acceleration is along the positive direction,the control system activates the piezoelectric actuators to produce control moments along the negative direction to prevent the acceleration from increasing,and then thezwingtip acceleration is reduced.Being aware of the relationship that the inertia moment is in direct proportion to acceleration,therefore,the inertia moment is also reduced as shown in Fig.12(a).Since the starting movement tendencies of the direct control moments and the aerodynamic moment are reversed and the direct control moments suppress the vibration ofthewingtip acceleration,theaerodynamic moment can be led to decrease as well,which is evident in Fig.12(b).In the light of D’Alembert principle,the root bending moment is a consequence of the inertia moment combined with the aerodynamic moment,which comes from the reason that these three sorts of external applied moments acting on the wing are balanced at any moment.Therefore,as Fig.12(c)described,the root bending moment may be alleviated as a result of the comprehensive interaction of both the reduced inertia and aerodynamic moments.

Furthermore,Fig.13 depicts the frequency response functions(FRFs)from the gust velocity input to thezwingtip acceleration and root bending moment outputs respectively for both open-and closed-loop cases.It is obvious that the control strategy is not effective in the whole frequency range,but it works well in different specified frequency bands with respect to different control objectives.As for thezwingtip acceleration,the sensitive gust frequency range of the gust load alleviation control system is 2.0–5.5 Hz as presented in Fig.13(a),and for the root bending moment in Fig.13(b),the sensitive gust frequency range is limited to 2.0–4.3 Hz.In addition,what is worth mentioning is that the control system is valid at low frequencies and disabled at high frequencies for both of the two objects.

5.Wind tunnel testing activities

Wind tunnel tests are carried out to study the gust-response loads of the large-aspect-ratio flexible wing shown in Fig.5,and to verify the capability of active gust load alleviation techniques with piezoelectric control.Techniques of aeroelastic model design,manufacture,test,and measurement are also investigated.All tests of the flexible wing model are performed in a 3 m×3 m low-speed wind tunnel.

5.1.Design of test subsystem

5.1.1.Support system

The test model is vertically fixed on a support system in the wind tunnel to avoid the influence of gravity,as shown in Fig.14.The root of the model is clamped with a-0.2°angle of attack.At the joint between the support system and the wing model,there mounts a force balance to measure the forces and moments in six directions and an angular rate gyro to measure the incidence angle of the test model.The support system is designed to be absolutely rigid and its vibration frequency is more than three times over the frequency of the wing model so that its influence on the wing cannot be taken into account.Fig.15 shows the wing model being tested.

5.1.2.Gust generator device

A gust generator is designed to produce expected gust disturbance during the tunnel tests.The major parts of the gust generator are two rectangle blades as given in Fig.16.The NACA 0015 airfoil is used,the span length of the blades is 2000 mm,the chord length is 300 mm,and the distance between the two blades is 600 mm.The gust generator is placed in front of the test model at a certain position so that the wing model is 2000 mm downstream from the blades of the gust generator.The two blades driven by a direct current motor of 500 W deflect sinusoidally and synchronously,and they rotate about their own main beams located at the 25%chord line.The deflecting angle range is 0–±7°and the deflecting frequency is 1–7 Hz.

According to the results in Ref.38,when the blades deflect sinusoidally at a certain frequency,the lateral gust which is approximatively sinusoidal can be generated in the test field,and the gust velocity can be written as

whereamis the amplitude of the blades deflecting angle,andAgis the gust disturbance coef ficient which is relevant to the flow velocityVand the blades de flecting frequencyfand is calibrated by the test.

5.1.3.Measure-control system

The functions of the measure-control system in the wind tunnel test contain gust load alleviation control,vibration monitor,and data recording,as given in Fig.17.Hardware devices used in the test include data acquisition cards,dynamic strain gauges,and low-pass anti-mix filters.The software module is developed on NI Labview software.The gains of the gust load alleviation control loop can be adjusted independently as well as the switches.During the test,the gust load alleviation control loop can be switched between on and off in order to validate the effect of the gust load alleviation system.

5.2.Gust responses wind tunnel test

5.2.1.Experimental conditions

The gust responses wind tunnel test aims to validate the correctness of the aeroelastic modeling of the large-aspect-ratio flexible wing with piezoelectric modules and to have an insight into the characteristics of the wing test model.The wing model are tested in a flow velocity range of 15–32 m/s and a gust frequency range of 2.0–6.5 Hz.Table 5 shows the actual test conditions,and for each flow velocity,the test model is disturbed by the sinusoidal gust from 2.0 to 6.5 Hz.Gust responses includingzandxwingtip accelerations and the root bending moment are recorded.

5.2.2.Comparison between numerical results and test results

The comparisons between the numerical results and the test results corresponding to thezwingtip acceleration and the root bending moment at a flow velocity of 15 m/s and a gust frequency of 3.5 Hz are shown in Fig.18,where the test results are filtered data after 12 Hz low-pass filtering.It can be seen that the test results of both objects coincide well with respective numerical results and the maximum error is less than 5.07%.In addition to the above comparisons in the time domain,they are also compared in the frequency domain.As illustrated in Fig.19,the peak values of responses with respect to thezwingtip acceleration and the root bending moment,when the wing model is tested at different velocities velocities with gust disturbance in the whole frequency range,are compared with their counterparts in numerical simulations.From Fig.19,it can be observed that most of the test data agree well with the theoretical numerical results except for several bad data points whose motional tendencies deviate from their neighboring data obviously.The disturbed data acquisition equipment or unstable sensors may bring about the appearance of bad data.According to the comparisons above,it can be said that the aeroelastic modeling method of this wing model is valid.

Table 5 Test conditions of gust responses wind tunnel test.

5.2.3.Effects of gust frequency on gust responses

Gust responses are relevant to gust frequency and flow velocity;here,the effects of gust frequency are discussed firstly.Three objects of concern are thezwingtip acceleration,thexwingtip acceleration,and the root bending moment.Figs.20 presents gust responses of these three objects vs gust frequency at different flow velocities.

According to Figs.20(a)and(b),for all flow velocities,the response of thezwingtip acceleration rises up to the peak increasingly and then fluctuates,and with regard to thexwingtip acceleration,its response generally increases to the maximum and then decreases with the gust frequency.With the wind speeding up,both thezandxaccelerations at the wingtip have their peak values when the frequency changes from 3.5 to 5.0 Hz.The major reason for the phenomenon is that the responses of the wingtip accelerations at low flow velocities are excited by the first bending mode of the wing which is about 3.5 Hz;at high flow velocities,however,by the first bending mode in-plane which is about 5.0 Hz.As for the fact shown in Fig.20(c)that the root bending moment is more obvious at a frequency of 2.0–3.5 Hz than that of 4.0–6.5 Hz,that is mainly because this object is sensitive to gust of low frequencies.

5.2.4.Effects of flow velocity on gust responses

In the above section,the effects of gust frequency on gust responses have been analyzed.In this section,the effects of flow velocity which is the other factor in fluencing gust responses will be explored.Fig.21 presents the tendencies ofzandxwingtip accelerations and the root bending moment vs flow velocity,respectively.Fig.21 indicates that all of these three objects increase generally with the flow velocity,and their peak values are achieved at 32 m/s.This follows the common sense that at a certain frequency of gust disturbance,the gust responses become greater with the flow velocity increasing.

5.3.Gust load alleviation wind tunnel test

5.3.1.Experimental objective

The objective of the gust load alleviation wind tunnel test is to verify the active control technique that employs piezoelectric control to reduce the gust-response loads including thezandxaccelerations at the wingtip of the wing and the bending moment at the section of the wing root.

The signal used as a feedback to the control system is thezwingtip acceleration.The control system for gust load alleviation utilizes two pairs of piezoelectric actuators located at the root and middle of the wing respectively as its control driving devices.A classical PID controller used in the control scheme treats the feedback signal as its input signal and its out signal is the driving voltages to actuate piezoelectric patches to generate control moments by which to alleviate the gust-response loads.Detailed information about the gust load alleviation control scheme refers to Section 3.1 above.

The capability of the control method proposed in this study is investigated when the test model is at different flow velocities along with gust disturbance of different frequencies.Abundant experimental data and control law parameters of various test conditions are recorded and analyzed.In this paper,the gust load alleviation analysis at an operating point that the flow velocity is 15 m/s is taken to make intensive discussion,which is explored overall here to evaluate the effectiveness of the active control technique.As for other flow velocity conditions,the alleviation effectiveness and the trend with gust frequency are generally similar to those of 15 m/s,besides some numerical deviation.Table 6 shows specific test conditions.Aiming at this low flow velocity test status,in order to avoid complexity,a set of effective gain values is obtained through an analysisadjust procedure as shown in Table 7.

Table 6 Test conditions of gust load alleviation wind tunnel test.

5.3.2.Gust load alleviation analysis of z wingtip acceleration

The test results with respect to thezwingtip acceleration including both open-and closed-loop cases are shown in Fig.22.According to the comparison curves illustrated in Fig.22,it can be noticed that thezwingtip acceleration is alleviated at specific frequencies including 2.5,3.5,4.0,5.5,and 6.5 Hz,which take up half of the whole frequency range.That is to say,the active control scheme is capable of alleviating thezwingtip acceleration since the scope of its efficacy is up to 50%.Although the control system is not able to alleviate thezwingtip acceleration at a frequency of 4.5–5.0 Hz,even making them larger than the open-loop results,but for the invalid frequencies left,the closed-loop results are nearly equivalent to the open-loop results without increasing them.The reduction rate which is defined by Eq.(27)evidently achieves the maximum 28.32%at 4.0 Hz,and the control system can also alleviate the peak value at 3.5 Hz of the openloop results by 20.10%.According to the previous analysis that thezwingtip acceleration at a low flow velocity is excited mainly by the first bending mode of the wing about 3.3 Hz,it can be said that the control scheme functions well to suppress the vibration of this mode.Furthermore,comparing the experimental response curves in the frequency domain illustrated in Fig.22 with the theoretical FRF curves shown in Fig.13(a),it is clear that the dynamic tendencies of the test results basically coincide with those of the numerical simulations for both open-and closed-loop cases.The test results indicate that the control system is functional for most frequencies below 5.5 Hz and is out of work for high frequencies,which is consistent with the theoretical control effectiveness analysis results as elucidated in Section 4.4 as well.Hence,the theoretical study of control efficacy and the effective frequency interval is partly verified by tests.Fig.23 presents the time-domain original signal of gust responses of thezwingtip acceleration with the control system on and off when the gust frequency is 3.5 Hz.Fig.24(a)shows the single-sided PSD of the original unprocessed test data and Fig.24(b)shows the filtered data after 12 Hz low-pass filtering.

The alleviation efficacy of the control scheme acting on thezwingtip acceleration is shown in Table 8.It can be observed that the scheme gains a better effect at low and middle frequencies than at high frequencies,and most of the reduction rate are over 20%.

According to the analysis above,it comes to a conclusion that the control method proposed here that takes advantage of piezoelectric patches as control actuators to alleviate thezwingtip acceleration is proven feasible.

5.3.3.Gust load alleviation analysis of x wingtip acceleration

As far as the long large-aspect-ratio straight wing is concerned,when it is in gust disturbance,the structural damping of inplane modes is always so small that the transverse gust response is large enough not to be ignored.Moreover,the sweep angle of the wing can have an effect upon the transverse dynamic response as well,for the reason that with an increase in the sweep angle,the degree of coupling between in-plane modes and torsional modes gets stronger,which leads to a larger transverse dynamic response for such a wing.In terms of the wing model tested in this study,according to the results of gust responses wind tunnel tests shown in Figs.20(b)and 21(b),the first bending mode in-plane can excite a large gust response of thexwingtip acceleration which is in the same order of magnitude with that of thezwingtip acceleration.As a consequence,the gust load alleviation effectiveness of transversexwingtip acceleration should also be investigated.

The test results corresponding to thexwingtip acceleration are shown in Fig.25 which illustrates both open-and closedloop cases.It can be seen from Fig.25 that the control scheme alleviates thexwingtip acceleration at a frequency range of 2.5–4.5 Hz and 5.5 Hz greatly,but as for the rest of the frequency points,their closed-loop results are virtually equal to the open-loop results,and the reduction rate reaches the maximum 64.68%at 3.5 Hz.In accordance with thezwingtip acceleration,the first bending moment mode about 3.3 Hz also acts an important role in the gust response of thexwingtip acceleration,and the reduction rate exceeding 50%at 3.5 Hz proves that the vibration of this major mode is suppressed by the control system again.Fig.26 shows the time-domain original open-loop gust response of thexwingtip acceleration at 3.5 Hz in comparison to the closed-loop result.Fig.27(a)and(b)are the single-sided PSD of measurements of the original and 12 Hz-filtered test data,respectively.

Table 9 presents the alleviation efficacy of the control scheme acting on thexwingtip acceleration.According to Table 9,the reduction rates at low and middle frequencies can exceed 50%,which proves that the control system has a good performance on the alleviation of thexwingtip acceleration.

Based on the results above,it can be said that the active control strategy designed in this study is an efficient mean to alleviate thexwingtip acceleration caused by gust.

Table 8 Open-and closed-loop results comparison of z wingtip acceleration.

5.3.4.Gust load alleviation analysis of root bending moment

Fig.28 depicts practically the measured open-and closed-loop results concerning the root bending moment.As can be seen in Fig.28,the gust responses of the root bending moment are much stronger at low frequencies,and the control scheme functions well at gust frequencies of 2.5 and 3.5 Hz;besides,the responses of the root bending moment are smaller at 4.0–6.5 Hz,and the gust load alleviation efficacy is less.Although the scheme is not able to alleviate the peak value of the open-loop results at 3.0 Hz,it is quite capable of alleviating the secondary maximum of the root bending moment at 3.5 Hz over 45%.Furthermore,for the invalid statuses in the whole frequency range,the closed-loop results are almost the same as the open-loop results without making them greater.Through the comparison between the experimental response curves in the frequency domain described in Fig.26 and the theoretical FRF curves shown in Fig.13(b),it should be noticed that the overall experimentally measured dynamic tendencies of open-and closed-loop results are generally in agreement with the theoretical numerical simulations,except for the frequency point of 3.0 Hz at the closed-loop condition,hence,this test point is supposed to be bad data.According to the test results,the control system works relatively well for frequencies below 4.0 Hz and loses efficacy for high frequencies,which is basically in line with the predictions analyzed in Section 4.4.So far,the theoretical evaluation of the control system’s performance and characteristics is proven through tests to some extent.Fig.29 shows the original time-domain comparison curves of the root bending moment between open-and closed-loop resultsat3.5 Hzwherethereduction rate also reaches the maximum.Figs.30(a)and(b)are the single-sided PSD of the original test data and that after 12 Hz-filtering,respectively.Takenoticeofthepreload 2.4 N·m of the root bending moment,which is caused by the initial nonzero angle of attack of the test model.

The alleviation efficacy of the control scheme acting on the root bending moment is shown in Table 10.It can be seen that at a low frequency range,the control system can achieve a reduction rate of 23.53%–47.31%,and even at a high frequency of 5.5 Hz,it can also alleviate the load by 22.70%.On account of the analysis above,the responses of the root bending moment concentrate on low frequencies and the control system works well in this frequency range;hence,the conclusion is drawn out that alleviating the root bending moment by the control scheme designed is applicable.

Table 9 Open-and closed-loop results comparison of x wingtip acceleration.

Table 10 Open-and closed-loop results comparison of root bending moment.

6.Conclusions

Focusing on a large-aspect-ratio flexible wing,an active control technique using piezoelectric actuators to alleviate gust-response loads is investigated in this paper.Applying Hamilton’s principle with the modal approach,the motion equation of the wing with piezoelectric patches is obtained.An acceleration feedback control strategy with PID controllers is used to realize gust load alleviation.The gust responses and gust load alleviation characteristics of the wing model are analyzed by a numerical method in time-domain and an effectiveness evaluation criterion of gust load alleviation according to Dryden PSD is put forward;furthermore,the alleviation mechanism analysis of piezoelectric control is explored qualitatively.Based on the numerical studies,gust responses and gust load alleviation wind tunnel tests are carried out in a low-speed wind tunnel.Conclusions are drawn as follows:

(1)The test results agree well with the numerical simulation results,which verifies that the aeroelastic modeling method and the gust response analysis method of the flexible wing with piezoelectric actuators proposed in this paper are valid.

(2)Gust responses are affected by gust frequency and flow velocity.In general,with the gust frequency increasing,thezandxwingtip accelerations and the root bending moment rise up to the peaks and then decrease;however,they have their maximums at different frequencies,because different quantities have different sensitive frequencies.Besides,during the gust disturbance,all of the three objects generally increase with the flow velocity.

(3)The active control strategy that employs piezoelectric patches as control actuators,uses wingtip acceleration as the feedback signal,and adopts the classic PID controllers to alleviate gust-response loads is proven feasible,not only by numerical simulations but also by the wind tunnel test.

(4)The control scheme functions well to suppress the wing vibration which is excited by the sinusoidal gust disturbance,and the peak values ofzandxwingtip accelerations and the root bending moment can be alleviated by 20.10%–64.68%.

(5)The theoretical predictions of control system performance and characteristics are proven through the wind tunnel test.The gust load alleviation control system only works well at a certain range of gust frequency in alleviatingzandxwingtip accelerations and the root bending moment.For measured data like the bending moment,the same alleviation control law works better at low frequencies than at high frequencies.Test results also indicate that at specific gust frequencies,the control system is effective to alleviate these three control objectives at the same time.

The relevant work in this study is only a preliminary exploration,but it is of significant value for future engineering applications.There are still some disadvantages for piezoelectric actuators,for example,they have strong extension strength but weak shearing,their working voltages are a little higher,which requires special requests for the airborne energy,and moreover their layouts and installations on an airplane structure also need serious consideration.In follow-up work,we will explore further into the various aspects of piezoelectric control,such as utilizing piezoelectric patches to obtain torsion control,optimizing the positions of piezoelectric actuators,considering the control law optimization for the wing model,and so on.

Acknowledgements

The study was supported by the National Key Research and Development Program(2016YFB 0200703).The first author wishes to acknowledge all of the fellows in the Aeroelastic Laboratory at Beihang University.This study could not have been completed without their help.

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24 May 2016;revised 26 July 2016;accepted 4 September 2016

Available online 21 December 2016

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*Corresponding author.

E-mail addresses:15810538220@163.com(Y.Bi),xiechangc@163.com(C.Xie),ac_buaa@163.com(C.An),yangchao@buaa.edu.cn(C.Yang).

Peer review under responsibility of Editorial Committee of CJA.