Wind tunnel test of gust load alleviation for a large-scale full aircraft model

Dongqing ZHAO, Zhihun YANG, Xinng ZENG, Jinge YU,Yining GAO, Guoning HUANG

aSchool of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China

bAVIC The First Aircraft Institute, Xi’an 710089, China

cAVIC Aerodynamics Research Institute, Harbin 150001, China

KEYWORDSAlleviation;Full model;Gust generator;Suspension system;Wind tunnel

AbstractWind tunnel test is an important way to test the performance of Gust Load Alleviation(GLA).At present, some component-level wind tunnel tests have been carried out in big aviation countries, but there is a lack of full aircraft model GLA tests.In this study, a set of large-scale GLA test system in low-speed wind tunnel is developed, which includes a gust generator, a fivedegree-of-freedom suspension system, a full elastic aircraft model with control system, and gust load measuring devices.Two control schemes based on closed-loop feedback control and openloop feed forward control are respectively designed and verified by the full-model GLA tests in the wind tunnel.The experimental results show that the designed gust generator can generate a stable wideband, wide-area gust wind field; the suspension support system can sustain static and dynamic stability during wind tunnel test,and enables the model moving in the horizontal,vertical,pitching,rolling and yawing directions.The results show that the closed-loop feedback control can obtain good control performance of reducing the peak values of elastic vibration response induced by gust excitation, but has little effect on suppressing the rigid body motion excited by lowfrequency gust, while the open-loop feed forward control presents superior performance in alleviating the high-frequency elastic vibration as well as the low-frequency rigid body motion with more than 40% overall reduction rate.

1.Introduction

The gust during flight imposes dynamic load on aircraft and reduces the riding comfort of passengers1,2.From the perspective of structural strength,the aircraft may be damaged due to overload under severe gust3.For aircraft with high-aspectratio and high-flexibility wing, Gust Load Alleviation (GLA)using active control is important for the flight safety and flight quality of aircraft, which can suppress the airframe response under gust excitation, reduce the structural load, and improve the riding comfort and fatigue life of structures4,5.At present,the main targets of GLA are to suppress rigid body motion and wing elastic vibration6,7.

Since the 1960s,the United States has been carrying out the design and test verification of GLA,and has developed mature low-speed wind tunnel GLA test capabilities.The flight test and verification of GLA control have been completed on aircraft such as L1011,B-52,and C-5A8–12.Some large civil airplanes, such as Boeing B787 and Airbus A380, have successfully applied GLA control13.

In the wind tunnel test of GLA, gust generator is an essential device.Many research institutions and universities have developed different devices to generate gust field,such as rotating slotted cylinder type14,oscillating vane15–18,cascade oscillating airfoil19, oscillating flap on the wing20, and some special ways such as miniature surplus computer cooling fans to generate random gust21,a wire grid to generate continuous gust22, etc., among which oscillating vane is the most commonly used.Russia and the United States have developed mature gust wind test equipment and technical capability.The capability of low-speed wind tunnel gust test in China has also been preliminarily developed23–29.Kuznetsov introduced the gust wind generating device of the T103 wind tunnel in Russia30.Due to the inertia of the vane and the power limit of the oil pump of the hydraulic actuator,the deflection velocity of the vane is half of the desired velocity.Moreover, the suspension system in the wind tunnel is not flexible enough,and its rigid body frequency is close to the modal frequency of elastic model and hence affects the dynamic load measurement.In T104 wind tunnel of Russia, the transverse distribution of gust wind is not uniform, and the gust amplitude at the side wall is almost twice as much as that at the center at most.In most studies,single elastic-wing or half-wingspan aircraft model was adopted, such as the low-speed wind tunnel gust load response test at Delft University in the Netherlands17, the wind tunnel X-DIA gust load test at Milan University of Technology in Italy31,the two-dimensional airfoil GLA test at ONERA S3 wind tunnel in France32, the semi-modal gust load test at ARA-TWT wind tunnel in the United Kingdom33,and the GLA test at TDT wind tunnel in the United States34.Wind tunnel tests of GLA for the full aircraft model are less reported in the existing literature.However,there are some disadvantages in the GLA test of single wing or half model.The effect of the rigid body motion cannot be taken into account with single wing,and the performance of fuselage acceleration and attitude alleviation cannot be determined.For half model,vertical support of the wind tunnel floor is usually used to eliminate the influence of gravity and to realize free rigid body motion of the model on the supporting mechanism; however,the force and deformation of the half model change with air speeds, and the unexpected force between the model and the supporting mechanism results in the inflexibility and even hysteresis of the longitudinal motion.Also, the influence of antisymmetric modes cannot be considered.Therefore, it is necessary to develop a large-scale low-speed test device of gust load in wind tunnel,and carry out the study of full-model GLA test.

In the study, a set of large-scale GLA test system in lowspeed wind tunnel is developed, which includes a gust generator, a five-degree-of-freedom (five-DOF) suspension system, a full elastic model with control system,and gust load measuring devices.Two control schemes, namely, closed-loop feedback control and open-loop feed forward control, are designed,and their GLA performances are verified by wind tunnel test.

2.Computation scheme

2.1.Simulation model

The aeroelastic equation of aircraft motion under gust load is

where ξ is the generalized modal coordinates of the elastic aircraft that includes the rigid body motion and elastic vibration modes,Mξξ,Cξξand Kξξare the generalized mass matrix,generalized damping matrix and generalized stiffness matrix,respectively, and fξand fgare the generalized unsteady aerodynamic forces caused by aircraft motion and gust excitation

where q is the air density,V is the free stream velocity,ωgis the gust velocity,Aξand Agare the generalized aerodynamic coefficient matrixes, and their frequency domain form can be obtained by Double Lattice Method (DLM).

By transforming Eq.(1)into the frequency domain,the following equation is obtained:

In the design of GLA control system, the elastic aircraft system has multiple inputs (e.g., gust disturbance and control surface deflection) and multiple outputs (e.g., structural responses).Therefore,the control law cannot be simply decoupled, and thus the frequency domain form has to be transformed into time domain for control synthesis.Therefore, it is necessary to transform the discrete form of unsteady aerodynamic coefficient matrix in frequency domain into a continuous form capable of state-space modeling by Rational Function Approximation (RFA).The RFA mainly includes Least Square (LS) method, Minimum State (MS) method and fit state-space Matrix Approximation(MA)method.Considering the model order and fitting precision, MS method is selected to fit the unsteady aerodynamic coefficient matrix.

In the present study,Aξis approximated by MS method as

where b is the reference half-chord length,s is the Laplace variable,R is the aerodynamic lag term diagonal matrix,I is the unit matrix,and Aξ0;Aξ1;Aξ2and D;E are the fitting rational coefficient matrices.By introducing the aerodynamic lag state vector,Eq.(3)can be transformed into the state space equation as

In Eq.(1),since fgis not a time domain form and cannot be solved directly,the generalized gust aerodynamic vector in the time domain is obtained by Fourier transform, and then the ordinary differential Eq.(5) are solved by numerical method to obtain the motion response of the aircraft under gust wind.By combining the state space equation of the elastic aircraft model,the actuator model,and the gust model,the state space model of the aircraft with actuator system under gust excitation can be obtained.Furthermore,the closed-loop state space equation can be obtained in conjunction with the state space equation of feedback control law35.

2.2.Gust model

The gust model includes discrete gust and continuous gust in most studies36.Typical forms of discrete gust are step gust,‘‘sine”gust, ‘‘1-cos”gust and so on37.The ‘‘sine”gust is generally chosen for wind tunnel test,because it is easy to generate and avoids some uncertainties caused by the complex gust forms.Moreover,the positive and negative fluctuations caused by the‘‘sine”gust offset the energy and are more favorable for the model to maintain at a certain height.

The ‘‘sine”gust, as shown in Fig.1, is expressed as

where wg0is the amplitude of the gust,L is the scale of the gust,x0is the distance of the model from the gust field,and V is the free stream velocity.

3.Control law design

3.1.Closed-loop feedback control

Fig.1 ‘‘sine”gust model.

Fig.2 Schematic diagram of closed-loop GLA control.

Fig.3 Flowchart of closed-loop feedback control.

Based on the state-space model of aircraft with actuator under gust excitation, the gust load response and the design of control system can be implemented by simulation program.The diagram of closed-loop feedback control is shown in Fig.2.In the wind tunnel test,the gust induced wing-tip vibration signals acquired by the sensor are sent to the control system, the control commands are sent to the actuator controller,and then the aileron deflection re-distributes the wing load to reduce the structural responses.As velocity sensor is not installed at wing tip in the wind tunnel test, the velocity is constructed by integrating the wing tip acceleration signal,and the low-frequency signal drift caused by the integral is eliminated by a high-pass filter.The controller structure is shown in Fig.3,where awtand vwtare the vertical acceleration and the wing tip velocity respectively, ω1is the cut-off frequency of the first-order high-pass filter, ω2is the characteristic frequency of the lowpass filter, δais the aileron deflection, and Kais the feedback gain.The gain is adjusted to reduce the wing tip acceleration while maintain aeroservoelastic stability.The low-frequency signal drift generated by the integrator could be partially eliminated by the high-pass filter.If the noise has a strong effect,other control methods such as approximate integrator could be used.

3.2.Open-loop feed forward control

The open-loop feed forward control presets the position of control surface according to the real-time measured gust field to directly offset the aerodynamic increment produced by the gust wind.When the model encounters low-frequency longitudinal gust,the gust field can be equivalent to the superposition of the uniform vertical gust and the pitching gust.The uniform vertical gust is equivalent to applying an additional angle of attack αgto the model,and the effect of pitching gust is equivalent to the aerodynamic force generated by the pitching motion of the model with corresponding pitch rateqg.

The increment of lift LIand pitching moment MIgenerated by longitudinal gust are shown as follows:

In order to suppress the increment of aerodynamic force caused by gust wind, the effect of control surface deflection is to produce an equal and opposite aerodynamic force.The best control surface for this task is the elevator.Due to the response delay of the angle of attack to elevator input, it is impossible to instantaneously suppress the effect of the gust wind.Therefore, direct lift is generated to counteract the impulse force through the combined deflection of the control surfaces.Based on this scheme, the equations of gust suppression are established as follows:

For the dynamic load induced by gust, the feed forward control needs to eliminate this effect by aileron deflection to produce incremental bending moment of equal size and opposite direction.The transfer function Gag（s ）is a complex highorder block of the vertical wing-tip acceleration awtto the vertical gust velocitywgn.Gaδ（s ）is the transfer function of awtto the aileron deflectionδa.At main concerned frequency,such as the 1st wing bending frequencyωb,the controller C is designed,and thus we have

Based on the principle of rigid body motion and elastic vibration suppression, the feed forward control law is designed to integrate direct force control of rigid motion and reverse force control of elastic vibration as shown in Fig.4, where wgis the vertical gust velocity at the reference point, wgnis the vertical gust velocity lags behind wgat the measured point, and τ=x0/V is the lag time constant of aileron deflection to gust velocity.Compared with the closed-loop control, the openloop control has no effect on the stability of the model itself,the elastic stability of the aeroservoelasticity, and the flutter characteristics.

4.Experimental setup

4.1.Model description

In the wind tunnel test,the most commonly used elastic model is the flutter model38.The gust load model is similar to flutter model,but has some difference.The basic design requirements of the full gust load model are: accurately simulating the stiffness and mass characteristics of the aircraft;having connecting mechanism with the wind tunnel suspension system; having controllable control surface and equipped with actuators that meet the requirements of frequency bandwidth; installing attitude sensor, strain gauge and acceleration sensor.Weight is also a key concern in wind tunnel model design.The model cannot be too heavy, so that, under available wind speed,the model lift can counteract partial gravity and realize rigid body motion.According to the aircraft size,weight,wind tunnel size and wind speed range, the selected length scale and velocity scale are 1:8 and 1:6 respectively.The basic characteristic parameters of the model are shown in Table 1.The model structure,as shown in Fig.5,adopts several materials to accu-rately simulate the quality and stiffness characteristics and to meet the strength requirements.

Table 1 Test model specification.

Fig.4 Block diagram of open-loop feed forward control law.

Fig.5 Design of test model.

The test model was manufactured based on the design,and Ground Vibration Test (GVT) was conducted to obtain the vibration characteristics of the model, as shown in Fig.6.The comparison of the calculated and the GVT measured maximum rigid body mode and low-order elastic modal frequencies of the model with spring suspension are shown in Table 2.The frequency of the maximum rigid body mode is 1.01 Hz, less than one third of the lowest order elastic mode frequency.The frequency of the 1st wing symmetric bending mode, the key mode that affects the structural responses, is 3.07 Hz.The error between the calculation and the experimental results is less than 5%, which demonstrates that the established dynamic finite element model can reflect the vibration characteristics of the test model, and can be applied for the gust load analysis and control law design.

In order to ensure the safety of the model,the wind speed of the GLA test is generally below the flutter speed,so the flutter characteristics of the model are calculated.The calculated results are shown in Fig.7, and the flutter speed is above 50 m/s.

To realize attitude control and gust load alleviation of the test model, six control surfaces including left/ right ailerons,left/ right flaps and left/right elevators were designed.Electric-servo actuator includes motor, gearbox and numbering apparatus, and the detailed parameters are shown in Table 3.Each control surface is operated by a separate electric-servo actuator through a set of four-bar mechanisms,as shown in Fig.8.

4.2.Five-DOF suspension system design

Fig.6 Ground vibration test setup of test model.

The classical types of elastic model support system used in wind tunnel test include the double cable suspension system of the United States39,40and the five-DOF tension suspension support system originated from Russia30.The double-cable suspension system needs complex auxiliary cable, and relatively more structural interface and pulley mechanism are installed on the upper and lower wall of the tunnel.Moreover,it is difficult to support heavy model.The five-DOF tension suspension support system has complex mechanism and large blockage degree.

To simplify the complexity of the mechanism and reduce the blockage degree,a new type of five-DOF double-cable suspension support system was designed for the full aircraft model wind tunnel test.Fig.9 demonstrates the full aircraft model support system that consists of two parts: the spring suspension system and the double-cable support system.The spring suspension system consists of a vertical cable and aspring system.On the symmetrical plane, two cables are used to hang the model.The upper end of each cable is connected with the suspension point at the top of the wind tunnel, and the lower end of the cable is directly suspended on the fuselage.The double-cable support system is supported by two sets of cables:one is located upstream in the vertical plane of the wind tunnel and is connected by pulley to the top and bottom of the wind tunnel;the other is located downstream in the horizontal plane and is driven to the outside of the wind tunnel by a pulley connected to the fuselage beam and a pulley fixed to the side wall of the wind tunnel.The two free ends of the cable are connected to balance weights,which are generally adjusted to be the same weight as the model to maintain stability during the test,as well as to ensure the elastic modal frequency of the model not affected by excessive additional stiffness.In addition, the stability of the system can be adjusted by changing the position of the pulley on the side wall of the wind tunnel.The combination of the spring suspension system and the double-cable support system enables five-DOF movements of the model, namely in the horizontal, vertical, pitching, rolling and yawing directions.

Table 2 Comparison of calculated and measured vibration characteristics.

Fig.7 V-f and V-g plots of flutter.

Table 3 Electric-servo actuator specification.

Fig.8 Illustration of control surface mechanism.

Fig.9 Five-DOF double-cable suspension support system.

The five-DOF double-cable suspension support system consists of spring, front cable, back cable and weight device that simulates the free-flying state and prevents the model from large attitude change.The lower end of the vertical cable is located at the two joints of the first-order vertical bending mode of the fuselage,thus reducing the influence of the suspension device on the inherent vibration characteristics of the model.The pulley mounted on the fuselage is close to the fuselage skin, which can not only provide a large pitch and roll moment,but also does not affect the flow field of the fuselage.By adjusting the stiffness of the spring,the requirements of different rigid body frequencies can be satisfied.By adjusting the fixed position of the pulley on the side wall of the wind tunnel,the position of the back cable can be adjusted so as to change the stability of the system.Furthermore, the stability of the system can be adjusted by changing the balance weight.

4.3.Gust generator design

To obtain satisfactory quality of the gust field, the geometric parameters, flow field characteristics, and blockage degree of the wind tunnel should be considered in the design of gust generator.Moreover, the performance requirements such as fatigue and reliability requirements to bear the alternating load caused by high-frequency motion, the elastic modal frequency requirement of the vane to avoid resonance with the test model and the tunnel body should also be taken into account.Based on the moving multi-block chimera structure grid technique41,the structural dynamic response of the gust generator is calculated by CFD/ CSD time-domain coupling method, and the effect of the elastic deformation of the gust generator on the flow field is analyzed.Finally,through the optimization design of vane characteristics, the quality of the gust flow field is guaranteed.

The cascade gust generator,widely used in the wind tunnel,adopts the linkage mechanism or cam mechanism to ensure synchronized motion.However, many links of the driving mechanism,the large vibration response of the gust generator,and the multiple resonance points of the system induce poor reliability and greatly limit the test ability.In order to increase the available frequency range of the test, a single-vane independent drive scheme as shown in Fig.10 is designed to reduce the transmission link, and synchronized motion is ensured by the joint control system.In addition, through the single-vane independent drive, any combination of gust can be obtained.Considering the geometry of large-scale wind tunnel, the vane airfoil adopts NACA0015 that has large stall angle and large airfoil space suitable for hardware installation.The vane structure uses composite material and meets the requirements of performance,stiffness and strength through reasonable design.Considering the constraints of 70%available width of the 8 m wide wind tunnel,the vane is designed to be 6 m in length and is divided into three identical sections to facilitate manufacture and installation in the wind tunnel.To improve the vane stiffness, two vertical supports are designed at the vane butt joint.Fig.11 demonstrates the installation of the gust generator in the wind tunnel.

4.4.Measuring system and test procedure

The experiment was carried out in the FL-10 8×6 low-speed wind tunnel of AVIC Aerodynamics Research Institute.The full aircraft model is suspended in the center of the wind tunnel by the five-DOF suspension system, with its nose three meters away from the gust generator.In order to realize the attitude control and GLA control,the model is equipped with the control surfaces including ailerons,flaps,elevators and rudders,as well as control stabilization system to realize the model leveling.The angle sensor is installed on the fuselage, the acceleration sensor is installed on the wing tip, and the strain gauge is installed on the wing root, as shown in Fig.12.

To ensure the safety of the test system,some measures were implemented before the formal test: (A) the rigid body frequency test of the suspension system;(B)the start-up and emergency shut-off test of the blast generator;(C)the calibration of the wind speed of the five-hole probe; (D) the consistency check of the control system and the actuator deflection; (E)the frequency response test of all the control surfaces; (F)the stability test of the full model and suspension system with increasing free stream velocity.

Fig.10 Gust generator structure and installation form.

Fig.11 Installation of gust generator in wind tunnel.

Fig.12 Installation of model in wind tunnel with marked sensor locations.

Fig.13 Gust load alleviation test system.

The test system is shown in Fig.13 during the test,and the gust generator is controlled by the gust generator computer to oscillate at desired amplitude and frequency; the gust velocity is measured by the five-hole detection, and the measurement accuracy could reach 0.2 m/s; the full model supported by the five-DOF suspension system is excited by the gust wind,and the attitude sensor located on the fuselage, the acceleration sensor on the wing, and the wing root strain gauge sense the motion signal and transmit the signal to the simulator through the AD/DA switch box; the simulator carries on real-time numerical calculation of the simulation system program, transforms the calculated command into the analog voltage signal by D/A conversion, and transmits the signal to the actuator control box; the control surface such as the ailerons is deflected according to the given command; the industrial computer connected with the simulator implements the display, the control law design, and the simulation system compilation.

5.Results and discussion

5.1.Wind tunnel flow field

Fig.14 Gust generator installed in wind tunnel.

Fig.15 Smoke laser display of sinusoidal gust field.

Fig.16 Gust velocity versus gust frequency under different vane deflections (v=40 m/s).

The gust generator is manufactured and installed in the wind tunnel as shown in Fig.14.The vane oscillating form can be sinusoidal function, step function, trigonometric function,etc.In the present test, the flow field generated by sinusoidal oscillation of the vane creates a sinusoidal gust field with stable shape displayed by smoke laser, as shown in Fig.15.The gust generator can produce a stable gust field of high amplitude in a wide range.Under air speed of 40 m/s, gust velocities were measured with varying frequency and vane deflection as shown in Fig.16, the amplitude of the gust velocity varies linearly with the frequency of the vane oscillation under different deflection angles.The maximum gust frequency can reach 10 Hz, and maximum velocity 12 m/s in the wind tunnel.

Comparison of the gust velocity between the two ends of the vane and the center position under air speed v=40 m/s and vane oscillation amplitude θ=2?is made, as shown in Fig.17, and it is shown that the difference between the two ends of the vane and the center position is less than 25%,superior to 100% of the Russia T104 wind tunnel30.

5.2.Gust load measuring test

To obtain proper response amplitude and avoid static strength failure of the model,it is necessary to set moderate flow velocity and vane deflection amplitude in the gust load measuring test.The gust test is carried out with air speeds v equal to 20 m/s and 30 m/s, respectively.The vane deflection angle θ is set to 2 °, as the corresponding gust velocity vgis less than 1 m/s, the wing tip acceleration Nwtis less than 2 g, and the wing root bending moment Mwris less than 40 N?m.The frequency range of the vane oscillation is selected considering three aspects:(A)including the longitudinal rigid body motion frequency of the whole model and the pitching mode frequency of the model under suspension support at 1 Hz; (B) covering the 1st wing bending mode frequency; (C) not exceeding the available frequency range of the actuator.Based on the above principles, the gust vane oscillating frequency ωgis chosen to vary from 1.0 Hz to 6.0 Hz with an increment of 0.5 Hz.The wind tunnel test conditions are listed in Table 4.

Fig.17 Comparison of gust velocity at different vane locations(θ=2?, v=40 m/s).

Under the above test conditions,the gust load test was conducted to measure the elastic vibration response of wing tip acceleration Nwtand the variation of wing root bending momentMwr,as well as acceleration and pitch rate of the center of gravityNc.g.,qc.g., due to the rigid body motions.The measured dynamic loads are compared to the calculated results by frequency domain method, as shown in Fig.18 and Fig.19.It is seen that the calculated gust loads agree well with the test data.The error of Mwris less than 15%.The absolute difference of Nwtis less than 0.2g.Due to the small absolutevalue of Nwtand system error transmitting signals,the relative error of the low frequency at 1 Hz is relatively large,while that of other frequency points is less than 20%.The most severe structural loads appear between 3 Hz and 4 Hz, which corresponds to the frequency of the 1st wing bending mode.SinceNc.g.,qc.g.are small, only absolute errors are compared,the absolute difference of qc.g.is less than 0.5 (°)/s, and theabsolute difference of Nc.g.is less than 0.04g.The calculated variation trend ofNc.g.,qc.g.along with ωgis basically the same as the test results.

Table 4 Gust load test conditions.

Fig.18 Comparisons of test and calculated gust load RMS (GTest-20).

Fig.19 Comparisons of test and calculated gust load RMS (GTest-30).

Table 5 Closed-loop feedback control law parameters.

5.3.Gust load alleviation test

Based on the block diagram of the control law in Section 3,the closed-loop feedback control law and the open-loop feed forward control law of the model are designed, and the detailed parameters about the gains and cut-off frequencies are shown in Table 5 and Table 6.In fact, some parameters in the table such as Kcand τcvary with wind speed and gust frequency,but the moderate fixed values are calculated by Eq.(14)to take into account the overall frequency-domain mitigation effect at each given wind speed,

Table 6 Open-loop feed forward control law parameters.

Fig.20 Comparisons of gust load control effect (GTest-20).

Fig.21 Comparisons of gust load control effect (GTest-30).

Fig.22 Comparisons of gust load reduction rate.

Fig.23 Frequency response of wing root bending moment to aileron deflection.

Fig.24 Comparisons of GLA off and closed-loop feedback control (v=20 m/s, ωg= 3.5 Hz, θ=2°).

where ωgiis the gust frequency,ωbis the 1st wing bending frequency,η is the weight factor(the general value of η is 1,and it can be adjusted according to the frequency range of concern),and yiis Kcor τcwith different gust frequency.The gust loads in terms of the acceleration and pitch rate of the center of gravityNc.g.,qc.g., due to the presence of rigid body motions, affect the riding comfort of passengers, and wing root bending moment Mwrand wing tip acceleration Nwtrelated to the load and fatigue life of the airplane structure were measured under the test conditions in Table 4.The control performance of closed-loop feedback and open-loop feed forward control about acceleration of the center of gravityNc.g., pitch rateqc.g.,wing root bending momentMwr,and wing tip acceleration Nwtare compared, as shown in Fig.20 and Fig.21.The reduction rate of qc.g.and Mwrare shown in Fig.22.It is shown that the overload at the center of gravity is small and the reduction is not obvious, and the peak response of pitch rate oscillation appear in the low-frequency range near 1 Hz, where the closed-loop feedback control has no alleviation effect, while the open-loop feed forward control has obvious suppression effect, even with reduction rate of more than 50%atωg=1 Hz.However, the open-loop feed forward control does not take effect over 4 Hz, as the rigid motion control is only aimed at the low-frequency gust and the cut-off frequency of low-pass filter is set to 4 Hz.Both control laws have significant alleviation effects for peak gust loads within 4.5 Hz,while the feed forward control presents better performance with Mwrreduction over 40%.Both control schemes have little effect,even magnifying effect on Mwrover 5 Hz.The main reason is that the frequency response characteristic of Mwrto aileron deflection δahas a positive and negative transformation in phase, i.e.from lag to lead, as shown in Fig.23, and the phase transition point is 5 Hz at v=20 m/s and 5.2 Hz at v=30 m/s respectively.This is consistent with the positive and negative law of the wing root bending moment in Fig.22.Overall, the open-loop feed forward control performs better than the closed-loop feedback control in alleviating both rigid body motion and elastic vibration under gust excitation.

The measured time-domain responses of gust loads with and without active control atωg=3.5 Hz (near 1st wing bending frequency), v=20 m/s are compared in Fig.24 and Fig.25.Fig.24 shows that the influence of the gust disturbance is reduced by the deflection of the aileron with closed-loop feedback control.Fig.25 shows that the open-loop feed forward control reduces the effect of gust load by the combined deflection of ailerons, flaps and elevators.

Fig.25 Comparisons of GLA off and open-loop feed forward control (v=20 m/s, ωg=3.5 Hz, θ=2°).

6.Conclusions

Through the design of a set of large-scale GLA test system including a gust generator, a five-DOF suspension system, a full elastic model,control system and test device,the gust load test based on two control schemes is conducted in the wind tunnel to verify the reliability of the system,and test the effectiveness of the alleviation performance.The following conclusions can be drawn:

(1) A stable wideband,wide-area gust field can be generated by the designed gust generator.The maximum gust frequency of 10 Hz and maximum velocity of 12 m/s can be reached in the wind tunnel, and the velocity deviation between the two ends of the vane and the center of the wind tunnel is less than 25%.

(2) A set of five-DOF double-cable suspension support system is designed and manufactured.It can realize static and dynamic stability during wind tunnel test by adjusting spring stiffness, suspension position and balance weight with small support stiffness, and enables five-DOF motions of the model in the horizontal, vertical, pitching, rolling and yawing directions.

(3) The closed-loop feedback control can achieve good control performance of reducing the gust induced elastic vibration of the model within 4.5 Hz,but has little effect on suppressing the rigid body motion excited by lowfrequency gust.

(4) The open-loop feed forward control presents superior alleviation performance in high-frequency elastic vibration as well as the low-frequency rigid body motion.Through the joint control of ailerons, flaps and elevators, over 40% reduction rate of structural responses can be achieved in a wider range.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was co-supported by the National Natural Science Foundation of China (No.11972296) and the Major Project Foundation of China (No.2017-F-08).