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

CJA 768 26 December 2016 Chinese Journal of Aeronautics, (2016), xxx(xx): xxx–xxx No of Pages 19 Chinese Society of Aeronautics and Astronautics & Beihang University Chinese Journal of Aeronautics cja@buaa.edu.cn www.sciencedirect.com 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 100183, China Received 24 May 2016; revised 28 July 2016; accepted September 2016 11 12 KEYWORDS 13 Active control; Aeroelastic wing; Gust load alleviation; Gust response; Piezoelectric actuators; Wind tunnel test 14 15 16 17 18 19 Abstract 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 the z and x wingtip 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% Ó 2016 Production and hosting by Elsevier Ltd on behalf of Chinese Society of Aeronautics and Astronautics This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/) * 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 Production and hosting by Elsevier Introduction 20 High-altitude long-endurance unmanned aerial vehicles (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 slender 21 http://dx.doi.org/10.1016/j.cja.2016.12.028 1000-9361 Ó 2016 Production and hosting by Elsevier Ltd on behalf of Chinese Society of Aeronautics and Astronautics This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 22 23 24 25 26 27 28 CJA 768 26 December 2016 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 wings) 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 Cesnik2 investigated 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.3,4 developed an approach to rapidly predict the worst case gust loads for aircraft, which could significantly 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.6,7 performed 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.8 studied 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.9 applied optimal control allocation techniques on a nonlinear simulation of a generic transport aircraft to alleviate gust loads Cook et al.10 conducted 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 Liu11 completed 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.12 employed 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 conventional aerodynamic control surfaces 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 significantly Hence, gust load alleviation control which can accomplish multi-objective alleviation 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 No of Pages 19 Y Bi et al 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 Weisshaar13,14 studied wing surface divergence control using piezoelectric actuators Khot et al.15,16 employed 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.17 Scott18 and Hajela19 et al validated the feasibility and validity of wing surface active control by means of piezoelectric actuators The earliest wind tunnel tests taking advantage of piezoelectric actuators to suppress flutter was completed by Heeg.20 Crawley et al.21,22 made 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.23 Chen et al.24,25 utilized piezoelectric materials to perform single-input-single-output (SISO) and multi-inputmulti-output (MIMO) flutter suppression wind tunnel tests Hui et al.26 studied wing surface thermal flutter suppression with distributed piezoelectric actuators Nam et al.27 designed 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 Karpel28 alleviated gust response and performed wind tunnel test validation Except for the traditional linear condition, Tsushima and Su29 tried 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 Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 CJA 768 26 December 2016 No of Pages 19 Gust load alleviation wind tunnel tests 155 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 156 Mathematical modeling 151 152 153 154 nal applied voltage, and h is 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 Z t2 dT U ỵ Wị ẳ 4ị t1 157 158 159 160 161 162 163 164 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 165 2.1 Structural modeling 166 In this study, the large-aspect-ratio flexible wing is modeled as a cantilever beam Fig 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 167 168 169 170 171 @ w @x2 173 174 175 176 177 179 180 181 182 183 184 185 186 188 189 190 191 ey ¼ Àz ð1Þ where ey is the strain along the z axis and w is the transverse displacement of the beam The stress-strain relationship is given by ry ẳ Eey 2ị where ry is the stress and E is the elastic modulus of the material The polarization direction of the piezoelectric material is in the z axis An outer voltage is applied across the piezoelectric layer thickness The constitutive equations of the piezoelectric patch are written as ( p r ey ẳ Ey ỵ e31 Ez 3ị Dz ẳ e31 rpy þ k33 Ez where rpy is the stress, e31 is the piezoelectric constant, k33 is the dielectric constant, Dz is the electric displacement, Ez ¼ V0 =h is the electric intensity along the z direction,30–33 V0 is the exter- Fig where t1 and t2 are the integration time limits, dðÁÞ indicates the first variation, T and U are the total kinetic energy and total potential energy of the beam with the piezoelectric patch system, respectively, and W is the work done by external loads The formulations of T, U, and W are 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 Z Z 1 T¼ qs w_ dV ỵ q w_ dV 5ị Vs Vp p where qs and qp are the mass densities of the base beam and piezoelectric patch, respectively, Vs and Vp are 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 Z Z Z 1 Uẳ ry ey dV ỵ rpy ey dV À Dz Ez dV ð6Þ Vs Vp VP 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 Z Z dW ẳ qs dwdA ỵ qg dwdA ð7Þ A A where qs and qg represent the aerodynamic load components per unit area along the z direction induced by the structural vibration and the gust, respectively, and A is the surface area of the beam The modal approach is applied here to establish the structural dynamics equation, which assumes that the structural Schematic diagram of a cantilever beam with a piezoelectric patch Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 192 193 194 195 196 197 199 200 201 202 203 204 205 206 207 208 209 210 212 213 214 215 216 217 218 219 220 221 222 224 225 226 227 228 229 231 232 233 234 235 236 237 CJA 768 26 December 2016 No of Pages 19 238 239 240 242 243 244 245 246 247 248 249 251 Y Bi et al displacement vector is a linear combination of some lowfrequency normal modes of the structure That is, wx; y; tị ẳ Ux; yịqtị 8ị where Ux; yị is the structural mode shapes and qðtÞ is the generalized coordinate Substituting Eqs (1)–(3) and (8) into Eqs (5)–(7), the kinetic energy, potential energy, and virtual work are expressed in terms of the normal modes and the generalized coordinate as T ẳ q_ T Mm q_ 9ị 252 254 255 257 258 259 260 261 262 263 264 265 266 267 268 269 270 272 1 U ẳ qT Km q ỵ V0 Ks/ q ỵ K0 V20 2 10ị dW ẳ qs Ps dq ỵ qg Pg dq ð11Þ where Mm and Km are the modal mass and stiffness matrices of the whole cantilever beam with the piezoelectric patch system, respectively, Ks/ and K0 are the electromechanical coupling matrix and the piezoelectric capacitance of the piezoelectric patch, respectively, and Ps and Pg are 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 UT yields the dynamic motion equation of the whole beam with the piezoelectric patch system as follows: ^ Mq ỵ Cq_ ỵ Kq ẳ Fq ỵ Fg ỵ BV 12ị 292 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 Fq and Fg are the generalized unsteady aerodynamic forces induced by the structural vibration and the atmospheric gust, respectively, ^ ¼ ÀUT Ks/ is the generalized driving matrix of the piezoand B electric patch In this study, the generalized matrices M, C, and K as well as the mode shapes U 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 voltage V0 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) 293 2.2 Aerodynamic modeling 294 Unsteady aerodynamics is modeled using the subsonic double lattice method (DLM).36 Unsteady aerodynamic forces excited by structure vibration and atmospheric gust in the frequency domain under the generalized coordinate system are given by 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 295 296 297 298 300 Fq ỵ Fg ẳ qV2 Qq q ỵ Qg wg ị 13ị where 1=2qV2 represents the dynamic pressure, q is the air density, V is the flight speed, Qq and Qg are the aerodynamic influence coefficient matrices with respect to the structural and gust modes, respectively, which are complex functions of reduced frequency, and wg denotes 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 À1 QðsÞ % A0 ỵ A1s ỵ A2s ỵ Ds Is Rs Þ Ess ð14Þ where s ¼ sb=V, in which s is the Laplace variable and b represents the reference chord, An n ẳ 0; 1; 2ị, Ds , and Es are the polynomial fitting coefficient matrices solved by a leastsquares fitting, and Rs is a diagonal matrix with aerodynamic lag roots Furthermore, An n ẳ 0; 1; 2ị and Es matrices are column partitioned as & An ẳ ẵ Aqn Agn n ẳ 0; 1; 2ị : Es ẳ ½ Eq Eg Š To facilitate time-domain formulation, an augmenting aerodynamic state vector is defined by its Laplace transform as follows:  1 V xa sị ẳ sI Rs Eq sqsị ỵ Eg swg sịị 15ị b Its Laplace inverse transform is given below: V _ ỵ Eg w_ g tị ỵ Rs xa tị x_ a tị ẳ Eq qðtÞ b 303 304 305 306 307 308 309 310 311 313 314 315 316 317 318 319 320 322 323 324 325 326 328 329 330 ð16Þ Substituting Eq (14) and Eq (15) into Eq (13) and completing the Laplace inverse transform lead to the timedomain aerodynamics b Fq ỵ Fg ẳ qV2 Aq0 q ỵ Ag0 wg ị ỵ Aq1 q_ ỵ Ag1 w_ g ị V ! b2 g ị ỵ Ds xa ỵ Aq2 q ỵ Ag2 w V 301 302 ð17Þ 332 333 334 335 336 338 2.3 Synthesized modeling 339 Synthesized modeling of the flexible wing with piezoelectric control completes the connection between structural modeling and aerodynamic modeling Substituting Eq (17) into Eq (12), the time-domain aeroelastic equation of the whole system can be expressed as   b b2 M q ỵ Cq_ ỵ Kq ẳ qV Aq0 q ỵ Aq1 q_ ỵ Aq2 q V V   b ỵ qV2 Ag0 wg ỵ Ag1 w_ g V ^ 18ị ỵ qV2 Ds xa ỵ BV 340 The outputs of the aeroelastic system are sensor readings of wingtip accelerations and the root bending moment It is assumed that sensor measurements are perfect The outputs are assumed to be linear combinations of the state response The accelerometer readings € uk and root bending moment Fr can be expressed by 348 Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 341 342 343 344 345 347 349 350 351 352 353 CJA 768 26 December 2016 No of Pages 19 Gust load alleviation wind tunnel tests 354 356 357 358 359 360 361 362 363 365 366 367 ( € uk ¼ /Tk €q Fr ¼ Kr uk ð19Þ where /k is the modal displacement matrix at the sensor location, Kr is the element stiffness matrix of the wing root, and uk is the wingtip displacement at the sensor location 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 & x_ ¼ Ax ỵ Bu 20ị y ẳ Cx ỵ Du where  À1 Ds qV2 M 5; I ÀM À1  À1    K À M C A¼4 2 Eq 0  À1 B ¼ qV M Ag0 V R b s  qVbMÀ1 Ag1 " 370 C¼ " D¼   À1 K À/Tk M Kr /Tk  À1 B ^7 M 5; Eg 369 372   À1 C À/Tk M  À1 Ds /Tk 12 qV2 M 0 # ;  À1 Ag0 /Tk 12 qV2 M  À1 Ag1 /Tk 12 qVbM  À1 B ^ /Tk M 0 # ; 373 x ẳ ẵ q q_ xa ; u ¼ ½ wg w_ g V0 Š ;  ¼ C À qVbAq1 ; K  ¼ K À qV2 Aq0 :  ¼ M À qb2 Aq2 ; C M 2 T T 375 376 377 378 379 380 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 Fig piezoelectric patch, the process applies to multiple piezoelectric patches as well, in which case, the external applied voltage scalar V0 turns into the voltage vector V0 381 Active control strategy 384 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 385 3.1 Control architecture 390 The gust load alleviation control law is based on a feedback loop as shown in Fig 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, the z wingtip 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 Ỉ750 V 391 SIMULINK model of gust load alleviation controller architecture Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 382 383 386 387 388 389 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 CJA 768 26 December 2016 No of Pages 19 413 414 415 416 418 419 420 421 422 423 424 425 426 427 428 430 431 432 433 435 436 437 438 439 440 441 443 444 445 446 448 449 450 451 452 453 454 455 456 457 Y Bi et al Denoting aðsÞ as the Laplace transformation of the z wingtip acceleration u€kz , the control law is expressed with a transfer function in the following way: #" # ! " 50 kp1 ksi1 V01 sị sỵ50 ẳ asị 21ị 50 V02 sị kp2 ksi2 sỵ50 where V0 ðsÞ is the Laplace transformation of the piezoelectric patches control voltages V0 ðtÞ, kp and ki are 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 ! ! ! V01 ðtÞ ki1 eÀ50t ð50kp1 À ki1 ị ukz ỵ u_ kz ẳ 50t 22ị V02 tị ki2 e ð50kp2 À ki2 Þ Substituting the acceleration u€kz in Eq (19) into Eq (22), the control voltage vector V0 can be written as V0 tị ẳ Mk /Tkz q ỵ Ck /Tkz q_ 23ị 50t T where Mk ẳ e 50kp1 ki1 ị e50t 50kp2 ki2 ị , Ck ẳ ẵ ki1 ki2 T , and /kz is the z modal displacement vector at the wingtip Substituting Eq (23) into Eq (12), the following equation of motion with active mass and active damping is obtained M ỵ Mp ịq ỵ C ỵ Cp ịq_ ỵ Kq ẳ Fq ỵ Fg 24ị where Mp and Cp are the active mass and damping matrices due to the piezoelectric patches and are expressed as ( ^ k /T Mp ẳ BM kz 25ị ^ k /T Cp ẳ ÀBC kz 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 gains kp and ki , the active mass Mp and the active damping Cp are 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 458 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 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., 459 eGA ¼ l X ej s j 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 26ị 487 jẳ1 where eGA is the gust load alleviation evaluation indicator, while ej is the reduction rate at the frequency point j and sj is the weighting coefficient derived from the Dryden PSD, which are given as e ẳ Ropen Rclosed ị=Ropen 100% > < j , l X 27ị > pjị : sj ẳ pjị jẳ1 where Ropen and Rclosed are the peak values of the gust responses when the gust load alleviation control system is open and closed, respectively, pðjÞ is the PSD at the frequency point j, and l is the sum of all the frequency points considered Based on the gust load alleviation evaluation indicator eGA , the effectiveness evaluation criterion of gust load alleviation in a specified frequency range can be completely described as eGA P 20% Fig 460 ð28Þ 488 489 490 491 492 494 495 496 497 498 499 500 501 502 504 In this study, the optimized control parameters kp and ki are chosen from specified intervals to satisfy the effectiveness evaluation criterion 505 Numerical studies 508 In Sections 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 509 Dryden spectrum Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 506 507 510 511 512 513 CJA 768 26 December 2016 No of Pages 19 Gust load alleviation wind tunnel tests Fig Fig Catia model of large-aspect-ratio flexible wing Wind tunnel test model of large-aspect-ratio flexible wing Table Design parameters of flexible wing model Item Value Weight (kg) Semi-span (m) Root chord (m) Tip chord (m) Torsion angle (°) Aspect ratio Taper ratio Airfoil of wing 3.167 1.542 0.261 0.069 À2.0 9.3 3.8 Supercritical airfoil 515 open-loop gust responses analysis and closed-loop gust load alleviation effects will be presented 516 4.1 Model description 517 The semi-span flexible wing model which is used during the numerical analysis and wind tunnel test is shown in Figs and The design parameters of the large-aspect-ratio flexible wing are given in Table 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 514 518 519 520 521 522 523 524 525 526 Table Item w (mm) t1 (mm) H (mm) t2 (mm) 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 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 shows the layout of these sensors and piezoelectric actuators, and the detailed information of the piezoelectric patches is given in Table 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 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 In order to figure out the safe range of flow speed, flutter analysis for the FEM is conducted beforehand Fig 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 speed range of 15–32 m/s 527 4.2 Open-loop results 558 Open-loop gust response is defined as the response of the wing while the gust load alleviation control system is opened The simulated flow speed 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 Fig 8(a) and (b) represent the z acceleration of the wingtip and the root bending moment, respectively It can be seen that with the flow speed increasing, the z acceleration at the wingtip 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 bending moment at the root section is more obvious at a frequency of 2.0–3.5 Hz 559 Parameters of ‘ + ’ cross-sections along spar Section Dimension 10 11 21.0 5.5 21.0 5.9 19.0 4.7 19.0 5.4 17.8 4.4 18.0 4.9 16.0 4.0 16.3 4.5 15.1 4.0 14.0 4.0 13.8 4.0 11.3 3.4 12.9 3.5 9.3 3.4 10.9 3.5 9.0 3.4 10.0 3.5 7.9 3.4 9.0 3.5 7.9 3.4 7.4 3.1 6.9 3.4 Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 560 561 562 563 564 565 566 567 568 569 570 571 572 CJA 768 26 December 2016 No of Pages 19 Y Bi et al Table Parameters of piezoelectric patches Item A1 A2 B1 B2 Length (mm) Width (mm) Thickness (mm) Distance from root (mm) 20 4.5 78.6 20 4.5 153.5 20 3.5 817.3 20 3.5 885.8 Figure Entity and installation Structural finite element model Fig Table Mode number Main modal parameters Frequency (Hz) 3.37 5.21 10.08 17.22 Mode shape 1st bending mode 1st bending mode in-plane 2nd bending mode 2nd bending mode in-plane 574 than that of 4.0–6.5 Hz, and the first bending mode of the wing happens around a frequency of 3.3 Hz 575 4.3 Closed-loop results 576 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 the z wingtip acceleration and the root bending moment to be alleviated at least 20% The design space of control gains is S ¼ SðÀ0:02 kp 0; À6:5 ki 0Þ, which means that the main parameters 573 577 578 579 580 581 582 583 584 585 Aerodynamic model of interest kp and ki are varied from À0.02 to and À6.5 to 0, respectively, and the satisfactory gains will be chosen in those ranges In order to simplify, the control parameters kp and ki in 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 speed 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 the z wingtip acceleration and the root bending moment are shown respectively in Fig (a) and (b) Here, the reduction rate is calculated by Eq (26) According to Fig 9, the optimized parameters range is À0:02 kp along with À6:5 ki À4:5 In this range, any control gains combination satisfies the effectiveness evaluation criterion of gust load alleviation, i.e., it can alleviate both the z wingtip 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 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 4.4 Control mechanism analysis 603 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 the z wingtip 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 the z wingtip acceleration, direct control moments produced by piezoelectric actuators, and the inertia moment, aerodynamic moment, and root bending moment exerting at the wing 604 Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 CJA 768 26 December 2016 No of Pages 19 Gust load alleviation wind tunnel tests Fig Fig Fig 10 620 621 622 623 624 625 626 Open-loop gust response results Reduction rates with different control gains pairs Gust response of z wingtip acceleration 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 the z wingtip 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 Fig 11 Direct control moments produced by piezoelectric actuators the z wingtip 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 Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 627 628 629 630 631 632 CJA 768 26 December 2016 No of Pages 19 10 Y Bi et al Fig 12 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 Gust responses of different sorts of moments vibration of the wingtip acceleration, the aerodynamic 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 the z wingtip 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 the z wingtip 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 Fig 13 Wind tunnel testing activities 657 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 m  m low-speed wind tunnel 658 5.1 Design of test subsystem 665 5.1.1 Support system 666 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 À0.2° 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 667 Frequency response functions (FRFs) from gust velocity input to different response outputs Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 659 660 661 662 663 664 668 669 670 671 672 673 674 675 676 677 CJA 768 26 December 2016 No of Pages 19 Gust load alleviation wind tunnel tests 11 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 wg tị ẳ Ag am sin2pftị Fig 14 Fig 15 Wing model installation Wing model in a test 678 5.1.2 Gust generator device 679 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 680 681 682 683 684 685 Fig 16 Gust generator placed in wind tunnel ð29Þ 686 687 688 689 690 691 692 693 694 695 696 698 where am is the amplitude of the blades deflecting angle, and Ag is the gust disturbance coefficient which is relevant to the flow speed V and the blades deflecting frequency f and is calibrated by the test 699 5.1.3 Measure-control system 703 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 704 5.2 Gust responses wind tunnel test 714 5.2.1 Experimental conditions 715 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 speed range of 15–32 m/s and a gust frequency range of 2.0–6.5 Hz Table shows the actual test conditions, and for each flow speed, the test model is disturbed by the sinusoidal gust from 2.0 to 6.5 Hz Gust responses including z and x wingtip accelerations and the root bending moment are recorded 716 Fig 17 Measure-control system diagram of wind tunnel test Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 700 701 702 705 706 707 708 709 710 711 712 713 717 718 719 720 721 722 723 724 725 CJA 768 26 December 2016 No of Pages 19 12 Table Y Bi et al Test conditions of gust responses wind tunnel test Flow speed (m/s) 15 20 Gust frequency (Hz) 24 28 32 2.0 2.5 3.0 726 5.2.2 Comparison between numerical results and test results 727 748 The comparisons between the theoretical results and the experimental measurements corresponding to the z wingtip acceleration and the root bending moment at a flow speed of 15 m/s and a gust frequency of 3.5 Hz are shown in Fig 18, where the experimental measurements are filtered data after 12 Hz lowpass filtering It can be seen that the experimental 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 the z wingtip acceleration and the root bending moment, when the wing model is tested at different flow speeds 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 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 749 5.2.3 Effects of gust frequency on gust responses 750 Gust responses are relevant to gust frequency and flow speed; here, the effects of gust frequency are discussed firstly Three objects of concern are the z wingtip acceleration, the x wingtip acceleration, and the root bending moment Fig 20 presents gust responses of these three objects vs gust frequency at different flow speeds According to Fig 20(a) and (b), for all flow velocities, the response of the z wingtip acceleration rises up to the peak increasingly and then fluctuates, and with regard to the x wingtip acceleration, its response generally increases to the maximum and then decreases with the gust frequency With the 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 751 752 753 754 755 756 757 758 759 760 Fig 18 3.5 4.0 4.5 5.0 5.5 6.0 6.5 wind speeding up, both the z and x accelerations 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 761 5.2.4 Effects of flow speed on gust responses 772 In the above section, the effects of gust frequency on gust responses have been analyzed In this section, the effects of flow speed which is the other factor influencing gust responses will be explored Fig 21 presents the tendencies of z and x wingtip accelerations and the root bending moment vs flow speed, respectively Fig 21 indicates that all of these three objects increase generally with the flow speed, 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 speed increasing 773 5.3 Gust load alleviation wind tunnel test 783 5.3.1 Experimental objective 784 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 the z and x accelerations 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 the z wingtip 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 785 Comparisons between numerical results and test results at a flow speed of 15 m/s Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 762 763 764 765 766 767 768 769 770 771 774 775 776 777 778 779 780 781 782 786 787 788 789 790 791 792 793 CJA 768 26 December 2016 No of Pages 19 Gust load alleviation wind tunnel tests Fig 19 13 Comparisons between numerical results and test results in frequency domain Fig 20 Fig 21 794 795 796 797 798 799 800 801 Effects of gust frequency on gust responses Effects of flow speed on gust responses 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 speed 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 speed conditions, the alleviation effectiveness and the trend with gust frequency Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 802 803 804 805 806 807 808 809 CJA 768 26 December 2016 No of Pages 19 14 Table Y Bi et al Test conditions of gust load alleviation wind tunnel test Flow speed (m/s) Gust frequency (Hz) 15 2.0 Table 2.5 3.0 3.5 Proportion Integral Proportion Integral 0.001 The experiment results with respect to the z wingtip 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 the z wingtip 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 the z wingtip acceleration since the scope of its efficacy is up to 50% Although the control system is not able to alleviate the z wingtip 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 open-loop results by 20.10% According to the previous analysis that the z wingtip acceleration at a low flow speed 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 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 6.5 0.001 816 817 6.0 Control law 5.3.2 Gust load alleviation analysis of z wingtip acceleration 813 5.5 Root of wing 815 812 5.0 Location of piezoelectric patches and control gain category 814 811 4.5 Gust load alleviation control system are generally similar to those of 15 m/s, besides some numerical deviation Table shows specific test conditions Aiming at this low flow speed test status, in order to avoid complexity, a set of effective gain values is obtained through an analysisadjust procedure as shown in Table 810 4.0 Fig 22 Gust response of z wingtip acceleration in frequency domain Middle of wing Fig 22 with the theoretical FRF curves shown in Fig 13(a), it is clear that the dynamic tendencies of the experiment results basically coincide with those of the numerical simulations for both open- and closed-loop cases The experiment 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 experiments Fig 23 presents the timedomain original signal of gust responses of the z wingtip 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 the z wingtip acceleration is shown in Table 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 the z wingtip acceleration is proven feasible 838 5.3.3 Gust load alleviation analysis of x wingtip acceleration 862 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 863 Fig 23 Original signal of z wingtip acceleration under 3.5 Hz gust disturbance Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 864 865 CJA 768 26 December 2016 No of Pages 19 Gust load alleviation wind tunnel tests Fig 24 Table Gust response of z wingtip acceleration under 3.5 Hz gust disturbance Open- and closed-loop results comparison of z wingtip acceleration Status number 15 Gust frequency (Hz) 2.5 3.5 4.0 5.5 6.5 z wingtip acceleration (m/s2) Open loop Closed loop 2.4205 6.5148 6.2215 4.1644 3.0044 1.7469 5.2053 4.4596 3.1354 2.8636 Fig 25 Gust response of x wingtip acceleration in frequency domain 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 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 the x wingtip acceleration which is in the same order of magnitude with that of the z wingtip acceleration As a consequence, the gust load alleviation effectiveness of transverse x wingtip acceleration should also be investigated The experiment results corresponding to the x wingtip acceleration are shown in Fig 25 which illustrates both Reduction rate (%) 27.83 20.10 28.32 24.71 4.69 Fig 26 Original signal of x wingtip acceleration under 3.5 Hz gust disturbance open- and closed-loop cases It can be seen from Fig 25 that the control scheme alleviates the x wingtip 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 the z wingtip acceleration, the first bending moment mode about 3.3 Hz also acts an important role in the gust response of the x wingtip 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 the x wingtip acceleration at 3.5 Hz in comparison to the closed-loop result Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 881 882 883 884 885 886 887 888 889 890 891 892 893 CJA 768 26 December 2016 No of Pages 19 16 Y Bi et al Fig 27 Table Open- and closed-loop results comparison of x wingtip acceleration Status number Gust response of x wingtip acceleration under 3.5 Hz gust disturbance Gust frequency (Hz) 2.5 3.0 3.5 4.0 4.5 5.5 x wingtip acceleration (m/s2) Open loop Closed loop 0.2204 0.5617 0.7196 0.5857 0.2891 0.1940 0.1098 0.2416 0.2542 0.2063 0.2243 0.1430 Fig 28 Gust response of root bending moment in frequency domain 904 Fig 27(a) and (b) are the single-sided PSD of measurements of the original and 12 Hz-filtered test data, respectively Table presents the alleviation efficacy of the control scheme acting on the x wingtip 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 the x wingtip 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 the x wingtip acceleration caused by gust 905 5.3.4 Gust load alleviation analysis of root bending moment 906 Fig 28 depicts practically the measured open- and closed-loop results concerning the root bending moment As can be seen in 894 895 896 897 898 899 900 901 902 903 907 Reduction rate (%) 50.16 56.99 64.68 64.78 22.42 26.30 Fig 29 Original signal of root bending moment under 3.5 Hz gust disturbance 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 Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 908 909 910 911 912 913 914 915 916 917 918 919 920 921 CJA 768 26 December 2016 No of Pages 19 Gust load alleviation wind tunnel tests Fig 30 Table 10 17 Gust response of root bending moment under 3.5 Hz gust disturbance Open- and closed-loop results comparison of root bending moment Status number Gust frequency (Hz) 2.5 3.5 5.5 Root bending moment (N m) Open loop Closed loop 0.5444 0.6475 0.0977 0.4163 0.3412 0.0755 949 noticed that the overall experimentally measured dynamic tendencies of open- and closed-loop results are generally in agreement with the theoretical 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 experiments to some extent Fig 29 shows the original time-domain comparison curves of the root bending moment between open- and closed-loop results at 3.5 Hz where the reduction rate also reaches the maximum Fig 30(a) and (b) are the single-sided PSD of the original test data and that after 12 Hz-filtering, respectively Take notice of the preload 2.4 NÁm 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 950 Conclusions 951 Focusing on a large-aspect-ratio flexible wing, an active control technique using piezoelectric actuators to alleviate gust- 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 952 Reduction rate (%) 23.53 47.31 22.70 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: 953 (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 speed In general, with the gust frequency increasing, the z and x wingtip 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 speed (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 966 Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 954 955 956 957 958 959 960 961 962 963 964 965 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 CJA 768 26 December 2016 18 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 Y Bi et al (4) The control scheme functions well to suppress the wing vibration which is excited by the sinusoidal gust disturbance, and the peak values of z and x wingtip 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 alleviating z and x wingtip 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 1001 1014 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 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FM Active aeroelastic flutter suppression of a supersonic plate with piezoelectric material Int J Eng Sci 2012;51(2):190–203 36 Albano E, Rodden WP A doublet-lattice method for calculating lift distributions on oscillating surfaces in subsonic flows AIAA J 1969;7(2):279–85 No of Pages 19 19 37 Karpel M Design for active and passive flutter suppression and gust alleviation Washington, D.C.: NASA Report No.: NASA CR-3482; 1981 38 Liu XY, Wu ZG, Yang C Flow field analysis and experimental investigation on gust generator J Beijing Univ Aeronaut Astronaut 2010;36(7):803–7 [Chinese] Bi Ying is a Ph.D candidate in the School of Aeronautic Science and Engineering at Beihang University, where she received her B.S degree in 2011 Her area of research includes aeroelasticity, gust responses, gust alleviation, and active control 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 Xie Changchuan is an instructor in the School of Aeronautic Science and Engineering at Beihang University His major research interests are aeroelasticity and flight dynamics of flexible aircraft, aerodynamics, and structure dynamics 1146 An Chao is a Ph.D candidate in the School of Aeronautic Science and Engineering at Beihang University, where he received his B.S degree in 2014 His main research areas are aeroelasticity and flight dynamics of flexible aircraft 1151 Yang Chao is a professor and Ph.D advisor in the School of Aeronautic Science and Engineering at Beihang University, where he received his Ph.D degree in 1996 His current research interests are aeroelasticity and active control 1156 Please cite this article in press as: Bi Y et al Gust load alleviation wind tunnel tests of a large-aspect-ratio flexible wing with piezoelectric control, Chin J Aeronaut (2016), http://dx.doi.org/10.1016/j.cja.2016.12.028 1147 1148 1149 1150 1152 1153 1154 1155 1157 1158 1159 1160