The stable flight region can be extended by adding control flap at the wing trailing edge and combined with active control technology. We studied the active flutter control by considering the input constraints. By designing the data-driven optimal controller, the limit cycle oscillations of a typical two-dimensional airfoil wing can be suppressed with single trailing edge control surface. The traditional control methods always need a precise mathematical model of the system, which put high requirements on system modeling. In this study, a novel data-driven optimal controller is proposed by using the input–output data and without depending on the nonlinear system dynamic model. This model-free approach avoids the effects of modeling errors and system uncertainty. When the data-driven controller is applied, the limit cycle oscillation phenomenon of the airfoil wing is eliminated within several seconds. It can be seen from the numerical simulation result that the data-driven adaptive dynamic programming control method possess superiority and feasibility.
AbdelkefiAVasconcellosRMarquesFD, et al. (2012) Modeling and identification of freeplay nonlinearity. Journal of Sound and Vibration331(8): 1898–1907.
2.
AbouheafMGueaiebWLewisF (2018) Model-free gradient-based adaptive learning controller for an unmanned flexible wing aircraft. Robotics7(4): 66.
3.
AsadiDFarsadiT (2020) Active flutter control of thin walled wing-engine system using piezoelectric actuators. Aerospace Science and Technology, 102: 105853.
4.
BaoXMaoZHSharmaN (2018) A Supplementary Condition for the Convergence of the Control Policy during Adaptive Dynamic Programming. arXiv preprint arXiv:07743.
5.
ChenC-LChangC-WYauH-T (2012) Terminal sliding mode control for aeroelastic systems. Nonlinear Dynamics70(3): 2015–2026.
6.
CuiLXieXWangX, et al. (2019) Event-triggered single-network adp method for constrained optimal tracking control of continuous-time non-linear systems. Applied Mathematics and Computation352: 220–234.
7.
DingQCooperJELeungAYT (2005) Application of an improved cell mapping method to bilinear stiffness aeroelastic systems. Journal of fluids and structures20(1): 35–49.
8.
DowellEH (2015) A Modern Course in Aeroelasticity: Fifth Revised and Enlarged Edition. Cham: Springer International Publishing, 487–529.
9.
FramptonKDClarkRL (2000) Experiments on control of limit-cycle oscillations in a typical section. Journal of Guidance, Control, and Dynamics23(5): 956–960.
10.
GöhrtTOsinenkoPStreifS (2019) Adaptive dynamic programming using Lyapunov function constraints. IEEE Control Systems Letters3(4): 901–906.
11.
GuoHCaoSYangT, et al. (2018) Aeroelastic suppression of an airfoil with control surface using nonlinear energy sink. Nonlinear Dynamics94(2): 857–872.
12.
HeSYangZGuY (2016) Nonlinear dynamics of an aeroelastic airfoil with free-play in transonic flow. Nonlinear Dynamics87(4): 1–27.
13.
HouZ-SWangZ (2013) From model-based control to data-driven control: survey, classification and perspective. Information Sciences235: 3–35.
14.
HuangRHuHZhaoY (2013) Nonlinear aeroservoelastic analysis of a controlled multiple-actuated-wing model with free-play. Journal of Fluids and Structures42: 245–269.
15.
HuangRQianWHuH, et al. (2015) Design of active flutter suppression and wind-tunnel tests of a wing model involving a control delay. Journal of Fluids and Structures55: 409–427.
16.
JiangYFanJChaiT, et al. (2018) Data-driven flotation industrial process operational optimal control based on reinforcement learning. IEEE Transactions on Industrial Informatics14(5): 1974–1989.
17.
JiffriSFicheraSMottersheadJE, et al. (2017) Experimental nonlinear control for flutter suppression in a nonlinear aeroelastic system. Journal of Guidance, Control, and Dynamics40(8): 1925–1938.
18.
LiuDYangG-H (2018) Model-free adaptive control design for nonlinear discrete-time processes with reinforcement learning techniques. International Journal of Systems Science49(11): 2298–2308.
19.
LivneE (2017) Aircraft active flutter suppression: state of the art and technology maturation needs. Journal of Aircraft55(1): 410–452.
20.
LuoBWuH-NHuangT, et al. (2015) Reinforcement learning solution for hjb equation arising in constrained optimal control problem. Neural Networks71: 150–158.
21.
LuoMGaoMCaiG (2016) Delayed full-state feedback control of airfoil flutter using sliding mode control method. Journal of Fluids and Structures61: 262–273.
22.
MalherATouzéCDoaréO, et al. (2017) Flutter control of a two-degrees-of-freedom airfoil using a nonlinear tuned vibration absorber. Journal of Computational and Nonlinear Dynamics12(5) 051016.
23.
MannarinoADowellEHMantegazzaP (2017) An adaptive controller for nonlinear flutter suppression and free-play compensation. Journal of Vibration and Control23(14): 2269–2290.
24.
MarsdenCCPriceSJ (2005) The aeroelastic response of a wing section with a structural freeplay nonlinearity: an experimental investigation. Journal of Fluids and Structures21(3): 257–276.
25.
ModaresHLewisFL (2014) Optimal tracking control of nonlinear partially-unknown constrained-input systems using integral reinforcement learning. Automatica50(7): 1780–1792.
26.
MukhopadhyayV (2003) Historical perspective on analysis and control of aeroelastic responses. Journal of Guidance, Control, and Dynamics26(5): 673–684.
27.
NguyenNTSweiSSM (2015) Adaptive linear quadratic gaussian optimal control modification for flutter suppression of adaptive wing. In: AIAA infotech@ aerospace, Kissimmee, Florida, 5–9 January 2015, Virginia: ARC, 0118.
28.
O’NeilTStrganacTW (1998) Aeroelastic response of a rigid wing supported by nonlinear springs. Journal of Aircraft35(4): 616–622.
29.
OuyangYHeWLiX (2017) Reinforcement learning control of a single‐link flexible robotic manipulator. IET Control Theory & Applications11(9): 1426–1433.
30.
PrasadLBGuptaHOTyagiB (2014) Application of policy iteration technique based adaptive optimal control design for automatic voltage regulator of power system. International Journal of Electrical Power & Energy Systems63: 940–949.
31.
SanchesLGuimarãesTAMMarquesFD (2019) Aeroelastic tailoring of nonlinear typical section using the method of multiple scales to predict post-flutter stable lcos. Aerospace Science and Technology90: 157–168.
32.
SinghKVBlackCKolonayR (2019) Active aeroelastic output feedback control with partial measurements by the method of receptances. Aerospace Science and Technology86: 47–63.
33.
SongRLiJ (2018) A single-nn iterative adaptive dynamic programming algorithm for continuous-time nonlinear zero-sum games. In: 2018 37th chinese control conference (CCC), Wuhan, China, 25–27 July 2018, New York: IEEE, 2848–2853.
34.
SongZChenYLiZ, et al. (2019) Axially functionally graded beams and panels in supersonic airflow and their excellent capability for passive flutter suppression. Aerospace Science and Technology92: 668–675.
35.
StrganacTWKoJThompsonDE, et al. (2000) Identification and control of limit cycle oscillations in aeroelastic systems. Journal of Guidance, Control, and Dynamics23(6): 1127–1133.
36.
KurdilaBHeMWangY, et al. (2018) A data-driven optimal control approach for solution purification process. Journal of Process Control68: 171–185.
37.
SvobodaFHromcikM (2019) Active flutter suppression by means of fixed-order h-infinity control: results for the benchmark active control technology (bact) wing. In: 2019 18th european control conference (ECC), Naples, Italy, 25–28 June 2019, New York: IEEE, 119–124.
38.
TanaskovicMFagianoLNovaraC, et al. (2017) Data-driven control of nonlinear systems: an on-line direct approach. Automatica75: 1–10.
39.
TangDChenLTianZF, et al. (2017) Nonlinear optimal control for active suppression of airfoil flutter via a novel neural-network-based controller. In: 2017 25th mediterranean conference on control and automation (MED), Valletta, Malta, 03–06 July 2017, New York: IEEE, 253–258.
40.
TangDChenLTianZF, et al. (2018) Adaptive nonlinear optimal control for active suppression of airfoil flutter via a novel neural-network-based controller. Journal of Vibration and Control24(22): 5261–5272.
41.
VerstraelenEKerschenGDimitriadisG (2017) Flutter and limit cycle oscillation suppression using linear and nonlinear tuned vibration absorbers. In: Shock & Vibration, Aircraft/Aerospace, Energy Harvesting, Acoustics & Optics. New York: Springer, Vol. 9, 301–313.
42.
WangYZhangQZhuL (2015) Active control of hypersonic airfoil flutter via adaptive fuzzy sliding mode method. Journal of Vibration and Control21(1): 134–141.
43.
WeiQZhangHDaiJ (2009) Model-free multiobjective approximate dynamic programming for discrete-time nonlinear systems with general performance index functions. Neurocomputing72(7): 1839–1848.
44.
WerbosPJ (2007) Using adp to understand and replicate brain intelligence: the next level design?. In: 2007 IEEE international symposium on approximate dynamic programming and reinforcement learning, Honolulu, HI, 1–5 April 2007, 109–123. New York: IEEE.
45.
XiangJYanYLiD (2014) Recent advance in nonlinear aeroelastic analysis and control of the aircraft. Chinese Journal of Aeronautics27(1): 12–22.
46.
XiaoGZhangHLuoY, et al. (2017) General value iteration based reinforcement learning for solving optimal tracking control problem of continuous-time affine nonlinear systems. Neurocomputing245: 114–123.
47.
XueWTLiJZ (2016) An adaptive backstepping sliding mode control method for aeroelastic system. In: Industrial electronics society, IECON 2016-42nd annual conference of the IEEE, Florence, Italy, 23–26 October 2016, New York: IEEE, 6764–6769.
48.
YaghmaieFABraunDJ (2019) Reinforcement learning for a class of continuous-time input constrained optimal control problems. Automatica99: 221–227.
49.
YangNWangNZhangX, et al. (2016) Nonlinear flutter wind tunnel test and numerical analysis of folding fins with freeplay nonlinearities. Chinese Journal of Aeronautics29(1): 144–159.
50.
YangXHeHZhongX (2018) Adaptive dynamic programming for robust regulation and its application to power systems. IEEE Transactions on Industrial Electronics65(7): 5722–5732.
51.
YangXLiuDWangD (2014) Reinforcement learning for adaptive optimal control of unknown continuous-time nonlinear systems with input constraints. International Journal of Control87(3): 553–566.
52.
YuMHuH (2012) Flutter control based on ultrasonic motor for a two-dimensional airfoil section. Journal of Fluids and Structures28: 89–102.
53.
YuanJQiNQiuZ, et al. (2018) Adaptive rbf observer-sliding mode controller design for a two dimensional aeroelastic system with unsteady aerodynamics. Aerospace Science and Technology80: 482–495.
54.
ZhangHJiangHLuoY, et al. (2017) Data-driven optimal consensus control for discrete-time multi-agent systems with unknown dynamics using reinforcement learning method. IEEE Transactions on Industrial Electronics64(5): 4091–4100.
55.
ZhangKBehalA (2016) Continuous robust control for aeroelastic vibration control of a 2-d airfoil under unsteady flow. Journal of Vibration and Control22(12): 2841–2860.
56.
ZhangWLvZDiwuQ, et al. (2019a) A flutter prediction method with low cost and low risk from test data. Aerospace Science and Technology86: 542–557.
57.
ZhangZSongRCaoM (2019b) Synchronous optimal control method for nonlinear systems with saturating actuators and unknown dynamics using off-policy integral reinforcement learning. Neurocomputing356: 162–169.
58.
ZhaoHCaoDZhuX (2010) Aerodynamic flutter and limit cycle analysis for a 2-d wing with pitching freeplay in the supersonic flow. In: International symposium on systems and control in aeronautics and astronautics, Harbin, China, 8–10 June 2010, New York: IEEE, 1105–1109.
59.
ZhengGYangY (2008) Chaotic motions and limit cycle flutter of two-dimensional wing in supersonic flow. Acta Mechanica Solida Sinica21(5): 441–448.
