Abstract
The objective of aeroelastic control, i.e., aeroservoelasticity, is either suppression of instability, such as flutter, or impeding the effect of external excitation, e.g., due to a gust. In the present work, a robust active feedback controller for a NACA64A010 airfoil model under sub- and transonic flow conditions is designed to impede flutter. The airfoilmodel has an elastic heave and pitch suspension and is equipped with an active aerodynamic control surface. The control design is based on linear reduced-order models (ROM) derived from a coupled computational fluid dynamics (CFD)-computational structural mechanics (CSM) simulation environment. Because the control design should be robust across a range of flow conditions, a collection of ROMs, which span the desired operational envelope, is considered. For each condition, the stability region for a three-term controller is determined with a parameter space approach. Building the intersection area for certain flow regimes allows determining the area of robust stability. The possibility of shifting the flutter boundary with a robust controller compared to adaptive control designs is discussed. To determine finally a set of control parameters chosen from within the stabilizing area, an optimization approach is used. Comparisons of the response of the investigated airfoil model under control between ROM and CFD–CSM shows that the linear ROM is able to predict the response very accurately, despite nonlinearities due to shocks in the flow field.
Similar content being viewed by others
References
Stickan, B., Johannes, D., Jens, N.: Limit-cylcle-oscillation simulations of AEROSTABIL Windtunnel experiments. In: 17th International forum on aeroelasticity and structural dynamics (IFASD), Saint Petersburg, Russia, 2015
Kroll, N., et al.: DLR project digital-X: towards virtual aircraft design and flight testing based on high-fidelity methods. CEAS Aeronaut. J. 7(1), 3–27 (2015). https://doi.org/10.1007/s13272-015-0179-7
Lucia, D.J., Beran, P.S., Silva, W.A.: Reduced-order modeling: new approaches for computational physics. Progress Aerosp. Sci. 40(1–2), 51–117 (2004). https://doi.org/10.1016/j.paerosci.2003.12.001
Dowell, E.H.: Some recent advances in nonlinear aeroelasticity: fluid-structure interaction in the 21st century. In: 51st AIAA/ASME/-ASCE/AHS/ASC structures, structural dynamics, and materials conference. 3137. American Institute of Aeronautics and Astronautics, (2010). https://doi.org/10.2514/6.2010-3137
Widhalm M., et al.: Efficient computation of dynamic stability data with a linearized frequency domain solver. In: Pereira, J. C. F., Sequeira, A. (eds.) European conference on computational fluid dynamics ECCOMAS CFD, Lisbon, Portugal (2010)
Da Ronch, A., et al.: Linear frequency domain and harmonic balance predictions of dynamic derivatives. J. Aircr. 50(3), 694–707 (2013). https://doi.org/10.2514/1.C031674
Zimmermann, R.: A locally parametrized reduced-order model for the linear frequency domain approach to time-accurate computational fluid dynamics. SIAM J. Sci. Comput. 36(3), B508–B537 (2014). https://doi.org/10.1137/130942462
Poncet-Montanges, A., et al.: Frequency-domain approach for transonic unsteady aerodynamics modelling. In: 17th international forum on aeroelasticity and structural dynamics (IFASD), Saint Petersburg, Russia (2015)
Lassila, T., Manzoni, A., Quarteroni, A., Rozza, G.: Model order reduction in fluid dynamics: challenges and perspectives. In: Quarteroni, A., Rozza, G. (eds.) Reduced order methods for modeling and computational reduction. MS&A - Modeling, Simulation and Applications, vol. 9, pp. 235–273. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-02090-7-9
Rowley, C.W., Colonius, T., Murray, R.M.: Model reduction for compressible flows using pod and Galerkin projection. Phys. D Nonlinear Phenom. 189(1–2), 115–129 (2004). https://doi.org/10.1016/j.physd.2003.03.001
Bourguet, R., Braza, M., Dervieux, A.: Reduced-order modeling of transonic flows around an airfoil submitted to small deformations. J. Comput. Phys. 230(1), 159–184 (2011). https://doi.org/10.1016/j.jcp.2010.09.019
Barone, M.F., et al.: Stable Galerkin reduced order models for linearized compressible flow. J. Comput. Phys. 228(6), 1932–1946 (2009). https://doi.org/10.1016/j.jcp.2008.11.015
Hall, K.C., Thomas, J.P., Dowell, E.H.: Proper orthogonal de-composition technique for transonic unsteady aerodynamic flows. AIAA J. 38(10), 1853–1862 (2000). https://doi.org/10.2514/2.867
Amsallem, D., Farhat, C.: On the stability of reduced-order linearized computational fluid dynamics models based on POD and Galerkin projection: descriptor vs non-descriptor forms. In: Reduced order methods for modeling and computational reduction, pp. 2014–2233. Springer, New York (2014)
Amsallem, D., Farhat, C., Zahr, M.: On the robustness of residual minimization for constructing POD-based reduced-order CFD models. In: Proceedings of the 43rd AIAA fluid dynamics conference and exhibit, San Diego, CA (2013)
Silva, W.: Reduced-order models based on linear and nonlinear aero-dynamic impulse responses. In: 40th structures, structural dynamics, and materials conference and exhibit. American Institute of Aeronautics and Astronautics (AIAA), 1999. https://doi.org/10.2514/6.1999-1262
Kaiser, C., et al.: Time-linearized analysis of motion-induced and gust-induced airloads with the DLR TAU Code. In: Deutscher Luft- und Raumfahrtkongress, Rostock, Germany (2015)
Raveh, D.E.: Reduced-order models for nonlinear unsteady aerodynamics. AIAA J. 39(8), 1417–1429 (2001). https://doi.org/10.2514/2.1473
Winter, M., Breitsamter, C.: Nonlinear reduced-order modeling of unsteady aerodynamic loads based on dynamic local linear neuro-fuzzy models. In: I7th international forum on aeroelasticity and structural dynamics (IFASD), Saint Petersburg, Russia (2015)
Silva, W.A.: Simultaneous excitation of multiple-input/multiple-output CFD-based unsteady aerodynamic systems. J. Aircr. 45(4), 1267–1274 (2008). https://doi.org/10.2514/1.34328
Silva, W.A., Vatsa, V.N., Biedron, R.T.: Development of unsteady aerodynamic and aeroelastic reduced-order models using the FUN3D Code. In: 14th international forum on aeroelasticity and structural dynamics (IFASD), p. 030. Seattle, USA (2009)
Munteanu, S., et al.: A Volterra Kernel reduced-order model approach for nonlinear aeroelastic analysis. In: 46th AIAA/ASME/ASCE/AHS/-ASC structures, structural dynamics and materials conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, pp. 1–19. (2005). https://doi.org/10.2514/6.2005-1854
Lucia, D.J., Beran, P.S., Silva, W.A.: Aeroelastic system development using proper orthogonal decomposition and Volterra theory. J. Aircr. 42(2), 509–518 (2005). https://doi.org/10.2514/1.2176
Cowan, T.J., Arena, A.S., Gupta, K.K.: Accelerating computational fluid dynamics based aeroelastic predictions using system identification. J. Aircr. 38(1), 81–87 (2001). https://doi.org/10.2514/2.2737
Silva, W., Raveh, D.: Development of unsteady aerodynamic state-space models from CFD-based pulse responses. In: 19th AIAA applied aerodynamics conference. American Institute of Aeronautics and Astronautics (AIAA), 2001. https://doi.org/10.2514/6.2001-1213.
Rampurawala, A., Badcock. K., Marques, S.: ANN based RIM for the prediction of unsteady aeroelastic instabilities. In: 14th international forum on aeroelasticity and structural dynamics (IFASD), Seattle, USA (2009)
Mannarino, A., Mantegazza, P.: Multifidelity control of aeroelastic systems: an immersion and invariance approach. J. Guid. Control Dyn. 37(5), 1568–1582 (2014). https://doi.org/10.2514/1.G000329
Librescu, L., Marzocca, P.: Advances in the linear/nonlinear control of aeroelastic structural systems. Acta Mech. 178(3–4), 147–186 (2005). https://doi.org/10.1007/s00707-005-0222-6
Lee, K.W., Singh, S.N.: Global robust control of an aeroelastic system using output feedback. J. Guid. Control Dyn. 30(1), 271–275 (2007). https://doi.org/10.2514/1.22940
Giesseler, H. et al.: Gust load alleviation based on model predictive control. In: 16th international forum on aeroelasticity and structural dynamics (IFASD), Bristol, United Kingdom, pp. 1–18 (2013)
Mukhopadhyay, V.: Historical perspective on analysis and control of aeroelastic responses. J. Guid. Control Dyn. 26(5), 673–684 (2003). https://doi.org/10.2514/2.5108
Dowell, E.H., et al.: A modern course in aeroelasticity. In: Dowell, E.H. (ed.) Solid Mechanics and its Application, vol. 116, 4th edn. Kluwer Academic Publishers, Dordrecht (2004)
Wang, Z., Behal, A., Marzocca, P.: Adaptive and robust aeroelastic control of nonlinear lifting surfaces with single/multiple control surfaces: a review. Int. J. Aeronaut. Space Sci. 11(4), 285–302 (2010). https://doi.org/10.5139/IJASS.2010.11.4.285
Gaspari, A.D., et al.: Active aeroelastic control over a multisurface wing: modeling and wind-tunnel testing. AIAA J. 47(9), 1995–2010 (2009). https://doi.org/10.2514/1.34649
Allen, C.B., et al.: A comparison of full non-linear and reduced order aerodynamic models in control law design using a two-dimensional aerofoil model. Int. J. Numer. Methods Eng. 64(12), 1628–1648 (2005). https://doi.org/10.1002/nme.1421
Gang, C., Yueming, L., Guirong, Y.: Active control law design for flutter/LCO suppression based on reduced order model method. Chin. J. Aeronaut. 23(6), 639–646 (2010). https://doi.org/10.1016/S1000-9361(09)60265-X
Chen, G., Sun, J., Li, Y.-M.: Adaptive reduced-order-model-based control-law design for active flutter suppression. J. Aircr. 49(4), 973–980 (2012). https://doi.org/10.2514/1.C031236
Bendiksen, O.: Modern developments in computational aeroelasticity. Proc. Inst. Mech. Eng. 218(3), 157–177 (2004). https://doi.org/10.1243/0954410041872861
Dowell, E.H., Bliss, D.B., Clark, R.L.: Aeroelastic wing with leading- and trailing-edge control surfaces. J. Aircr. 40(3), 559–565 (2003)
Singh, K.V., et al.: Receptance-Based Active Aeroelastic Control Using Multiple Control Surfaces. J. Aircr. 51(1), 335–342 (2014). https://doi.org/10.2514/1.C032183
Mukhopadhyay, V.: Transonic flutter suppression control law design and wind-tunnel test results. J. Guid. Control Dyn. 23(5), 930–937 (2000). https://doi.org/10.2514/2.4635
Damen, A., Weiland, S.: Robust Control. Department of Electrical Engineering, Eindhoven University of Technology, Measurement and Control Group (2002)
Bhattacharyya, S.P., Chapellat, H., Keel, L.H.: Robust Control: The Parametric Approach, p. 648. Prentice Hall, Upper Saddle River (1995)
Zhou, K., Doyle, J.: Essentials of Robust Control. Prentice Hall, Upper Saddle River (1999)
Zhou, K., Doyle, J., Glover, K.: Robust and Optimal Control. Prentice Hall, Upper Saddle River (1996)
Bhattacharyya, S.: Robust control under parametric uncertainty: an overview and recent results. Ann. Rev. Control (2017). https://doi.org/10.1016/j.arcontrol.2017.05.001
International Electrotechnical Commission (IEC): International electrotechnical vocabulary Part 351: Control technology (IEC 60050-351:2013). 2014
Ackermann, J.: Robust Control—The Parameter Space Approach Communications and Control Engineering. Springer, London (2002). https://doi.org/10.1007/978-1-4471-0207-6
Brüderlin, M., Hosters, N., Behr, M.: Robust active control of a winglet with elastic suspension at transonic flow. J. Guid. Control Dyn. 41, 526–534 (2017)
Farhat, C., Lesoinne, M., LeTallec, P.: Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal dis-cretization and application to aeroelasticity. Comput. Methods Appl. Mech. Eng. 157(1–2), 95–114 (1998). https://doi.org/10.1016/S0045-7825(97)00216-8
Felippa, C.A., Park, K., Farhat, C.: Partitioned analysis of coupled mechanical systems. Comput. Methods Appl. Mech. Eng. 190(24–25), 3247–3270 (2001). https://doi.org/10.1016/S0045-7825(00)00391-1
Reimer, L. et al.: Development of a modular method for computational aero-structural analysis of aircraft. In: Schröder, W. (ed.) Summary of flow modulation and fluid–structure interaction findings. Notes on numerical fluid mechanics and multidisciplinary design, Vol. 109, pp. 205–238. Springer, Berlin (2010). https://doi.org/10.1007/978-3-642-04088-7
Schwamborn, D., Gerhold, T., Heinrich, R.: The DLR TAU-code : recent applications in research. In: Wesseling, P., Onate, E., Periaux, J. (eds.) European conference on computational fluid dynamics ECCOMAS CFD, Egmond aan Zee, Netherlands (2006)
Barnewitz, H., Stickan, B.: Improved mesh deformation. In: Eisfeld, B. et al. (eds.) Management and minimisation of uncertainties and errors in numerical aerodynamics. Notes on numerical fluid mechanics and multidisciplinary design, Vol. 122, pp. 219-243. Springer, Berlin (2013). https://doi.org/10.1007/978-3-642-36185-2-9
Meinel, M., Einarsson, G.: The FlowSimulator framework for massively parallel CFD applications. In: PARA 2010 state of the art in scientific and parallel computing—extended abstract no. 44. University of Iceland, Reykjavik (2010)
Rugh, W.J.: Nonlinear system theory–the Volterra/wiener approach. The Johns Hopkins University Press, Baltimore (1981)
Juang, J.-N., Pappa, R.S.: An eigensystem realization algorithm for modal parameter identification and model reduction. J. Guid. Control Dyn. 8(5), 620–627 (1985). https://doi.org/10.2514/3.20031
Kim, T.: Efficient reduced-order system identification for linear systems with multiple inputs. AIAA J. 43(7), 1455–1464 (2005). https://doi.org/10.2514/1.11225
Ma, Z., Ahuja, S., Rowley, C.W.: Reduced-order models for control of fluids using the eigensystem realization algorithm. Theor. Comput. Fluid Dyn. 25(1–4), 233–247 (2011)
Ackermann, J., Kaesbauer, D.: Design of robust PID controllers. In: Proceeding of European control conference, Porto, pp. 522–527 (2001)
Bajcinca, N., Hulin, T.: Menge aller robust stabilisierenden PID-Regler: Methodik und Software (Teil I). at Automatisierungstechnik 53, 556–564 (2005)
Schrödel, F., Manickavasagam, S.K., Abel, D.: A comparative overview of different approaches for calculating the set of all stabilizing PID controller parameters. IFAC-PapersOnLine 48(14), 43–49 (2015). https://doi.org/10.1016/j.ifacol.2015.09.431
Ho, M.: Synthesis of \(h_{\infty }\) PID controllers : a parametric approach. Automatica 39, 1069–1075 (2003). https://doi.org/10.1016/S0005-1098(03)00078-5
Apkarian, P., Gahinet, P., Buhr, C.: Multi-model, multi-objective tuning of fixed-structure controllers. Eur. Control Conf. ECC 2014, 856–861 (2014). https://doi.org/10.1109/ECC.2014.6862200
Djayapertapa, L., Allen, C.: Numerical simulation of active control of transonic flutter. In: Proceeding of 23rd ICAS congress, Toronto (2002)
Yang, T., Batina, J.: Transonic time-response analysis of three D.O.F. conventional and supercritical airfoils. In: 23rd structures, structural dynamics and materials conference, New Orleans, LA, USA, p. 0688 (1982)
Batina, J., Yang, T.: Transonic calculation of airfoil stability and response with active controls. In: 25th structures, structural dynamics and materials conference, Palm Springs, CA, USA, p. 0873 (1984)
Batina, J., Yang, T.: Application of transonic codes to aeroelastic modeling of airfoils including active controls. J. Aircr. 21(8), 623–630 (1984)
Schulze, S.: Transonic aeroelastic simulation of flexible wing section. In: AGARD REPORT 822, numerical unsteady aerodynamic and aeroelastic simulation, papers presented at the 85th meeting of the AGARD structures and materials panel, Denmark (1998)
Allan, M., Badcock, K., Richards, B.: CFD based simulation of longitudinal flight mechanics with control. In: 43rd AIAA aerospace sciences meeting and exhibit, Reno, USA. 0046. American Institute of Aeronautics and Astronautics (2005)
Marzocca, P., Silva, W., Librescu, L.: Nonlinear open-/closed-loop aeroelastic analysis of airfoils via Volterra series. AIAA J. 42(4), 673–686 (2004)
Ghiringhelli, G., Lanz, M., Mantegazza, P.: Active flutter suppression for a wing model. J. Aircr. 27(4), 334–341 (1990). https://doi.org/10.2514/2.2319
Acknowledgements
Gratefully acknowledged is the funding of parts of this work within the LARC project funded by Luftfahrtforschungsprogramm of the German Federal Ministry for Economic Affairs and Energy. Computing resources were provided by the RWTH Aachen University IT Center and supported by the German Research Foundation under GSC 111 (Aachen Institute for Advanced Study in Computational Engineering Science) and Jülich Aachen Research Alliance-HPC. The authors are also grateful to the German Aerospace Center (DLR) and the Institute of Automatic Control of RWTH Aachen University for providing software tools.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Brüderlin, M., Hosters, N. & Behr, M. Reduced-order model for robust aeroelastic control. CEAS Aeronaut J 10, 367–384 (2019). https://doi.org/10.1007/s13272-018-0322-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13272-018-0322-3