Analytical design of damping system for flexural aeroelastic vibrations of the wings of airliner

Аuthors

Rybnikov S. I.^*, Nguyen T. S.^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: kaf301@mai.ru
**e-mail: thanhson0410@gmail.com

Abstract

The analytical design of the active system of damping of flexural aeroelastic oscillations of the wing, which is optimal according to the extended variational criterion of generalized work.

The first tone of aeroelastic oscillations of wing airliner often have frequencies of the same order with the natural frequency of undamped oscillations of the steering gear. Therefore, the synthesis and analysis of the dynamics of the stabilization systems of the airliner dynamics such the angular position of the wing is expedient to take into account and to ensure high quality in these adjustment systems may be required to build the system damping vibrations of aeroelastic wing independent or internal in relation to systems organized on the basis of the aileron channels. The assumption of the symmetry of the oscillations of the wing considered the synthesis of active system of damping of flexural vibrations of a wing of the airliner. For the synthesis of the damping system uses the method of analytical design of optimal regulators (AKOR) according to the criterion of the generalized work, the extended variable energy members of the penalty function, which takes into account the work of the control forces to move the controlled object. The joint variation in energy of the members of the penalty function is intended for counter control the level of damping wing in the transitional processes of the system, on the one hand, control-related energy consumption.

Damping of flexural vibrations of the wing is constructed using as the executive bodies of external ailerons, or specially imposed limit deflected surfaces mounted on the wing. Steering was adopted with a minor, about 15% excess frequency undamped oscillations over the frequency of the third tone aeroelastic oscillations of the wing that allows you to build a complicated damping system oscillations, which includes the first and third tones. In the mathematical model of the damping system first and the third tone of Flexural vibrations of a semi-wing and working steering aileron are described by differential equations of the second order. The control is constructed as linear, in variants with complete information about the control object and with incomplete information containing signals only of the total velocities and displacements of the console.

Performed parametric synthesis of the system damping with the current settings of the extended control object, it is shown that the choice of coefficients criterion, if sufficient control actions, it is possible to reduce vibration of the object, providing an unambiguous or even its monotonous transition function with its adjustable duration. The change in the coefficient k_m for the energy the members of the penalty function in the process of designing the system is an effective impact on the nature of the transition process in it. With its growth, the absolute values of the feedback coefficients in the system, its natural frequencies, the level and efficiency of the control action decrease, and the transient process in the system approximates to free fluctuations of the object. With decreasing k_m, conversely, the moduli of the feedback coefficients in the system and its natural frequencies increase, as well as the values of the control actions and their efficiency, the oscillation of the transient process decreases, then the process becomes single-valued and then goes monotonous. Tightening restrictions on the derivatives of the deviations from the ends of the console from a stable state to be performed in the form of an increase in the coefficients in front of them, with sufficient energy, leads to a decrease in variability transients in the system, in extreme cases , to its complete elimination . The handling qualities transients change in the coefficient k_m is maintained.

Keywords:

analytical design, control, aeroelastic vibrations, tone of aeroelastic, the penalty function

References

1. Letov A.M. Avtomatika i telemekhanika, 1960, no. 4, pp. 436-441; no. 5, pp. 561-568; no. 6, pp. 651-655; 1961, no. 4, pp. 425-435; 1962, no.11, pp. 1405-1413.

2. Letov A.M. Dinamika poleta i upravleniye (Flight Dynamics and Control), Moscow, Nauka, 1969, 360 p.

3. Krasovskiy A.A. Analiticheskoye konstruirovaniye konturov upravleniya letatel’nymi apparatami (Analytical design of control loops for aircraft), Moscow, Mashinostroyeniye, 1969, 240 p.

4. Pupkov K.A., Yegupov N.D. Metody klassicheskoy i sovremennoy teorii avtomaticheskogo upravleniya (Methods of the classical and modern theory of automatic control), Moscow, Izd. MGTU im. N.E.Baumana, 2004, 744 p.

5. Bukov V.N., Sizykh V.N. Avtomatika i telemekhanika, 1999, no.12, pp. 16-32.

6. Ageyev A.M., Sizykh V.N. Nauchnyy vestnik NGTU, 2014, vol. 56, no. 3, pp.7-22.

7. Aleksandrov A.G. Avtomatika i telemekhanika, 2015, no. 5, pp. 27-42.

8. Khlebnikov M.V., Shcherbakov N.S., Chestnov V.N. Avtomatika i telemekhanika, 2015, no. 12, pp. 65-79.

9. Lebedev G. N., Yeliseyev V. D., Ivashova N. D. Trudy MAI, 2013, no. 70, available at: http://trudymai.ru/eng/published.php?ID=44508

10. Ketkov Yu.L., Ketkov A.Yu., Shul’ts M.M. Matlab 7: programmirovaniye, chislennyye metody (Matlab 7: programming, numerical methods), SPb, BKHV-Peterburg, 2005, 752 p.

11. Grishanina T.V., Shklyarchuk F.N. Izbrannyye zadachi aerouprugosti (Aeroelastic problems), Moscow, Izd-vo MAI, 2007, 48 p.

12. Belotserkovskiy S.M., Kochetkov Yu.A., Krasovskiy A.A., Novitskiy V.V. Vvedeniye v aeroavtouprugost’ (Introduction to aero-autoelasticity), Moscow, Nauka, 1980, 384 p.

13. G.S.Byushgens A.V. Dinamika poleta (Flight dynamics), Moscow, Mashinostroyeniye, 2011, 776 p.

14. Timakov S.N., Zhirnov A.V. Vestnik MGTU im. N.E.Baumana. Priborostroyeniye, 2014, no. 3(96), pp. 37-53.

15. Stepanov A.V. Prikladnaya matematika i mekhanika, 1999, vol. 63, no.1, pp. 61.

16. Rybnikov S.I. Analiticheskoye konstruirovaniye optimal’nykh regulyatorov na osnove uravneniya Eylera-Puassona (Analytical construction of optimal regulators based on the Euler-Poisson equation), Moscow, Izd. MAI, 1993, 28 p.

17. Rybnikov S.I., Khoang Min’ Dak. Vestnik Moskovskogo aviatsionnogo instituta, 2008, vol. 15, no.3, pp. 154-164.

Download