ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Stability of forced oscillations in manned aircraft systems

Author(s):

Julia Sergeevna Zaitceva

ITMO University
Russia, 197101, St.Peterburg, Kronverksky pr. 49
PhD student

juliazaytsev@gmail.com

Leonid Sergeevich Chechurin

LUT University
Finland, 53850, Lappeenranta, Yliopistonkatu 34

leonid.chechurin@lut.fi

Abstract:

In the paper the oscillatory modes of a non-autonomous flight control system are considered. The phenomenon of pilot induced oscillations in the presence of non-linearities such as " saturation" and backlash in the system is studied under conditions of active control and a significant value of the time delay. The conditions for the occurrence of self-oscillations are established by using the harmonic stationary method, the robustness of forced oscillations in the first harmonic approximation in the class of amplitudes and frequencies of the reference signal is studied.

Keywords

References:

  1. Anderson M. R., Schmidt D. K. Closed-Loop Pilot Vehicle Analysis of the Approach and Landing Task. J. Guidance, Control, and Dynamics. 1987. Vol. 10, no. 2. P. 187–194.
  2. Hess R. A. Analysis of aircraft attitude control systems prone to pilot-induced oscillations. J. of Guidance, Control, and Dynamics. 1984. Vol. 7, no. 1. P. 106 – 112.
  3. Efremov A. V., Ogloblin A. V., Predtechenskij A. N., Rodchenko V. V. Letchik kak dinamicheskaya sistema [Pilot as a dynamic system] М.: Mashinostroenie. 1992. 330 p. (In Russian)
  4. Efremov A. Analysis of Reasons for Pilot Induced Oscillation Tendency and Development of Criteria for Its Prediction: Tech. Rep. Contract SPC-94-4028. Moscow, Russia: Pilot-Vehicle Laboratory, Moscow Aviation institute, 1995.
  5. Aerodinamika, ustojchivost' i upravlyaemost' sverhzvukovyh samoletov. Pod red. G.S. Byushgensa [Aerodynamics, stability and controllability of supersonic aircraft. Ed. G.S. Buesgens.] М.: Nauka. Fizmatlit. 1998. 816 p. (In Russian)
  6. Aviation Safety and Pilot Control: Understanding and Preventing Unfavorable Pilot-Vehicle Interactions / Ed. by D. T. McRuer, J. D. Warner. Washington, DC: Committee on the Effects of Aircraft-Pilot Coupling on Flight Safety Aeronautics and Space Engineering Board Commission on Engineering and Technical Systems National Research Council. National Academy Press, 1997. URL: http://www.nap.edu/catalog/5469.html.
  7. Duda H. Effects of Rate Limiting Elements in Flight Control Systems – A New PIO Criterion. Effects of Rate Limiting Elements in Flight Control Systems – A New PIO Criterion / in Proc. of the AIAA Guidance, Navigation and Control Conf. Baltimore, Maryland: 1995.—August. P. 288– 298.
  8. Lindsey S. W. Prediction of longitudinal pilot induced oscillations using the optimal control model. Master's thesis, School of Engineering Air Force Institute of Technology Air University, Ohio, 1989.
  9. Klyde D., McRuer D., Myers T. Unified Pilot-Induced Oscillation Theory. Vol. I: PIO Analysis with Linear and Nonlinear Effective Vehicle Characteristics, Including Rate Limiting: Tech. Rep. WL-TR 96-3028:Wright-Patterson Air Force Base, Ohio: Wright Laboratory, 1995.
  10. Katayanagi R. Pilot-Induced Oscillation Analysis with Actuator Rate Limiting and Feedback Control Loop. Trans. Japan Soc. Aero. Space Sci. 2001. Vol. 44, no. 143. P. 48 – 53.
  11. McRuer D. T., Klyde D. H., Myers T. T. Development of a Comprehensive PIO Theory. AIAA paper 96-3433. 1996. P. 581 – 597.
  12. McRuer D., Krendel E. Mathematical Models of Human Pilot Behavior. AGARD AG-188, 1974.
  13. Efremov A.V., Koshelenko A.V., Tyaglik M.S., Tyumencev YU.V., Tyan' V.C. Matematicheskoe modelirovanie harakteristik upravlyayushchih dejstvij letchika pri issledovanii zadach ruchnogo upravleniya [Mathematical modeling of the characteristics of pilot control actions in the study of manual control tasks]. Izvestiya vysshih uchebnyh zavedenij. Aviacionnaya tekhnika. 2015. Vol. 2. pp. 34–40. (In Russian)
  14. Andrievsky B., Kuznetsov N., Kuznetsova O. et al. [Localization of hidden oscillations in flight control systems]. Trudy SPIIRAN [SPIIRAS Proceedings]. 2016. Vol. 6, no. 49. P. 5–31. (In Russian)
  15. Andrievsky B., Arseniev D. G., Kuznetsov N. V., Zaitceva I. S. Pilot-Induced Oscillations and Their Prevention. Cyber-Physical Systems and Control. CPS&C 2019 / Ed. by D. Arseniev, L. Overmeyer, H. Kalviainen, B. Katalinic. Springer, Cham, 2013. Vol. 95 of Lecture Notes in Networks and Systems. P. 108–123. URL: https://link.springer.com/chapter/10.1007\%2F978-3-030-34983-7_11.
  16. Federal Aviation Administration. Pilot Induced Oscillations. URL: https://www.skybrary.aero/index.php/Pilot_Induced_Oscillation (дата обращения: 2017-10-24).
  17. Mandal T., Gu Y., Chao H., Rhudy M. B. Flight Data Analysis of Pilot-Induced-Oscillations of a Remotely Controlled Aircraft. Proc. AIAA Guidance Navigation and Control Conf. (GNC 2013), Boston, MA. AIAA, 2013.—Aug. P. 1–15.
  18. Mandal T., Gu Y. Analysis of Pilot-Induced-Oscillation and Pilot Vehicle System Stability Using UAS Flight Experiments. Aerospace. 2016. Vol. 3, no. 42. P. 1–23. URL: https://www.mdpi.com/2226-4310/ 3/4/42.
  19. McRuer D., Graham D., Krendel E., Reisener, Jr. W. Human pilot dynamics in compensatory systems-theory, models, and experiments with controlled element and forcing function variations: Tech. Rep. AFFDLTR-65-15: Franklin Inst., 1965.—January.
  20. Derusso P., Roj R.YU, Klouz CH. Prostranstvo sostoyanij v teorii upravleniya (dlya inzhenerov). [State variables for engineers] М.: Gl. red. fiziko-matematicheskoj literatury izd-va .Nauka. publ., 1970. 620 p.
  21. Metody klassicheskoj i sovremennoj teorii avtomaticheskogo upravleniya. Pod red. Pupkova K. A., Egupova N. D. [Methods of the classical and modern theory of automatic control] М.: MGTU im. N. E. Baumana, 2004. 584 p. (In Russian)
  22. Popov E.P. Teoriya nelinejnyh sistem avtomaticheskogo regulirovaniya i upravleniya [Theory of nonlinear systems of automatic regulation and control] М.: Nauka publ., 1988. 256 p. (In Russian)
  23. Popov E.P. Prikladnaya teoriya processov upravleniya v nelinejnyh sistemah [Applied Theory of Control Processes in Nonlinear Systems] М.: Nauka publ., 1973. 584 p. (In Russian)
  24. Bogolyubov N.N., Mitropol'skij YU.A. Asimptoticheskie metody v teorii nelinejnyh kolebanij. [Asymptotic methods in the theory of nonlinear oscillations]. М.: Gos. izd-vo fiziko-matematicheskoj literatury.1957. 407 p. (In Russian)
  25. Ajzerman M. A., Gantmaher F.R. Absolyutnaya ustojchivost' reguliruemyh sistem [Absolute stability of regulated systems] М.: Akademiya Nauk SSSR, 1963. 139 p. (In Russian)
  26. Barkin A.I., Zelencovskij A.L. Absolute stability criterion for nonlinear control systems. Avtomat. i telemekh. 1981. p. 5–10. (In Russian)
  27. Andronov A. A. Predel'nye cikly Puankare i teoriya avtokolebanij. Sobranie trudov Andronova A. A. [Poincare limit cycles and theory of self-oscillations. Collection of works by Andronov A.A.] Izd. Akademiya Nauk SSSR. 1956. 41 p. (In Russian)
  28. Yakubovich V. A. Frequency conditions of self-oscillations in nonlinear systems with a single time-invariant nonlinearity. Sibirskij matem. zhurnal. 1973. Vol. 14, № 5. pp. 1100–1129. (In Russian)
  29. Kuznetsov N. V. [Theory of hidden oscillations and control systems stability]. XII Vserossijskij s"ezd po fundamental'nym problemem teoreticheskoj i prikladnoj mekhaniki. Bashkirskij gosudarstvennyj universitet. [Proc. of XII All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics. Bashkir State University]. 2019. pp. 46–48. (In Russian)
  30. Bragin V., Vagaitsev V., Kuznetsov N., Leonov G. Algorithms for Finding Hidden Oscillations in Nonlinear Systems. The Aizerman and Kalman Conjectures and Chua's Circuits J. Computer and Systems Sciences Intern. Izvestiya Rossijskoj Akademii Nauk. Teoriya i sistemy upravleniya. 2011. Vol. 50, no. 4. P. 511–543. (In Russian)
  31. Tzypkin Ya. Z. Relejnye avtomaticheskie sistemy [Relay automatic systems]. М.: Nauka publ., 1974. P. 576 (In Russian)
  32. Khlypalo E. I. Nelinejnye korrektiruyushchie ustrojstva v avtomaticheskih sistemah. L.: Energiya, 1973. 344 p. (In Russian)
  33. Duda H. Prediction of Pilot-in-the-Loop Oscillations due to Rate Saturation J. of Guidance, Navigation, and Control. 1997.—May–June. Vol. 20, no. 3.
  34. Glattfelder A., W.Scaufelberger. Stability analysis of single loop control systems with saturation and antireset-windup circuits IEEE Trans. Automat. Contr. 1983.—Dec. Vol. 28, no. 12. P. 1074–1081.
  35. Andrievsky B., Kuznetsov N., Leonov G., Pogromsky A. Hidden Oscillations in Aircraft Flight Control System with Input Saturation. IFAC Proceedings Volumes (IFAC-PapersOnline). Vol. 5(1). IFAC: 2013. P. 75–79.
  36. Zames G., Falb P. Stability conditions for systems with monotone and slope-restricted nonlinearities. SIAM J. 1968. Vol. 6, no. 1. P. 89–108.
  37. Evdokimov S., Klimanov S., Korchagin A. et al. Terminal control algorithm for the downrange motion of a descent module with load factor constraints. J. Computer and Systems Sciences Intern. 2012. Vol. 51, no. 5. pp. 715–731.
  38. Evdokimov S.N., Klimanov S.I., Korchagin A.N., Mikrin E.A., Siharulidze Yu.G. Control of longitudinal and lateral movement of the descent vehicle in the corridor of entry angles with overload restriction. Izvestiya Rossijskoj akademii nauk. Teoriya i sistemy upravleniya. 2012. № 6. pp. 63–79. (In Russian)
  39. Mikrin E.A., Zubov N.E., Negodyaev S.S., Bogachev A.V. [Optimal control of the orbital orientation of a spacecraft based on an algorithm with a predictive model]. Trudy Moskovskogo fiziko-tekhnicheskogo instituta [Proceedings of the Moscow Institute of Physics and Technology]. 2010. Vol. 2, no 3 (7), pp. 189–195. (In Russian)
  40. Amato F., Iervolino S., Pandit M. et al. Analysis of Pilot-in-the-Loop Oscillations Due to Position and Rate Saturations. In: Proc. 39th IEEE Conf. on Decision and Control (CDC 2000), Sydney, Australia. IEEE, 2000. P. 6.
  41. Amato F., Iervolino R., Scala S., Verde L. Category II pilot-in-the-loop oscillations analysis from robust stability methods. J. of Guidance, Control and Dynamics. 2001.—May–June. Vol. 24, no. 3.
  42. Teoriya avtomaticheskogo upravleniya: Nelinejnye sistemy upravleniya pri sluchajnyh vozdejstviyah [Theory of Automatic Control: Nonlinear Control Systems under Stochastic Actions]. Pod redakciej A.V. Netushila. М.: Vysshaya shkola publ., 1983. 432 p. (In Russian)
  43. Nguen Ch. K. The effect of backlash and dry friction on the stability of the mechatronic drive (analytical study). Nauchno-tekhnicheskij vestnik Universiteta ITMO. 2006. № 28. pp. 157–162. (In Russian)
  44. Belova L. A., Netushil A. V. On the absolute stability of control systems with multivalued nonlinearities such as backlash and limiter. Avtomat. i telemekh. 1967. Vol. 12. pp. 58–63.
  45. Brusin V. A. Absolute stability of a backlash tracking system. Izv. vuzov. Radiofizika. 1964. № 3. pp. 7–16. (In Russian)
  46. Petrov P. V., Koeva A. A. The study of self-oscillations in hydromechanical drives operating under the friction. Vestnik UGATU [Bulletin of the Ufim state aviation technical university]. 2014. Vol. 18, no 4 (65), pp. 183–190. (In Russian)
  47. Tarbourieh S., Queinnec I., Prieur C. Nonstandard use of anti-windup loop for systems with input backlash. IFAC J. of Systems and Control. 2018. Vol. 6. P. 33–42.
  48. Nadzharov E. M. An approximate determination of periodic modes in automatic control systems containing several nonlinearities. Trudy 2-go Vsesouznogo soveshaniya po TAR. [Proc. of the 2nd All-Union meeting on the theory of automatic control]. 1955. Vol. 1. (In Russian)
  49. McRuer D. T. Pilot-Induced Oscillations and Human Dynamic Behavior: Tech. rep. Hawthorne, CA, USA: NASA, 1995.—July.
  50. Gol'dfarb L. S., Baltrushevich A. V., Netushil A. V. Teoriya avtomaticheskogo upravleniya [Theory of Automatic Control]. М.: Vysshaya shkola publ., 1976. 430 p. (In Russian)
  51. Berko V.S., Zhivov Yu.G., Poedinok A.M. An approximate criterion for the stability of forced oscillations of controlled objects with a nonlinear drive. Uchenye zapiski CAGI. 1984. Vol. ХV, № 4. Pp. 72–80. (In Russian)
  52. Leonov G.A. Efficient methods for searching for periodic oscillations in dynamical systems. Prikladnaya matematika i mekhanika. 2010. Vol. 74, № 1. pp. 37–73. (In Russian)
  53. Leonov G. A., Kuznetsov N. V., Vagaitsev V. I. Localization of hidden Chua's attractors. Physics Letters A. 2011. Vol. 375, no. 23. P. 2230–2233.
  54. Leonov G. A., Kuznetsov N. V. Analytical-numerical methods for investigation of hidden oscillations in nonlinear control systems. IFAC Proceedings Volumes (IFAC-PapersOnline). 2011. Vol. 18, no. 1. P. 2494–2505.
  55. Leonov G. A., Kuznetsov N. V. Hidden attractors in dynamical systems. From hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractors in Chua circuits. Int J. Bifurcation and Chaos. 2013. Vol. 23, no. 1. P. 1–69.
  56. Kuznetsov N., Leonov G. Hidden attractors in dynamical systems: systems with no equilibria, multistability and coexisting attractors. IFAC Proceedings Volumes (IFAC-PapersOnline). 2014. Vol. 47, no. 3. P. 5445–5454. Proc. 19th IFAC World Congress. URL: https://www.sciencedirect.com/science/article/pii/S1474667016424614.
  57. Dudkowski D., Jafari S., Kapitaniak T. et al. Hidden attractors in dynamical systems. Physics Reports. 2016. Vol. 637. P. 1 –50. URL: http://www.sciencedirect.com/science/article/pii/S0370157316300928.
  58. Chechurin S. L. Parametricheskie kolebaniya i ustojchivost' periodicheskogo dvizheniya. [Parametric oscillations and stability of periodic motion]. SPb.: LGU publ., 1983. 220 p. (In Russian)
  59. Byushgens G. S., Studnev R. V. Aerodinamika samoleta: Dinamika prodol'nogo i bokovogo dvizheniya. М.: Mashinostroenie, 1979. 352 p. (In Russian)
  60. Chechurin L., Chechurin S. Physical Fundamentals of Oscillations. Frequency Analysis of Periodic Motion Stability. Springer, 2017. 220 P.

Full text (pdf)