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

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

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Methods for Pilot-induced Oscillation Prevention. A Survey

Author(s):

Boris Rostislavich Andrievsky

Doctor of Technical Sciences, Leading Research Fellow Control of Complex Systems Lab,
Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences
(IPME RAS),
Bolshoy pr., 61, St. Petersburg, 199178;
Principal Research Fellow, Department of Applied Cybernetics,
Faculty of Mathematics and Mechanics, St. Petersburg State University (SPbSU),
Universitetskiy pr., 28, Old Peterhof, St. Petersburg, 198504;
Principal Research Fellow, Baltic State Technical University (BSTU. Voenmekh.)
1st Krasnoarmeyskaya St., 1, 198005

boris.andrievsky@gmail.com

Julia Sergeevna Zaitceva

Ph.D. student,
Department of control systems and robotics, ITMO University.
Kronverksky pr.49, St. Petersburg, 197101, Russia

juliazaytsev@gmail.com

Elena Vladimirovna Kudryashova

Ph.D., leading researcher, St.Petersburg State University.
Universitetsky pr., 28., St. Petergof, 198504, Russia

kudryashova.helen@gmail.com

Nikolay Vladimirovich Kuznetsov

Sc.D., Professor, Head of the Applied Cybernetics Department,
Saint Petersburg State University
Head of the Lab, the Institute of Problems in Mechanical
Engineering of RAS (IPME RAS);
Universitetsky pr., 28., St. Petergof, 198504, Russia

nkuznetsov239@mail.ru

Olga Aleksandrovna Kuznetsova

Ph.D., chief researcher of the Applied Cybernetics Department,
St.Petersburg State University.
Universitetsky pr., 28., St. Petergof, 198504, Russia
o_a_kuznetsova@mail.ru; Universitetsky pr.28, St. Petersgof, 198504

Abstract:

The phenomenon of aircraft Pilot-Induced Oscillation (PIO) is well known from the very beginning of aviation development. It led to accidents and incidents in military aviation, and also served as a factor contributing to incidents and accidents in civil aviation. At the present stage, the problem of PIO is becoming increasingly important, affecting various classes of automated control systems, for example, such as remote control of drones, as well as spacecraft. This review attempts to characterize the phenomenon of PIO and give an idea of the available methods for its elimination. The article describes the PIO phenomenon and classifies its types, notes the connection between PIO and the technology of electric steering, presents the existing methods for preventing PIO, including organizational and technical measures for pilots training, conducting flight tests, and criteria for evaluating the aircraft flight quality. Particular attention is paid to algorithmic methods for PIO suppression implemented in the flight control system. Some numerical examples are presented.

Keywords

References:

  1. Ajerodinamika, ustojchivost' i upravljaemost' sverhzvukovyh samoletov [Aerodynamics, stability and controllability of supersonic aircraft] Ed. Bjushgens G. S. M. : Nauka. Fizmatlit, 1998. 816 p
  2. Efremov A. V., Ogloblin A. V., Predtechenskij A. N., Rodchenko V. V. Letchik kak dinamicheskaja sistema [Aerodynamics, stability and controllability of supersonic aircraft] M. : Mashinostroenie, 1992
  3. Efremov A. V., Zaharchenko V. F., Ovcharenko V. N., Suhanov V. L. Dinamika poleta: uchebnik dlja studentov vysshih uchebnyh zavedenij [Flight dynamics: textbook for students of higher educational institutions] Ed. Bjushgens G. S. M. : Mashinostroenie, 2011. 776 p
  4. Efremov A. V., Koshelenko A. V., Tjaglik M. S., Tjumencev Ju. V., Tjan' V. C. Mathematical modeling of the characteristics of the pilot's control actions during the study of problems of manual control. Izvestija vysshih uchebnyh zavedenij. Aviacionnaja tehnika. 2015. vol. 2. pp. 34-40. (in Russian)
  5. Ashkenas I. L., Jex H. R., McRuer D. T. Pilot-induced oscillations: their cause and analysis: Tech. rep. Inglewood, CA USA: DTIC Document, 1964. No. STI-TR-239-2
  6. McRuer D. T. Pilot-Induced Oscillations and Human Dynamic Behavior: Tech. rep. Hawthorne, CA, USA: NASA, 1995. —July
  7. Aviation Safety and Pilot Control: Understanding and Preventing Unfavorable Pilot-Vehicle Interactions. Ed. by D. T. McRuer, J. D. Warner. Washington, DC: The National Academies Press, 1997
  8. McRuer D., Krendel E. Mathematical Models of Human Pilot Behavior. 1974. AGARD AG-188
  9. Klyde D., McRuer D., Myers T. Unified Pilot-Induced Oscillation Theory. PIO Analysis with Linear and Nonlinear Effective Vehicle Characteristics, Including Rate Limiting. Ohio: Wright Laboratory: Wright-Patterson Air Force Base, 1995. Vol. I. WL-TR 96-3028
  10. 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
  11. Mikrin E. A. Bortovye kompleksy upravlenija kosmicheskih apparatov: Uchebnoe posobie [Onboard spacecraft control systems: Textbook] M. : Publishing House of MSTU. N. E. Bauman, 2014
  12. Mikrin E. A. Prospects for the development of domestic manned space exploration. Kosmicheskaja tehnika i tehnologija. 2017. no 1(16). pp. 5-11. (In Russian)
  13. Mikrin E. A., Beljaev M. Ju. Manned space exploration is an area of development and application of advanced control technologies. Proc. XIII All-Russian Meeting on Control Problems (VSPU-2019), IPU RAS, Moscow. M . : IPU RAS, 2019. — June 17-20. S. 393-397. (In Russian)
  14. Mikrin E. A. Scientific and technical problems of the project. Manned space systems and complexes. Kosmicheskaja tehnika i tehnologii. 2019. no 3(36). pp. 5-19. (In Russian)
  15. McRuer D. T., Smith R. E. PIO - A historical perspective. Flight Vehicle Integration Panel Workshop on Pilot Induced Oscillations. Neuilly-sur-Seine: AGARD, 1995. AGARD-AR-335
  16. McRuer D., Graham D., Krendel E., Reisener W. Human pilot dynamics in compensatory systems: Theory, models, and experiments with controlled element and forcing function variations.. (AFFDL-TR-65-15). 1965
  17. Deppe R. P. Flight evaluation of software rate limiter concept: Report 8091-1. Buffalo, New York: Calspan Advanced Technology Center, 1993
  18. Bjushgens G. S., Studnev R. V. Ajerodinamika samoleta: Dinamika prodol'nogo i bokovogo dvizhenija [Aerodynamics of aircraft. Dynamics of longitudinal and lateral motion]. M. : Mechanical Engineering, 1979. 352 p
  19. Lebedev A. A., Chernobrovkin L. S. Dinamika poleta bespilotnyh letatel'nyh apparatov. Uchebnoe posobie. [Flight dynamics of unmanned aerial vehicles. Tutorial] M. : Mashinostroenie, 1973. 616 p
  20. Bogoslovskij S. V., Dorofeev A. D. Dinamika poleta letatel'nyh apparatov. Uchebnoe posobie [Flight dynamics of aircraft. Tutorial] SPb. : GUAP, 2002. S. 64
  21. Topcheev Y. N., Potemkin V. G., Ivanenko V. G. Sistemy stabilizacii [Stabilization systems] M. : Mashinostroenie, 1974
  22. Bodner V. A. Sistemy upravlenija letatel'nymi apparatami [Control systems for aircraft] M. : Mashinostroenie, 1973. 698 p
  23. Sannikov V. A., Jureskul A. G. Osnovnye principy postroenija modelej dvizhenija letatel'nyh apparatov: ucheb. pos. [The basic principles of building aircraft motion models: textbook] SPb. : BSTU., 2008. 135 p
  24. Efremov A. V., Korovin A. A. Modifikacija kriteriev ocenki pilotazhnyh harakteristik i javlenija raskachki samoleta letchikom [Modification of the criteria for assessing aerobatic characteristics and the phenomenon of pilot-induced oscillations]. Proc. Moscow Aviation Institute. 2012. no 55. pp. 1-12. (In Russian)
  25. Parhomovskij Ja. M., Popov L. S. Issledovanija M. V. Keldysha v CAGI po avtokolebanijam samoletnyh konstrukcij [Research of M. V. Keldysh at TsAGI on self-oscillations of aircraft structures. ] Uch. zap. TsAGI. 1971. vol. 2, no 1. pp. 3-8. (In Russian)
  26. Berko V. S., Zhivov Ju. G., Poedinok A. M. Priblizhennyj kriterij ustojchivosti vynuzhdennyh kolebanij reguliruemyh ob’’ektov s nelinejnym privodom [An approximate stability criterion for forced oscillations of controlled objects with a nonlinear drive] Uchenye zapiski TSAGI. 1984. vol. XV, no 4. pp. 72-80. (In Russian)
  27. Popov E. P., Pal'tov I. P. Priblizhennye metody issledovanija nelinejnyh avtomaticheskih sistem. [Approximate methods for the study of nonlinear automatic systems. ] M. : Fizmatlit, 1960
  28. Bjushgens G. S., Goman M. G., Fedulova E. V., Hramcovskij A. V., Usol'cev S. P. Metod funkcij Ljapunova v dinamike poleta. Sintez universal'nyh zakonov upravlenija: Teh. doklad. 140160, Moskovskaja obl., g. Zhukovskij-3: TsAGI, 1994. URL: https://elibrary.ru/item.asp?id=223060 (In Russian)
  29. Bjushgens G. S., Goman M. G., Kolesnikov E. N., Sidorjuk M. E., Fedulova E. V., Hramcovskij A. V. Metod funkcij Ljapunova v dinamike poleta. Robastnye algoritmy upravlenija prostranstvennym dvizheniem. [Lyapunov function method in flight dynamics. Synthesis of universal control laws:] Tech. report. 140160, Moscow Region, Zhukovsky-3: TsAGI, 1994. URL: https://elibrary.ru/item.asp?id=223060 (In Russian)
  30. Goman M. G., Bjushgens S. G. Osnovnye metody analiza dinamiki poleta. Ajerodinamika, ustojchivost' i upravljaemost' sverhzvukovyh samoletov. [Basic methods of analysis of flight dynamics. Aerodynamics, stability and controllability of supersonic aircraft] Eds. Bjushgens G. S., Chernyshev S. L., Goman M. G., Kuvshinov V. M., Fedosov E. A. M. : RAS, 2016. pp. 309-340. (In Russian)
  31. Keldysh M. V. O dempferah s nelinejnoj harakteristikoj. [On dampers with a nonlinear characteristic] TsAGI. 1944. vol. 557. pp. 26-37. (In Russian)
  32. Grossman E. P., Keldysh M. V., Parhomovskij Ja. M. Vibracii kryla s jeleronom. [Vibration of the wing with aileron] Uch. zap. TsAGI. 1937. no 337
  33. Keldysh M. V. Izbrannye trudy. Mehanika. [Selected Works. Mechanics] M. : Nauka, 1985
  34. Parhomovskij, Ja. M. O dempfirovanii flattera. Proc. TsAGI. 1944. pp. 1-25. (In Russian)
  35. Leonov G. A., Kuznetsov N. V. On Flutter Suppression in the Keldysh Model. Doklady Physics. 2018. vol. 63, no 9. pp. 366-370
  36. McRuer D. T., Ashkenas I. , Graham D. Aircraft dynamics and automatic control. Princeton, N. J., 1973
  37. McRuer D., Jex H. A review of quasi-linear pilot models. IEEE Transactions on Human Factors in Electronics. 1967. Vol. HFE-8, no. 3. P. 231-249
  38. McRuer D. T., Klyde D. H., Myers T. T. Development of a Comprehensive PIO Theory. AIAA paper 96-3433. 1996. P. 581 - 597
  39. McRuer D. T., Krendel E. S. The human operator as a servo system element. J. Franklin Inst. 1959. —May. Vol. 267. P. 381-403
  40. Dornheim M. A. Report pinpoints factors leading to YF-22 crash. Aviation Week and Space Technology. 1992. Vol. 137, no. 19. P. 53-54
  41. Dornheim M. A. Boeing corrects several 777 PIOs. Aviation Week and Space Technology. 1992. Vol. 142, no. 19. P. 32-33
  42. Gibson J. Piloted Handling Qualities Design Criteria for High Order Flight Control Systems in Criteria for Handling Qualities of Military Aircraft: Tech. Rep. AGARDCP-333. 800 Elkridge Landing Road, Linthicum Heights, Maryland: Available from NASA Center for AeroSpace Information, 1982
  43. Hirsch D., McCormick R. Experimental investigation of pilot dynamics in pilotinduced oscillation situation. Journal of Aircraft. 1966. Vol. 3. P. 567-573
  44. Hamel P. Rotocraft-pilot coupling: A critical issue for highly augmented helicopters?. AGARD Symposium on Advances in Rotorcraft Technology, Ottawa, Canada. Linthicum Heights, Maryland, USA: NASA Center for AeroSpace Information, 1996. —May. AGARD-CP-592
  45. Anackij V. S., Astapenko V. A., Lebedev S. I. Koncepcija manevrennosti [The concept of maneuverability]. Military scientific and practical bulletin. 2015. vol. 1, no 2. pp. 4-10. (In Russian)
  46. 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
  47. Smith R. Effects of control system dynamics on fighter approach and landing longitudinal flying qualities (Vol. 1): Tech. Rep. AFFDL-TR-122: Wright-Patterson Air Force Base, Ohio: Wright Laboratory, 1978
  48. Cooke N. J. Human factors of remotely operated vehicles. Human factors of remotely operated vehicles. In Proc. of the Human Factors and Ergonomics Society Annual Meeting. Vol. 50. San Francisco, CA, USA: 2006. —October. P. 166 - 169
  49. 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
  50. DoD. Flying qualities of Piloted Aircraft. MIL STD-1797A. Philadelphia, Pensylvania: Department of Defense Military Specifications and Standarts, 1990
  51. 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
  52. Duda H. Open Loop Onset Point: A New Qualities Parameter to Predict A-PC Problems due to Rate Saturation in FCS: Tech. Rep. DLR IB 111-96/1. Braunschweig, Germany: DLR Institut fur Flugmechanik, 1996
  53. Efremov A. V., Koshelenko A. V., Tjaglik M. S., Aleksandrov V. V. Razvitie v MAI stendovoj bazy dlja issledovanij sistemy samolet-letchik. [Development of a bench base at the Moscow Aviation Institute for studies of the pilot-aircraft system] Polet. All-Russian scientific and technical journal. 2014. vol. 1. pp. 58-64. (In Russian)
  54. Animica O. V., Gajfullin A. M., Ryzhov A. A., Sviridenko Ju. N. Modelirovanie na pilotazhnom stende dozapravki samoleta v polete. [Modeling at the flight bench for refueling an aircraft in flight]. Proc. Moscow Institute of Physics and Technology. 2015. vol. 7, no 1 (25). pp. 3-15. (In Russian)
  55. Vyshinskij V. V., Ivanov V. K., Terpugova A. V. Modelirovanie slozhnyh rezhimov poleta na pilotazhnyh stendah s uchetom atmosfernoj turbulentnosti. [Modeling of complex flight modes on aerobatic stands taking into account atmospheric turbulence]. Proc. Moscow Institute of Physics and Technology. 2015. vol. 7, no 1 (25). pp. 36-43. (In Russian)
  56. Mikrin E. A., Korvjakov V. P., Klimanov S. I. Razrabotka trenazhera spuska korablja . Sojuz TMA-M. dlja bortovogo leptopa mezhdunarodnoj kosmicheskoj stancii. [Development of a simulator for launching a ship. Union TMA-M. for the onboard laptop of the international space station]. Bulletin of computer and information technology. 2013. vol. 1 (103). pp. 12-16. (in Russian)
  57. Mitchell D., Hoh R., Aponso B., Klyde D. Proposed Incorporation of Mission-Oriented Flying Qualities into MIL STD-1797A: Tech. Rep. WL-TR-94-3162: Wright-Patterson Air Force Base, Ohio: Air Force Flight Dynamics Laboratory, 1994
  58. Mitchell D., Hoh R. Development of a unified method to predict tendencies for pilot-induced oscillations: Tech. Rep. WL-TR-95-3049: Wright-Patterson Air Force Base, Ohio: Air Force Flight Dynamics Laboratory, 1995
  59. Buchacker E., Galleithner H., Koehler R., Marchand M. Development of MIL-8785C into a Handling Qualities Specification for a New European Fighter Aircraft: Tech. Rep. AGARD-CP508: Proc. of Flight Mechanics Panel Symposium, Turin, Italy, May 9-13, 1994. (Available from NASA Center for AeroSpace Information, 800 Elkridge Landing Road, Linthicum Heights, Maryland), 1990
  60. Gibson J. The Prevention of PIO by Design. Proc. Flight Mechanics Panel Symposium, Turin, Italy, May 9-13, 1994. Vol. AGARD-CP-560. 1995
  61. Gibson J. Definition, Understanding, and Design of Aircraft Handling Qualities: Tech. Rep. LR-756. Delft, Netherlands: Delft University of Technology, 1995
  62. Smith R. The Smith-Geddes Criteria. The Smith-Geddes Criteria. Presented at the SAE Aerospace, Control and Guidance Systems Symposium. Reno, Nevada: Mojave, California: High Plains Engineering, 1993. —March
  63. Smith R., Geddes N. Handling Quality Requirements for Advanced Aircraft Design: Longitudinal Mode: Tech. Rep. AFFDL-TR-78-154: Wright-Patterson Air Force Base, Ohio: Air Force Flight Dynamics Laboratory, 1979
  64. Neal P., Smith R. An In-Flight Investigation to Develio Control System Design Criteria for Fighter Aircraft: Tech. Rep. AFFDL-TR-70-74: Wright-Patterson Air Force Base, Ohio: Air Force Flight Dynamics Laboratory, 1970
  65. Mitchell D., Hoh, Klyde D. Recommended Practices for Exposing Pilot-Induced Oscillations of Tendecies in the Development Process. USAF Developmental Test and Evaluation Summit, AIAA. 2004
  66. Mitchell D., Hoh, Klyde D. A critical examination of PIO prediction criteria. AIAA Atmospheric Flight Mechanics Conference and Exhibit. 1998
  67. Mitchell D. G., Hoh, Klyde D. Bandwidth Criteria for Category I and II PIOs. Bandwidth Criteria for Category I and II PIOs. NASA. Vol. 1. 1999. —April. P. 17 - 29
  68. Duda H. Prediction of Adverse Aircraft-Pilot Coupling in the Roll Axis due to Rate Limiting in Flight Control Systems: Tech. Rep. DLR IB 111-96/13. Braunschweig, Germany: DLR Institut fur Flugmechanik, 1996
  69. 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
  70. Hanke D. Handling qualities analysis on rate limiting elements in flight control systems: Tech. Rep. AGARD-AR-335. 800 Elkridge Landing Road, Linthicum Heights, Maryland: Available from NASA Center for AeroSpace Information [CASI], 1995
  71. Smith J., Berry D. Analysis of Longitudinal Pilot-Induced Oscillation Tendencies of YF-12 Aircraft: Tech. Rep. NASA TN D-7900. Washington, D. C. : NASA, 1975
  72. Zaitseva I. S., Chechurin L. S. Ustojchivost' vynuzhdennyh kolebanij v pilotiruemyh sistemah letatel'nyh apparatov. [Stability of forced oscillations in manned aircraft systems]. Differential Equations and Control Processes. 2019. no 4. pp. 159-176. (In Russian)
  73. Taylor J., O’Donnell J. Syntethis of nonlinear controlers with rate feedback via sinusoidal - input describing function method. Proc. American Control Conf. 1990. P. 2217-2222
  74. 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
  75. Daniel O., Matthias H., Oliver B. Enhancement of the Nonlinear OLOP-PIOCriterion Regarding Phase-Compensated Rate Limiters. Enhancement of the Nonlinear OLOP-PIO-Criterion Regarding Phase-Compensated Rate Limiters. AIAA Atmospheric Flight Mechanics Conf. and Exhibit. Honolulu, Hawaii: 2008. —Aug
  76. Amato F., Iervolino S. Actuator design for aircraft robustness versus category II PIO. Proc. 7th Mediterran. Conf. on Control and Automation (MED’99), Haifa, Israel. IEEE Press, 1999. P. 1804 - 1820
  77. 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. P. 531-538
  78. Baily R. E., Bidlack T. J. A quantitative criterion for pilot-induced oscillations: time domain Neal-Smith Criterion. A quantitative criterion for pilot-induced oscillations: time domain Neal-Smith Criterion. AIAA Atmospheric Flight Mechanics Conf. AIAA-96-3434-CP. San Diego, CA: 1996. —July
  79. Брагин В. О., Вагайцев В. И, Кузнецов Н. В., Леонов Г. А. Алгоритмы поиска скрытых колебаний в нелинейных системах. Проблемы Айзермана и Калмана и цепи Чуа. Известия РАН. Теория и Системы Управления. 2011. no 4. С. 3-36. [V. O. Bragin, V. I. Vagaitsev, N. V. Kuznetsov, G. A. Leonov, Algorithms for Finding Hidden Oscillations in Nonlinear Systems. The Aizerman and Kalman Conjectures and Chua’s Circuits, J. of Computer and Systems Sciences Intern. , 50(4), 2011, pp. 511-543 (doi:10. 1134/S106423071104006X)]
  80. Leonov G., Kuznetsov N. Hidden attractors in dynamical systems: From hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits. Int. J. Bifurcation and Chaos. 2013. Vol. 23, no. 1. P. 1330002
  81. 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. Intern. J. Bifurc. Chaos. 2013. Vol. 23, no. 1. art. no. 1330002
  82. Andrievsky B. R., Kuznetsov N. V., Kuznetsova O. A., Leonov G. A., Mokaev T. N. Lokalizacija skrytyh kolebanij v sistemah upravlenija poletom. [Localization of latent vibrations in flight control systems]. SPIIRAS Proc. 2016. vol. 6, no. 49. pp. 5-31
  83. Hess R. Feedback control models - manual control and tracking. Handbook of Human Factors and Ergonomics. Ed. by G. Salvendy. New York: John Wiley and Sons., 1996
  84. Kleinman D. L., Baron S., Levison W. H. An optimal control model of human response part II: Prediction of human performance in a complex task. Automatica. 1970. Vol. 6, no. 3. P. 357 - 383
  85. 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
  86. Toader A., Ursu I. Pilot modeling based on time-delay synthesis. J. of Aerospace Engineering. 2013. Vol. 228. P. 740 - 754
  87. 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
  88. Tran A. T., Sakamoto N., Kikuchi Y., Mori K. Pilot induced oscillation suppression controller design via nonlinear optimal output regulation method. Aerospace Science and Technology. 2017. Vol. 68. P. 278 - 286
  89. Anderson M. R., Schmidt D. K. Closed-Loop Pilot Vehicle Analysis of the Approach and Landing Task. J. of Guidance, Control, and Dynamics. 1987. Vol. 10, no. 2. P. 187 - 194
  90. Taylor J. A systematic nonlinear controller design approach based on quasilinear system models. Proc. American Control Conf. 1983. —June. P. 141-145
  91. Meyer G., Su R., Hunt L. Application of nonlinear transformations to automatic flight control. Automatica. 1984. Vol. 20, no. 1. P. 103-107
  92. Krylov N., Bogoliubov N. Introduction to Nonlinear Mechanics. Annals of Mathematics Studies. Princeton, N. J. : Princeton University Press, 1947. Vol. 11
  93. Pavlov A., van de Wouw N., Pogromsky A. et al. Frequency domain performance analysis of nonlinearly controlled motion systems. Proc. 46th IEEE Conf. Decision and Control. New Orleans, LA, USA: IEEE, 2007. —Dec. 12-14
  94. Pogromsky A. Y., van den Berg R. A., Rooda J. E. Performance analysis of harmonically forced nonlinear systems. Proc. 3rd IFAC Workshop on Periodic Control Systems (PSYCO’07), IFAC Proceedings Volumes (IFAC-PapersOnline). Vol. 3. Saint Petersburg: IFAC, 2007. —August
  95. van den Berg R., Pogromsky A., Rooda J. Well-posedness and Accuracy of Harmonic Linearization for Lur’e Systems. Proc. 46th IEEE Conf. Decision and Control. New Orleans, USA: 2007
  96. Pogromsky A., Van Den Berg R. Frequency domain performance analysis of Lur’e systems. IEEE Trans. Control Syst. Technol. 2014. —Sep. Vol. 22, no. 5. P. 1949- 1955
  97. Andrievsky B., Kravchuk K., Kuznetsov N. et al. Hidden oscillations in the closed-loop aircraft-pilot system and their prevention. IFAC-PapersOnLine. 2016. Vol. 49. P. 30-35. URL: https://www.sciencedirect.com/science/article/pii/S2405896316312587
  98. Garber E. D., Rozenvasser E. N. On Studies of Periodical Regimes of Non-Linear Systems on the Basis of Filter Hypothesis. Automation and Remote Control. 1965. Vol. 26, no. 2. P. 274-284
  99. Andrievsky B., Kuznetsov N., Leonov G. Convergence-based Analysis of Robustness to Delay in Anti-windup Loop of Aircraft Autopilot. Proc. IFAC Workshop on Advanced Control and Navigation for Autonomous Aeroespace Vehicles (ACNAAV 2015). IFAC Proceedings Volumes (IFAC-PapersOnline). Seville, Spain: IFAC, 2015. —June 10 - 12
  100. Andrievsky B., Kuznetsov N., Leonov G., Pogromsky A. Hidden Oscillations in Aircraft Flight Control System with Input Saturation. Proc. 5th IFAC Intern. Workshop on Periodic Control Systems (PSYCO 2013), IFAC Proceedings Volumes (IFAC-PapersOnline). Vol. 5(1). Caen, France: 2013. P. 75-79
  101. Perng J. -W. Application of parameter plane method to pilot-induced oscillations. Aerospace Science and Technology. 2012. Vol. 23, no. 1. P. 140-145
  102. Bollt E., Marzocca P., Ahmadi G. The application of nonlinear pre-filters to prevent aeroservoelastic interactions due to actuator rate limiting. 53rd Structures, Structural Dynamics, and Materials Conf. 2012
  103. Brieger O., Kerr M., Postlethwaite I. et al. PIO suppression using low-order antiwindup: flight-test evaluation. J. of Guidance, Control, and Dynamics. 2012. Vol. 35, no. 2. P. 471- 483
  104. Brieger O., Kerr M., Leiß ling D. et al. Flight testing of a rate saturation compensation scheme on the ATTAS aircraft. Aerospace Science and Technology. 2009. — March. Vol. 13, no. 2-3. P. 92-104
  105. Gatley S., Postlethwaite I. , Turner M., Kumar A. A comparison of rate-limit compensation schemes for PIO avoidance. Aerospace Science and Technology. 2006. Vol. 10, no. 1. P. 37-47
  106. Hanley J. A comparison of nonlinear algorithms to prevent PIO caused by actuator rate limiting. Master Thesis, Air Force Institute of Technology Air University. 2003
  107. Sofrony J., Postlethwaite I. , Turner M. Anti-windup synthesis for systems with ratelimits using Riccati equation. Intern. J. of Control. 2008. Vol. 83. P. 233-245
  108. Smith J., Edwards J. Design of nonlinear adaptive filter for suppression of shuttle PIO tendencies. NASA Technical Memorandum 81349. 1980
  109. Alcala I., Gordillo F., Aracil J. Phase compensation design for prevention of PIO due to actuator rate saturation. Proc. American Control Conf. (ACC 2004). Boston, Massachusetts, USA: AACC, 2004. —June 30-July 2. P. 4686-4691
  110. Brieger O., Kerr M., Leiß ling D. et al. Anti-windup compensation of rate saturation in an experimental aircraft. Proc. American Control Conf. (ACC 2007). AACC, 2007. —July. P. 924-929
  111. Brieger O., Kerr M., Postlethwaite J. et al. Flight testing of low-order anti-windup compensators for improved handling and PIO suppression. American Control Conf. (ACC 2008). AACC, 2008. —June. P. 1776-1781
  112. Rundqwist L., St˚ ahl-Gunnarsson K. Phase compensation of rate limiters in unstable aircraft. Proc. Int. Conf. Control Applications (CCA’96). Dearborn, MI, USA: IEEE Press, Piscataway, NJ, 1996. P. 19-24
  113. Rundqwist L., Stahl-Gunnarsson K., Enhagen J. Rate limiters with phase compensation in JAS 39 Gripen. Control Conference (ECC), 1997 European. 1997. — July. P. 3944-3949
  114. Queinnec I., Tarbouriech S., Biannic J. -M., Prieur C. Anti-Windup algorithms for pilot-induced-oscillation alleviation. AerospaceLab. 2017
  115. Pogromsky A., Andrievsky B., Rooda J. Aircraft flight control with convergencebased anti-windup strategy. Proc. IFAC Workshop Aerospace Guidance, Navigation and Flight Control Systems (AGNFCS 09). Samara, Russia: 2009. —June, 30
  116. Andrievsky B., Kuznetsov N., Leonov G., Pogromsky A. Convergence Based Antiwindup Design Method and Its Application to Flight Control. Proc. IV Int. Congress on Ultra Modern Telecom. and Control Systems (ICUMT 2012). St. Petersburg, Russia: IEEE, 2012. —October 3-5. P. 219-225. art. no. 6459667
  117. Leonov G. A., Andrievskij B. R., Kuznecov N. V., Pogromskij A. Ju. Upravlenie letatel'nymi apparatami s AW-korrekciej . [ Control of aircraft with AW correction. ] Differential equations and control processes. 2012. no 3. p 36. (in Russian)
  118. Leonov G. A. Effektivnye metody poiska periodicheskih kolebanij v dinamicheskih sistemah. [Effective methods of searching for periodic oscillations in dynamical systems. ] Applied mathematics and mechanics. 2010. vol. 74, no 1. pp. 37-73. (in Russian)
  119. Andrievskij B. R., Kuznecov N. V., Kuznecova O. A., Leonov G. A., Mokaev T. N. Lokalizacija skrytyh kolebanij v sistemah upravlenija poletom. [Localization of latent vibrations in flight control systems. ] SPIIRAS Proceedings. 2016. no 49. pp. 5-31. (in Russian)
  120. Leonov G., Andrievskii B., Kuznetsov N., Pogromskii A. Aircraft control with Anti-Windup compensation. Differential equations. 2012. vol. 48, no. 13. pp. 1700-1720
  121. Hlypalo E. I. Uchet dinamicheskoj nelinejnosti magnitnyh usilitelej pri proektirovanii avtomaticheskih sistem. [Taking into account the dynamic nonlinearity of magnetic amplifiers in the design of automatic systems] Avtomatika i Telemehanika. 1963. vol. 24, no 11. pp. 1394-1401. (in Russian)
  122. Nelinejnye korrektirujushhie ustrojstva v sistemah avtomaticheskogo upravlenija. [Nonlinear correction devices in automatic control systems. ] Ed. Popov E. P. M. : Mashinostroenie, 1971
  123. Sharov A. N., Sharov S. N. Issledovanie parametrov chastotnyh svojstv nekotoryh nelinejnyh dinamicheskih korrektirujushhih ustrojstv. [The study of the parameters of the frequency properties of some nonlinear dynamic correction devices. ] Avtomatika i Telemehanika. 1974. vol. 35, no 8. pp. 1219-1225. (in Russian)
  124. Filatov I. V., Sharov S. N. Issledovanie parametricheskoj chuvstvitel'nosti nelinejnyh dinamicheskih korrektirujushhih ustrojstv. [Parametric sensitivity study nonlinear dynamic corrective devices. ] Tecknicheskaya kibernetika. 1977. vol. 15, no 2. pp. 166-169. (in Russian)
  125. Zel'chenko V. Ja., Sharov S. N. Nelinejnaja korrekcija avtomaticheskih sistem. [Parametric sensitivity studynonlinear dynamic corrective devices. ] L. : Sudostroenie, 1981
  126. Zel'chenko V. Ja., Sharov S. N. Raschet i proektirovanie avtomaticheskih sistem s nelinejnymi dinamicheskimi zven'jami. [Calculation and design of automatic systems with non-linear dynamic links. ] Mashinostroenie, 1986
  127. Zajtseva I. S. Podavlenie nelinejnyh kolebanij v pilotiruemyh sistemah upravlenija letatel'nymi apparatami. [Non-linear vibration suppression in manned aircraft control systems. Sat Proceedings of the VII Congress of Young Scientists. St. Petersburg: ITMO University, 2018. pp. 69-72. (in Russian)
  128. Andrievsky B., Kuznetsov N., Kuznetsova O. et al. Nonlinear Phase Shift Compensator for Pilot-Induced Oscillation Prevention. Prepr. 9th IEEE Europ. Modeling Symp. on Mathematical Modeling and Computer Simulation (EMS 2015). Madrid, Spain: 2015. —6 - 8 October. P. 225-231. URL: http://uksim.info/ems2015/start.pdf
  129. Zaitseva I. S., Kuznetsov N. V. Podavlenie avtokolebanij pri distancionnom upravlenii BPLA. In Youth. Technics. Space: proc. XI All-Russian Youth Scientific and Technical conf. Ser. Library of the magazine " Voenmekh. Bulletin of BSTU". No. 56. v. 1. St. Petersburg: Balt. state tech. Univ., 2019. pp. 245-248. (in Russian)
  130. Andrievsky B. R., Zajtseva Ju. S., Kuznetsov N. V., Kudrjashova E. V. Predotvrashhenie avtokolebanij v konture operator-BPLA posledovatel'noj nelinejnoj korrekciej. [Prevention of self-oscillations in the UAV-operator loop by sequential nonlinear correction]. Proc. III-rd scientific-practical conference RARAN. Radio-electronic and missile weapons of the Navy: a look into the future. Appendix to the scientific and technical collection. Ship and airborne multichannel information management systems . St. Petersburg: JSC. Concern. Granit-Electron., 2018. pp. 73-80
  131. Taylor J., Strobel K. Application of nonlinear controller design approach based on quasilinear system models. Proc. American Control Conf. 1984. P. 817-824
  132. Taylor J., Astrom K. A nonlinear PID autotuning algorithm. Proc. American Control Conf. 1986. —June. P. 2118-2123
  133. Nassirharand A., Firdeh S. Design of nonlinear lead and/or lag compensators. Intern. J. of Control, Automation and Systems. 2008. Vol. 6. P. 394-400
  134. Gelb A., Vander Velde W. E. Multiple-Input Describing Functions and Nonlinear System Design. New York: McGraw-Hill, 1968
  135. Gibson J., di Tada E. S. On the inverse describing function problem. On the inverse describing function problem. Vol. 1. 1963. P. 29 - 34
  136. Lane S., Stengel R. Flight control design using non-linear inverse dynamics. Automatica. 1988. Vol. 24, no. 4. P. 471-483
  137. Rysdyk R., Calise A. Robust nonlinear adaptive flight control for consistent handling qualities. IEEE Trans. Control Syst. Technol. 2005. Vol. 13, no. 6. P. 896-910
  138. Burken J., Williams-Hayes P., Kaneshige J., Stachowiak S. Adaptive Control Using Neural Network Augmentation for a Modified F-15 Aircraft. Adaptive Control Using Neural Network Augmentation for a Modified F-15 Aircraft. 14th Mediterranen Conf. on Control and Automation. 2006
  139. Itoh E., Suzuki S. A New Approach to Automation That Takes Account of Adaptive Nature of Pilot Maneuver. Automation Congress, 2006. WAC ’06. World. 2006. — July. P. 1-8
  140. de Lamberterie P., Perez T., Donaire A. A low-complexity flight controller for Unmanned Aircraft Systems with constrained control allocation. Australian Control Conference (AUCC), 2011. 2011. —Nov. P. 284-289
  141. Yildiz Y., Kolmanovsky I. A Control Allocation Technique to Recover From Pilot-Induced Oscillations (CAPIO) due to Actuator Rate Limiting. Proc. American Control Conf. (ACC 2010). Baltimore, MD, USA: AACC, 2010. —June 30-July 02,. P. 516-523
  142. Acosta D. M., Yildiz Y., Craun R. W. et al. Piloted Evaluation of a Control Allocation Technique to Recover from Pilot-Induced Oscillations. J. of Aircraft. 2015. — Jan. Vol. 52, no. 1. P. 130-140
  143. Yildiz Y., Kolmanovsky I. , Acosta D. A control allocation system for automatic detection and compensation of phase shift due to actuator rate limiting. Proc. American Control Conference (ACC 2011). 2011. —June. P. 444-449
  144. Smeur E., De Wagter C., Hoppener D. Prioritized Control Allocation for Quadrotors Subject to Saturation. Prioritized Control Allocation for Quadrotors Subject to Saturation. 9th Int. Micro Air Vehicle Competition and Conf. Toulouse, France: 2017. P. 37-43
  145. Andrievsky B., Andrievsky A., Zaitceva I. Adaptive Zooming Strategy in Discrete-time Implementation of Sliding-mode Control. IFAC Proceedings Volumes (IFACPapersOnline). Vol. 48. IFAC, 2015. P. 319-326
  146. Balas G., Hodgkinson J. Control design methods for good flying qualities. presented at the AIAA Atmospheric Flight Mechanics Conf. 2009. —August
  147. Pahle J., Wichman K., Foster J., Bundick W. An overview of controls and flying qualities technology on the F/A-18 high alpha research vehicle: Tech. Rep. NASAH-2123: NASA Dryden technical report, 1996
  148. Stengel R. Princeton University, Lecture Notes : Flying qualities criteria. Aircraft flight dynamics. 2014. URL:http://www. princeton. edu stengel-MAE331Lecture18a. pdf
  149. McCarley J. S., Wickens C. D. Human Factors Concerns in UAV Flight: Tech. rep. Urbana, IL, USA: Champaign Institute of Aviation, Aviation Human Factors Division, University of Illinois at Urbana, 2004
  150. Stapleford R. L., Peters R. A., Alex F. R. Experiments and a Model for Pilot Dynamics with Visual and Motion Inputs. NASA. 1969
  151. Pool D. M., Zaal P. M., Damveld H. J. et al. Pilot equalization in manual control of aircraft dynamics. Proc. IEEE Intern. Conf. on Systems, Man and Cybernetics (SMC 2009). San Antonio, TX, USA: 2009. —October. P. 2480 - 2485
  152. Zaal P. M. T., Pool D. M., Chu Q. et al. Modeling human multimodal perception and control using genetic maximum likelihood estimation. J. Guid. Control. Dyn. 2009. Vol. 32. P. 1089-1099
  153. Klyde D., Mitchell D. Investigating the role of rate limiting in pilot-induced oscillations. J. of Guidance, Control, and Dynamics. 2004. Vol. 27, no. 5. P. 804-813
  154. Acosta D. M., Yildiz Y., Klyde D. H. Avoiding Pilot-Induced Oscillations in Energy-Efficient Aircraft Designs. The Impact of Control Technology - 2nd Ed.. Ed. by T. Samad, A. Annaswamy. IEEE CSS, 2014. URL: http://ieeecss.org/sites/ieeecss.org/files/CSSIoCT2Update/IoCT2-RC-Acosta-1.pdf
  155. Grodzovskij G. L., Ivanov Ju. N., Tokarev V. V. Mehanika kosmicheskogo poleta s maloj tjagoj. [Low-thrust space flight mechanics. ] M. : Fizmatgiz, 1966
  156. Raushenbah B. V., Tokar' E. N. Upravlenie orientaciej kosmicheskih apparatov. [Spacecraft orientation control] M. : Nauka, 1974. 600 p
  157. Kargu L. I. Sistemy uglovoj stabilizacii kosmicheskih apparatov. [Systems of angular stabilization of spacecraft. ] 2nd rev. M: Mashinostroenie, 1980. 172 pp
  158. Teoreticheskie osnovy proektirovanija informacionno-upravljajushhih sistem kosmicheskih apparatov. [Theoretical foundations for the design of information and control systems for spacecraft] Ed.. Mikrin E. A. M. : Nauka, 2006
  159. Zubov N. E. Algoritmicheskoe obespechenie avtomaticheskogo rezhima orbital'noj orientacii kosmicheskogo apparata. [Algorithmic support for the automatic mode of the orbital orientation of the spacecraft. ] Izv. USSR Academy of Sciences. Tech. Cybernetics. 1990. no 2. pp. 193. (In Russian)
  160. Mikrin E. A., Zubov N. E., Negodjaev S. S., Bogachev A. V. Optimal'noe upravlenie orbital'noj orientaciej kosmicheskogo apparata na osnove algoritma s prognozirujushhej model'ju. [Optimal control of the orbital orientation of a spacecraft based on an algorithm with a predictive model. ] Proc. Moscow Institute of Physics and Technology. 2010. Vol. 2, no 3 (7). pp. 189-195. (In Russian)
  161. Zubov N. E., Mikrin E. A., Negodjaev S. S., Lavrent'ev I. N. Sintez upravlenija sblizheniem kosmicheskogo apparata s poljarnoj shemoj dvigatel'noj ustanovki po metodu svobodnyh traektorij na osnove algoritma optimal'nogo upravlenija s prognozirujushhej model'ju. [Synthesis of approaching a spacecraft with a polar scheme of a propulsion system using the free trajectory method based on an optimal control algorithm with a predictive model. Proc. Moscow Institute of Physics and Technology. 2010. Vol. 2, no 3 (7). S. 168-173. (In Russian)
  162. Mikrin E. A., Mihajlov M. V., Rozhkov S. N. Autonomous navigation and rendezvous of spacecraft in lunar orbit. Gyroscopy and navigation. 2010. vol. 1, no 4. P. 310-320
  163. Pittet C., Despre N., Tarbouriech S., Prieur C. Nonlinear controller design for satellite reaction wheels unloading using anti-windup techniques. Proc. AIAA Guidance, Navigation, and Control Conference and Exhibit. Honolulu, USA: 2008. — August 18-21
  164. Boada J., Prieur C., Tarbouriech S. et al. Anti-windup design for satellite control with microthrusters. Proc. AIAA Guidance, Navigation, and Control Conference and Exhibit. Chicago, USA: 2009. —August 10-13
  165. Boada J. Satellite control with saturating inputs. Mathematics. ISAE: Ph. D. thesis. LAAS-CNRS. Toulouse, France: LAAS-CNRS, 2010. URL:. /tel. archives-ouvertes. fr/tel-00564267
  166. Boada J., Prieur C., Tarbouriech S. et al. Multi-saturation anti-windup structure for satellite control. Proc. 2010 American Control Conference (ACC 2010). Baltimore, USA: 2010. —30 June - 2 July 2010. P. 5979-5984
  167. Boada J., Prieur C., Tarbouriech S. et al. Extended Model Recovery Anti-windup for Satellite Control. Proc. 18th IFAC Symposium on Automatic Control in Aerospace (ACA 2010). IFAC Proceedings Volumes (IFAC-PapersOnline). Ed. by Y. Ochi, H. Siguerdidjane, S. Nakasuka. Nara-ken Shinkokaido, Japan: IFAC, 2010
  168. Boada J., Prieur C., Tarbouriech S. et al. Formation flying control for satellites: anti-windup based approach. Modeling and optimization in space engineering. Series Springer Optimization and Its Applications. Ed. by G. Fasano, J. D. Pint’er. London: Springer, 2013. Vol. 73. P. 61-83
  169. Zubov, N. E., Vorob'Eva, E. A., Mikrin, E. A., Misrikhanov, M. S., Ryabchenko, V. N., Timakov, S. N. Synthesis of stabilizing spacecraft control based on generalized Ackermann's formula. J. Computer and Systems Sciences International. 2011, vol. 50, no 1, pp. 93-103
  170. Mikrin E. A., Zubov N. E., Lapin A. V., Rjabchenko V. N. Analiticheskajaformula vychislenija reguljatorov dlja linejnyh SIMO-sistem. [Analytical formula for calculating controllers for linear SIMO systems. ] Differential Equations and Control Processes. 2020. no 1. pp. 1-11. (in Russian)
  171. Zubov N., Mikrin E., Misrikhanov M., Ryabchenko V. Synthesis of controls for a spacecraft that optimize the pole placement of the close-loop control system. J. Computer and Systems Sciences International. 2012. Vol. 51. P. 431-444
  172. Zubov N. E., Mikrin E. A., Misrihanov M. Sh., Rjabchenko V. N., Timakov S. N. Primenenie algoritma tochnogo razmeshhenija poljusov pri reshenii zadach nabljudenija i identifikacii v processe upravlenija dvizheniem kosmicheskogo apparata. [The application of the algorithm for the exact placement of the poles in solving the problems of observation and identification in the process of controlling the motion of a spacecraft]. Proceedings of the Russian Academy of Sciences. Theory and control systems. 2013. no 1. pp. 135-150. (in Russian)
  173. Zubov, N. E., Mikrin, E. A., Misrikhanov, M. Sh., Ryabchenko, V. N. Modification of the exact pole placement method and its application for the control of spacecraft motion. J. Computer and Systems Sciences International. 2013, vol. 52, no 2, pp. 279-292

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