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

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

Design of Nonlinear Correcting Device to Prevent Oscillations of Pilot-vehicle Systems


Iuliia Zaitceva

PhD student
Institute for problems in mechanical engineering
of the Russian Academy of Sciences
Russia, 199178, St-Petersburg, Bol'shoj pr. V.O., 61
St-Petersburg State University
Russia, 199034, St-Petersburg, Universitetskaya nab., 7-9


It is known from engineering practice that the actuators of the aircraft control surfaces have physical limits of thrust which are manifested in the nonlinear effects of actuator rate and the level saturation. In turn, the influence of nonlinearities causes a negative phase shift between the actual and control pilot signal, which negatively affects the stability of the aircraft. As a result, nonlinear oscillations of the aircraft's angular motion may arise, which endanger flight safety. To prevent fluctuations various methods have been developed, but there is no general approach to modeling. In this paper, the nonlinear correcting device synthesis methods is proposed. It is illustrated by the example of stabilizing the pitch angle in a piloted aircraft control system. The synthesis is implemented on the base of the optimization of system parameters and uses the Matlab/Simulink dynamic modeling software package. As a result of the study, the algorithm for the synthesis of a nonlinear correcting device is presented on the example of a remotely controlled UAV. The parameters of the pilot model, at which pilot-induced oscillations occur, are obtained. The properties of the optimal system are illustrated and evaluated using frequency response, pitch transients, and flight characteristics.



  1. 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, pp. 278-286
  2. Zaitceva, I., Chechurin, L. The estimation of aircraft control system stability boundaries by the describing function method. Cybernetics and Physics, 2020, vol. 9, no. 2, pp. 117- 122. Available at:
  3. Zaitseva, I. S., Chechurin, L. S. Stability of forced oscillations in manned aircraft systems. Differencialnie Uravnenia i Protsesy Upravlenia, 2019, no. 4. (In Russian) Available at:
  4. 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, pp. 30-35. Available : at
  5. Andrievskij, B. R., Kuznecov, N. V., Leonov, G. A. Methods for suppressing nonlinear oscillations in astatic systems of autopilot control of aircraft. Izv. RAN. Teoriya i Sistemy Upravleniya, 2017, no. 3, pp. 118-134. (In Russian)
  6. Andrievskij, B. R., Zajceva, I. S., Kudryashova, E. V., Kuznetsov, N. V., Kuznetsova, O. A. Methods for pilot-induced oscillation prevention. A survey. Differencialnie Uravnenia i Protsesy Upravlenia, 2020, no. 2. (In Russian) Available at:
  7. Andrievsky, B., Arseniev, D., Kuznetsov, N., Zaitceva, I. Pilot-Induced Oscillations and Their Prevention. Proc. of Cyber-Physical Systems and Control, Springer International Publishing, Cham, 2020, pp. 108-123
  8. Queinnec, I., Tarbouriech, S., Biannic, J. -M., Prieur, C. Anti-Windup algorithms for pilot-induced-oscillation alleviation. AerospaceLab, 2017, 35 p. Available at:
  9. 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, pp. 37-47
  10. Leonov, G. A., Andrievskij, B. R., Kuznetsov, N. V., Pogromskij, A. Y. Control of aircraft with AW-compensation. Differencialnie Uravnenia i Protsesy Upravlenia, 2012, no. 3. (In Russian) Available at:
  11. Zel’chenko, V. J, Sharov, S. N. Nelinejnaja korrekcija avtomaticheskih sistem. [Parametric sensitivity study nonlinear dynamic corrective devices. ] L. : Sudostroenie Publ., 1981, 167 p. (In Russian)
  12. Andrievskij, B. R., Kuznetsov, N. V., Kuznetsova, O. A., Leonov, G. A., Mokaev, T. N. Localization of hidden oscillations in ight control systems. Trudy SPIIRAN, 2016, no 49, pp. 5-31. (In Russian)
  13. Skorospeshkin, M. V., Skorospeshkin, V. N., Avramchuk, V. S. An adaptive correcting device for automatic control systems. Problemy informatiki, 2011, vol. 2, no. 10, pp. 68- 75. Available at:
  14. Hlypalo, E. I. Taking into account the dynamic nonlinearity of magnetic amplifiers in the design of automatic systems. Avtomatika i Telemekhanika, 1963, vol. 24, no 11, pp. 1394-1401. (In Russian)
  15. Nelinejnye korrektiruyushchie ustrojstva v sistemah avtomaticheskogo upravleniya / pod red. Popova E. P. [Nonlinear correcting devices in automatic control systems / ed. Popova E. P. ] M. : Mashinostroenie Publ., 1971, 466 p. (In Russian)
  16. Sharov, A. N., Sharov, S. N. Investigation of the parameters of the frequency properties of some nonlinear dynamic correcting devices. Avtomatika i Telemekhanika, 1974, vol. 35, no 8, pp. 1219-1225. (In Russian)
  17. Filatov, I. V., Sharov, S. N. Investigation of the parametric sensitivity of nonlinear dynamic correcting devices. Inzhenernaya kibernetika, 1977, vol. 15, no 2, pp. 166-169. (In Russian)
  18. Zel’chenko, V. Ya., Sharov, S. N. Raschet i proektirovanie avtomaticheskih sistem s nelinejnymi dinamicheskimi zven’yami. [Calculation and design of automatic systems with nonlinear dynamic links. ] Mashinostroenie Publ., 1986, 174 p. (In Russian)
  19. Berzin, B. P., Matyuhina, L. I., Mihalev, A. S. Non-linear correcting device. Certificate of authorship, SU 411430 A1, SSSR, 1974. number: 1680846/18-24, date: 08. 07. 1971, date of publ. : 15. 01. 1974. Applicant: Ryazan Radio Engineering Institute
  20. Skorospeshkin, M. V., Skorospeshkin, V. N., Avramchuk, V. S. [Pseudo-linear PID controller for second order system. ] Sb. trudov 13-oj mezhdunarodnoj nauchn. -prakt. konf. studentov, aspirantov i molodyh uchenyh [Proc. of the 13th international scienti c-practical. conf. students, graduate students and young scientists. ], 2016, pp. 181-182. (In Russian)
  21. Skorospeshkin, M. V., Sukhodoev, M. S., Timoshenko, E. A., Lenskiy, F. V. Adaptive pseudolinear compensators of dynamic characteristics of automatic control systems. IOP Conf. Ser. : Mater. Sci. Eng, 2016, vol. 124, pp. 012028
  22. Kryzhanovskij, G. A., Shestakov, I. N. A method of increasing the security of the application of the technology of automatic dependent observation from induced targeted interference. Trudy XXIII Vserossijskoj nauch. -prakt. konf. RARAN «Aktual’nye problemy zashchity i bezopasnosti», [Proceedings of XXIII All-Russian scientific-practical. conf. RARAN «Actual problems of protection and security», ] 2020, pp. 342-344. (In Russian)
  23. 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), 2015, pp. 225-231
  24. Zaitceva, I. S. Nonlinear oscillations prevention in unmanned aerial vehicle. Proc. of XI Majorov Int. Conf. on Software Engineering and Computer Systems, 2019, vol. 2590, 8 p
  25. Zajceva, I. S. Suppression of oscillations in the control loop « unmanned aerial vehicle-operator ». Trudy XXI konf. molodyh uchenyh «Navigaciya i upravlenie dvizheniem» [Proceedings of the XXI Conf. young scientists « Navigation and traffic control »], 2019, pp. 222-223. (In Russain)
  26. Efremov, A. V., Zaharchenko, V. F., Ovcharenko, V. N., Suhanov, V. L. Dinamika poleta: uchebnik dlya studentov vysshih uchebnyh zavedenij/Pod redakciej Byushgensa G. S. [Flight dynamics: a textbook for university students / Edited by Byushgens G. S. ] М. : Mashinostroenie Publ., 2011, 776 p
  27. Efremov, A. V., Ogloblin, A. V., Predtechenskij, A. N., Rodchenko, V. V. The pilot as a dynamic system. [Letchik kak dinamicheskaya sistema. ] М. : Mashinostroenie Publ., 1992, 331 p. (In Russian)
  28. Mitchell, D., Klyde, D. This Is Pilot Gain. Proceedings AIAA SciTech Forum, 2019, 17 p
  29. 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: Tech. Rep. (AFFDL-TR-65-15), 1965
  30. McRuer, D., Krendel, E. Mathematical models of human pilot behaviour: Tech. Rep. (AGARD-AG-188), 1974, 67 p
  31. McRuer, D., Jex, H. A review of quasi-linear pilot models. IEEE Transactions on Human Factors in Electronics, 1967, vol. HFE-8, no. 3, pp. 231-249
  32. Byushgens, G. S., Studnev, R. V. Aircraft aerodynamics. The dynamics of the longitudinal and lateral movement. [Aerodinamika samoleta. Dinamika prodol’nogo i bokovogo dvizheniya. ] М. : Mashinostroenie Publ., 1979, 352 p. (In Russian)
  33. McRuer, D. T. Pilot-Induced Oscillations and Human Dynamic Behavior: Tech. rep., 1995
  34. Romanovskij, I. V. Algorithms for solving extreme problems. [Algoritmy resheniya ekstremal’nyh zadach. ] М. : Nauka Publ., 1977, 352 p. (In Russian)
  35. Nelder, J., Mead, R. A simplex method for function minimization. Computer J. , 1965, vol. 7, pp. 308-313
  36. Zaitceva, I. Parameter setting of pilot behavioral dynamic model in aircraft control loop. Nauchno-tekhnicheskij vestnik informacionnyh tekhnologij, mekhaniki i optiki, 2020, vol. 20, no. 2, p. 200-205. (In Russian)
  37. Zaitceva, I. S., Andrievsky, B. R. Optimization of the pitch control of a manned aircraft. Materialy konf. «Matematicheskaya teoriya upravleniya i ee polozheniya». XIII mul’tikonferenciya po problemam upravleniya. [Proc. of the conference " Mathematical theory of control and its provisions". XIII multiconference on management problems. Optimization of the pitch control of a manned aircraft. ], 2020, pp. 276-280. (In Russian)
  38. Bodner, V. A. Sistemy upravleniya letatel’nymi apparatami. [Aircraft control systems. ] М. : Mashinostroenie Publ., 1973, 698 p. (In Russian)
  39. Besekerskij, V. A., Popov, E. P. Teoriya sistem avtomaticheskogo regulirovaniya. [Theory of automatic control systems. ] М. : Nauka Publ., 1975, 768 p. (In Russian)
  40. Bejker, Dzh., ml., Grejvs-Morris, P. Approksimacii Pade / Pod red. A. A. Gonchara. [Pade approximants / Ed. A. A. Gonchar. ] М. : «Mir» Publ., 1986. (In Russian)
  41. Andrievskij, B. R., Fradkov, A. L. Izbrannye glavy teorii avtomaticheskogo upravleniya s primerami na yazyke Matlab. [Selected chapters of automatic control theory with examples in sc Matlab. ] SPb. : «Nauka» Publ., 1999, 467 p. (In Russian)
  42. Zaitseva, I. S., Kuznetsov, N. V., Andrievsky, B. R. A program for simulating pilot behavior in a closed loop flight control systems (Imitator-Flight). Certificate of state registration of a computer program No. 2020663322 dated 26. 10. 2020, application no. 2020662371 dated 14. 10. 2020
  43. Mandal, T., Gu, Y. Analysis of Pilot-Induced-Oscillation and Pilot Vehicle System Stability Using UAS Flight Experiments. Aerospace, 2016, vol. 3, no. 42, 23 p. Available at:
  44. Pavlov, A., van de Wouw, N., Pogromsky, A. et al. Frequency domain performance analysis of nonlinearly controlled motion systems. Proc. of 46th IEEE Conf. Decision and Control, 2007, pp. 1621-1627
  45. Fradkov, A. Kiberneticheskaya zika: principy i primery. [Cybernetic physics: principles and examples. ] SPb. : Nauka Publ., 2003, 208 p. (In Russian)
  46. Andrievsky, B. Computation of the Excitability Index for Linear Oscillators. Proceedings of the 44th IEEE Conference on Decision and Control. 2005, pp. 3537- 3540
  47. Andrievsky, B., Kudryashova, E., Kuznetsov, N., Kuznetsova, O. Aircraft wing rock oscillations suppression by simple adaptive control. Aerosp. Sci. Technol, 2020, vol. 105, 10 p

Full text (pdf)