Skip to main content

Nonlinear Stability Region Determination of Pilot-Aircraft Closed-Loop Based on Differential Manifold Theory

  • Conference paper
  • First Online:
Advances in Guidance, Navigation and Control

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 644))

  • 168 Accesses

Abstract

To deal with the severely flight safety problem for the modern high gain civil transport aircraft caused by instability, which affected by the activated actuator rate saturation, the stability region of pilot-aircraft closed-loop system was studied. Taking actuator rate saturation into account, a nonlinear pilot-aircraft closed-loop dynamic model was established. Through introducing manifold theory, the accuracy stability region of the system has been obtained. The validity and accuracy of the method were proved by validity verification and dynamic simulation. What’s more, the influence of different pilot-gain values and rate-limited values on the stability region was studied. The research results can be applied to flight safety risk assessment and provide theoretical guidance for design of flight control system.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 429.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 549.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Keller, J., McKillip, R., Kim, S.: Aircraft flight envelope determination using upset detection and physical modeling methods, AIAA Paper 2009–6259 (2009)

    Google Scholar 

  2. Urnes, J.M., Reichenbach, E.Y.: Dynamic flight envelope assessment and prediction. Biochem. Biophys. Res. Commun. 353(3), 848 (2007)

    Article  Google Scholar 

  3. Schuet, S., Lombaerts, T., Acosta, D., et al.: An adaptive nonlinear aircraft maneuvering envelope estimation approach for online applications. AIAA Guidance, Navigation, and Control Conference (2014)

    Google Scholar 

  4. Allen, R., Massey, R.: Longitudinal instability in braked landing gear. J. Dyn. Syst. Meas. Contr. 103(3), 259–265 (1981)

    Article  Google Scholar 

  5. Sharma, V., Petros, G., et al.: Aircraft autopilot analysis and envelope protection for operation under icing conditions. J. Guid. Control Dyn. 27(2), 454–465 (2004)

    Article  Google Scholar 

  6. Merret, J., Hossain, K., Bragg, M.: Envelope protection and atmospheric disturbances in icing encounters, AIAA Paper 2002–0814 (2002)

    Google Scholar 

  7. Ossmann, D., Heller, M., Brieger, O.: Enhancement of the nonlinear OLOP-criterion regarding phase-compensated rate limiters, Aiaa-afm (2008)

    Google Scholar 

  8. David, K., Duane, M.: Smart-Cue and smart-Gain concepts development to alleviate loss of control. J. Guid. Control Dyn. 32(5), 471–483 (2009)

    Google Scholar 

  9. Cao, Q., Li, Y., Xu, H.: Stability region for closed-loop pilot-vehicle system with actuator rate saturation. J. Beijing Univ. Aeronaut. Astronaut. 39(2), 1237–1253 (2013)

    Google Scholar 

  10. David, K., Liang, C., Daniel, A.: Mitigating unfavorable pilot Interactions with adaptive controllers in the presence of failures/damage. J. Vib. Acoust. 119(4), 563–572 (1997)

    Article  Google Scholar 

  11. Katayanagi, R.: Pilot-induced oscillation analysis with actuator rate limiting and feedback control loop. Trans. Japan Soc. Aeron. Space Sci. 44(143), 48–53 (2005)

    Article  Google Scholar 

  12. Boskovic, J., Knoebel, N., Jackson, J,: An initial study of pilot-adaptive controller interactions in flight control, AIAA Paper 2010–8016 (2010)

    Google Scholar 

  13. Popov, M.: Absolute stability of nonlinear systems of automatic control. Automat Remote Control 22(8), 857–875 (1961)

    MathSciNet  MATH  Google Scholar 

  14. Edwards, C., Postlethwaite, I.: An anti-windup scheme with closed-loop stability consideration. Automatica 35(4), 761–765 (1999)

    Article  MathSciNet  Google Scholar 

  15. Pandita, R., Chakraborty, A., Seiler, P.: Reachability and region of attraction analysis applied to GTM dynamic flight, AIAA Paper 2009–6258 (2009)

    Google Scholar 

  16. Cao, Q., Li, Y., Xu, H.: Stability Region of closed-loop pilot-vehicle System for fly-by-wire aircraft based on linear matrix inequalities. Acta Aeronaut. Et Astronaut. Sinica 34(1), 19–27 (2013)

    Google Scholar 

  17. Chaichi, M., Garcia-Rio, E.: Three-dimensional lorentz manifolds admitting a parallel null vector field. Inst. Phys. Publishing 38(4), 841–850 (2005)

    MathSciNet  MATH  Google Scholar 

  18. Hinke, M.O.: Two-dimensional invariant manifolds in four-dimensional dynamical systems. Comput. Graph. 29, 289–297 (2005)

    Article  Google Scholar 

  19. Holger, D.: Prediction of pilot-in-the-loop oscillations due to rate saturation. J. Guid. Control Dyn. 20(3), 581–587 (1997)

    Article  Google Scholar 

  20. McRuer, D.T., Krendel, E.S.: Mathematical models of human pilot behavior, AGARDograph no. 188 (1974)

    Google Scholar 

  21. McRuer, D.T.: Human dynamics in man-machine systems. Automatica 16(3), 237–253 (1980)

    Article  Google Scholar 

  22. Chiang, H.D., Hirsch, M.W., Wu, F.F.: Stability region of nonlinear autonomous dynamical system. IEEE Trans. Autom. Control 33(1), 16–27 (1988)

    Article  MathSciNet  Google Scholar 

  23. Li, Q., Yang, X.: A new algorithm computation of two-dimensional unstable manifolds and its applications. J. phys. 59(3), 1416–1422 (2010)

    MATH  Google Scholar 

  24. Kwatny, H., Dongmo, J., Chang, B.: Nonlinear analysis of aircraft loss of control. J. Guid. Control Dyn. 36(1), 149–162 (2014)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Haojun Xu .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Dong, Z., Li, Y., Zheng, W., Zhou, C., Xu, H., Li, Z. (2022). Nonlinear Stability Region Determination of Pilot-Aircraft Closed-Loop Based on Differential Manifold Theory. In: Yan, L., Duan, H., Yu, X. (eds) Advances in Guidance, Navigation and Control . Lecture Notes in Electrical Engineering, vol 644. Springer, Singapore. https://doi.org/10.1007/978-981-15-8155-7_5

Download citation

Publish with us

Policies and ethics