Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-12T06:37:06.586Z Has data issue: false hasContentIssue false
  • English
  • Français

Analytical Volterra-based models for nonlinear low order flight dynamics approximation systems

Published online by Cambridge University Press:  27 January 2016

A. Omran and
B. Newman
A. Omran
Affiliation:
CNH-Fiat Industrial, Burr-Ridge, Illinois, USA
B. Newman
Affiliation:
Dept of Mechanical and Aerospace Engineering, Old Dominion University, Norfolk, Virginia, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Analytical methodology is presented to conduct dynamical assembly of simple low order nonlinear responses for system synthesis and prediction using Volterra theory. The procedure is set forth generically and then applied to several atmospheric flight examples. A two-term truncated Volterra series, which is enough to capture the quadratic and bilinear nonlinearities, is developed for first and second order generalised nonlinear single degree of freedom systems. The resultant models are given in the form of first and second kernels. A parametric study of the influence of each linear and nonlinear term on kernel structures is investigated. A step input is then employed to quantify and qualify the nonlinear response characteristics. Uniaxial surge and pitch motions are presented as examples of the low order flight dynamic systems. These examples show the ability of the proposed analytical Volterra-based models to predict, understand, and analyse the nonlinear aircraft behaviour beyond that attainable by linear-based models. The proposed analytical Volterra-based model offers an efficient nonlinear preliminary design tool in qualifying the aircraft responses before computer simulation is available or invoked.

Information

Type
Research Article
Information
The Aeronautical Journal , Volume 116 , Issue 1185 , November 2012, pp. 1123 - 1153
Copyright
Copyright © Royal Aeronautical Society 2012 

References

1. Liebst, S. and Nolan, C. A simplified wing rock prediction method, August 1993, AIAA-1993-3662, Atmospheric Flight Mechanic Conference, Monterey, CA, USA.Google Scholar
2. Jahnke, C. and Culick, C. Application of bifurcation theory to the high-angle-of-attack dynamics of the F-14, AIAA J Aircr, January-February 1994, 31, (1), pp 26–34.Google Scholar
3. Ananthkrishnan, N. and Sudhakar, K. Characterization of periodic motions in aircraft lateral dynamics, AIAA J Guidance, Control, and Dynamics, May-June 1996, 19, (3), pp 680–685.Google Scholar
4. Nandan, S. Applications of bifurcation methods to F-18 HARV open-loop dynamics in landing configuration, Defense Science J, April 2002, 52, (2), pp 103–115.Google Scholar
5. Go, T. and Ramnath, R. Analytical theory of three-degree-of-freedom aircraft wing rock, AIAA J Guidance, Control, and Dynamics, July-August 2004, 27, (4), pp 657–664.Google Scholar
6. Richardson, S. and Lowenberg, M. A continuation design framework for nonlinear flight control problems, Aeronaut J, February 2006, 110, (1104), pp 85–89.Google Scholar
7. Sanchez, G. Dynamics and control of single-line kites, Aeronaut J, 2006, 110, (1111), pp 615–621.Google Scholar
8. Raghavendra, P., Sahai, T., Kumar, P., Chauhan, M. and Ananthkrishnan, N. Aircraft spin recovery, with and without thrust vectoring, using nonlinear dynamic inversion, AIAA J Aircr, November-December 2005, 42, (6), pp 1492–1503.Google Scholar
9. Mehra, K., Woburn, M., Prasanth, K. and Woburn, M. Bifurcation and limit cycle analysis of nonlinear pilot induced oscillations, August 1998, AIAA Atmospheric Flight Mechanics Conference, Boston, MA, USA.Google Scholar
10 Newman, B. Dynamics and control of limit cycling motions in boosting rockets, AIAA J Guidance, Control, and Dynamics, March-April 1995, 18, (2), pp 280–286.Google Scholar
11 Duda, H. Effects of rate limiting elements in flight control systems a new PIO-criterion, August 1995, AIAA Guidance, Navigation and Control Conference, Baltimore, MD, USA.Google Scholar
12 Klyde, H., McRuer, T. and Myers, T. PIO analysis with actuator rate limiting, July 1996, AIAA Atmospheric Flight Mechanics Conference, San Diego, CA, USA.Google Scholar
13 Go, T. Lateral-Directional aircraft dynamics under static moment nonlinearity, AIAA J Guidance, Control, and Dynamics, January–February 2009, 32, (1), pp 305–309.Google Scholar
14 Mehra, K., Washburn, B. and Carrol, V. A study of the application of singular perturbation theory, 1979, NASA CR-3167.Google Scholar
15 Naidu, D. and Calise, A. Singular perturbations and time scales in guidance and control of aerospace systems: a survey, AIAA J Guidance, Control, and Dynamics, 2001, 24, (6), pp 1057–1078.Google Scholar
16 Raghavan, B. and Ananthkrishnan, N. Small perturbation analysis of airplane dynamics with dynamic stability derivatives redefined, August 2005, AIAA Atmospheric Flight Mechanic Conference, San Francisco, CA, USA.Google Scholar
17 Mease, K., Bharadwaj, S. and Iravanchy, S. Timescale analysis for nonlinear dynamical systems, AIAA J Guidance, Control, and Dynamics, 2003, 26, (2), pp 318–330.Google Scholar
18 Desai, P. and Conway, B. Two timescale discretization scheme for collocation, AIAA J Guidance, Control, and Dynamics, 2008, 31, (5), pp 1316–1322.Google Scholar
19 Volterra, V. Theory of Functionals and of Integral and Integro-Differential Equations, 1958, Dover, New York, USA.Google Scholar
20 Rugh, J. W. Nonlinear System Theory: The Volterra/Wiener Approach, 1981, John Hopkins University Press.Google Scholar
21 Wiener, N. Response of a nonlinear device noise, 1942, Technical Report No 165, Massachusetts Institute of Technology Radiation Laboratory, Cambridge, MA, USA.Google Scholar
22 Brilliant, M. Theory of the analysis of nonlinear systems, 1958, Technical Report No 345, Massachusetts Institute of Technology Radiation Laboratory, Cambridge, MA, USA.Google Scholar
23 George, D. Continuous nonlinear systems, 1959, Technical Report No 355, Massachusetts Institute of Technology Radiation Laboratory.Google Scholar
24 Mohler, R.R. Nonlinear stability and control study of highly maneuverable high performance aircraft, 1991, NASAOSU-ECE Report No 91-01.Google Scholar
25 Stalford, H., Baumann, W., Garrett, E.F. and Herman, T. Accurate modeling of nonlinear system using volterra series submodels, July 1987, ACC American Control Conference, pp 886–891, Minneapolis, MN, USA.Google Scholar
26 Suchomel, C.F. Nonlinear flying qualities — one approach, January 1987, AIAA Aerospace Sciences Meeting, Reno, NV, USA.Google Scholar
27 Omran, A. and Newman, B. Full envelope nonlinear parameter-varying model approach for atmospheric flight dynamics, AIAA J Guidance, Control, and Dynamics, January-February 2012, 35, (1), pp 270–283.Google Scholar
28 Omran, A. and Newman, B. Piecewise global Volterra nonlinear modeling and characterization for aircraft dynamics, AAIJ J Guidance, Control, and Dynamics, May-June 2009, 32, (3), pp 749–759.Google Scholar
29. Nguyen, L., Ogburn, M., Gilbert, W., Kibler, K., Brown, P. and Deal, P. Simulator study of stall/post-stall characteristics of a fighter airplane with relaxed longitudinal static stability, 1979, NASA TP-1538.Google Scholar
30. Stevens, B. and Lewis, F. Aircraft Control and Simulation, 1992, John Wiley & Sons, New York, USA.Google Scholar
31. Franz, M. and Scholkopf, B. A unifying view of Wiener and Volterra theory and polynomial kernel regression, Neural Computation, December 2006, 18, (12), pp 3097–3118.Google Scholar
32. Gilbert, E. Functional expansions for the response of nonlinear differential systems, IEEE Transactions on Automatic Control, December 1977, 22, (6), pp 909–921.Google Scholar
33. Nguyen, T., Whipple, D. and Brandon, J. Recent experience of unsteady aerodynamic effect on flight dynamics at high angle of attack, May 1985, AGARD Conference Proceedings, Symposium on Unsteady Aerodynamics-Fundamentals and Applications to Aircraft Dynamics, Gottingen, Germany.Google Scholar
34. Omran, A. and Newman, B. Analytical nonlinear analysis methodology for reduced aircraft dynamical systems, 2010, ICAS 2010 Annual International Council of the Aeronautical Sciences Conference, 19-24 September 2010, Nice, France.Google Scholar
35. Omran, A. and Newman, B. On dynamical assembly of nonlinear uniaxial atmospheric flight mechanics, 10-13 August 2009, AIAA Atmospheric Flight Mechanics Conference and Exhibition, Chicago, IL, USA.Google Scholar
36. Zill, D., Wright, W. and Cullen, M. Advanced Engineering Mathematics, 2011, Jones & Bartlett Learning.Google Scholar