Advertisement

Longitudinal Aerodynamic Coefficients Estimation and Identifiability Analysis for Hypersonic Glider Controlled by Moving Mass

  • Pengxin Wei
  • Changsheng GaoEmail author
  • Wuxing Jing
Original Paper

Abstract

This paper presents a composite Bank-To-Turn (BTT) control mode with a moving mass and non-redundant Reaction Control System (RCS) for a hypersonic unpowered glider vehicle. This type of control mode can not only preclude the aerodynamic control surfaces ablation, but also optimize the internal space of flight vehicle. The identification of the aerodynamic coefficients for gliders under the novel control mode remains an important research focus. As a key part of system identification, input design greatly affects the identification results. Taking into account the flight characteristics and composite control strategy, the longitudinal dynamic characteristics considering the cubic nonlinearities of hypersonic glider are analyzed and the motion form of internal moving mass is designed based on multi-sine input method. The identifiability and identifiability degree of each longitudinal parameter are evaluated using singular value decomposition of the measure matrix. Simulation results demonstrate that the designed input form improves the accuracy of the estimated parameters, and show the identification order from the most identifiable parameter to the least identifiable parameter.

Keywords

Hypersonic glider Moving mass control Input design Identifiability analysis 

Abbreviations

\( \alpha \)

Angle-of-attack (AOA), deg

\( \beta \)

Sideslip angle, deg

\( \phi \)

Roll angle, deg

\( \theta \)

Pitch angle, deg

\( \psi \)

Yaw angle, deg

\( L \)

Reference length, m

\( S_{B} \)

Cross-sectional area, m2

\( \omega_{x} \)

Roll angular velocity, rad/s

\( \omega_{y} \)

Yaw angular velocity, rad/s

\( \omega_{z} \)

Pitch angular velocity, rad/s

\( v \)

Magnitude of inertial velocity vector, m/s

\( q \)

Dynamic pressure, kg/(m s2)

\( \rho \)

Air density, kg/m3

\( I_{x} \)

Moments of inertia about x-body axes, kg/(m s2)

\( I_{y} \)

Moments of inertia about y-body axes, kg/(m s2)

\( I_{z} \)

Moments of inertia about z-body axes, kg/(m s2)

\( \delta \)

Displacement of moving mass along the rail, m

\( \dot{\delta } \)

Velocity of the moving mass along the rail, m/s

\( \ddot{\delta } \)

Acceleration of the moving mass, m/s2

\( l \)

Axial coordinate of the moving mass in body frame, m

\( m_{\text{p}} \)

Mass of the moving mass, kg

\( m_{\text{S}} \)

Mass of the system, kg

\( \mu \)

Ratio of the moving mass relative to the system

\( C_{x} \)

Aerodynamics drag coefficient

\( C_{y}^{\alpha } \)

Partial derivatives of the normal forces coefficients with respect to AOA

\( C_{z}^{\beta } \)

Partial derivatives of the normal forces coefficients with respect to sideslip angle

\( m_{x}^{i} \)

Rolling moment coefficients derivatives attributable to i, \( i = \beta ,{\kern 1pt} {\kern 1pt} \omega_{x} ,{\kern 1pt} {\kern 1pt} \omega_{y} \)

\( m_{y}^{i} \)

Yaw moment coefficients derivatives attributable to i, i = \( \beta ,{\kern 1pt} {\kern 1pt} \omega_{x} ,{\kern 1pt} {\kern 1pt} \omega_{y} \)

\( m_{z}^{i} \)

Pitch moment coefficients derivatives attributable to i, i = \( \alpha ,{\kern 1pt} {\kern 1pt} \omega_{z} \)

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (NNSFC) through Grant nos. 10902026 and 11572097. The first author was also supported by the China Scholarship Council (CSC) under Grant 201406120080.

References

  1. 1.
    DARPA (2010) DARPA concludes review of falcon HTV-2 flight anomaly. DARPA news releaseGoogle Scholar
  2. 2.
    Atkins BM (2014) Mars precision entry guidance using internal moving mass actuators. Diss. Virginia Polytechnic Institute and State University, BlacksburgGoogle Scholar
  3. 3.
    Chen L, Zhou G, Yan XJ, Duan DP (2012) Composite control strategy of stratospheric airships with moving masses. J Aircr 49(3):794–801.  https://doi.org/10.2514/1.c031364 CrossRefGoogle Scholar
  4. 4.
    Rogers J, Costello M (2008) Control authority of a projectile equipped with a controllable internal translating mass. J Guidance Control Dyn 31(5):1323–1333.  https://doi.org/10.2514/1.33961 CrossRefGoogle Scholar
  5. 5.
    Menon PK, Sweriduk GD, Ohlmeyer EJ, Malyevac DS (2004) Integrated guidance and control of moving-mass actuated kinetic vehicles. J Guidance Control Dyn 27(1):118–126.  https://doi.org/10.2514/1.9336 CrossRefGoogle Scholar
  6. 6.
    Chesi S, Gong Q, Pellegrini V et al (2014) Automatic mass balancing of a spacecraft three-axis simulator: analysis and experimentation. J Guidance Control Dyn 37(1):197–206.  https://doi.org/10.2514/1.60380 CrossRefGoogle Scholar
  7. 7.
    Gao CS, Jing WX, Wei PX (2013) Research on application of single moving mass in the reentry warhead maneuver. Aerosp Sci Technol 30(1):108–118.  https://doi.org/10.1016/j.ast.2013.07.009 CrossRefGoogle Scholar
  8. 8.
    Sun BC, Park YK, Roh WR et al (2010) Attitude controller design and test of Korea space launch vehicle-I upper stage. Int J Aeronaut Space Sci 11(4):303–312.  https://doi.org/10.5139/ijass.2010.11.4.303 CrossRefGoogle Scholar
  9. 9.
    Morelli EA (2003) Multiple input design for real-time parameter estimation in the frequency domain. In: 13th IFAC symposium on system identification, Rotterdam, The NetherlandsGoogle Scholar
  10. 10.
    Morelli EA (2009) Flight-test experiment design for characterizing stability and control of hypersonic vehicles. J Guidance Control Dyn 32(3):949–959.  https://doi.org/10.2514/1.37092 CrossRefGoogle Scholar
  11. 11.
    Morelli EA, Derry SD, Smith MS (2005) Aerodynamic parameter estimation of the X-43A (Hyper-X) from flight test data. In: AIAA atmospheric flight mechanics conference and exhibit, San Francisco, California.  https://doi.org/10.2514/6.2005-5921
  12. 12.
    Zipfel HP (2007) Modelling and simulation of aerospace vehicle dynamic. In: AIAA education series, Reston, VAGoogle Scholar
  13. 13.
    Frost G, Costello M (2004) Linear theory of a projectile with a rotating internal part in atmospheric flight. J Guidance Control Dyn 27(5):898–906.  https://doi.org/10.2514/1.1115 CrossRefGoogle Scholar
  14. 14.
    Jauberthie C, Denis-Vidal L, Joly-Blanchard G (2005) Identifiability and estimation of aircraft parameters and delays by using optimal input design. In: Proceedings of the 44th IEEE conference on decision and control, Seville, Spain.  https://doi.org/10.1109/cdc.2005.1583371
  15. 15.
    Albisser M, Dobre S, Berner C (2013) Identifiability investigation of the aerodynamic coefficients from free flight tests. In: AIAA atmospheric flight mechanics conference, Boston, MA,  https://doi.org/10.2514/6.2013-4922
  16. 16.
    Saccomani MP, Audoly S, D’Angio L (2003) Parameter identifiability of nonlinear system: the role of initial conditions. Automatica 39(4):619–632.  https://doi.org/10.1016/S0005-1098(02)00302-3 MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Peeters RL, Hanzon B (2005) Identifiability of homogeneous systems using the state isomorphism approach. Automatica 41(3):513–529.  https://doi.org/10.1016/j.automatica.2004.11.019 MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Brun R, Kühni M, Siegrist H, Reichert P (2002) Practical identifiability of ASM2d parameters-systmatic selection and tuning of parameter subsets. Water Res 36(16):4113–4127.  https://doi.org/10.1016/s0043-1354(02)00104-5 CrossRefGoogle Scholar
  19. 19.
    Ni ZY, Wu ZG, Wu SN (2016) Time-varying modal parameters identification of large flexible spacecraft using a recursive algorithm. Int J Aeronaut Space Sci 17(2):184–194.  https://doi.org/10.5139/ijass.2016.17.2.184 CrossRefGoogle Scholar
  20. 20.
    Li CY, Jing WX, Gao CS (2009) Adaptive backstepping-based flight control system using integral filters. Aerosp Sci Technol 13(1):105–113.  https://doi.org/10.1016/j.ast.2008.05.002 CrossRefzbMATHGoogle Scholar
  21. 21.
    Klein V, Morelli EA (2006) Aircraft system identification—theory and practice. In: AIAA education series, Reston, VAGoogle Scholar
  22. 22.
    Press WH, Teukolsky SA, Vettering WT et al (1992) Numerical recipes in FORTRAN: the art of scientific computing, vol 2. Cambridge University Press, New YorkzbMATHGoogle Scholar
  23. 23.
    Hermann R, Krener AK (1977) Nonlinear controllability and observability. IEEE Trans Autom Control 11(5):728–740.  https://doi.org/10.1109/tac.1977.1101601 MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Qian YJ, Li CY, Jing WX et al (2013) Sun-Earth-Moon autonomous orbit determination for quasi-periodic orbit about the translunar libration point and its observability analysis. Aerosp Sci Technol 28(1):289–296.  https://doi.org/10.1016/j.ast.2012.11.009 CrossRefGoogle Scholar
  25. 25.
    Yim JR (2002) Autonomous spacecraft orbit navigation. Diss. Texas A&M UniversityGoogle Scholar

Copyright information

© The Korean Society for Aeronautical & Space Sciences 2019

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringHarbin Institute of TechnologyHarbinChina
  2. 2.Automation Engineering Center, Research Institute of China Shipbuilding Industry CorporationHarbinChina

Personalised recommendations