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Control-Oriented Modeling of a Three-Dimensional Hypersonic Vehicle with Rigid/Flexible Coupling


Modeling for a hypersonic vehicle is a great challenging task due to its tightly integrated airframe/propulsion system and flexible structure. A three-dimensional, six-degree-of-freedom, physics-based hypersonic vehicle model is being established that can capture the real physical characteristics for control studies. Flexible effects, aerodynamic loads and viscous effects are calculated using or combining variation method, shock/expansion theory and Eckert’s reference temperature method. Based on curve fit approximation of the forces and moments of the vehicle, a control-oriented six-degree-of-freedom model is then developed. The simulations illustrate that the surrogate model contain aerodynamic/structure/propulsion interactions of the vehicle, and can support designing of the model-based control.

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  1. Mirmirani M, Kuipers M, Levin J, Clark AD (2009) Flight dynamic characteristics of a scramjet-powered generic hypersonic vehicle. In: Proceedings of the 2009 American Control Conference, pp 2525–2532

  2. Ricketts RH, Noll TE, Jr, WW, Huttsell L (1993) An overview of aeroelasticity studies for the national aero-space planes. In: AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Washington, DC, USA, pp 152–162.

  3. Chavez FR, Schmidt DK (1994) Analytical aeropropulsive/aeroelastic hypersonic vehicle model with dynamic analysis. J Guid Control Dyn 17(6):1308–1319

    Article  Google Scholar 

  4. Bolender MA, Doman DB (2007) Nonlinear longitudinal dynamical model of an air-breathing hypersonic vehicle. J Spacecr Rocket 44(2):374–386

    Article  Google Scholar 

  5. Bolender MA, Oppenheimer MW, Doman DB (2007) Effects of unsteady and viscous aerodynamics on the dynamics of a flexible air-breathing hypersonic vehicle. In: AIAA Atmospheric Flight Mechanics Conference and Exhibit, Hilton Head, USA,

  6. Clark AD, Mirmirani MD, Wu C, Choi S, Kuipers M (2006) An aero-propulsion integrated elastic model of a generic air-breathing hypersonic vehicle. In: AIAA, GNC Conference and Exhibit, Keystone, Colorado, USA.

  7. Zong Q, You M, Zeng FL, Dou LQ (2016) Aeroservoelastic modeling and analysis of a six-DOF hypersonic flight vehicle. Proc Imeche Part G: Aerosp Eng 230(7):1240–1251

    Google Scholar 

  8. Frendreis SGV, Cesnik CES (2010) 3D simulation of flexible hypersonic vehicles. In: AIAA Atmospheric Flight Mechanics Conference, Toronto, Ontario Canada.

  9. Sudalagunta PR, Sultan C, Kapania RK, Watson LT, Raj P (2018) Aeroelastic control-oriented modeling of an airbreathing hypersonic vehicle. J Guid Control Dyn 41(5):1136–1149

    Article  Google Scholar 

  10. Parker JT, Serrani A, Yurkovich S, Bolender MA, Doman DB (2007) Control-oriented modeling of an air-breathing hypersonic vehicle. J Guid Control Dyn 30(3):402–406

    Article  Google Scholar 

  11. Shen HD, Liu YB, Chen BY, Lu YP (2018) Control-relevant modeling and performance limitation analysis for flexible air-breathing hypersonic vehicles. Aerosp Sci Technol 76:340–349

    Article  Google Scholar 

  12. Zhang D, Tang S, Cao L, Cheng F, Deng F (2019) Research on control-oriented coupling modeling for air- breathing hypersonic propulsion systems. Aerosp Sci Technol 84:143–157

    Article  Google Scholar 

  13. Zhang XB, Zong Q (2014) Modeling and analysis of an air-breathing flexible hypersonic vehicle. Math Probl Eng 6:759–765

    Google Scholar 

  14. Fiorentini L, Serrani A (2012) Adaptive restricted trajectory tracking for a non-minimum phase hypersonic vehicle model. Automatica 48(7):1248–1261

    MathSciNet  Article  Google Scholar 

  15. Zong Q, Wang J, Tian BL, Tao Y (2013) Quasi- continuous high-order sliding mode controller and observer design for flexible hypersonic vehicle. Aerosp Sci Technol 27(1):127–137

    Article  Google Scholar 

  16. Williams T, Bolender MA, Doman DB, Morataya O (2006) An aerothermal flexible mode analysis of a hypersonic vehicle. In: AIAA Atmospheric Flight Mechanics Conference and Exhibit, Keystone, Colorado, USA,

  17. Jason Levin J, Ioannou PA, Mirmirani MD (2008) Adaptive mode suppression scheme for an aeroelastic air-breathing hypersonic cruise vehicle. In: AIAA Guidance, Navigation and Control Conference and Exhibit 18–21 August 2008, Honolulu, Hawaii

  18. Oppenheimer MW, Doman DB, McNamara JJ, Culle AJ (2008) Viscous effects for a hypersonic vehicle model. In: AIAA Atmospheric Flight Mechanics Conference and Exhibit, Hawaii, USA.

  19. Sigthorsson DO, Serrani A (2009) Development of linear parameter-varying models of hypersonic, air-breathing vehicles. In: AIAA Guidance, Navigation, and Control Conference, Chicago, USA.

  20. Zhang D, Tang S, Zhu QJ, Wang RG (2016) Analysis of dynamic characteristics of the rigid body/elastic body coupling of air-breathing hypersonic vehicles. Aerosp Sci Technol 48:328–341

    Article  Google Scholar 

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This work was supported by the Fundamental Research Funds for the Universities of Tianjin (2018KJ112).

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Correspondence to Xi-bin Zhang.

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Zhang, Xb., Ding, Ym. & Zhang, Zx. Control-Oriented Modeling of a Three-Dimensional Hypersonic Vehicle with Rigid/Flexible Coupling. Int. J. Aeronaut. Space Sci. 23, 354–362 (2022).

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  • Three-dimensional hypersonic vehicle
  • Six-degree-of-freedom
  • Flexible effects
  • Control-oriented model
  • Rigid/flexible coupling