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Hypersonic Reentry Dynamics

S P A C E Structures, Propulsion, And Control Engineering C e n t e r. Hypersonic Reentry Dynamics. Student Assistants: Katie Demko, UCI Shing Chi Chan, CSULA. Faculty Advisors: Professor Mease, UCI Dr. Helen Boussalis, CSULA. Overview. Objective Current Goals

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Hypersonic Reentry Dynamics

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  1. S P A C E Structures, Propulsion, And Control Engineering C e n t e r Hypersonic Reentry Dynamics Student Assistants: Katie Demko, UCI Shing Chi Chan, CSULA Faculty Advisors: Professor Mease, UCI Dr. Helen Boussalis, CSULA NASA Grant URC NCC NNX08BA44A

  2. Overview • Objective • Current Goals • Background/Theory • Simulations without a Controller • Nonlinear Control Law Derivation • Simulations with a Controller • Simulations from Perturbations • Atmospheric Density Modeling • Timeline NASA Grant URC NCC NNX08BA44A

  3. Mission NASA Grant URC NCC NNX08BA44A

  4. Current Goals Research: • Evaluation of current knowledge of atmospheric density modeling of Earth and Mars NASA Grant URC NCC NNX08BA44A

  5. Background NASA Grant URC NCC NNX08BA44A Image and Video from reference 6

  6. Orion vs. Apollo NASA Grant URC NCC NNX08BA44A

  7. Basic Forces AIRPLANE NASA Grant URC NCC NNX08BA44A

  8. Basic Forces ORION SPACE CAPSULE NASA Grant URC NCC NNX08BA44A

  9. Trajectory Control via Drag Tracking γ In order to calculate Range in Matlab, use numerical integration Note: -The vehicle is modeled as a point mass - Total mechanical energy per unit mass NASA Grant URC NCC NNX08BA44A

  10. Derivation of Range in terms of Drag Horizontal Velocity Horizontal Distance Step 3: Change dV to dE Step 1: Change dt to dV Step 2: Substitute dV back into range equation Assume Υ is very small, so NASA Grant URC NCC NNX08BA44A

  11. Equations of Motion for Reentry (Drag) NASA Grant URC NCC NNX08BA44A

  12. Simulation Parameters NASA Grant URC NCC NNX08BA44A

  13. Simulation Conditions NASA Grant URC NCC NNX08BA44A

  14. Matlab: Calculating State Variables NASA Grant URC NCC NNX08BA44A

  15. Matlab: Calculating State Variables • In order to find the state variables, use ode45 in Matlab to numerically integrate the equations of motion • Ode45 uses Runge-Kutta fourth order methods NASA Grant URC NCC NNX08BA44A

  16. Lifting Entry with σ=0° NASA Grant URC NCC NNX08BA44A

  17. Lifting Entry with σ=0° NASA Grant URC NCC NNX08BA44A

  18. Lifting Entry with σ=60° NASA Grant URC NCC NNX08BA44A

  19. Lifting Entry with σ=60° NASA Grant URC NCC NNX08BA44A

  20. Lifting Entry with σ=60° Heading Convention (UCI): 90° = N 0 °= E 180° = W 270 ° = S NASA Grant URC NCC NNX08BA44A

  21. Lifting Entry with σ=60° NASA Grant URC NCC NNX08BA44A

  22. Advantages to Skip Entry Earth Moon Landing Spot Entry into the Atmosphere Downrange Distance NASA Grant URC NCC NNX08BA44A

  23. Planning Function Path Constraints in terms of Drag Range: NASA Grant URC NCC NNX08BA44A

  24. Tracking-Jacobian Linearization Starting from and The first derivative is The second derivative is NASA Grant URC NCC NNX08BA44A

  25. Tracking continued Desired Error Dynamics Control Law Substituting the control law back into the dynamics Closed Loop Dynamics NASA Grant URC NCC NNX08BA44A

  26. Tracking-Feedback Linearization 1) Feedback Linearization: Take (x1,x2,x3)=(r, γ,V) so that Original Dynamics : 2) State Transformation: Let y=z1=D in order to transform system into: Where, NASA Grant URC NCC NNX08BA44A

  27. Tracking-Feedback Linearization 2) State Transformation: cont. 4) Inverse Control Transformation: 5) Closed-Loop Dynamics: 3) Control Transformation: Where ζ, ω are positive to ensure asymptotic stability NASA Grant URC NCC NNX08BA44A

  28. Bank Angle Limits on the bank angle: www.fas.org/man/dod-101/sys/ac/intro.htm NASA Grant URC NCC NNX08BA44A

  29. Actual Drag vs. Reference Drag Normalized Energy NASA Grant URC NCC NNX08BA44A

  30. Bank Angle vs. Energy NASA Grant URC NCC NNX08BA44A

  31. Actual Range vs. Planned Range NASA Grant URC NCC NNX08BA44A

  32. Simulations from Flight Path Angle Perturbations NASA Grant URC NCC NNX08BA44A

  33. Simulations from Density Perturbations NASA Grant URC NCC NNX08BA44A

  34. Atmospheric Density Modeling NASA MSFC Earth Global Reference Atmospheric Model 2007 (Earth GRAM07) • Standardized atmospheric profile for use in mission planning and design • Global measurements of pressure, temperature, winds, seasonal effects and seasonal variations • Three distinct atmospheric regions: lower atmosphere (0-27km), middle atmosphere (20-120km), upper atmosphere (90km and above) NASA Grant URC NCC NNX08BA44A

  35. Atmospheric Density Modeling • Lower Atmosphere: • Data from Upper Air Climatic Atlas (GUACA) • Data from 1980-1991, measurements 2X a day • Data from radiosondes, aircraft and satellites • Monthly means and standard deviations in temperature, density, dewpoint, sea-level pressure, geopotential height and eastward and northward wind components • Data gridded globally at 2.5 deg by 2.5 deg resolution NASA Grant URC NCC NNX08BA44A

  36. Atmospheric Density Modeling • Middle Atmosphere: • Data from Middle Atmosphere Program (MAP) • Data from 1985 • Data from rocketsonde, aircraft and radar measurements • Monthly means and standard deviations in temperature, density, dewpoint, sea-level pressure, geopotential height and eastward and northward wind components • Data gridded globally at 10 deg latitude increments with 5 km height increments • Standing wave perturbation models for atmospheric variables NASA Grant URC NCC NNX08BA44A

  37. Atmospheric Density Modeling • Upper Atmosphere: • 3 Thermosphere Models: • Marshal Engineering Thermosphere (MET-07) • Naval Research Labs Mass Spectrometer, Incoherent Scatter Radar Extended (NRL MSISE-00) • Jachia-Bowman 2006 thermosphere model (JB 2006) • All three contain lower boundary conditions, diurnal variations, annual and semi-annual variations, solar activity variations, and geomagnetic activity variations • 10-15% error in normal conditions NASA Grant URC NCC NNX08BA44A

  38. Atmospheric Density Modeling-Mars • NASA MSFC Mars Global Reference Atmospheric Model 2005 (Mars GRAM05) • Three altitude ranges (only lower atmosphere relevant for reentry 0-80km) • Lower atmosphere data from NASA Ames General Circulation Model (MGCM) which uses surface topography from Mars Global Surveyor Mars Orbiter Laser Altimeter (MOLA) • Accounts for tidal components, longitude-dependent wave model, dust optical depth, perturbation model, background dust level, dust storm conditions NASA Grant URC NCC NNX08BA44A

  39. Timeline (2009-2010) NASA Grant URC NCC NNX08BA44A

  40. Timeline (2010-2011) NASA Grant URC NCC NNX08BA44A

  41. References • Bairstow, Sarah H., and Gregg H. Barton. "Reentry Guidance with Extended Range Capability for Low L/D Spacecraft." AIAA Guidance, Navigation and Control Conference and Exhibit Hilton Head, SC, August 2007. • Benito, Joel, and Kenneth D. Mease. "Nonlinear Predictive Controller for Drag tracking in Entry Guidance." American Institute of Aeronautics and Astronautics :14. • Mease ,K.D., and Kremer, JP., “Shuttle Entry Guidance Revisited Using Nonlinear Geometric Methods.” Journal of Guidance and Control, Vol. 17, No. 6, 1994 pp.1350-1356. • Harpold, J.C., and Graves, C. A., Jr., “Shuttle Entry Guidance,” Journal of the Astronautical Sciences, Vol. 27, No. 3, 1979, pp.239-268. • Lickly, D.J., H.R. Morth, and B.S. Crawford. "Apollo Reentry Guidance." MASSACHUSETTS INSTITUTE OF TECHNOLOGY N73-7461 (1963): 23. • "NASA - Constellation Main." NASA - Constellation Main. 26 Oct. 2009 <http://www.nasa.gov>. • Akins, K., Healy, L., Coffey, S., and Picone, M., “Comparison of Msis And Jacchia Atmospheric Density Models For Orbit Determination And Propagation”, Naval Research Laboratory, Paper AAS 03-165, February 2003. • Bergstrom, S. E. (2002, June). An Algorithm for Reducing Atmospheric Density Model Errors Using Satellite Observation Data in Real-Time. Massachusetts Institute of Technology. • Guide to Reference and Standard Atmosphere Models. (2004). ANSI/AIAA . • Justh, H. L., & Justus, C. Mars Global Reference Atmospheric Model (Mars-GRAM 2005) Applications for Mars Science Laborator • Mission Site Selection Processes. Seventh International Conference on Mars. • Justus, C. G., & James, B. F. (2000, May). Mars Global Reference Atmospheric Model 2000 Version (Mars-GRAM 2000) Users Guide. • NASA Center for AeroSpace Information. • Justus, C. G., & Leslie, F. W. (2008, November). The NASA MSFC Earth Global Reference Atmospheric Model-2007 Version. NASA. • Justus, C. G., Duvall, A. L., & Johnson, D. L. (2005). Global MGS TES data and Mars-GRAM validation. Advances in Space Research , 4-7. • Justus, C. G., James, B. F., Bougher, S. W., Bridger, A. F., Haberle, R. M., Murphy, J. R., et al. (2002). Mars-GRAM-2000: A Mars Atmospheric Model For Engineering Applications. Advances in Space Research , 193-202. • Leavitt, J. M. (2007). Feasible Trajectory Generation for Atmospheric Entry Guidance. Journal of Guidance, Control and Dynamics , Vol. 30, No. 2, 473-481. • Leslie, F. W., & Justus, C. G. (n.d.). Earth Global Reference Atmospheric Model 2007 (Earth-GRAM07) Applications for the NASA Constellation Program. NASA Grant URC NCC NNX08BA44A

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