INSTITUTO SUPERIOR TCNICO Mestrado Integrado em Engenharia Fisica

INSTITUTO SUPERIOR TÉCNICO Mestrado Integrado em Engenharia Fisica Tese de Mestrado, Dezembro 2012 Control and command of non-powered liftenabled vehicles in planetary atmospheres. João Luis Pinto da Fonseca Presidente de júri: Prof. Carlos Renato de Almeida Matos Ferreira Orientador: Prof. Rui Manuel Agostinho Dilão Co-orientador: Prof. Ana Maria Ribeiro Ferreira Nunes Vogal: Prof. Luís Manuel Braga da Costa Campos Vogal: Prof. José Manuel Gutierrez Sá da Costa 1/17

Spacecrafts: Two different ways of reentering Earth’s atmosphere “Ballistic” Soyuz (Russia) Travelling from altitudes of 120 km (Earth’s atmosphere limit) Shenzhou (China) “Lift-Enabled” Space Shuttle (US) X-37 (US) Dragon (Space X-US) Apollo (US) X-37 B (US) 11 th Dec 2012 Range Tens of Kms Hundreds of Kms Flight Time Minutes Tens of Minutes Accelerations Up to 8 -10 g´s Up to 2 -4 g´s Flight Angle Steep Wide Landing scheme Parachutes, Rockets Gliding (no fuel!) 2/17

Command & Control: The difference between being dynamic or not! “Spirit” & Opportunity : Mars 2004 (7 minutes) “Curiosity”: Mars 2012 (7 minutes) 1 2 1 3 2 3 Hard Landing Soft Landing 3/17

Dinamically controlling the TAEM phase of the Space Shuttle’s atmospheric reentry (h 0~40 km) Main Assumptions • Flat 1 non moving earth • Constant mass with no Thrust • Glider is a mass point with Lift and Drag Derived Model Equations of Motion New coordinate system • Spheric coordinates for the velocity (not on the position!) Using a specific reality Control Variables Attack Angle Bank Angle • Structural limits of the Space Shuttle • Wind Tunnel data for the Space Shuttle (up to 5 Mach, adequate to TAEM) • Earth’s atmospheric profile (US 1976) 1 40 km altitute vs 6. 4 x 103 km for Earth radius 4/17

Using a specific reality: Earth’s Atmosphere (US 1976) Temperature Not Constant Density Sound Speed Not constant (impacts on Ma) Pressure “Almost” exponential 5/17

Using a specific reality: Structural Limits Heat Flux Limiting Factor: Shuttle Nose (smallest curvature) Result: Imposes a minimum attack angle Load Limiting Factor: Shuttle Wings (biggest surface) Result: Imposes a maximum attack angle Acceleration Limiting Factor: Cargo and human occupants (not the fuselage) Result: Imposes a “smoothness condition” on the speed of the Space Shuttle 6/17

Space Shuttle´s Heat Insulation Numbered Tile System 7/17

Using a specific reality: Wind tunnel data for the Space Shuttle A “window of opportunity”. Can not go down too steep nor too shallow Aerodynamic Coefficients Key angles for the control “No Lift” attack angle: When lift is null (independent of Mac number) “Max Glide” attack angle: When L/D is max (maximizes range travelled) “Stall” attack angle: When lift peaks (and the induced drag also!) 8/17

Equations of Motion: Basic Dynamics Phase Space • 1 fixed point (or limit cycle) for each combination of relevant parameters • Stable fixed points (negative eigenvalues for all situations) • Different convergence regimes for different situations (to “roll or not to roll” around the fixed point) Fixed Point (or limit cycle) • • Earth profiles: g, ρ, Vsound (Ma) Areodynamic: CL and CD (α, Ma) Vehicle parameters: m, S Controls: α and μ Conceptual graph for CL=CD=1 and g=9. 8 m/s 2 Dynamics Space Shuttle case • “Rolled convergence” or “Straigh-line” converge to the fixed point (or limit cycle) 9/17

Algorithm: Minimize distance subject to aerodynamic & structural contraints Attack Angle Bank Angle • Heading Control (base control) • Heat Flux Control (if needed: imposes minimum angle) • Anti-Stall Control (if needed: forces a curved approach) • Load Factor Control (if needed: imposes maximum angle) • Energy Control (if needed: forces a dynamic S-turn to prevent climbs) • Heat and load controls only intervene should heading try to breach limits • Anti-stall and energy only intervene should heading try to breach limits 10/17

Simulations: From 30, 000 m to 3, 000 m (TAEM phase) Initial Conditions Analysis Made 1 • Range and error reaching specific targets at 3, 000 meters Physical Constraints Algorithm’s Parameters 2 • Typical trajectories generated by the algorithm 3 • Sensitivity analysis to initial conditions and control time interval 4 • Structural limits check on excessive speed entries 11/17

1 Simulations: TAEM Range and Error reaching the target point (HAC) Maximum Range • Hundreds of kilometers of range in any direction (highest range for straight flight) • Symmetric ranges for symmetric alignments with initial velocity • Different ranges for different alignments with initial velocity Distance Error • Typical error of the order of magnitude of 100 meters or below • Confirmation that any point inside MR is achievable (small error) • Angular symmetry of the error distribution follows the angular symmetry of the range 12/17

Simulations: Typical Trajectories 2 Long Range Trajectory • When the flight is made mostly in straight line (typical Shuttle strategy) Short Range Trajectory • When the HAC is “too close” to the xy origin the algorithm initiates a whirlpool approach while the altitude “slowly” decreases • Changed: HAC position Possible through dynamic S-turns Excessive Energy Trajectory • Without the energy control (dashed) we have caotic trajectories and the HAC is NOT reached • Changed: 3, 300 m/s entry speed 13/17

Simulations: Long Range Zoom-in 3 Almost always at equilibrium (v=v*) Speed and forces History Initial condition quickly changed Commands History Final approach Maximum glide until reachable in straight-line Diminishing turn Sonic boom 14/17

Simulations: Sensitivity Analysis 4 Initial Energy • Crucial to have enough speed to reach the target Initial Orientation • Crucial to start with the “right” trajectory descent angle (γ) Control Time • Selfrecovering • Low errors up to 30 seconds of control time interval 15/17

Simulations: Structural limits check Thermic • Three different initial speeds (V 0=1, 100 m/s; V 0=1, 650 m/s; V 0=2, 200 m/s) Mechanical • Three different initial speeds (V 0=1, 100 m/s; V 0=1, 650 m/s; V 0=2, 200 m/s) Maximum temperature for highest entry speed Maximum load for highest entry speed Maximum flux for highest entry speed Maximum g’s for highest entry speed 16/17

Conclusions & Next Steps Conclusions • The algorithm works well with control times intervals up to 30 seconds and is by nature self-recoverable at all control times • Any point inside the Maximum Range curve can be reached with minimum error (around or below 100 meters) • Three main types of trajectory are designed dependent on the HAC distance (close or far) and whether or not the glider has excessive speed • Sensitivity to initial conditions is limited and the glider will always reach the HAC should the initial speed be enough and the trajectory angle γ adequate Next steps Improve Extend Upgrade Lower Error reaching HAC Higher Speeds (up to 30 M) HAC Velocity Direction Landing maneuvers Thurst (and variable mass) Moving Non-Flat Earth & Wind 17/17