Mestrado Integrado em Engenharia Fisica
INSTITUTO SUPERIOR TÉCNICO
Tese de Mestrado, Dezembro 2012
Control and command of non-powered lift-enabled 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
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!)
Travelling from altitudes of
120 km (Earth’s
atmosphere limit)
“Ballistic”Soyuz (Russia)
Dragon (Space X-US)Apollo (US)
Shenzhou (China)
2/17
“Lift-Enabled”
Space Shuttle (US)
X-37 (US)
X-37B (US)
11th Dec 2012
Command & Control: The difference between being dynamic or not!
3/17
“Curiosity”: Mars 2012(7 minutes)
1 2
3
Soft Landing
“Spirit” & Opportunity : Mars 2004 (7 minutes)
HardLanding
1 2
3
Dinamically controlling the TAEM phase of the Space Shuttle’s atmospheric reentry (h0~40 km)
Derived Model
• Flat 1 non moving earth• Constant mass with no Thrust• Glider is a mass point with Lift and Drag
Main Assumptions
• 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)
Using a specific reality
1 40 km altitute vs 6.4 x 103 km for Earth radius
• Spheric coordinates for the velocity (not on the position!)
New coordinate system
Equations of Motion
Control Variables
Attack Angle Bank Angle
4/17
Using a specific reality: Earth’s Atmosphere (US 1976)
Pressure“Almost”
exponential“Almost”
exponential
Density
Sound SpeedNot Constant Not constant(impacts on Ma)
Temperature
5/17
Using a specific reality: Structural Limits
Load
Limiting Factor: Shuttle Wings (biggest surface)Result: Imposes a maximum attack angle
AccelerationLimiting Factor: Cargo and human occupants (not the fuselage)Result: Imposes a “smoothness condition” on the speed of the Space Shuttle
6/17
Heat Flux
Limiting Factor: Shuttle Nose (smallest curvature)Result: Imposes a minimum attack angle
Space Shuttle´s Heat Insulation Numbered Tile System
7/17
Key angles for the control
Using a specific reality: Wind tunnel data for the Space Shuttle
“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!)
Aerodynamic Coefficients
A “window of opportunity”. Can not go down too steep
nor too shallow
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) Conceptual graph for CL=CD=1 and g=9.8 m/s2
Fixed Point (or limit cycle) Dynamics
• Earth profiles: g, ρ, Vsound (Ma)• Areodynamic: CL and CD (α, Ma)• Vehicle parameters: m, S• Controls: α and μ
• “Rolled convergence” or “Straigh-line” converge to the fixed point (or limit cycle)
Space Shuttle case
9/17
Algorithm: Minimize distance subject to aerodynamic & structural contraints
Attack Angle Bank Angle
• Heading Control (base control) • Heading Control (base control)
• Heat and load controls only intervene should heading try to breach limits
• Heat Flux Control (if needed: imposes minimum angle)
• Load Factor Control (if needed: imposes maximum angle)
• Anti-stall and energy only intervene should heading try to breach limits
• Anti-Stall Control (if needed: forces a curved approach)
• Energy Control (if needed: forces a dynamic S-turn to prevent climbs)
10/17
Simulations: From 30,000 m to 3,000 m (TAEM phase)
Analysis Made
• Range and error reaching specific targets at 3,000 meters
• Typical trajectories generated by the algorithm
• Sensitivity analysis to initial conditions and control time interval
• Structural limits check on excessive speed entries
1
2
3
4
Initial Conditions
Physical Constraints
Algorithm’s Parameters
11/17
Simulations: TAEM Range and Error reaching the target point (HAC)
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
1
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
12/17
Simulations: Typical Trajectories2
Long Range Trajectory
• When the flight is made mostly in straight line (typical Shuttle strategy)
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
Possible through dynamic S-turns
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
13/17
Simulations: Long Range Zoom-in3
Speed and forces
History
Almost always at equilibrium (v=v*)
Maximum glide until reachable in
straight-line
Commands History
Sonic boom
Final approach Diminishing turn
Initial condition quickly changed
14/17
Simulations: Sensitivity Analysis4
Initial Orientation
• Crucial to start with the “right” trajectory descent angle (γ)
Initial Energy
• Crucial to have enough speed to reach the target
Control Time
• Self-recovering
• Low errors up to 30 seconds of control time interval
15/17
Simulations: Structural limits check
ThermicMaximum
temperature for highest entry speed
• Three different initial speeds (V0=1,100 m/s; V0=1,650 m/s; V0=2,200 m/s)
Maximum flux for highest
entry speed
MechanicalMaximum load
for highest entry speed
Maximum g’s for highest
entry speed
• Three different initial speeds (V0=1,100 m/s; V0=1,650 m/s; V0=2,200 m/s)
16/17
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
Conclusions & Next Steps
ImproveLower Error
reaching HACHigher Speeds (up to 30 M)
ExtendHAC Velocity
DirectionLanding
maneuvers
UpgradeThurst (and
variable mass)Moving Non-Flat
Earth & Wind
Next steps
17/17
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