Mestrado Integrado em Engenharia Fisica INSTITUTO SUPERIOR TÉCNICO Tese de Mestrado, Dezembro 2012...
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Transcript of Mestrado Integrado em Engenharia Fisica INSTITUTO SUPERIOR TÉCNICO Tese de Mestrado, Dezembro 2012...
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