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