Versatile Electro-dynamic Tethers Dynamics Simulator...
Transcript of Versatile Electro-dynamic Tethers Dynamics Simulator...
Versatile Electro-dynamic Tethers Dynamics Simulator for Debris Mitigation Tools Design
Michèle Lavagna, Amedeo Rocchi
POLITECNICO DI MILANO
Agenda
POLITECNICO DI MILANO ASTRA 2015 Amedeo Rocchi 1
• Introduction on Electrodynamic Tethers
• Simulator Requirement and Models
• Configuration Selection
• Instability and Control
• Design and Control Influence on Performance
• Conclusions
Space Debris Problem Solution
POLITECNICO DI MILANO
Solution: Remediation + Mitigation
Active Debris Removal (ADR) future missions
Electro-Dynamic Tethers (EDTs) = very promising concept
EDT = long conductive cables
energy and momentum transfer through Lorentz force
Missions and Studies: • 6 mission flown (since 1993, TSS-1, NASA-ASI) • 1 international project (BETs project = UPM,
CISAS, et al., 2012-current) • 2 active companies (Electrodynamic
Technologies, 1996-current, Tethers Unlimited, 1994-current)
Operating principle: • relative velocity v w.r.t. Earth magnetic field B
voltage difference ΔV
• e- collected and remitted
electric current I
• I x B along the tether
distributed Lorentz force FL
• FL opposed to v
decrease of orbital semi-major axis
de-orbiting
No electrical energy input required
partially or completely passive system
ASTRA 2015 Amedeo Rocchi 2
EDTs Features and Study Goals
EDTs used as electrodynamic drag augmentation devices (passive thrusters)
Compared to classical propulsion alternatives:
POLITECNICO DI MILANO
ADVANTAGES
• low mass • low volume • easily scalable • possibly independent from satellite • no impact on satellite design
DISADVANTAGES
• instability • long re-entry • large cross section • deployment and survivability issues • applicability domain
However:
• no best solution for control • previously simple models when studying the instabilities and control
Goals:
• develop an accurate but versatile simulator • compare configuration alternatives • compare and develop control alternatives • investigate influence of design and control on the performance/stability ASTRA 2015 Amedeo Rocchi 3
Simulator Requirements
Different missions design
versatility
Dynamical and Electrical non-linearity
high accuracy
POLITECNICO DI MILANO
MODEL NON-NEGLIGIBLE CONTRIBUTIONS
Tether Dynamics Flexibility Tether Elasticity Damping
Electrodynamics Current Profile Lorentz Forces
ED Torques
Environment Perturbation Frequencies Perturbation Intensity
SYSTEM FEATURE ALTERNATIVES
Deployment Direction
anode
cathode Down Up
Tether Section
Cable Tape Reinforced Tape
Tether Coating
Bare Coated
Tether Inert Portion
FL None Close to anode
SAT
SAT
SAT SAT
ASTRA 2015 Amedeo Rocchi 4
Simulator Scheme and Mechanical Model
Tethers mechanical model
lumped parameters method:
flexibility, elasticity and damping
End-masses model
extended bodies:
attitude coupling
POLITECNICO DI MILANO
1 Developed under ESA contract by the Department of Aerospace Science and Technology, PoliMi. Based on SimMechanics and included in GAST.
Orbital Propagator
MUST toolbox1
Mechanical Models: extended bodies, tethers,
appendages, etc…
Environment and Perturbations
Simulator core
Environment and Perturbations
Ionospheric and Magnetic Models
Electrodynamical Models
Newly introduced:
electrodynamic interaction EDT control
ASTRA 2015 Amedeo Rocchi 5
Electrodynamic Interaction: Bare Tethers Current profile
BARE TETHERS
POLITECNICO DI MILANO
No analytical solution
Options:
• numerical method • asymptotic semi-analytical method (Bombardelli, 2010)
FEATURES:
• Fast • Precise
I = current ΔV = voltage difference p = cross section perimeter Ne = electron density ΔVCE = cathodic voltage drop Zl = cathodic load σ = tether conductivity = σ(T)
non linear, coupled
conditions within domain
Assumptions:
• Orbital Motion Limited (OML)
• Constant properties along tether
• Rectilinear tether
NEWLY INTRODUCED:
Approximation for non-rectilinear tethers (condition relaxed)
Et reduced based on curvature
ASTRA 2015 Amedeo Rocchi 6
experimental validation required
Current Profile and Lorentz Forces
POLITECNICO DI MILANO
Distributed Lorentz force
Profile example, bare tether
Considered:
• Torques (non-uniform current distribution) • Tether elements orientation
Validated (Bombardelli, 2010)
ASTRA 2015 Amedeo Rocchi 7
Environmental and Thermal Models
POLITECNICO DI MILANO
Environmental Models Available/Implemented options
Atmospheric density (drag) • NRLMSISE-00 (Picone, 2003) • Simpler alternative (Panwar,1999)
Gravitational field • Higher harmonics • Uniform
Magnetic field • IGRF-11 (IAGA, 2010) • Tilted dipole (IGRF linear coefficients)
Plasma density in ionosphere Data from IRI and NeQuick profiler • 2 available accuracies
Thermal model needed conductivity σ(T) non-linear Assumptions:
• uniform tether temperature T • no heat exchange end-bodies
{ {
Perturbations
Electrodynamic interaction
All major fluxes considered in dynamical model:
• Sun radiation • emission to deep space • Earth radiation and albedo • Joule effect
ASTRA 2015 Amedeo Rocchi 8
Ionosphere Model
POLITECNICO DI MILANO
Not off-the-shelf available for Matlab/Simulink Ne according to NeQuick profiler (Radicella, 2001): • analytical in altitude variation Ne(h)
• based on Epstein layers
• data required: peak frequencies fF2, fF1, fE, M(3000) and R12
Database + Interpolation (in lat, long and time) ASTRA 2015 Amedeo Rocchi 9
Advantages of the method implemented: • fast but verified profiler • precise data, acquired a priori from International Reference Ionosphere (IRI)
(Bilitza, 2012)
System Architecture
Simulation campaign
POLITECNICO DI MILANO
CHOICE REASON
Hanging Tether (equilibrium // local vertical) Simplicity, high Technology Readiness Level (TRL)
Small end-mass Deployment, stabilization, equipment inside
Bare tether High collection efficiency (high current low de-orbiting time)
Reinforced Tape tether High collection efficiency, high tear resistance, high survivability
Field Emission Cathode (FEC) Hollow Cathode (HC) Most feasible options (currently available)
Sensitivity analysis on design parameters
Literature study
System Architecture Selection
NOTE: high performance system = low de-orbiting time ASTRA 2015 Amedeo Rocchi 10
Ideal Performances
POLITECNICO DI MILANO
Real cases selected, based on:
• debris threat (Rossi, 2014) • applicability of EDT systems
Debris a [km] i [°] e [--]
Cosmos sat. 7378 64.98 0.003
SL-16 r. b. 7228 71 0.001
Globalstar-2 7778 52 0
nano-sat 6978 28.5 0
Ideal performances to verify suitability: large fake end-mass/satellite mass ratio
(passive stabilization)
EDT system feasible for all cases
EDT system tailored: Cosmos: 7.5 km EDT, 15 kg end-mass system mass = 0.7% of tot. mass Nano-sat = 50 m EDT, 0.1 kg end-mass, system mass = 14% of tot. mass Final condition: different for each case: safe re-entry in 10 days (even with no EDT)
ASTRA 2015 Amedeo Rocchi 11
Real Cases and Instability
POLITECNICO DI MILANO
Issues:
• large libration amplitude tension peaks breaking slingshot effect anode-cathode reversed • system tumbling no current loss in efficiency system spinning Cause:
• FL continuously pumps energy in IP libration due to OOP/IP libration coupling
Faster onset of instability if:
• stronger FL • lower mass ratio • longer tether
instability example, system tumbling
For all cases considered (except nano-sat) instability detected
ASTRA 2015 Amedeo Rocchi 12
REAL MASS RATIO
POLITECNICO DI MILANO
Never tested in detail on accurate tether models
Current control, Lyapunov approach
system rotational energy estimation adimensional stability function V (threshold value imposed VTH) current I decrease V / VTH if positve energy inflow: libration direction = electrodyanmic torque direction
Control Technique Selected
PROS:
• simple • easily implementable (practical) • tunable parameters and alternatives
CONS:
• non-optimal (but tending to optimum with right threshold selection)
sensors: GPS receivers, optical or other actuators: cathodic varystor Zl or cathodic emitter ΔVCE
ASTRA 2015 Amedeo Rocchi 13
Control Available Parameters and Methods
POLITECNICO DI MILANO
Parameter/Method Options Description
Rotational Energy H Estimation
exact
H = Hkinetic+Hgrav-gradient+Helastic+Hinertial-ref V = (H-H0)/H0 H0 = H at equilibrium (tether // local vertical)
approx
H and V analytically derived θ and ϕ IP and OOP libration angles
Libration Direction and
ED Torque Direction Estimation
exact or
approx
According to H estimation exact approx
Control Scheme
on-off I = 0 if V/VTH > 1
continuous I = 0 if V/VTH > 1 if α < V/VTH < 1
VTH and α selection values VTH selected based on admissible libration domain α selected based on control action strength
tether node masses considered
only end-bodies considered
tether node masses considered
only end-bodies considered
complex sensors low TRL
ASTRA 2015 Amedeo Rocchi 14
Δa = 69.54 km tot. semi-major axis decrease
Δa = 81.25 km tot. semi-major axis decrease
Δa = 80.75 km tot. semi-major axis decrease
POLITECNICO DI MILANO
• Globalstar-2 sat • 1400 km altitude • 7.5 km aluminum + Dyneema tether • 15 kg end-mass • Other data • Initial conditions: equilibrium, tether // local vertical • 20 days
No control:
• large IP libration • large V, both
exact and approx
Approx. control on-off, VTH =
0.8:
• smaller IP libration
• V ≤ VTH always
Long Term Results Example
Exact control on-off, VTH =
0.8:
• slightly smaller libration
• smoother
ASTRA 2015 Amedeo Rocchi 15
POLITECNICO DI MILANO
• Cosmos sat • 800 km altitude • 7.5 km aluminum + Dyneema tether • 15 kg end-mass • Other data • Initial conditions: 25° OOP - 25° IP • 2 days
No control:
• increasing OOP libration
• IP libration acceptable
• large V
Δa = 3.51 km tot. semi-major axis decrease
Δa = 2.79 km tot. semi-major axis decrease
Approx. control,
on-off, VTH = 0.8:
• bounded OOP libration
• peaks V > VTH
Δa = 2.71 km tot. semi-major axis decrease
Exact. control, on-off, VTH =
0.8:
• very bounded libration
• V < VTH always
Δa = 2.61 km tot. semi-major axis decrease
Exact. control, continuous, VTH = 0.8:
• very smooth libration
Short Term Results Example
ASTRA 2015 Amedeo Rocchi 16
Control Methods Comparison
POLITECNICO DI MILANO
Conclusion:
• control required • Lyapunov most effective • open loop: not effective • simple threshold:
effective but low performance (low duty cycle)
Comparison with simpler controls:
• open-loop control (Lanoix, 2005) • simpler threshold (Kawamoto, 2006)
4 days simulation Globalstar-2 sat 800 km altitude System data as previous
TECHNIQUE NO control
Lyapunov control on-off, VTH 0.8
Open loop
Simpler threshold
Tumbling Time [days] 3.24 -- -- --
IP / OOP Final Amplitude [°]
-- / 30 30 / 7 12 / 24 50 / 13
DC [%] 98.8 96 100 43.2
Δa [km] -46.4 -60.6 -6.6 -25.9
ASTRA 2015 Amedeo Rocchi 17
Control Influence and Current Limitation
POLITECNICO DI MILANO
stable system till low altitude
Libration is influenced by:
• electrodynamic forces • aerodynamic drag • gravity gradient torques
NOT controllable
Libration energy can exceed threshold
Especially at low altitude
SOLUTION
Current Limitation + Control
NOTE:
• control reduces initial duty cycle DC, but higher in long term
• finer control
more effective
stronger control action lower DC lower Δa (?)
then natural re-entry (few days, even no EDT)
ASTRA 2015 Amedeo Rocchi 18
?
?
EDT Systems Applicability Domain
POLITECNICO DI MILANO
General case considered:
• Cubic satellite 3x3x3 m3, 1500 kg mass • 7.5 km aluminum + Dyneema tether with 15 kg end-mass (EDT system mass ~2% of total) • Exact control,VTH= 0.8, current limit = 1.5 A
Results:
• limit in inclination • cosine like trend • acceptable limit in altitude
(LEO denser regions included)
Are-time-product (tether large cross-section taken
into account)
applicability domain: • minimum altitude for EDT
use, depending on inclination
ASTRA 2015 Amedeo Rocchi 19
Nano-satellite Case
POLITECNICO DI MILANO
No feasible cathode:
• hollow cathode too massive • FEC1 too high power request
Solution: completely passive system
1 Field Emission Cathode
Advantages:
• no active element for cathode • lighter system
Disadvantages:
• no control available • lower current
Results:
• aerodynamic drag is the principal effect up to over 600 km • 25 years limit respected • no control need (high mass ratio and low current)
ASTRA 2015 Amedeo Rocchi 20
bare tether =
anodic and cathodic contactor (Hoyth, 2009)
Data:
• 900 km altitude • 60° inclination • 1500 kg sat. • 15 kg end-mass • continuous approx. control (VTH=0.8) current limit: 1.5 A
Data:
• 800 km altitude • 50° inclination • 1500 kg sat. • 15 kg end-mass • on-off exact control
(VTH=0.8)
SAT SAT
anode
cathode
down up
SAT
SAT
POLITECNICO DI MILANO
Results:
• undersized 2.5 km tether Length
[km]
EDT system mass [%]
2.5 1.37
5 1.74
7.5 2.10
PARAMETER VARIED Range
Tether length [km] 2.5 – 7.5
Deployment direction up - down
Inert tether portion ηinert 0 – 0.5
Design Parameters varied one at a time
Results:
• up: intrinsic more stable
• up: possibly higher mass
end-mass = dead-weight
Results:
• OOP amplitude increase with inert portion
• more stable
• not as much as expected
FL
none close to anode
SAT SAT
Design Influence on Performance/Stability Examples
ASTRA 2015 Amedeo Rocchi 21
Conclusions
POLITECNICO DI MILANO
EDTs: • valid alternative for mitigation • simple systems, but non-linear behaviors • light systems (1-2% mass) efficiently remove massive satellites
Further study should address:
• non-rectilinear tether current profile under OML regime experimental campaign • current limit selection general rules
Needed Control: • Lyapunov approach + current limitation = effective • Exact control = more effective but lower TRL sensors • Continuous control = more effective
Design: • Upward deployment = higher stability but arching problem and higher mass • Inert portion = not effective as expected • Longer tethers = more effective but less stable
First implementation of such control family on accurate tether models Deep study on interdependence stability/control/performance
ASTRA 2015 Amedeo Rocchi 22
Versatile Electro-dynamic Tethers Dynamics Simulator for Debris Mitigation Tools Design
Michèle Lavagna, Amedeo Rocchi
POLITECNICO DI MILANO
Available Control Techniques
POLITECNICO DI MILANO ASTRA 2015 Amedeo Rocchi 24
• periodic libration control no periodic orbit in reality
• open loop control difficult to select precisely a priori (availability of current)
• libration control not the goal of de-orbiting
• transfer optimization too high computational cost on-board (highly nonlinear)
• self balanced configuration high influence on satellite design
• libration containment and tumbling avoidance non optimal
Ionosphere Model Example and Validation
POLITECNICO DI MILANO
Validation results (compared to complete IRI): • accurate data interpolation max error < 10% • precise profile for h>hmF2 max error < 5% • Ne underestimation for h>hmF2 lower current available (not a problem, to be
diminished for control reasons)
temporal evolution example validation example
hmF2
ASTRA 2015 Amedeo Rocchi 25
Overall Simulator Validation
POLITECNICO DI MILANO
Two validation categories: 1. comparison of simulation outputs with
previous studies
2. analytical checks
general trends agreement with (Hoyt, 2001; Zanutto, 2013; etc..) libration frequency in-plane IP libration frequency out-of-plane OOP Lorentz force component along velocity
Analytical check example: IP libration peak at
Analytical check example:
negative FL component along v
ASTRA 2015 Amedeo Rocchi 26
Current Profile: Bare Tether
POLITECNICO DI MILANO
BARE TETHERS
I = current ΔV = voltage difference p = cross section perimeter Ne = electron density ΔVCE = cathodic voltage drop Zl = cathodic load σ = tether conductivity = σ(T)
ASTRA 2015 Amedeo Rocchi 27
Assumptions:
• Constant tether properties along length • Constant environmental properties along length • Rectilinear tether • Orbital Motion Limited (OML) regime
Verified in cases considered (conductive portion only) Negligible variations along tether length (average value considered) Relaxed, method to be verified Major assumption, usually done when dealing with bare tethers (Zanutto,2013; Hoyt,2001; al.)
Optimal case for cylindrical probes: length dimension preponderant tether = uniformly polarized cylinder
OML regime assumption valid if:
• d<λDebye or w<4λDebye (if t<<w) verified with IRI (random locations and times) • λDebye<<le (electrothermal gyroradius)
Experimentally confirmed when relative velocity lower than electron thermal velocity
Non-rectilinear Bare Tether
POLITECNICO DI MILANO ASTRA 2015 Amedeo Rocchi 28
relative velocity
magnetic field
vector
cathode to anode versor
• mimics real behavior • properties of the cable not
affected
Highly non-rectilinear dangerous configurations monitored
N.B.: original direction maintained
Current Profile Scheme: Bare Tether
POLITECNICO DI MILANO
Courtesy of Journal of Propulsion and Power
BARE TETHERS
I = current ΔV = voltage difference p = cross section perimeter Ne = electron density ΔVCE = cathodic voltage drop Zl = cathodic load σ = tether conductivity = σ(T)
ASTRA 2015 Amedeo Rocchi 29
Current Profile Complete Passive EDT (nano-sat)
POLITECNICO DI MILANO ASTRA 2015 Amedeo Rocchi 30
IRI Data Interpolation Example
POLITECNICO DI MILANO ASTRA 2015 Amedeo Rocchi 31
IRI Data Interpolation Error Example
POLITECNICO DI MILANO ASTRA 2015 Amedeo Rocchi 32
Thermal Model Need
POLITECNICO DI MILANO
Aluminum σ(T)
ASTRA 2015 Amedeo Rocchi 33
Thermal Model Result Example
POLITECNICO DI MILANO ASTRA 2015 Amedeo Rocchi 34
Damping Influence
POLITECNICO DI MILANO
Amplified to highlight effect NO CONTROL
ASTRA 2015 Amedeo Rocchi 35
Threshold Selection
POLITECNICO DI MILANO
V approximated VTH=0.8 20°/25° both IP and OOP
ASTRA 2015 Amedeo Rocchi 36
Power Sign Estimation
POLITECNICO DI MILANO
Power = dot product of ED torque and Libration direction
ASTRA 2015 Amedeo Rocchi 37
Tether Conductive/Reinforcing Material Fraction
POLITECNICO DI MILANO
Completely Aluminum 50% Aluminum 50% Dyneema (in volume)
ASTRA 2015 Amedeo Rocchi 38
Tether Length and Deployment Direction Influence
POLITECNICO DI MILANO
• upward deployment: higher passive stabilization
• longer tethers: less stable (interaction of gravity gradient, ED torque and masses)
• duty cycles: driven by the control algorithms and natural switching offs (easier for shorter tethers)
• altitude decrease higher for the downward deployment alternative
tether is constantly exposed to a slightly higher electron density
• approximated control used: the exact stability function can exceed the threshold imposed
ASTRA 2015 Amedeo Rocchi 39
Real Cases Performance Influence
POLITECNICO DI MILANO
Ideal performance: large fake mass ratio
(passive stabilization)
Acceptable in all cases
stronger current reduction due to control is at lower altitudes, where
de-orbiting rate is higher
50 days increase for a 1 year mission, Cosmos
ASTRA 2015 Amedeo Rocchi 40
Sensitivity Analysis on Average Current
POLITECNICO DI MILANO
Preliminary sensitivity analysis: design parameters influence on average current
• Natural switching off
ASTRA 2015 Amedeo Rocchi 41
Sensitivity Analysis on Average Current
POLITECNICO DI MILANO
Preliminary sensitivity analysis: design parameters influence on average current
• Non-linear • Strong ZL variation required
ASTRA 2015 Amedeo Rocchi 42
Sensitivity Analysis on Average Current
POLITECNICO DI MILANO
Preliminary sensitivity analysis: design parameters influence on average current
• If possible better than ZL • Linear dependence • Large ΔV
ASTRA 2015 Amedeo Rocchi 43
Sensitivity Analysis on Average Current
POLITECNICO DI MILANO
Preliminary sensitivity analysis: design parameters influence on average current
ASTRA 2015 Amedeo Rocchi 44
Sensitivity Analysis on Average Current
POLITECNICO DI MILANO
Preliminary sensitivity analysis: design parameters influence on average current
ASTRA 2015 Amedeo Rocchi 45
Sensitivity Analysis on Average Current
POLITECNICO DI MILANO
Preliminary sensitivity analysis: design parameters influence on average current
ASTRA 2015 Amedeo Rocchi 46