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


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:


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


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


Simulator Scheme and Mechanical Model

Tethers mechanical model

lumped parameters method:

flexibility, elasticity and damping

End-masses model

extended bodies:

attitude coupling


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


Electrodynamic Interaction: Bare Tethers Current profile

BARE TETHERS


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


experimental validation required

Current Profile and Lorentz Forces


Distributed Lorentz force

Profile example, bare tether

Considered:

• Torques (non-uniform current distribution) • Tether elements orientation

Validated (Bombardelli, 2010)


Environmental and Thermal Models


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


Ionosphere Model


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


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


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)


Real Cases and Instability


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


REAL MASS RATIO


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


Control Available Parameters and Methods


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


Δa = 69.54 km tot. semi-major axis decrease




• 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



• 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



Approx. control,

on-off, VTH = 0.8:

• bounded OOP libration

• peaks V > VTH


Exact. control, on-off, VTH =

0.8:

• very bounded libration

• V < VTH always


Exact. control, continuous, VTH = 0.8:

• very smooth libration

Short Term Results Example


Control Methods Comparison


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


Control Influence and Current Limitation


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)


?

?

EDT Systems Applicability Domain


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


Nano-satellite Case


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)


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


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


Conclusions


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


Versatile Electro-dynamic Tethers Dynamics Simulator for Debris Mitigation Tools Design

Michèle Lavagna, Amedeo Rocchi


Available Control Techniques


• 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


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


Overall Simulator Validation


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


Current Profile: Bare Tether


BARE TETHERS



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


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


Courtesy of Journal of Propulsion and Power

BARE TETHERS



Current Profile Complete Passive EDT (nano-sat)


IRI Data Interpolation Example


IRI Data Interpolation Error Example


Thermal Model Need


Aluminum σ(T)


Thermal Model Result Example


Damping Influence


Amplified to highlight effect NO CONTROL


Threshold Selection


V approximated VTH=0.8 20°/25° both IP and OOP


Power Sign Estimation


Power = dot product of ED torque and Libration direction


Tether Conductive/Reinforcing Material Fraction


Completely Aluminum 50% Aluminum 50% Dyneema (in volume)


Tether Length and Deployment Direction Influence


• 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


Real Cases Performance Influence


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


Sensitivity Analysis on Average Current


Preliminary sensitivity analysis: design parameters influence on average current

• Natural switching off





• Non-linear • Strong ZL variation required





• If possible better than ZL • Linear dependence • Large ΔV


versatile electro-dynamic tethers dynamics simulator...

Documents