Optimal Reconfiguration for Capacity Expansion of Communication Satellites

Constellations

Afreen SiddiqiJason Mellein

May 3, 2004

16.888 Final Presentation

2

Overview

• Motivation

• Goals

• Optimal Inter-satellite reconfiguration

• Optimal intra-satellite reconfiguration

• Conclusions

3

Motivation

Iridium may have succeeded ifit could ‘reconfigure’ for data as well as voice transmission

Reconfigurable communication satellite systems can mitigate risks and provide greater benefits

Definition: Reconfigurability is a system’s ability to reversibly achieve distinct configurations*, in order to produce new or modified system form and/or function, within an application specific time constant.

*relationships between system elements in the distinct configurations maybe physical, spatial etc.

• Reconfigurable satellite systems can meet new requirements

• Reconfiguration allows capitalization of economic opportunities, or fulfillment of new needs that may arise over time

4

Goals

• Two classes of reconfiguration studied:

• Inter-Satellite reconfiguration– Change in spatial relationships between constellation

satellites– Variation of orbital characteristics (altitude, elevation)

• Intra-Satellite reconfiguration– Change in internal satellites’ sub-systems – Variation of component characteristics to achieve desired

system requirements

5

Inter-Satellite Reconfiguration: Problem Definition

• What is the optimal orbital reconfiguration for an existing satellite constellation to undergo in order to meet a new (and higher) capacity demand?

aa

desiredB

b

b

andhgivenCC

kmhts

ationCostReconfigurJ

ε

ε=

≤≤≤≤

=

(deg)205)(2000400

..min

hb = altitude of B (km)εb = elevation angle of B (deg)Cb = system lifetime capacity (minutes)

N(B)-N(A) satellites on the ground

Constellation A Constellation B

N(B) satellites Earth N(A)

satellites Earth

Orbital transfer

Launch

⎥⎦

⎤⎢⎣

⎡=

b

bhε

x

Design vector:

Formulation:

6

Optimization on two levels

Constellation

Constellation

hbεb

haεa

N,s,p (B)

N,s,p (A) Astrodynamics

parameters

Design vector (x)

∆Vi,j , Ti,j

Optimizer(Auction algorithm)

# of additional sats needed

Launch Fuel

Orbital Assignments

Fuelconsumption

Launch cost/satellite

J = reconfig cost

Cost

Constellation

Link Budget

Optimizer

g(x)= capacity

x*

Function Evaluator

Legend:N: # of satellitesS: # of sats/planesP: # of planes∆V: matrix of ∆VsT: time matrix

Orbit Reconfiguration: SOO - Simulation Model

7

3.1x10114.5x1011System Lifetime Capacity [min]

17921100Voice circuits/sat

250240FDMA channels

10.510.5Bandwidth [MHz]

8.63-Beamwidth [deg]

400400Transmit power [W]

25.5724.3Transmit gain [W]

4.95x10-111010Power flux [Jv]

780780Altitude [km]

6 6# orbital planes

1.62131.6212Frequency [GHz]

6666# of sats

SimulatedActualCharacteristic

Benchmarked against Iridium data

Orbit Reconfiguration: Benchmarking

8Note: y-axes in billions of dollars.

• Strong effects of altitude and inclination → both used in design vector

Orbit Reconfiguration: DOE Analysis

9

Orbit ReconfigurationSingle Objective Optimization - I

Full Factorial Computation with ∆h=50[km] and ∆ε=1[deg]

Highly non-linear design space and constraint

10

Algorithm: SQP (fmincon)

Optimizer: MATLAB

x*:J*:

Actual Capacity:

[1066, 5]$587 Million1.008 x 1011[min]

Parameter Values:Cdesired = 1011 minhA = 2000 kmεA = 5 deg

Assumptions:- Polar constellation- Global, single fold coverage

Constellation A:2000 km, 5o

→ 21 satellites3 planes7 sats/plane

CA= 1.5 x 1010 min

Constellation B:1066 km, 5o

→ 40 satellites5 planes8 sats/plane

CB= 1.008 x 1011 min

Optimal orbital reconfiguration

Sensitivity:⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡∂∂∂∂

=∇0.0899 0.00005-

eJhJ

J

⎥⎦

⎤⎢⎣

⎡=∇=∇

0.7653 0.8569-

. *

*

JJJ x

Orbit Reconfiguration: SO Optimization - II

11

0 10 20 30 40 50 60 70 80 900.5

1

1.5

2

2.5

3

3.5

Iteration Number

Sys

tem

Ene

rgy

SA convergence history

current configurationnew best configuration

10 20 30 40 50 60 70

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

Iteration Number

Sys

tem

Ene

rgy

SA convergence history

current configurationnew best configuration

x* : [1085, 5]J* : $587 MillionActual Capacity: 9.92 x 1010 [min]

Iterations: 30J* std dev: 0.56%

Algorithm: Simulated Annealing

Optimizer: MATLAB

Best solution very close to one obtained from SQP

Orbit Reconfiguration: SO Optimization - II

12

desiredB

B

B

mo

CCand

kmhts

CJCostJ

JJJ

≥

<≤≤≤

==

−−=

(deg)205)(2000400

..

)1(min

2

1

21

ε

λλ

• Capacity Constraint changed from equality to inequality

• Objectives:

J1 = minimize reconfiguration cost

J2 = maximize capacity

• Scaling on the capacity objective due to O(11) difference between J1 and J2:

))((log*)1( 2101 JJJmo λλ −−=

• log10 used due to the variability of J2 over many orders of magnitude in the design space

Orbit Reconfiguration: MO Optimization

13

• Competing Objectives:

- System Capacity optimized at bounds of altitude and inclination (400 km, 20o) farthest from initial constellation

- Reconfiguration Cost optimized at bounds of altitude and inclination (2000 km, 5o) closest to initial Constellation

Orbit Reconfiguration: MOO Pareto Front

14

Goals

• Two classes of reconfiguration studied:

• Inter-Satellite reconfiguration– Change in spatial relationships between constellation

satellites– Variation of orbital characteristics (altitude, elevation)

• Intra-Satellite reconfiguration– Change in internal satellites’ sub-systems – Variation of component characteristics to achieve desired

system requirements

15

Intra-Satellite Reconfiguration: Problem Definition

Parameters:h: altitude (km)ε: elevation (deg)xA: satellite component design vector of

constellation A

Design Vector:x: vector of satellite component characteristics

Constellationh, ε

N(# of Sats)

Link BudgetCapacity

Objective Evaluator

x

xA

J

Constants

• What is the optimal reconfiguration the communication components of satellites of an existing constellation should undergo in order to meet a new (and higher) capacity demand?

Simulation Structure

16

Satellite Reconfiguration: DOE Analysis• Several variables affect communication system capacity

– DOE used to determine driving factors

Receiver gain discarded from design vector due to negligible effect on capacity

Chosen design vector:

DA: antenna diameter (m)Pt: transmit power (W)R: single user data rate (kbps)Tsat: satellite lifetime (yrs)Gr: Receiver gain

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

sat

t

a

TRPD

x

17

Satellite Reconfiguration: Problem Formulation

Formulation:

desiredB

sat

t

a

BA

CCand

yearsTkbpsRWPmD

tsJ

=

≤≤≤≤≤≤≤≤

−=

)(155)(104.2

)(80050)(101.0

..min xx

• Two algorithms used

• SQP:– all DVs continuous– repeatable – several ICs used

• Simulated Annealing: – well established heuristic technique – computationally cheaper than GAs

18

Satellite Reconfiguration: Single Objective Optimization

[ ]min107.9075.1

24.552.4

03.4005.2

11

*

*

xCJ

TRPD

B

sat

t

a

B

=

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=x

Parameter Values:Cdesired = 1012 minhA = 780 kmεA = 8.2 degxA =[1.5, 400, 4.8, 5]T

Note: xA had values of Iridium components

CA = 3.1 x 1011 min

Assumptions:- No orbital reconfiguration- On-orbit servicing

Da increased by 1mR decreased by small amountTsat increased by 3 months

Algorithm: SQP (fmincon)

Optimizer: MATLAB

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−=∇=∇

09.109.1

019.2

. *

*

JJJ x

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

∂∂∂∂∂∂∂∂

=∇

22.026.0

094.0

////

sat

t

a

TJRJPJDJ

J

Sensitivity:

Antenna diameteris highest driver

19

Satellite Reconfiguration: SO Optimization -II

x* : [2.5, 400.9, 4.4, 5]J* : 1.48Actual Capacity: 9.86 x 1011 [min]Iterations: 30

J* std dev: 2.42

Algorithm: Simulated Annealing

Optimizer: MATLAB

Best solution close to one obtained from SQP

20

Satellite Reconfiguration: Multi-Objective Optimization

desiredB

sat

t

a

BBA

CCand

yearsTkbpsR

WPmD

tsCJandJ

≥

≤≤≤≤

≤≤≤≤

=−=

)(155)(104

)(1200200)(105.0

..maxmin 21 xx

21 )1( JJz λλ −−=

Competing objectives:- higher capacity →

greater change in component values- lower cost →

smaller change in component values

21

BULLITNUTSBULLITNUTS

High probability that global optimum found

Post Optimality Analysis

• Conditioning and Optimization– Gradient Algorithm started from

various initial conditions – Heuristic Algorithm yielded

feasible design very close to Gradient method results.

• Termination Criteria– Gradient Algorithm converged

consistently– Heuristic Algorithm achieved

Stagnation in Fitness consistently

22

Conclusions

• Orbital and component reconfigurations can be used to increase system capacity if costs can be justified

• Reconfiguration cost vs capacity charts can be used in Constellation Design for Reconfigurability

– Staged deployment followed by reconfiguration

Future Work• Improve:

– capacity calculation– reconfiguration cost estimation– objective for intra-satellite reconfiguration

• Analysis with fixed quality of service, i.e. R not a variable• Explore technologies for intra-satellite reconfiguration

Questions?

24

0

20

40

05001000

150020000

5

10

15

20

25

30

elevation (deg)

# of orbital polar planes on design space

altitude(km)

# of

orb

ital p

olar

pla

nes

010

2030

40

0500

10001500

20000

10

20

30

40

50

elevation (deg)

# of satellites/plane on design space

altitude(km)

# of

sat

ellit

es/p

lane

• Ridged surfaces due to discreet increments of: → number of orbital planes→ number of satellites per plane

Design Space of Orbital Reconfiguration

25

Intra-Satellite Reconfiguration Results

• 34 Initial conditions were used• In most cases the same optimal solution was calculated

– Can be assumed that global optimum was found