prof. s. ishkov, samara/ssau young engineers satellite 2 samara summer space school 2004 mission...

prof. S. Ishkov, SAMARA/SSAU

Young Engineers Satellite 2Young Engineers Satellite 2Samara Summer Space School 2004 Samara Summer Space School 2004

Mission Safety Analysis And Deployment ControlMission Safety Analysis And Deployment Control(theoretical substantiations)(theoretical substantiations)

SAMARA STATE AEROSPASE SAMARA STATE AEROSPASE UNIVERSITY, RUSSIAUNIVERSITY, RUSSIA

prof. S. Ishkov, SAMARA/SSAU

Mathematical ModelMathematical Model Assumptions:Assumptions:

– No any disturbances of FOTON-YES2 orbitNo any disturbances of FOTON-YES2 orbit

– The tether is always tenseThe tether is always tense

– FOTON and YES2 capsule are mass pointsFOTON and YES2 capsule are mass points

Y

θ’

Z

X

ξ

φ

η

ζ

СВ

А

r

θ’

θ

φ

prof. S. Ishkov, SAMARA/SSAU

Mathematical ModelMathematical Model

T – control tensionζ – dissipation coefficientS – tether cross-sectional aream – total massm2 – implicit massR - geocentric radius vector

ν – true anomaly of center of mass-r – undeformed tether length E – tether young modulus

prof. S. Ishkov, SAMARA/SSAU

SimulationsSimulations

Deployment trajectoryDeployment trajectory Deployment speed vs. Deployment speed vs. timetime

prof. S. Ishkov, SAMARA/SSAU

F(u)

Шаговый мотор

/Stepper motor

ОТС / OTSТ Х

Сравнивающее устройство

/The comparator

Программное устройство

/Onboard computer

u

Катушка фрикц. мех./Barberpole

spool

Фрикционный механизм

/Barberpole brake

Control systemControl system

a

l

l

)(tlnp)(tlnp

BI

n

u

0ntIn B

;,1

;,0

;,1

au

aua

au

I B

a

prof. S. Ishkov, SAMARA/SSAU

Simulation with barberpole brakeSimulation with barberpole brake

Tension vs. time with barberpole brake

without barberpole brake

Turns vs. time

prof. S. Ishkov, SAMARA/SSAU

Simulation with barberpole brakeSimulation with barberpole brake

Tension (zoomed) vs. time with barberpole brake

without barberpole brake

Turns (zoomed) vs. time

prof. S. Ishkov, SAMARA/SSAU

Jerk SimulationJerk Simulation

Deployment trajectoryDeployment trajectory Velocity vs. timeVelocity vs. time Tension vs. timeTension vs. time

Jerk after ~ 40Jerk after ~ 40thth second of deployment second of deployment

prof. S. Ishkov, SAMARA/SSAU

Jerk SimulationJerk Simulation

Deployment trajectoryDeployment trajectory Velocity vs. timeVelocity vs. time Tension vs. timeTension vs. time

Jerk after ~ 8Jerk after ~ 8thth second of deployment second of deployment

prof. S. Ishkov, SAMARA/SSAU

Jerk SimulationJerk Simulation

Deployment trajectoryDeployment trajectory Velocity vs. timeVelocity vs. time Tension vs. timeTension vs. time

Jerk after ~ 2Jerk after ~ 2ndnd second of deployment second of deployment