ASTOS for Low Thrust Mission Analysis

Transcription

1 ASTOS for Low Thrust Mission Analysis 3rd Astrodynamics Workshop, Oct. 26, ESTEC

2 Overview Low Thrust Trajectory Computation Description of the Optimal Control Problem Trajectory Optimization and Mission Analysis Minimum Time Transfer Subsynchronous Transfer Restricted Minimum Fuel Transfer Summary & Conclusion 2

3 Electric Propulsion Thrust levels: F <.5 N Exhaust velocity: 3-4 km/s Can thrust continuously Thrust direction steerable First used as AOCS Then interplanetary travel (deep space, Smart, etc.) Considered for orbit raising to GEO Transfer of system & fuel mass to payload mass Increased transfer duration through Van Allen radiation belt Increased overall complexity of trajectory geometry ATOS hydrazine arcjet (up) and one of the IMPD thrusters (bottom) 3

4 Solution Methods Elaborate Control Laws Koppel, Pollard: st step: semimajor 2nd step: eccentricity, inclination, a = const. Indirect Optimization Methods Identify relations for adjoint variables, if possible Averaging Techniques Reduce size of optimal control problem (parameterisation losses) Direct Optimization Methods Requires many parameters (-k) => SOCS 4

5 Core Objectives for Industrial Mission Analysis Determination of initial mission specifications is governed by Varying levels of sophistication Earth oblateness effects Perturbational bodies Radiation belt modelling, power degradation modelling Varying propulsion and system configurations Propulsion components, thruster characteristics System driven restrictions, e.g. Solar cells orientation, recharge cycle Trade-Off aspects Restrictions on orbit geometry, e.g. subsynchronous transfers Changing objectives, e.g. power output, payload, fuel, trip time Mission constraints Power management Geometrical path constraints, e.g. subsyncronous transfer Target orbit definition 5

6 Core Objectives for Industrial Mission Analysis Requirements for mission analysis software Allow quick modification/in-/exclusion of boundary and path constraints and cost components Time economic and reliable computation of transfer trajectories Robust with respect to changing dynamics Provide optimal results that can easily be compared Relieve user from tuning of optimiser setting 6

7 ASTOS Work Flow. Describe OCP 2. Initialize/Discretize 3. Transcription into NLP is done automatically 4. Optimize & Monitor 5. Simulate 6. Handle Data 7

8 Control Law vs Optimization apo peri. with the Control Laws suggested by Pollard with coasts: Semimajor Axis [km] 4.4 x 4.8 Eccentricity [-] 3 Inclination [deg] f Pollard ASTOS f coast Cont..9 d 9.5 kg days days days 8

9 Control Law vs Optimization Low-thrust transfer from a GTO with high inclination (see J.E. Pollard) GTO: h apo = 35,786 km; h peri = 85 km; i = 28.5 ; mass =4kg 4.4 x Semimajor Axis [km].8 3 f Pollard f 2. with the.7 Control Laws suggested by Pollard 25 without coasts:.6 coast.9 d kg.4 5 Cont. 2.3 d kg.2. Eccentricity [-] 5 Inclination [deg] ASTOS days days days 9

10 Control Law vs Optimization apo peri 3. Optimized with ASTOS/SOCS: Semimajor Axis [km] 4.4 x 4.8 Eccentricity [-] 3 Inclination [deg] f Pollard ASTOS f coast.9 d 9.5 kg Cont. 2.3 d 28.9 kg 96.7 d 27. kg days days days

11 Control Law vs Optimization apo peri 4. Optimized with ASTOS/SOCS allowing optimizable thrust: 4.6 x 4 Semimajor Axis [km].8 Eccentricity [-] 3 Inclination [deg] f Pollard ASTOS f coast Cont..9 d 9.5 kg 2.3 d 28.9 kg.9 d 67.3 kg 96.7 d 27. kg days days days

12 Central Body and Perturbation Equations of Motion comprehend: A central gravitational body (Earth) Perturbation vector in the radial frame EoM: Equinoctial Elements The Perturbation Vector can comprise: Thrust Oblateness models Third bodies (Sun, Moon, Mars, Jupiter, etc.) Solar wind pressure = T + g + q

13 Power Management Thrust and massflow are functions of the provided power P, per thruster: Thrust : F = f (P) Massflow: mdot = f 2 (P) Available power depends on: Solar array size and characteristics Power supply for secondary systems Power management during solar eclipses Reduction due to radiation damage Battery capacity and recharge cycles under consideration of eclipses 3

14 Boundary Conditions Initial Conditions Ariane 5 GTO orbit Final Conditions GEO Interbox Gap: Semimajor axis: 42, km 5. km Eccentricity:. Inclination:. V-bar excitation Longitude of GEO box 4

15 Radial Frame of the Control Variables T = T m u u u r th h a i th b i r i th i r z i th i h i r i th i r r x y u( t) = ( u r, u th, u h ) T vernal equinox u( t) = u 2 r + u 2 th + u 2 h 5

16 Initial Guess Generation Initial guess generation is based on a straight forward simulation Construction using standard control laws Generic control history is sufficient to allow steady optimization Enhanced performance with more sophisticated initial control histories Use of earlier trajectories of lower-level computations is possible Benefits: Non need to compute abstract adjoint variables Non need to newly generate model equations (see indirect/hybrid methods) Pure utilization of physical relations Preparation of optimization algorithm is not required ( minutes) Don t waste time on the initial guess (< 5 minutes) 6

17 Minimum Time Transfer Optimal overshooting km] 3 25 Radius 2 [

18 Minimum Time Transfer Semimajor Axis [ 3 km] Eccentricity [-] Inclination [deg] Min t f transfer: No eclipses No phasing 25. Radial Component Tangential Component Normal Component

19 Optimal Phasing Radial Component Tangential Component Normal Component λ Radial Component Tangential Component Normal Component λ Time optimal, but not fuel optimal!

20 Yaw and Pitch over Anomaly 2

21 Thrust Direction in each Revolution 2

22 Influence of Perturbations Semimajor Axis [ 3 km] Radial Component Eccentricity [-] Tangential Component Inclination [deg] Normal Component km] Apogee/Perigee 5 [ Unperturbed dynamics Perturbed dynamics Opt control unperturbed case Opt control perturbed case Is this influence much higher than that of thrust vector error? 22

23 Subsynchronous Transfer Time optimal subsynchronous transfer km] 25 2 Radius [ Time optimal but not fuel optimal because of permanent constant thrust! 23

24 Subsynchronous Transfer Optus B3, December Launch Semimajor Axis [ 3 km] Eccentricity [-] Inclination [deg] Subsync. transfer: With eclipses With phasing Radial Component Tangential Component Normal Component

25 Thrust Direction in each Revolution 25

26 Restricted Minimum Fuel Transfer I Time optimal 3 km] Propellant Mass [k g] 4 2 Cost: 7.6 days Benefit: 24.6 kg Perigee/Apogee [ Fuel optimal Upper bound: Max available power Lower bound: Min continuous thrust 26

27 Restricted Minimum Fuel Transfer II Transfer Costs & Benefits for Arrival on -Mar-29 Fuel Consumption [kg] days 2.5 days Subsynchronous Overshooting 2-May May-28 -Jun-28 -Jun-28 2-Jun-28 -Jul-28 -Jul-28 2-Jul-28 3-Jul-28 -Aug-28 2-Aug-28 3-Aug-28 Launch Date 27

28 Time Consumption Generation of an initial guess New missions with similar configurations: min New missions: 5-5 min Optimization of the trajectory Reliable solution for a standard mission: min Converged solution for standard mission: -2 hours Complex cases: Up to a few hours CPU time Research on new scenarios: takes days It all depends on the level of sophistication and the tolerances 28

29 Summary & Conclusion The NLP setup for GTO-GEO transfers in ASTOS/SOCS has proven to - be easily extendable/adaptable to new mission requirements - be reliable/stable with respect to the sophistication of the dynamics - produce solutions that are superior to control law applications NLP optimization is a well appropriate alternative for low-thrust GTO-GEO mission analysis 29

30 Thank you! 3