Attachment_D_-_ACS3_Attitude_Control_Supplement.pdf

Advanced Composite Solar Sail System (ACS3) Attitude Control Supplement

ACS3 Project

ACS3-02-007

Table of Contents

1.0 Introduction

2.0 Intent of Use

3.0 ACS3 Bus and Solar Sail Payload Reference Configuration

4.0 Analysis Approach and Model Description

5.0 Results and Discussion

5.1. Disturbance Torques and Orbital Decay Rates – Controlled Flight

5.2. Disturbance Torques, Body Rates, Orbital Decay Rates – Uncontrolled Flight

6.0 Summary

7.0 References

1.0 Introduction

Estimates of on-orbit disturbance torques acting on the ACS3 solar sail vehicle with sail deployed are provided in this supplement. Disturbance estimates for all controlled flight modes with sail deployed are estimated via time domain simulations. Combined disturbances from solar radiation pressure, aerodynamic drag, and gravity gradient sources are included in the model estimates. Stability characteristics, disturbance torques, and body rates for uncontrolled flight with sail deployed are also assessed.

2.0 Intent of Use

The purpose of this document is to provide the spacecraft bus vendor with insight into the deployed solar sail spacecraft system to aid in the design of their attitude control system. Specifically, the data in this document is intended to inform requirements 6.1.9 (Mission Orbit), 6.4.1 (Pointing Accuracy), and 6.4.6 (Recover from Tumble). Per the rationale in those requirements, the spacecraft bus vendor is encouraged to design their attitude control system to enable as low a minimum altitude (within the required range), and as tight a pointing accuracy, as possible, while successfully being able to recover from a tumble at the proposed minimum altitude (as a bounding case).

Please note, if any discrepancies are found between this document and the Payload-to-Spacecraft Bus Interface Control Document and/or Spacecraft Bus Level 3 Requirements document, the ICD and requirements document shall take priority.

3.0 ACS3 Bus and Solar Sail Payload Reference Configuration

Tyvak 12U payload specifications were assumed for the central spacecraft dimensions. The ACS3 solar sail system deployer and sail stowage are located on the anti-sunward end of the spacecraft (Figure 1). All remaining volume is allocated to bus avionics, and the sail camera diagnostic system and solar sail payload control electronics (labeled as “ACS3 Trunk”). A uniform density of 1.43 kg/l was assumed for the bus avionics (approximately 4U). The center of solar radiation pressure (Cp) is located approximately 86 mm behind (anti-sunward direction) the spacecraft center of mass (Cm) and 45 mm behind the payload boom reference plane.

As a bounding case, the lightest estimated mass of the complete ACS3 spacecraft (16 kg) together with the largest sail structure (7.0 m booms with an 82 m2 deployed solar sail) currently under consideration for ACS3 was assumed. This can be expected to produce the largest disturbance torques and greatest deorbiting rates on the spacecraft.

4.0 Analysis Approach and Model Description

MATLAB with Princeton Satellite Systems Spacecraft Control Toolbox and Solar Sail module was used for on-orbit disturbance analysis (Reference 2). The ACS3 spacecraft (bus and deployed sail) is modeled as an assembly of rigid bodies, as shown in Figure 2. Bus, booms, and sail quadrant inertias and geometries are accounted for properly. Solar panels inertias are not modelled in this analysis, but can be included in future analyses. Calculated rotational inertias for the spacecraft with solar sail deployed are summarized in Table 1. Off-diagonal inertia terms were negligible.

Figure 1. ACS3 Reference Configuration for Disturbance Analyses.

Figure 2. ACS3 Spacecraft Attitude Control Reference Coordinate System.

Table 1. Rotational Inertias of Spacecraft with Sail Deployed.

Ixx [kg-m2] 17.26 Iyy [kg-m2) 8.73 Izz (kg-m2) 8.73

Aerodynamic drag, solar radiation pressure, and gravity gradient are accounted for (largest disturbance sources). A simple atmospheric density model used. Solar cycle effects are not included. Realistic, non-ideal optical properties are used to model the solar sail radiation pressure forces. Disturbance forces acting upon the boom and bus are neglected in this analysis, but can be included if desired in future analyses.

5.0 Results and Discussion

Plots and tables summarizing orbital decay rates, magnitudes of disturbance torques acting on the spacecraft, and, in the case of uncontrolled, tumbling flight, peak body angular rates, are provided below.

Behavior of the ACS3 spacecraft at altitudes between 500 km and 1000 km was examined. Summary data is derived from time domain simulations performed for each orbital altitude and control condition. An initial dawn-dusk sun synchronous orbit (DD-SSO) with 270 degree RAAN and launch date ca. 20 March 2021 was used for all cases.

5.1. Disturbance Torques and Orbital Decay Rates – Controlled Flight

Orbital decay rates and mean and oscillatory disturbance torque amplitudes for controlled flight cases are shown in Figure 3 through Figure 5 and Table 2 through Table 4.

Spacecraft attitude in the local horizontal-local vertical (LVLH) frame is constrained throughout each simulation. The +Z boom of the spacecraft is nadir pointing at all times, with a fixed rotation about the +Z axis. +Z rotation angle for normal flight is typically 0 degrees, i.e., the sail plane is aligned with the local horizontal plane. This minimizes aerodynamic drag effects and mean disturbance torques acting on the spacecraft. Non-zero +Z rotations may also be commanded to evaluate the orbit lowering characteristics of the spacecraft, and in some cases, the orbit raising capabilities of the solar sail.

Simulation duration for all cases was 10 days, initialized from the nominal DD-SSO altitude. Mean and maximum oscillatory amplitude of disturbance torques produced by atmospheric drag, gravity gradients, and solar radiation pressure are computed as the spacecraft orbit is propagated.

Note that in the provided tables orbit decay rates for the nominal, zero +Z rotation attitude are highlighted in green, maximum orbit raising rates are highlighted in blue, and maximum orbit lowering rates are highlighted in red.

AC

S3

P ro je ct

At tit ud e Co nt ro l S up pl em en t

AC

S3

-0 2-

Pa ge of

Ta bl e 2.

O rb ita l D ec ay

R at es v s.

+Z

Ro ta tio n An gl e

(C on tr ol le d

Fl ig ht

Fi gu re

.O rb ita l D ec ay

R at es v s.

+Z

R ot at io n An gl e

(C on tr ol le d

Fl ig ht

P ro ud e Co nt ro l S up pl em en t

AC

S3

-0 2-

Pa ge of

Fi gu re

. M ea n D is tu rb an ce T or qu e vs

Z

Ro ta tio n

An gl e (C on tr ol le d Fl ig ht

Ta bl e 3.

M ea n D is tu rb an ce T or qu e vs

Z

Ro ta tio n

An gl e (C on tr ol le d Fl ig

P ro ud e Co nt ro l S up pl em en t

AC

S3

-0 2-

Pa ge of

Fi gu re

. O sc ill at or y

D is tu rb an ce

T or qu e

Am pl itu de v s.

Z

Ro ta ti on

A ng le (C on tr ol le d Fl ig ht

Ta bl e 4.

O sc ill at or y

D is tu rb an ce

T or qu e

Am pl itu de vs

Z

Ro ta tio n

An gl e (C on tr ol le d Fl ig

5.2. Disturbance Torques, Body Rates, Orbital Decay Rates – Uncontrolled Flight

Orbit altitude decay rates, maximum body angular rates, and mean and oscillatory disturbance torque amplitudes for uncontrolled flight cases are shown in Figure 6 through Figure 9. Results are also summarized in Table 5.

For all cases, spacecraft attitude was initialized in the DD-SS orbit at a nominal zero +Z rotation angle.

Attitude is unconstrained thereafter. Simulation duration for all altitude cases above 500 km was 10 days.

For the 500 km altitude case only, simulation duration was 1 day.

For altitude cases below 950 km, the spacecraft begins to tumble, generally within one orbit. At 950 km and above, atmospheric drag forces and resulting disturbance torques are relatively small and the spacecraft is stabilized in an approximately sun-pointing attitude by solar radiation pressure forces. This is expected for spacecraft configurations where the solar sail is located behind (i.e., anti-sunward) of the spacecraft center of mass.

Angular rates and disturbance torque amplitudes shown are applicable about both the Y and Z spacecraft axes.

Figure 6. Orbital Decay Rate (Uncontrolled Flight).

Figure 7. Maximum Body Angular Rate (Uncontrolled Flight).

Figure 8. Mean Disturbance Torques (Uncontrolled Flight).

Figure 9. Oscillatory Disturbance Torques Amplitude (Uncontrolled Flight).

Table 5. Uncontrolled Flight Orbital Decay Rates, Maximum Body Angular Rates, and Disturbance Torques.

6.0 Summary

The ACS3 solar sail may be flown without significant loss of altitude provided the sail plane is kept in the orbit plane (local vertical-local horizontal plane) at all times. In this flight attitude, oscillatory torque amplitudes about the Y and Z spacecraft axes will vary once per orbit and have zero mean.

If attitude control is lost, the sail plane will tend to drift out of the minimum drag orientation, typically within one orbit. At 500 km, the uncontrolled solar sail will begin to tumble within one orbit and lose altitude rapidly (30-40 km/day).

For altitudes cases between 700 km and 900 km, the uncontrolled solar sail oscillates at large amplitude about the mean sun angle, although does not completely overturn. For these cases, orbit altitude decays relatively slowly; < 2 km/day initially.

For the 950 km and 1000 km altitude cases, the uncontrolled solar sail is passively stabilized about the mean sun angle by solar radiation pressure. Oscillations remain relatively small.

For altitudes of 700 km and above, orbit raising and orbit lowering may be accomplished via a fixed rotation about the Z boom axis, although for configurations with non-zero Cm-Cp offset, a mean disturbance torque about the sail Z boom axis will be present. Reaction wheel momentum management will likely be required to maintain the fixed Z rotation angle for long durations.

7.0 References

1. McInnes, Colin R., Solar Sailing: Technology, Dynamics, and Mission Applications, Springer-Praxis, 1999.

2. Solar Sail Module for the Spacecraft Control Toolbox Professional Edition, v. 1.2, Princeton Satellite

Systems, Inc., 2012.

3. Wertz, J.R., Spacecraft Attitude Determination and Control, Kluwer, 1976, p. 820.

4. Boain, R. J., "A-B-Cs of Sun-Synchronous Orbit Mission Design“, 14th AAS/AIAA Space Flight Mechanics

Conference, Maui, Hawaii, February 8-12, 2004.

5. Wie, B., Murphy, D., Puluszek, M., Thomas, S., “Robust Attitude Control Systems Design for Solar Sails, Part 1: Propellantless Primary ACS,” AIAA Guidance, Navigation and Control Conference and Exhibit, 16-19 August 2004, Providence, RI.