Solar Sail Attitude Control using a Combination of a Feedforward and a Feedback Controller D. Romagnoli, T. Oehlschlägel

Solar Sail Attitude Control using a Combination of a

Feedforward and a Feedback Controller

D. Romagnoli, T. Oehlschlägel

2nd International Symposium on Solar SailingD. Romagnoli & T. Oehlschlägel

Agenda

1

2

3

Introduction

Simulations Results

Controller Structure

4 Conclusions


Introduction

1


Problem Statement

• Solar sail coupling between trajectory and attitude is crucial for performance analysis

• High performance reorientation maneuvers may be important for demanding missions (like those with close fly-by of the Sun or planetary ones)

• The control authority is a critical issue in selecting/designing the control system


Objectives

• Develop a controller that is able to perform attitude maneuvers around the three body axes of the sail

• Select and model a controller actuator which satisfies the requirements of high control authority and technological feasibility

• Study the performances during attitude maneuvers given the sail‘s parameters and the selected actuator

• Understand the reorientation capabilieties of a solar sail, independently from trajectory constraints


The CM-CP Control Technique

No Control TorqueClockwise Control TorqueCounter-Clockwise Control Torque

PM CC PC

MCMC


Controller Structure

2


[Ref. Wie B. and Murphy D. „Solar-Sail Attitude Control Design for a Solar Flight Validation Mission“, Journal of Spacecraft and Rockets, Vol. 144, No. 4, July-August 2007]

zextxSr

yxyxzz

xSr

zxxzyy

zyzyxx

TyFmM

mJJJ

TzFmM

mJJJ

TJJJ

,,

yext,,

xext,

Control Torques

External Torques

Equations of Motion for the Control Design


Equations of Motion for the Control Design

zoffset,,,

yoffset,yext,,

xext,

TTyFmM

mJJJ

TTzFmM

mJJJ

TJJJ

zextxSr

yxyxzz

xSr

zxxzyy

zyzyxx

+Y

+Z

CP

The contribution coming from the offset of the center of pressure is

the most significant source of disturbance

It MUST be included in the controller design to improve the performances!!


The Basic Loop Structure

Maneuver Parameters

Feed-ForwardController

Attitude Dynamics & Kinematics

Settings

Maneuver TimeControl Torque To Ballasts‘ Position

Feed-BackController

Measured/Simulated States

FF Control Torque

FF Predicted States Errors

FB Control Torque

Total Control Torque

Off - SetNon-Diagonal

InertiaExternal Torque

Feedforward‘s Fast Response + Feedback‘s Ability of Coping with Unpredicted Disturbances


The Feedforward: basics

Initial Quaternion

Final Quaternion

ftft ,, 0

Polynomial of 9th degree with boundary conditions on its derivatives up to the third order

43223495 12642054031570 ttttttp f


The Feedforward: basics

Assumptions for the feedforward design:

1. The effect of the offset is included

2. The inertia matrix is constant

3. The mass distribution leads to a diagonal inertia matrix


The Feedforward: an Example

+Y

+Z

Pitch (+Y) = 15°

Yaw (+Z) = 35°

+Y

+ZEuler Axis = 38°


38°

The Feedforward: an Example


The Feedforward Controller

Once the polynomial has been computed:

• All the (predicted) states of the system are known at each time-step

• All the (predicted) inputs to the system are known at each time-step

But:

• A detailed description of the system‘s dynamic is required

• The predicted/desired states and inputs do not consider disturbing effects coming from not included sources


The Feedback Controller

Error Dynamics

dtq

qq

e

q

realdesired

realdesired

ωωωX

qe

II

qq

ωωTω tot

1

2

1

The system can be linearized about the zero-point…


The Feedback Controller

…and controlled using a simple LQR approach!

101010555100100100diagQ

Weighting matrices are:

101010diagR

IDP KKKK

Gain Matrix

Diagonal submatrices


Simulations Reults

3


Simulations Results: Sail Parameters

Geometry

SizeBoom lengthSail area

4028

1200

mmm2

Masses

SailsBoomsBallasts (each)BusOther

Total

671

15020

185

kgkgkgkgkgkg

Inertia

Ix (roll)Iy (pitch)Iz (yaw)

434021712171

kg m2

kg m2

kg m2

[Ref. Wie B. and Murphy D. „Solar-Sail Attitude Control Design for a Solar Flight Validation Mission“, Journal of Spacecraft and Rockets, Vol. 144, No. 4, July-August 2007]


Simulations Results: Single Axis Maneuver

Roll: 0° 0°Pitch: 0° 0°Yaw: 0° 35°

Under the effects of:

• no offset

• no external torque

• a diagonal inertia matrix

+Y

+ZYaw (+Z) = 35°

Desired maneuver:



+Y

+ZYaw (+Z) = 35°



Maneuver Time: 3370 sec or about 57 min






VIDEO


Simulations Results: Two Axes Maneuver

+Y

+Z

Pitch (+Y) = 45°

Yaw (+Z) = 35° Roll: 0° 0°Pitch: 0° 45°Yaw: 0° 35°

Under the effects of:

• an offset of 0.1 m in both directions

• an external torque around the +Z axis

• a non-diagonal inertia matrix

Desired maneuver:









VIDEO


Conclusions

4


Conclusions

1. The problem of attitude control for solar sails has been introduced

2. A control strategy which uses both a feedforward and a feedback controller has been described

3. Some example maneuvers have been presented to describe the performances of the proposed controller


Model Improvement:

- include sailcraft (booms and membrane) flexibility in the model

- investigation of coupling effects between attitude and structure dynamics

- current approach involves cosimulation with structural analysis in ANSYS and dynamic simulation and control in MATLAB/SIMULINK

- any suggestions or comments on this topic are welcome!

Open Points

Controller Improvement:

- use of H-Infinity controller instead of LQR

- include better time optimization routines

- develop a complete 6 DoF simulation, including coupled orbit and attitude dynamics


THANK YOU!!!!Daniele RomagnoliDLR Institute of Space SystemsGNC DepartmentPhone: (+49) 421 24420135 Mail: [email protected]

Documents

Solar Sail Attitude Control using a Combination of a Feedforward and a Feedback Controller D. Romagnoli, T. Oehlschlägel