On the Problem of Jitter in Spacecraft

Richard W. LongmanColumbia University, New York City, USA

Edwin S. AhnAir Force Research Laboratory, Albuquerque, NM

Columbia is and Important University

First Spiderman movie starts on campus.

Spider gets loose in lab and bites him.

If scientist more careful – no Spiderman movies

Columbia Continues to be important (Filming latest Spiderman movie 4/5/2011 outside my bedroom window)

Spacecraft Often Have Requirements for High Pointing Accuracy

Design spec:

Maintain pointing accuracy to 5 milli arc seconds !

The Jitter Problem in Spacecraft Attitude control system actuators

Reaction Wheels Control Moment Gyros (CMG’s) Momentum Wheel

Cryo pump Disturb fine pointing equipment

Slight imbalance produces vibrations With periods that can be known

Various control methods make use of knowledge of a periodic disturbance to learn to cancel – e.g. Repetitive Control

There are other examples of systems with periodic disturbances

Jefferson National Accelerator Facility

Computer Disk Drives

Xerox Copy Machines

Examples of Periodic Disturbance Problems Jefferson National

Accelerator Facility, 8 Giga Electron Volt continuous beam accelerator – eliminate 60 Hz and harmonics from beam position

Examples (cont.) Computer disk storage Improved track following allows closer tracks

and more storage

Example: Constant Velocity Timing Belt Drive at Xerox

Velocity error frequency content before

Velocity error frequency content after (too good)

Another Application: Laser Communication Relay Satellite

Laser Communication Relay (LCR) Laser Communication (LaserCom) VS Radio

Frequency (RF) Communication 1) RF Communication:

High power is required for sending signal: Mars Reconnaissance Orbiter (MRO) requires 100 W for transmitting about 6 Mbps

Small accuracy required in pointing 2) LaserCom:

Less power required (< 1W) within space Data transmission rate up to 100 Mbps for HD video Large accuracy required in pointing

Challenge in LCR

Precision pointing is required for interplanetary laser communication link

Acquisition, Tracking, and Pointing (ATP) needed

Optical jitter induced by vibration in spacecraft hinders pointing accuracy

News Alert Lunar Laser Communication Demonstration Breaks Records.

The Los Angeles Times (10/23, Hubbard) “Science Now” blog continues coverage of NASA’s groundbreaking Lunar Laser Communication Demonstration aboard the LADEE spacecraft, as it just accomplished a “record-shattering” data download rate of 622 megabits per second.

In 2017, the Laser Communications Relay Demonstration “is going

to test the ability to relay data from one ground station at White Sands NM to another at NASA JPL through a laser communications terminal in geostationary orbit.”

The International Business Times (10/24, Poladian) reports the ISS

will also test its own laser communication system with the Optical Payload for Lasercomm Science (OPALS), which will send “video data” to the Jet Propulsion Laboratory.

Hardware Setup – Spacecraft #1

Three-axis simulator (TAS2) testebed:

Representing spacecraft #1

Mars orbiter

Optical setup on spacecraft platform TAS2 testbed

Hardware Setup Hardware representation

of Mars communication

tower and Earth orbiter –

Spacecraft #2

Communication tower:Generates main transmitting beam

Spacecraft #2:1)Records target error2)Transmits laser beacon beam Source and Target

Located 29 ft from TAS2

Hardware Setup

Communication link Star TrackerCamera

PSD

FSM

CMG

CMG

SOURCE

TARGETPSD

WIRELESSROUTER

LCD SCREENWITH STAR

IMAGE

Laser communication link setup

Optical Jitter Characteristics

Measuring error from the center of the onboard PSD: Voltage output readings

Primary peak within frequency spectrum (35.5 Hz) is correlated to rotor speed of CMG

Optical Jitter Characteristics

Modal surveying analysis

Identified structural modes are compared (Top plot) with averaged DFT magnitude data (Bottom plot) in order to identify reoccurring modes within optical jitter

Optical Scheme for Jitter Correction

Source path jitter correction loop (3-12) corrects jitter within beam at 13

Jitter Control Algorithms

Multiple-Period Repetitive Control (MPRC)

Repetitive Control (RC)

: A control method that utilizes past data history specifically for periodic signals.

Ex: Tracking periodic reference or rejecting periodic disturbances

( ) (( ) ) (( 1) )u kT u k p T e k p T

Jitter Control Algorithms Multiple-Period Repetitive Control (MPRC)

( )( )

( )j

j jj p

j

H zR z

z H z

: Repetitive controller for addressing period jp

2 2 21 2

0

[1 ( ) ( )][1 ( ) ( )]* ( )j j j j

Ni T i T i T i T

nj

J G e F e G e F e V a a a

1 2 0 ( 1) ( )1 2 1( ) m m n m n m

m n nF z a z a z a z a z a z : FIR filter RC compensator

H (z) akzk

k n

n

: FIR zero-phase low-pass filter JH [1 H (ei jT )]j0

jp

[1 H (ei jT )]* [H (ei jT )][H (ei jT )]*jjs

N 1

modelˆ ( ) ( ) ( )G z F z G z

( )G z : Plant: Model of plant multiplied by RC compensator

Jitter Control Algorithms Filtered X-LMS Algorithm (XLMS) – feedback

method

Stochastic gradient approach

- Cost function: J = “mean-square-error”2

2

2 1 1 1

Independant of weights Quadratic functi

( ) [ ( )] [( ( ) ( ) ( )) ( ( ) ( ) ( ))]

[( ( )] 2 ( ) ( ) ( ) ( ) ( )

[( ( )] ( ) ( ) ( ) ( ( ) ( ) ( )) ( )( ( ) ( ) ( ))

T T T

T T

T T

J k E e k E d k k k d k k k

E d k k k k k k

E d k k k k k k k k k k k

w

w x w x

p w w R w

p R p w R p R w R p on of weights w

( ) [ ( ) ( )]k E d k kp x

( ) [ ( ) ( )]Tk E k kR x x

Cross-correlation vector:

Auto-correlation matrix:

Target Track Loop

The effectiveness of adding the target track loop

ABM (source) and XLMS (target)

Conclusions Many control systems are subject to periodic disturbances Often the period of these disturbances can be known, e.g.

base on the inputs of three phase motors Control systems can be made smarter, to make use of

knowledge of the period of the disturbance In theory, such control laws can converge to zero tracking

error A challenging application is to Laser Communication. A

series of methods are tested, evaluated Each method has its own advantages and disadvantages,

and can be preferred on some class of problems