© 2009 SPACE LAB, California State University Los Angeles Fault Detection, Isolation of a Segmented Telescope Testbed Authors: Presenter: Jose D. Covarrubias

© 2009 SPACE LAB, California State University Los Angeles

Fault Detection, Isolation of a Segmented Telescope Testbed

Authors: Presenter: Jose D. Covarrubias (Student) Dr. Helen Boussalis Christian P. Torres (Student) Dr. Helen Boussalis (Advisor)

17th MediterraneanConference on Control and Automation 2009 June 24-26 2009

• James Web Space Telescope

• The SPACE Testbed

• Fault Detection and Isolation (FDI)

• Actuator & Sensor FDI

• Results

OutlineOutline

James Webb Space Telescope

Hubble Space Telescope

James Webb Space TelescopeJames Webb Space Telescope

The SPACE TestbedThe SPACE Testbed


• Top Level Requirements

› Within 1 micron rms

figure error (primary mirror)

› 2 arc second

pointing accuracy

• Primary dish is segmented into 7 panels› 1 static center panel› 6 actively controlled panels

1

2

3

4

5

6

C


• Decentralized control and fault detection technique› Testbed is divided into smaller subsystems› Separate control laws and fault detection for each subsystem

1

2

3

4

5

6

C


1 Subsystem per active panel

Total = 6

• 3 Actuators per panel (subsystem)• 6 Position sensors

Panel

Actuator

Position Sensor


ResidualGeneration

CONTROLLER ACTUATOR PLANT SENSORReference

ResidualEvaluation

FDI

ResidualGeneration

CONTROLLER ACTUATOR PLANT SENSOR

ResidualEvaluation

Control Loop

Fault DetectionAnd IsolationSubsystem

• Purpose› Diagnose a Problem (fault) within the system

› What component failed› How did the component fail› When did the failure occur

General Block Diagram

Fault Detection and IsolationFault Detection and Isolation

Two Types of Faults Considered

• Sensor Faults Actuator Faults


General Block Diagram of an Observer Filter

System A,B,C,D

System A,B,C,D

ObserverA,B,C,D

ObserverA,B,C,D

LLU(t)

Y(t)

Ỹ (t)

+

-

Error


•Residual Generation (output estimation) › An Observer Filter Approach Is Used

›One Observer Filter for each subsystem

)()(ˆ)(ˆ

)()()()1(

tDukxCky

yyLkBukxAkx

Observer Filter Equation:

Residual Generation

Definition

• Residual, r is near 0

• Residual , r > t (Threshold)

r

time

r

time

No fault

Fault

)(ˆ)()( kykykr

)(ky

)(ˆ ky

= Output signal

= Estimated Output signal


t

• Using an observer method alone will detect an actuator/sensor fault

but will not isolate the defective component (using a single observer per

subsystem)

System

Fault

SensorActuator

Output residual

Sensor Fault

System SensorActuator

FaultOutput residual

Actuator Fault

Both output residuals increase with sensor or actuator faults

• Sensor Relationship› Mathematically relates each sensor to other sensors in the

subsystem › Error generated from sensor relationship can be used to validate

the sensor output signals

One method to isolate sensor and actuator faults is the use of a sensor relationship

Sensor 1

Sensor 2

Sensor 3

Sensor 4

Relationship

Relationship

Error

Valid Sensor Signals

At Least One Invalid sensor

Signal

• Sensor Relationship (Continued)

› Each panel can be viewed as a bounded rigid plane

› Sensor output signals must be related to the plane that is being measured

› Planer Relationship is used

› It is assumed that the panel is rigid and panel flexing is insignificant Z

Center

X

Y

• Sensor Relationship (Continued)› Individual sensor values will vary; however, as a whole the four

sensor values must reside on the calculated panel plane

› If one sensor signal is invalid (fault), this value will not reside on the calculated plane and may indicate a sensor fault

= Sensor measurement

Possible sensor fault

All sensor values reside on the plane

One sensor value not residing on the plane


› Plane equation is defined as:

› a, b, c, d are plane coefficients› x, y, z : components of position vector S

› x, y : location of measuring point of sensor on panel (with respect to center)

› z measured value (sensor output value)

0 dczbyax

Z

Center

X

Y

z

y

x

S

= Sensor measurement

• Sensor Relationship (Continued)› Plane coefficients, a,b,c,d, can be determined using three sensor

values:

And the following equations

33

22

11

1

1

1

zy

zy

zy

a

33

22

11

1

1

1

zx

zx

zx

b 1

1

1

33

22

11

yx

yx

yx

c

333

222

111

zyx

zyx

zyx

d

1

1

1

1

z

y

x

S

2

2

2

2

z

y

x

S

3

3

3

3

z

y

x

S

• Sensor Relationship (Continued)› Once the coefficients a, b, c, d are determined, the 4th sensor

position value is tested to verify that it resides on the plane calculated by S1, S2, S3

› If right side of the equation is appox. 0 then 4th sensor value resides on the calculated plane, indicating valid signals for all 4 sensors

› If right side of the equation in not appox. 0 then 4th sensor value does not reside on calculated plane, indicating at least one sensor failure on the panel

4

4

4

4

z

y

x

S

0444 dczbyax


› Two scenarios will cause the plane equation to be non-zero› Scenario 1

› 3 sensors used to calculated the plane coefficients are valid› Calculated plane is correct

› 4th sensor used for testing is invalid

S4

S3

S2S1

Scenario 1

S1, S2, S3- Valid S4-Invalid

- Sensor measurement


› Scenario 2› 1 of 3 sensors used to calculate the plane coefficients is

invalid› Calculated plane is not correct

› 4th sensor used for testing is valid

S 4

S 3

S 2S 1

Scenario 2

Actual Plane

S1, S2, S4- ValidS3-Invalid

Calculated

Plane

- Sensor measurement

Sensor Relationship Method Overview

Input Output

Sensor

Residuals

Transform

Actuator

Residuals

Sensor

Fault

SensorRelationship

Observer

Testbed

• Sensor Relationship In Not Satisfied

Sensor Relation Error Is Non-Zero

Sensor

Relationship

Error

Sensor 2 Fault

Sensor Relationship Method Overview

Sensor

Residuals

Actuator

Residuals

Transform

Actuator

Fault

•Sensor Relationship Is Satisfied

Sensor Relation Error = 0

Sensor

Relationship

Error

Input Output

SensorRelationship

Observer

Testbed

Actuator 2 Fault

Implementation Results

• The actuator and sensor fault detection and isolation method (ASFDI) was

applied to panel 3 (subsystem 3) in an open loop control test.

• Actuator and sensor faults were simulated by physically disconnecting them

from the testbed while running the ASFDI program.

Output

SensorRelationship

Observer

Testbed

Input

• Sensor 16 Fault

› Absolute value of sensor 16

residual (black) is greater than

other sensor residuals

› Sensor relationship error is > 0

(Indicates sensor outputs

are NOT valid)

› Absolute values of actuator

residuals are > 0

› Using sensor relationship › Sensor 16 Fault Can Be Isolated


• Actuator 9 Fault

› Sensor residuals > 0

› Sensor relationship error is near 0

(Indicates sensor outputs ARE valid)

› Absolute value of actuator 9

residual (red) is greater than

the other actuator residuals

› Using sensor relationship › Actuator 9 Fault Can Be Isolated


Documents

© 2009 SPACE LAB, California State University Los Angeles Fault Detection, Isolation of a Segmented Telescope Testbed Authors: Presenter: Jose D. Covarrubias