Post on 21-Jan-2016
© 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
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
The SPACE TestbedThe SPACE Testbed
• 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
The SPACE TestbedThe SPACE Testbed
1 Subsystem per active panel
Total = 6
• 3 Actuators per panel (subsystem)• 6 Position sensors
Panel
Actuator
Position Sensor
The SPACE TestbedThe SPACE Testbed
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
Fault Detection and IsolationFault Detection and Isolation
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
Fault Detection and IsolationFault Detection and Isolation
•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
Fault Detection and IsolationFault Detection and Isolation
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
• Sensor Relationship (Continued)
› 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
• Sensor Relationship (Continued)
› 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
• Sensor Relationship (Continued)
› 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
Implementation Results
• 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
Implementation Results