1. © 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 Mediterranean Conference on Control and Automation 2009 June 24-26 2009

2. James Web Space Telescope The SPACE Testbed Fault Detection and Isolation (FDI) Actuator & Sensor FDI Results Outline

3. James Webb Space Telescope Hubble Space Telescope James Webb Space Telescope

4. The SPACE Testbed

5. Top Level Requirements › Within 1 micron rms figure error (primary mirror) › 2 arc second pointing accuracy

6. Primary dish is segmented into 7 panels › 1 static center panel › 6 actively controlled panels 1 2 3 4 5 6 C The SPACE Testbed

7. 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 Testbed 1 Subsystem per active panel Total = 6

8. 3 Actuators per panel (subsystem) 6 Position sensors Panel Actuator Position Sensor The SPACE Testbed

9. Residual Generation CONTROLLER ACTUATOR PLANT SENSOR Reference Residual Evaluation FDI Residual Generation CONTROLLER ACTUATOR PLANT SENSOR Residual Evaluation Control Loop Fault Detection And Isolation Subsystem 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 Isolation

10. Two Types of Faults Considered Sensor Faults Actuator Faults Fault Detection and Isolation

11. General Block Diagram of an Observer Filter System A,B,C,D System A,B,C,D Observer A,B,C,D Observer A,B,C,D L L U(t) Y(t) Ỹ (t) + - Error Fault Detection and Isolation Residual Generation (output estimation) › An Observer Filter Approach Is Used › One Observer Filter for each subsystem Observer Filter Equation :

12. Residual Generation Definition Residual, r is near 0 Residual, r > t (Threshold) r time r No fault Fault = Output signal = Estimated Output signal Fault Detection and Isolation t

13. 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 Sensor Actuator Output residual Sensor Fault System Sensor Actuator Fault Output residual Actuator Fault Both output residuals increase with sensor or actuator faults

14. 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 Error Valid Sensor Signals At Least One Invalid sensor Signal

15. 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

16. 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

17. 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) Z Center X Y = Sensor measurement

18. Sensor Relationship (Continued) › Plane coefficients, a,b,c,d, can be determined using three sensor values: And the following equations

19. Sensor Relationship (Continued) › Once the coefficients a, b, c, d are determined, the 4 th 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 4 th 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 4 th sensor value does not reside on calculated plane, indicating at least one sensor failure on the panel

20. 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 › 4 th sensor used for testing is invalid S4 S3 S2 S1 Scenario 1 S1, S2, S3- Valid S4-Invalid - Sensor measurement

21. Sensor Relationship (Continued) › Scenario 2 › 1 of 3 sensors used to calculate the plane coefficients is invalid › Calculated plane is not correct › 4 th sensor used for testing is valid S 4 S 3 S 2 S 1 Scenario 2 Actual Plane S1, S2, S4- Valid S3-Invalid Calculated Plane - Sensor measurement

22. Sensor Relationship Method Overview Input Output Sensor Residuals Transform Actuator Residuals Sensor Fault Sensor Relationship Observer Testbed Sensor Relationship In Not Satisfied  Sensor Relation Error Is Non-Zero Sensor Relationship Error Sensor 2 Fault

23. Sensor Relationship Method Overview Sensor Residuals Actuator Residuals Transform Actuator Fault Sensor Relationship Is Satisfied  Sensor Relation Error = 0 Sensor Relationship Error Input Output Sensor Relationship Observer Testbed Actuator 2 Fault

24. 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 Sensor Relationship Observer Testbed Input

25. 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

26. 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