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Control Team Welcome Dr. Spanos

S P A C E Structures, Propulsion, And Control Engineering C e n t e r. Control Team Welcome Dr. Spanos. Student Assistants Jessica Alvarenga Allison Bretaña. Faculty Advisors Dr. Helen Boussalis Dr. Charles Liu. State Estimation Methods: Observer and Kalman Filter.

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Control Team Welcome Dr. Spanos

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  1. S P A C E Structures, Propulsion, And Control Engineering C e n t e r Control TeamWelcome Dr. Spanos Student Assistants Jessica Alvarenga Allison Bretaña Faculty Advisors Dr. HelenBoussalis Dr. Charles Liu NASA Grant URC NCC NNX08BA44A

  2. State Estimation Methods:Observer and Kalman Filter NASA Grant URC NCC NNX08BA44A

  3. Outline • Objective • Project Background and Luenberger Observer • Kalman Filter • Single Panel Simulations • Noise Modeling • Future goals • Timeline • References NASA Grant URC NCC NNX08BA44A

  4. Fault Detection • Component Failures cannot be allowed to cause a total malfunction • Used to achieve a fault tolerant reconfigurable controller NASA Grant URC NCC NNX08BA44A

  5. Outline • Objective • Project Background and Luenberger Observer • Kalman Filter • Single Panel Simulation • Noise Modeling • Future goals • Timeline • References NASA Grant URC NCC NNX08BA44A

  6. Fault Detection and Isolation NASA Grant URC NCC NNX08BA44A

  7. Fault Detection and Isolation NASA Grant URC NCC NNX08BA44A

  8. State Observer Discrete System Model Observer Design Residual Error Dynamic State Error NASA Grant URC NCC NNX08BA44A

  9. State Observer Dynamic Error Equation PD Gains State Feedback (L) NASA Grant URC NCC NNX08BA44A

  10. State Observer Simulink Observer Realization NASA Grant URC NCC NNX08BA44A

  11. State Observer Simulink Simulation Results NASA Grant URC NCC NNX08BA44A

  12. State Observer Residual Error Initatied Actuator Fault Observer Simulated Output Observer Discrepencies Real System Output NASA Grant URC NCC NNX08BA44A

  13. Outline • Objective • Project Background and Luenberg Observer • Kalman Filter • Single Panel Simulation • Noise Modeling • Future goals • Timeline • References NASA Grant URC NCC NNX08BA44A

  14. Kalman Filter Methodology • Two Phases: • Predictions • Previous Estimate Current Estimate • Update • Current Measurement  Refines Current State estimate • “A numerical method used to track a time-varying signal in the presence of noise.”[1] • A method of estimating the internal states of a system Prediction Update [1] http://www.nps.gov/gis/gps/glossary.htm NASA Grant URC NCC NNX08BA44A

  15. Kalman Equations System State Equations A Priori Equations Noise Distributions A Posteriori Equations Noise Variances Kalman Gain Equation NASA Grant URC NCC NNX08BA44A

  16. + + ∑ ∑ + + + Delay Kalman Filter Realization + ∑ ∑ + - + Delay NASA Grant URC NCC NNX08BA44A

  17. Outline • Objective • Project Background and Luenberg Observer • Kalman Filter • Single Panel Simulations • Noise Modeling • Future goals • Timeline • References NASA Grant URC NCC NNX08BA44A

  18. Single Panel Model NASA Grant URC NCC NNX08BA44A

  19. Single Panel Model NASA Grant URC NCC NNX08BA44A

  20. Single Panel Kalman Filter NASA Grant URC NCC NNX08BA44A

  21. Single Panel Kalman Gain NASA Grant URC NCC NNX08BA44A

  22. No Noise, No Fault System Simulation Edge Sensor Estimates KF Edge Sensor Residuals KF Edge Sensor Estimates Magnified View of KF Edge Sensor Residuals NASA Grant URC NCC NNX08BA44A

  23. No Noise, Additive Sensor Fault System Simulation Edge Sensor Estimates KF Edge Sensor Residuals KF Edge Sensor Estimates NASA Grant URC NCC NNX08BA44A

  24. Simulated Noise and Additive Sensor Fault System Simulation Edge Sensor Estimates KF Edge Sensor Residuals KF Edge Sensor Estimates NASA Grant URC NCC NNX08BA44A

  25. Issues with Simulation • Long run times (10 sec took ~10 minutes) • Faulty residuals • Difficult to tune noise NASA Grant URC NCC NNX08BA44A

  26. Solution • Develop a new and efficient simulation code • Create accurate process and measurement noise models • Simulation of an open-loop system NASA Grant URC NCC NNX08BA44A

  27. Outline • Objective • Project Background and Luenberg Observer • Kalman Filter • Single Panel Simulation • Noise Modeling • Future goals • Timeline • References NASA Grant URC NCC NNX08BA44A

  28. Noise Scenarios • Case 1: Assume no process noise • All noise attributed to sensors • Case 2: Assume no sensors noise • All noise attributed to process • Case 3: Combination of process and sensor noise (Real Scenario) 28

  29. Case 1: No process noise w=0, v~N(0,R) Sensor noise is attributed to the measurements. NASA Grant URC NCC NNX08BA44A

  30. DIRECTMeasurement Noise NASA Grant URC NCC NNX08BA44A

  31. Edge Sensor Data (System at rest) 31

  32. Single Panel Edge Sensor Data (System at rest) 32

  33. Case 2: No Sensor Noise w~N(0,Q), v=0 Sensor noise is attributed to noise in the process. Are not directly observing states. NASA Grant URC NCC NNX08BA44A

  34. Inversion of State Space A: n x n B: n x m C: p x n However, C may not be square, as in our case, and is not invertible. NASA Grant URC NCC NNX08BA44A

  35. Moore-Penrose Pseudo Inverse • Use the Moore-Penrose Pseudo Inverse to invert the state space model and allow us to make process noise calculations using sensor measurements. NASA Grant URC NCC NNX08BA44A

  36. Noise Modeling • Use mathematical equation to determine process noise where • Calculate mean, standard deviation and variance of process noise using MATLAB 36

  37. Simulation focuses on Panel 1 • Apply the calculated variance to Gaussian White noise in simulation 37

  38. Simulated Noise 38

  39. Outline • Objective • Project Background and Luenberg Observer • Kalman Filter • Implementation into a SISO System • Initial simulations • Noise Modeling • Future goals • Timeline • References NASA Grant URC NCC NNX08BA44A

  40. Future Goals • Improve the noise model for the homogenous case • Noise analysis for non-homogenous cases • Step input • Impulse • Chirp • Sinusoid • Develop algorithm for Testbed implementation NASA Grant URC NCC NNX08BA44A

  41. Outline • Objective • Project Background and Luenberg Observer • Kalman Filter • Implementation into a SISO System • Initial simulations • Noise Modeling • Future goals • Timeline • References NASA Grant URC NCC NNX08BA44A

  42. Timeline NASA Grant URC NCC NNX08BA44A

  43. Timeline NASA Grant URC NCC NNX08BA44A

  44. Timeline NASA Grant URC NCC NNX08BA44A

  45. Outline • Objective • Project Background • Lyapunov Observer • Kalman Filter • Implementation into a SISO System • Initial simulations • Noise Modeling • Future goals • Timeline • References NASA Grant URC NCC NNX08BA44A

  46. References Andrews, A. and Grewal, M. (2001). Kalman Filtering: theory and practice using MATLAB. New York, NY: John Wiley and Sons Inc. Boussalis, H., “Stability of Large Scale Systems”, New Mexico, USA, November, 1979. Boussalis, H., Guillaume, D., Wu, C., Liu, C. (2009). Space URC Annual Report. NASA, 139. Boussalis, H., Mirmirani, M., Chassiako, A., Rad, K., “The Use of Decentralized Control in Design of a Large Segmented Space Reflector”, Control and Structures Research Laboratory, California. Cao, Yi (February 5, 2010 information retrieved). MATLAB Central. http://www.mathworks.com/matlabcentral/fileexchange/18465 Clark, B., Larson, E., Parker,E. Model-Based Sensor and Actuator Fault Detection and Isolation. NASA Langley Research Center,5. Greg, W. & Bishop, G. (2006). An Introduction to the Kalman Filter. University of North Carolina at Chapel Hill, NC 27599-3175. NASA. (November 30, 2009 revision). James Webb Space Telescope. Retrieved from www.jswt.nasa.gov/ Simon, D. (2001). Kalman Filtering. Embedded Systems Programming, 73-79.  Simon, D. (2006). Optimal State Estimation: Kalman, H Infinity and Nonlinear Approaches. Hoboken, NJ. John Wiley and Sons Inc. NASA Grant URC NCC NNX08BA44A

  47. Questions? Thank You NASA Grant URC NCC NNX08BA44A

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