1. Control Team Welcome Dr. Spanos Faculty Advisors Dr. Helen Boussalis Dr. Charles Liu Student Assistants Jessica Alvarenga Allison Bretaña 6/27/2015NASA Grant URC NCC NNX08BA44A1

2. State Estimation Methods: Observer and Kalman Filter 6/27/20152NASA Grant URC NCC NNX08BA44A

3. Outline Objective Project Background and Luenberger Observer Kalman Filter Single Panel Simulations Noise Modeling Future goals Timeline References 6/27/2015NASA Grant URC NCC NNX08BA44A3

4. Fault Detection Component Failures cannot be allowed to cause a total malfunction Used to achieve a fault tolerant reconfigurable controller 6/27/2015NASA Grant URC NCC NNX08BA44A4

5. Outline Objective Project Background and Luenberger Observer Kalman Filter Single Panel Simulation Noise Modeling Future goals Timeline References 6/27/2015NASA Grant URC NCC NNX08BA44A5

6. Fault Detection and Isolation 6/27/2015NASA Grant URC NCC NNX08BA44A6

7. Fault Detection and Isolation 6/27/2015NASA Grant URC NCC NNX08BA44A7

8. State Observer Discrete System Model Observer Design 6/27/20158NASA Grant URC NCC NNX08BA44A Residual Error Dynamic State Error

9. State Observer Dynamic Error Equation PD Gains State Feedback (L) 6/27/20159NASA Grant URC NCC NNX08BA44A

10. State Observer 6/27/2015NASA Grant URC NCC NNX08BA44A10 Simulink Observer Realization

11. State Observer 6/27/2015NASA Grant URC NCC NNX08BA44A11 Simulink Simulation Results

12. State Observer 6/27/201512NASA Grant URC NCC NNX08BA44A Residual Error Observer Simulated Output Real System Output Initatied Actuator Fault Observer Discrepencies

13. Outline Objective Project Background and Luenberg Observer Kalman Filter Single Panel Simulation Noise Modeling Future goals Timeline References 6/27/2015NASA Grant URC NCC NNX08BA44A13

14. Kalman Filter Methodology –Two Phases: –Predictions Previous Estimate  Current Estimate –Update Current Measurement  Refines Current State estimate PredictionPrediction UpdateUpdate 6/27/2015NASA Grant URC NCC NNX08BA44A14 [1] http://www.nps.gov/gis/gps/glossary.htm –“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

15. Kalman Equations 6/27/2015NASA Grant URC NCC NNX08BA44A15 System State Equations Noise Distributions Noise Variances A Priori Equations A Posteriori Equations Kalman Gain Equation

16. ∑ ∑ ∑ ∑ Delay + - + + ∑ ∑ ∑ ∑ + + + + + Kalman Filter Realization 6/27/2015NASA Grant URC NCC NNX08BA44A16

17. Outline Objective Project Background and Luenberg Observer Kalman Filter Single Panel Simulations Noise Modeling Future goals Timeline References 6/27/2015NASA Grant URC NCC NNX08BA44A17

18. Single Panel Model 6/27/201518NASA Grant URC NCC NNX08BA44A

19. Single Panel Model 6/27/201519NASA Grant URC NCC NNX08BA44A

20. Single Panel Kalman Filter 6/27/201520NASA Grant URC NCC NNX08BA44A

21. Single Panel Kalman Gain 6/27/201521NASA Grant URC NCC NNX08BA44A

22. No Noise, No Fault 6/27/2015NASA Grant URC NCC NNX08BA44A22 System Simulation Edge Sensor Estimates KF Edge Sensor Estimates KF Edge Sensor Residuals Magnified View of KF Edge Sensor Residuals

23. No Noise, Additive Sensor Fault 6/27/2015NASA Grant URC NCC NNX08BA44A23 System Simulation Edge Sensor Estimates KF Edge Sensor Estimates KF Edge Sensor Residuals

24. Simulated Noise and Additive Sensor Fault 6/27/2015NASA Grant URC NCC NNX08BA44A24 System Simulation Edge Sensor Estimates KF Edge Sensor Estimates KF Edge Sensor Residuals

25. Issues with Simulation Long run times (10 sec took ~10 minutes) Faulty residuals Difficult to tune noise 6/27/2015NASA Grant URC NCC NNX08BA44A25

26. Solution Develop a new and efficient simulation code Create accurate process and measurement noise models Simulation of an open-loop system 6/27/2015NASA Grant URC NCC NNX08BA44A26

27. Outline Objective Project Background and Luenberg Observer Kalman Filter Single Panel Simulation Noise Modeling Future goals Timeline References 6/27/2015NASA Grant URC NCC NNX08BA44A27

28. 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) 2/18/2010NASA Grant URC NCC NNX08BA44A28 Noise Scenarios

29. Case 1: No process noise 6/27/2015NASA Grant URC NCC NNX08BA44A29 w=0, v~N(0,R) Sensor noise is attributed to the measurements.

30. DIRECT Measurement Noise 6/27/201530 NASA Grant URC NCC NNX08BA44A

31. Edge Sensor Data (System at rest) 6/27/2015 NASA Grant URC NCC NNX08BA44A 31

32. Single Panel Edge Sensor Data (System at rest) 6/27/2015NASA Grant URC NCC NNX08BA44A32

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. 6/27/2015NASA Grant URC NCC NNX08BA44A33

34. Inversion of State Space A: n x nB: n x mC: p x n However, C may not be square, as in our case, and is not invertible. 6/27/2015NASA Grant URC NCC NNX08BA44A34

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. 6/27/2015NASA Grant URC NCC NNX08BA44A35

36. Use mathematical equation to determine process noise where Calculate mean, standard deviation and variance of process noise using MATLAB 2/18/2010NASA Grant URC NCC NNX08BA44A36 Noise Modeling

37. 2/18/2010NASA Grant URC NCC NNX08BA44A37 PANEL 1PANEL 2PANEL 3PANEL 4PANEL 5PANEL 6 STATEmeanstd. dev.variancemeanstd. dev.variancemeanstd. dev.variancemeanstd. dev.variancemeanstd. dev.variancemeanstd. dev.variance 1-6.163380.1516010.0229837.5496820.0947990.008987-0.506930.5412830.2929883.4421270.7636610.5831791.6134330.8456810.715177-1.667580.3064420.093907 2-0.027560.1315740.017312-1.233160.0601060.003613-1.293160.7894760.62327310.809160.6394890.4089476.0872630.6501410.4226842.3133671.2909441.666536 3-6.562020.3459140.1196574.7366390.1211530.0146783.1385320.5404690.2921071.7977970.3535350.1249872.3942281.019841.040073-1.254420.3101490.096192 4-4.609670.0876440.0076823.25910.0806880.0065111.3164030.0655770.00433.966950.1065950.0113622.086680.2151910.0463071.430540.4387640.192514 514.104293.0753659.45787113.380730.8249950.680617-32.9060.6836760.46741314.573792.7410447.513324-3.373812.5411546.457463-7.316381.7926573.21362 6-1.019440.9478980.8985119.3608590.2508730.062937-7.399440.8064680.650391-1.147791.5168442.300817-3.830950.6627590.439249-4.074331.2407671.539503 76.7328070.6826670.466034-0.906680.1879410.035322-8.552270.6104930.3727026.0713190.3064030.0938830.8668751.148481.319007-0.563790.58880.346686 8-31.44234.46480519.934481.0217531.2268681.50520633.655481.3191231.74008720.057312.2361045.00016128.000574.67001821.809071.5909313.43074111.76998 95.0572151.4929332.228856.7636590.3976790.158149-14.23270.3765540.1417936.6443271.2188531.485602-1.990291.2393441.535973-1.916050.7692430.591734 10-4.882850.9428250.888919-6.334530.2675850.07160210.816440.8293860.687882.6516261.5215322.3150584.5316530.5296140.2804916.8561231.6506372.724603 11-9.03530.6582590.4333057.205330.2622580.0687799.541121.8432493.397568-29.28561.7464273.050008-17.96831.6861152.8429851.0183852.6924637.249355 12-3.937290.9558420.913635-2.018740.2638140.0695983.484220.7797930.60807715.700211.068111.14085812.036150.3864680.1493571.7371631.8138733.290134 13-5.042781.2510151.56503911.923450.3619350.130997-8.277340.2966920.08802610.173561.2200091.4884220.6791030.7244120.5247731.2629260.6847810.468925 1413.170720.7503680.563052-5.278780.3230970.104391-2.89951.5689242.461523-33.43331.3684291.872599-20.26290.5550230.308051-7.149733.73723313.96691 15-32.16952.6464287.003581-0.139420.910320.82868225.350873.52685912.4387351.917974.14931617.2168236.174151.2569821.58000523.825748.26515668.3128 16-0.494360.7109940.505513-6.876840.1833270.0336098.6638780.2110370.044536-7.687651.0145741.029359-1.804460.4465350.1993933.2072530.424870.180515 17-1.366160.8207840.6736875.4656060.2307780.053258-3.240150.3622250.131207-3.678760.8311270.690772-5.145770.347530.1207770.3347650.6747790.455327 181.2592030.4930480.2430965.7844510.1437530.020665-10.53910.4172550.17410217.603790.8522020.7262497.9602390.627660.393957-2.945120.836180.699197 19-41.94642.1379264.57072724.38150.7774690.60445823.293071.9696313.87944817.174680.9473470.89746617.274594.91328724.140391.4197391.9932573.973072 2020.561581.3399861.795562-6.741630.4534230.205592-28.95813.74830914.0498249.383332.3019655.29904421.757454.763222.688072.1832854.65700321.68767 21-43.8432.2994615.28752161.16730.8717580.759962-6.38877.94112463.0614529.761937.60839857.8877328.4437511.83002139.9495-45.2266.18039438.19727 22-13.98880.8830450.7797693.866850.2945090.08673617.336331.6114912.596903-20.79481.0230121.046554-8.177252.3998215.759141.4266671.7561773.084156 2311.834781.8482393.4159897.6522120.506360.256401-23.95670.4266120.18199813.360271.8256113.3328540.7741121.6471242.713019-7.297331.1910571.418616 244.6931661.2623021.5934051.1441950.3511070.123276-3.047650.7132180.50868-20.01071.1347231.287596-15.74160.6724050.4521290.4708091.9095013.646193 2513.566460.9230290.851983-12.33270.4100510.168142-18.66244.63047521.441367.340643.80093614.4471138.49764.28038218.321675.0512076.91209647.77707 2656.905232.2520875.071897-21.88181.7193632.956211-12.36919.89666497.94397-118.8945.99190135.90288-53.1157.57116457.32252-66.018518.37947337.805 2720.352181.9178483.678142-7.473780.9732090.9471353.3046516.51597642.45794-70.18213.61162813.04386-28.24586.10096937.22182-37.652610.72388115.0016 28-7.452110.5560380.3091787.1123120.1798280.0323381.9284920.975470.9515424.3528160.7112350.5058564.9244431.6667092.777919-4.85560.6048230.36581 2912.435570.6007640.360917-11.61930.3090960.0955412.2832720.9250690.855753-22.95290.5748170.330415-9.867320.607870.369506-6.402422.3417025.48357 30-2.483962.523866.36987114.548490.7187920.516662-16.24461.2072371.45742216.304631.4633582.141416-1.32732.2829255.2117466.0441861.7183712.952798 3134.713091.1183921.250801-23.47680.8415220.70816-1.824153.43907611.82725-63.89231.6702492.78973-29.87421.9595693.83991-23.74847.78584760.61941 32-8.953410.4521410.20443218.763590.3665650.134375.4347455.87293434.49135-46.02024.61604221.30784-21.55356.21760738.65864-24.19517.93990263.04204 33-11.13081.9160753.671345-6.888490.5368430.288215.594391.5197652.30968718.108642.4783546.14223816.394690.8302820.6893699.2563283.49976512.24835 34-18.03030.3959190.1567529.5218290.3382340.1144028.6737570.4505290.20297611.926810.3040030.0924186.4271310.5463040.2984488.488871.9770683.908798 35-20.30662.3019245.298854-12.64360.6896150.47556944.353041.0406921.083039-44.96213.077839.473035-17.2162.6309956.92213716.454271.8350323.367342 3626.170343.82372514.62088-10.79611.0695261.143886-13.81371.4416272.078288-45.34061.5833232.506911-40.01764.52570620.482018.8176623.28077710.7635 37-3.33612.7405917.5108384.1009920.8688990.75498610.024664.83657923.39249-25.95822.277575.187325-1.449016.26467239.24611-27.22055.96134635.53765 38-48.16254.84836123.5066132.898021.4312492.04847542.338659.9142398.29195-50.03195.23849527.44183-5.3228314.17606200.9606-35.079710.08864101.7807 390.4690427.72210459.63089-36.59772.1369764.56666746.821793.50814412.30707-32.11434.08148916.6585513.73467.14894851.10745-18.44374.44582319.76534 40150.44213.42057911.70036-140.1672.9225798.54146920.501186.51970542.50655-280.5867.92367462.78462-144.0595.82204533.89621-36.595323.46778550.7366 412.6195081.548212.3969547.6124110.5595610.313109-12.88491.5837652.50831227.656881.8081883.26954322.265162.6486027.015094-21.16541.2189671.485881 42-18.6033.57637212.79044-11.59220.9654380.93207130.4611.3168251.73402713.556853.49487912.2141820.225112.1184914.48800510.186643.98024315.84233 4334.422115.02156225.6471224.12884.46293819.91781-269.08720.4383417.7242157.900638.988441520.09846.1911820.35599414.3663-201.51327.7892772.2396 4447.488993.65056113.32665.8474821.2761711.628612-55.15932.9203378.528368-15.30515.33426328.45436-18.31241.9403343.764896-37.68127.86697761.88932 45-59.75542.6741217.15092133.571741.5315252.345567-9.029219.90613698.13152209.767.77867460.50777119.34934.94283124.4315835.6177421.68449470.2172 464.2865488.01547764.2478717.511572.4489815.997507-64.604813.96711195.0801153.36455.45332229.7387247.6703217.01947289.662357.7827819.53231381.5113 4733.252648.76965976.90692-100.742.5006666.25333169.406794.16141917.31741-52.090112.48055155.76413.5302025.27918927.8698419.031355.0758625.76436 48-83.72872.3173895.3702919.499812.3458785.50314528.3343315.5565242.0048187.928611.05429122.197493.2088511.03403121.749898.792429.1192847.9278 PANEL 1 STATEmeanstd. dev.variance 1-6.163380.1516010.022983 2-0.027560.1315740.017312 3-6.562020.3459140.119657 4-4.609670.0876440.007682 514.104293.0753659.457871 6-1.019440.9478980.898511 76.7328070.6826670.466034 8-31.44234.46480519.93448 95.0572151.4929332.22885 10-4.882850.9428250.888919 11-9.03530.6582590.433305 12-3.937290.9558420.913635 13-5.042781.2510151.565039 1413.170720.7503680.563052 15-32.16952.6464287.003581 16-0.494360.7109940.505513 17-1.366160.8207840.673687 181.2592030.4930480.243096 19-41.94642.1379264.570727 2020.561581.3399861.795562 21-43.8432.2994615.287521 22-13.98880.8830450.779769 2311.834781.8482393.415989 244.6931661.2623021.593405 2513.566460.9230290.851983 2656.905232.2520875.071897 2720.352181.9178483.678142 28-7.452110.5560380.309178 2912.435570.6007640.360917 30-2.483962.523866.369871 3134.713091.1183921.250801 32-8.953410.4521410.204432 33-11.13081.9160753.671345 34-18.03030.3959190.156752 35-20.30662.3019245.298854 3626.170343.82372514.62088 37-3.33612.7405917.510838 38-48.16254.84836123.50661 390.4690427.72210459.63089 40150.44213.42057911.70036 412.6195081.548212.396954 42-18.6033.57637212.79044 4334.422115.02156225.6471 4447.488993.65056113.3266 45-59.75542.6741217.150921 464.2865488.01547764.24787 4733.252648.76965976.90692 48-83.72872.3173895.37029 Simulation focuses on Panel 1 Apply the calculated variance to Gaussian White noise in simulation

38. 2/18/2010 NASA Grant URC NCC NNX08BA44A 38 Simulated Noise

39. Case 3: Combination (Reality) w~N(0, αQ) v~N(0, ßR) Noise is a combination of both process and measurement disturbances. 6/27/2015NASA Grant URC NCC NNX08BA44A39

40. Outline Objective Project Background and Luenberg Observer Kalman Filter Implementation into a SISO System Initial simulations Noise Modeling Future goals Timeline References 6/27/2015NASA Grant URC NCC NNX08BA44A40

41. 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 6/27/2015NASA Grant URC NCC NNX08BA44A41

42. Outline Objective Project Background and Luenberg Observer Kalman Filter Implementation into a SISO System Initial simulations Noise Modeling Future goals Timeline References 6/27/2015NASA Grant URC NCC NNX08BA44A42

43. Timeline 6/27/2015NASA Grant URC NCC NNX08BA44A43 2009­MAR APRMAYJUN JUL Jessica Alvarenga Introduction to SPACE Laboratory and Testbed Kalman Filter Familiarization and Paper Surveying. DOCUMENTATIONDOCUMENTATION Learn Matlab, LabVIEW and C Chris Torres Observer

44. Timeline 6/27/2015NASA Grant URC NCC NNX08BA44A44 2009­AUG SEPOCTNOV DEC Jessica Alvarenga Kalman Filter Simulation in Matlab. Initial Simulation of Testbed Noise Finalize Matlab Simulation. DOCUMENTATIONDOCUMENTATION NSF GK-12 IMPACT LA Allison Bretaña Introduction to Testbed Initial Training Chris Torres Kalman Filter Design Testbed Noise AnalysisKalman Filter Simulation

45. Timeline 6/27/2015NASA Grant URC NCC NNX08BA44A45 ­ DECJANFEBMARAPRMAYJUNJUL Jessica Alvarenga Noise Modeling and Investigation of Plant Model Coding Implementation of KF in C code DOCUMENTATIONDOCUMENTATION NSF GK-12 IMPACT LA Allison Bretaña Familiarization with TestbedSimulink Modeling of KF FDI Schema Integration of sensor noise statistics into KF FDI Schema Initial training periodSensor Noise ModelingIntegration of Noise Model into C code

46. Outline Objective Project Background Lyapunov Observer Kalman Filter Implementation into a SISO System Initial simulations Noise Modeling Future goals Timeline References 6/27/2015NASA Grant URC NCC NNX08BA44A46

47. 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 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. 6/27/2015NASA Grant URC NCC NNX08BA44A47

48. Questions? Thank You 6/27/201548NASA Grant URC NCC NNX08BA44A

49. Preliminary Results 6/27/201549NASA Grant URC NCC NNX08BA44A System Simulation Output w/ Additive Noise & Actuated Faults Kalman Estimate

50. Residuals 6/27/201550NASA Grant URC NCC NNX08BA44A Kalman Residuals (System Simulation O/P) – (Kalman Estimate O/P) = Actuated Fault Discrepency Step Input