1. Calibration, Characterization, and Linear Quadratic Gaussian Estimation of Sensor Feedback Signals for a Novel Ocean Wave Energy Linear Test Bed M.S. Thesis Defense for Christopher A. Haller Electrical Engineering and Computer Science Major Advisor: Dr. Ted Brekken Oregon State University. 2010 June10 th 1

2. C.C.L.Q.G.E.S.F.S.N.O.W.E.L.T.B. - Agenda I.Background II.Load Cell Calibration III.Kalman Filtration [7] [8] 2

3. I.Background II.Load Cell Calibration III.Kalman Filtration [7] [8] 3

4. Wallace Energy Systems and Renewables Facility (WESRF) 4 [13]

5. Ocean Testing [1] 5

6. Renewable Energy from the Ocean [1] 6

7. OSU Wave Energy Linear Test Bed Tests ocean wave energy generators by creating relative linear motion between the center spar and surrounding float. Specifications [1] :  10kW with a 50% efficient device, and up to 19kW @ 95% efficiency  1m/sec @ 20,000 N Thrust (4500 lbf)  2m/sec @ 10,000 N Thrust (2250 lbf)  Modes: Point-Point (fixed or captured position//wave profile vs. time) & Force (load cell feedback)  2m relative motion/stroke (6.5 feet)  Upper & Lower Gimbal mounting (for alignment variation)  16.5ft tall x 10.5ft wide x 8.5ft deep 7 [7]

8. Force Control Scheme Linear Test Bed (LTB) External Control Computer Analog position command signal sent to Linear Test Bed. Analog feedback signals may be used to control force applied by LTB. [9],[10],[11] Position Command Acceleration Feedback Velocity Feedback Position Feedback Force Feedback [7] 8

9. Problem: Feedback Signals with Noise 9

10. Research Focus 10 To Advance the LTB Toward Closed-Loop Force Control  Construct L.Q.G. Estimator (Kalman Filter) to solve feedback noise issues  Develop LTB Calibration Procedure and Assess Force Sensor Accuracy (Load Cells) [8]

11. I.Background II.Load Cell Calibration III.Kalman Filtration [7] [8] 11

12. LTB Load Cell Calibration 12

13. Tension & Compression Measurement 13

14. Load Cell Accuracy 14

15. Right Load Cell Error for Points 4, 5, 6, and 7 15

16. Least Squares Best Fit Lines 16 R 2 = 0.9999 Left Load CellRight Load Cell

17. Load Cell Conclusion // Future Work 17

18. I.Background II.Load Cell Calibration III.Kalman Filtration [7] [8] 18

19. Problem: Feedback Signals with Noise 19

20. The Discrete Kalman Estimator 20 [5],[6][16] from LTB Transfer Functions  A, B, C Find: LTB Noise Analysis  R and Q

21. 21 [5],[6][16] Increment Time Start The Discrete Kalman Estimator Prediction Prior State Estimate Prior Error Covariance Correction State Estimate Error Covariance Observer Gain

22. 22 A, B, C  from LTB Transfer Functions Find: Step #1 for Construction of Kalman Estimator for LTB

23. Position Transfer Function Signal Path 23

24. Position Transfer Function (H P ) Bode Plot 24

25. Position Bode Plot 25

26. Position Bode Plot (ident 4 th order) 26

27. Velocity and Acceleration Transfer Functions 27

28. Force Transfer Function Signal Path 28

29. Force Step Response 29

30. 30 R  from LTB Noise Analysis Find: Step #2 for Construction of Kalman Estimator for LTB

31. System Noise Analysis

32. Covariance [4] :

33. 33 Step #3 Construct Kalman Estimator

34. Kalman Filter Matrices 34

35. Position Results 35 Simulated Wave Data File [14]

36. Position Results – Close Up 36 Simulated Wave Data File [14]

37. Velocity Results – Close Up 37 Simulated Wave Data File [14]

38. Force and Acceleration 38 Simulated Wave Data File [14]

39. Improvement Analysis 39

40. Improvement Analysis Data 40

41. Kalman Improvement Results 41

42. Conclusion // Future Work 42

43. References [1] “Wave Energy Opportunities and Developments,” [Online]. Available: http://eecs.oregonstate.edu/wesrf/projects/images/Wave%20Energy_Final.ppt. [Accessed: April 19, 2010]. http://eecs.oregonstate.edu/wesrf/projects/images/Wave%20Energy_Final.ppt [2] M. H. Patel and J. A. Witz, Compliant Offshore Structures. London: Butterworth-Heinemann Ltd., 1991. [3] M. S. Grewal and A. P. Andrews, Kalman Filtering: Theory and Practice. United States: Prentice-Hall, Inc., 1993. [4] D. C. Montgomery and G. C. Runger, Applied Statistics and Probability for Engineers. United States: John Wiley & Sons, Inc., 1999. [5] Stefani, Savant, Shahian, and Hostetter, Design of Feedback Control Systems. United States: Saunders College Publishing, 1994. [6] “Kalman” [Online]. Available: http://www.mathworks.com/access/helpdesk/help/toolbox/control/ref/kalman.html. [Accessed: April 20, 2010]. [7] “Linear Test Bed Pictures” [Image] provided by Ean Amon. May 2010. [8] Interface-Force Inc. Load Cell [Online Image]. Available: http://www.interfaceforce.com/includes/thumb.php?resize=275&img=images%2Floadcells%2FLOW_PROFa_000.jpg. [Accessed: April 20, 2010]. [9] Dell Monitor[Online Image]. Available: http://www.theinquirer.net/img/1177/dell_monitor.jpg. [Accessed: April 23, 2010]. [10] Industrial Computer [Online Image]. Available: http://img.diytrade.com/cdimg/960066/9655368/0/1247037540/Rack_Mount_Chassis_industrial_Computer_Case_4u450AT.j pg. [Accessed: April 23, 2010]. [11] Ocean Wave [Online Image]. Available: http://megroberts.files.wordpress.com/2008/12/ocean-wave-jj-001.jpg. [Accessed: April 23, 2010]. [12] Strain Gauge States [Online Image]. Available: http://http://en.wikipedia.org/wiki/Strain_gauge. [Accessed: June 3, 2010]. [13] WESRF Lab [Image]. WESRF Share Drive [Accessed: June 7, 2010]. [14] D. Elwood, \Simulated Ocean Wave Data Files," 2010, Oregon State University. [15] P. Hogan, Thesis. 2007, Oregon State University. [16] Kalman Filter [Website]. Available :http://bilgin.esme.org/BitsBytes/KalmanFilterforDummies. [Accessed: June 9, 2010]. [8] 43

44. Questions ? 44

45. Load Cell Composition Two load cells directly coupled to buoy. Each load cell is rated for 5000 lb-f in tension or compression. 45 [8] [12]

46. Typical Calibration Test 1.Measure zero point (no weight). 2.Measure five tension points to capacity. 3.Measure one return point (25% of capacity). 4.Measure zero point (no weight). 5.Measure five compression points to capacity. 6.Measure one return point (25% of capacity). 7.Measure zero point (no weight). [8] 46

47. Simulating Load Cell Response 47

48. Tuning the Kalman Filter 48 ω P = 0.8 ω V = 200π ω A = 400π Q N = 5000 ω P = 5.35 ω V = 10π ω A = 5π Q N = 10 Starting ValuesFinal Values

49. Mean Squared Error Analysis 49

50. Acceleration Results – Close Up 50 Simulated Wave Data File [14]

51. Force Results – Close Up 51 Simulated Wave Data File [14]

52. Force Results 52 Simulated Wave Data File [14]

53. Noisy Plant attached to Kalman Filter 53

54. Proposed Solution: Linear Quadratic Gaussian Controller 54

55. S-Type Load Cell with Readout Display Used for Calibration of the LTB Load Cells 55

56. Load Cell Suspension Arm 56 [15]