M.S. Thesis Defense for Christopher A. Haller Electrical Engineering and Computer Science

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 June10th

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

3. Background • Load Cell Calibration • Kalman Filtration [7] [8]

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

5. Ocean Testing [1]

6. Renewable Energy from the Ocean [1]

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]

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

9. Problem: Feedback Signals with Noise

10. Research Focus 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. Background • Load Cell Calibration • Kalman Filtration [7] [8]

12. LTB Load Cell Calibration

13. Tension & Compression Measurement

14. Load Cell Accuracy

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

16. Least Squares Best Fit Lines Left Load Cell Right Load Cell R2 = 0.9999 R2 = 0.9999

17. Load Cell Conclusion // Future Work

18. Background • Load Cell Calibration • Kalman Filtration [7] [8]

19. Problem: Feedback Signals with Noise

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

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

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

23. Position Transfer Function Signal Path

24. Position Transfer Function (HP) Bode Plot

25. Position Bode Plot

26. Position Bode Plot (ident 4th order)

27. Velocity and Acceleration Transfer Functions

28. Force Transfer Function Signal Path

29. Force Step Response

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

31. System Noise Analysis

32. System Noise Analysis Covariance[4]:

33. Step #3 Construct Kalman Estimator

34. Kalman Filter Matrices

35. Position Results Simulated Wave Data File [14]

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

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

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

39. Improvement Analysis

40. Improvement Analysis Data

41. Kalman Improvement Results

42. Conclusion // Future Work

43. References [8] [1] “Wave Energy Opportunities and Developments,” [Online]. Available: http://eecs.oregonstate.edu/wesrf/projects/images/Wave%20Energy_Final.ppt. [Accessed: April 19, 2010]. [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.jpg. [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].

44. Questions ?

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

46. Typical Calibration Test [8] • Measure zero point (no weight). • Measure five tension points to capacity. • Measure one return point (25% of capacity). • Measure zero point (no weight). • Measure five compression points to capacity. • Measure one return point (25% of capacity). • Measure zero point (no weight).

47. Simulating Load Cell Response

48. Tuning the Kalman Filter ωP = 0.8 ωV = 200π ωA = 400π QN = 5000 ωP = 5.35 ωV = 10π ωA = 5π QN = 10 Starting Values Final Values

49. Mean Squared Error Analysis

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