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

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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

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I.Background

II.Load Cell Calibration

III.Kalman Filtration

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Wallace Energy Systems and Renewables Facility (WESRF)

4[13]

Ocean Testing

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Renewable Energy from the Ocean

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OSU Wave Energy Linear Test BedTests 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 deep7

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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.

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Position Command

Acceleration Feedback

Velocity FeedbackPosition Feedback

Force Feedback

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Problem: Feedback Signals with Noise

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Research Focus

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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)

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I.Background

II.Load Cell Calibration

III.Kalman Filtration

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LTB Load Cell Calibration

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Tension & Compression Measurement

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Load Cell Accuracy

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

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Least Squares Best Fit Lines

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R2 = 0.9999 R2 = 0.9999

Left Load Cell Right Load Cell

Load Cell Conclusion // Future Work

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I.Background

II.Load Cell Calibration

III.Kalman Filtration

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Problem: Feedback Signals with Noise

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The Discrete Kalman Estimator

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[5],[6][16]

from LTB Transfer Functions A, B, C Find:

LTB Noise Analysis R and Q

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[5],[6][16]

Increment Time

Start

The Discrete Kalman Estimator

Prediction

Prior State Estimate

Prior Error Covariance

Correction

State Estimate

Error Covariance

Observer Gain

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A, B, C from LTB Transfer FunctionsFind:

Step #1 for Construction of Kalman Estimator for LTB

Position Transfer Function Signal Path

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Position Transfer Function (HP) Bode Plot

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Position Bode Plot

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Position Bode Plot (ident 4th order)

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Velocity and Acceleration Transfer Functions

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Force Transfer Function Signal Path

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Force Step Response

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R from LTB Noise AnalysisFind:

Step #2 for Construction of Kalman Estimator for LTB

System Noise Analysis

System Noise Analysis

Covariance[4]:

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Step #3 Construct Kalman Estimator

Kalman Filter Matrices

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Position Results

35Simulated Wave Data File [14]

Position Results – Close Up

36Simulated Wave Data File [14]

Velocity Results – Close Up

37Simulated Wave Data File [14]

Force and Acceleration

38Simulated Wave Data File [14]

Improvement Analysis

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Improvement Analysis Data

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Kalman Improvement Results

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Conclusion // Future Work

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References[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].

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Questions ?

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Load Cell Composition• Two load cells directly

coupled to buoy. • Each load cell is rated for

5000 lb-f in tension or compression.

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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).

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Simulating Load Cell Response

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Tuning the Kalman Filter

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ωP = 0.8

ωV = 200π

ωA = 400π

QN = 5000

ωP = 5.35

ωV = 10π

ωA = 5π

QN = 10 Starting

Values

Final Values

Mean Squared Error Analysis

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Acceleration Results – Close Up

50Simulated Wave Data File [14]

Force Results – Close Up

51Simulated Wave Data File [14]

Force Results

52Simulated Wave Data File [14]

Noisy Plant attached to Kalman Filter

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Proposed Solution:Linear Quadratic Gaussian Controller

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S-Type Load Cell with Readout DisplayUsed for Calibration of the LTB Load Cells

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Load Cell Suspension Arm

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