Methods of Analysis for Mathematical Modeling of a Synthetic Jet Actuator

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Methods of Analysis for Mathematical Modeling of
a Synthetic Jet Actuator

• Ben Mertz
• Dr. Kamesh Subbarao (advisor)
• Texas A M Department of Aerospace Engineering
• August 6, 2003

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Objectives

• Analyze data using 4 different methods
• Least squares approximation
• Radial basis functions
• MATLAB system identification toolbox
• Dynamic radial basis functions
• Compare methods of analysis
• Determine the best model

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Synthetic Jet Actuator
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Experimental Setup
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Notes About Experiment and Analysis

• Three data sets were collected
• Only input voltage frequency was varied
• Input voltage is sinusoidal
• Final model should be the same for all data sets

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System Identification Least Squares
General Form of Output
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Motor Frequency vs. Voltage with Best Fit line
For Case 2
Motor Frequency vs. Voltage with Best Fit line
For Case 3
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Error Between Best Fit Lines
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System Identification Radial Basis Functions
For sigma 0.5 and centers at mu 3.75, 4.00,
4.25, 4.50, 4.75, 3.90, 4.60
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Errors Between Best Fit Lines
These Values are similar to the ones found using
least squares
(51.44 Hz, 33.82 Hz, and 37.69 Hz)
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System Identification System Identification
Toolbox
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Case 2 Results
Motor Frequency
Motor Frequency
Time (sec)
Time (sec)
Discrete Time Step
Continuous Time Step
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Case 3 Results
Motor Frequency
Motor Frequency
Time (sec)
Time (sec)
Discrete Time Step
Continuous Time Step
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System Identification Dynamic Radial Basis
Functions

• Same basic equations as radial basis function
  method
• Neural network used to find parameters
• Weight vectors
• Center placements
• R-1
• Randomized data
• Monte Carlo algorithm

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Case 1 Results
Motor Frequency
Motor Frequency
Step Number
Step Number
1,000 Iterations
1 Iteration
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Case 2 Results
Motor Frequency
Motor Frequency
Step Number
Step Number
1,000 Iterations
1 Iteration
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Case 3 Results
Motor Frequency
Motor Frequency
Step Number
Step Number
1,000 Iterations
1 Iteration
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Summary

• Static vs. Dynamic Model
• And the winner is
• Where do we go from here?

Dynamic Radial Basis Function
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References

• Traub, L.W., Miller, A.C., Ukpai, U.I., and
  Rediniotis, O.K., Reconfigurable Synthetic Jet
  Actuation and Closed-Loop Flow Control, AIAA
  Paper 2003-0217, 41st Aerospace Sciences Meeting
  and Exhibit, Reno, NV, Jan. 6-9, 2003.
• Junkins, J.L. and Kim, Y., Introduction to
  Dynamics and Control of Flexible Structures,
  American Institute of Aeronautics and
  astronautics, Inc., Washnington, DC, 1993.
• Junkins, J.L, Intellignet Systems Radial Basis
  Function Neural Networks, 1st Annual TiiMS-URETI
  Review Meeting, Houston, TX, July 14-15, 2003.
• Rediniotis, O., Intellignet Systems Hingeless
  Control of a Wing, 1st Annual TiiMS-URETI Review
  Meeting, Houston, TX, July 14-15, 2003.

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Questions?