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Frequency-domain Least Squares System Identification of the TSU Hexapod

Frequency-domain Least Squares System Identification of the TSU Hexapod . Paul Ware Electrical and Computer Engineering Jiann-Shiun Lew Center of Excellence in Information Systems Tennessee State University. MOTIVATION AND APPROACH.

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Frequency-domain Least Squares System Identification of the TSU Hexapod

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  1. Frequency-domain Least Squares System Identification of the TSU Hexapod Paul Ware Electrical and Computer Engineering Jiann-Shiun Lew Center of Excellence in Information Systems Tennessee State University

  2. MOTIVATION AND APPROACH • Ultra-lightweight inflatable space structures offer several advantages over conventional structures for further space exploration and discovery • A 3m-diameter hexapod membrane structure was designed and built for research on modeling and vibration control of inflatable gossamer observatories. • Modeling this structure is a challenging task because of the flexibility of the structure and the substantial number of modes • This project presents a study of the application of a least-squares technique to curve fit experimental data collected from the hexapod.

  3. HEXAPOD STRUCTURE FOR TESTING

  4. HEXAPOD WITH DIMENSIONS

  5. TEST SET-UP • The torus is mounted vertically on a pair of steel rods. • One (Ling Dynamic Systems L.D.S. Va203) shaker, connected to the torus in the normal direction, is used to impart forces. • Displacement measurements were taken with a Keyence LK-503 single point laser displacement sensor. • HP analyzer is used for frequency-domain response testing.

  6. SHACKER SET-UP FOR TESTING

  7. LASER DISPLACEMENT SENSOR

  8. TRANSFER FUNCTION The dynamic equation of this single-degree system is • The transfer function of displacement measurement is

  9. LEAST-SQUARE APPROACH • In experiments we can get frequency response function (FRF) data (complex values) • The FRF data are used to form the cost function • This is a linear least-squares problem of variables ai, a unique solution can be obtained by minimizing this cost function.

  10. FRF DATA

  11. IDENTIFICATION RESULTS Gain=1  experimental data,  model, - - model error

  12. IDENTIFICATION RESULTS Gain=1.5  experimental data,  model, - - model error

  13. IDENTIFICATION RESULTS Gain=2  experimental data,  model, - - model error

  14. IDENTIFICATION RESULTS FROM FRF

  15. CONCLUSIONS • Testing of inflatable/rigidizable structures presents many challenges such as high modal densities, tension stiffened membranes. • A least-squares technique is developed to curve fit the FRF data. • The least-squares technique fits the experimental data well with model error one order of magnitude lower than that of the experimental data • The identified natural frequency decreases as the input force increases.

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