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L. Angrisani, R. Schiano Lo Moriello

Digital Signal Processing Approaches for Varying Magnetic Field Measurements through a Rotating Coils System. L. Angrisani, R. Schiano Lo Moriello. L. Bottura, A. Masi. Outline. Introductive notes Limitations of the standard Fourier analysis in the presence of analog bucking Proposals:

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L. Angrisani, R. Schiano Lo Moriello

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  1. Digital Signal Processing Approaches for Varying Magnetic Field Measurements through a Rotating Coils System L. Angrisani, R. Schiano Lo Moriello L. Bottura, A. Masi 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  2. Outline • Introductive notes • Limitations of the standard Fourier analysis in the presence of analog bucking • Proposals: • Quadrature demodulation-based method • Extrapolation-based method • Performance comparison in simulated conditions • Results in actual experiments • Conclusions 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  3. Introduction • In superconducting magnets, dynamic effects like snapback can be estimated only through measurements in ramping conditions. • Due to current variation, field harmonics are both time and ramp rate dependent (e.g. decay phenomena). • The conventional Fourier analysis does not work properly. Being addressed to DC measurements, it assumes field harmonics to be constant during a coil turn. 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  4. Introduction • Increasing coil speed is often impracticable, and it could prove unsuccessful in the presence of high ramp rates of the current. • To measure varying magnetic fields through a rotating coils system, two new digital signal-processing methods are proposed. • They both assume continuous coil rotation. 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  5. The standard Fourier analysis Constant during a coil turn Magnetic flux as a function of the angular position Integration of Vcoil in the angular domain Field Harmonics 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  6. Problems with the standard Fourier analysis • A periodic, magnetic flux characterized by constant envelope….. 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  7. Problems with the standard Fourier analysis • The envelope of the main component (fundamental) increases linearly with the angular position, B3 and B5 being constant ….. DFT results Imposed values 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  8. Problems with the standard Fourier analysis • Hardware solution: analog bucking Measurement problems with B3 still survive. Measurement problems with B5 still survive. 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  9. Typical test current evolution Standard Fourier analysis characterization LHC Cycle 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  10. Standard Fourier analysis characterization 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  11. Linear ramp: different ramp rates have been simulated Absolute difference for B1 -3 x 10 1.8 1.6 R=100A/s 1.4 R=90A/s 1.2 R=80A/s R=70A/s 1 Abs(B1-B1 avg) [T] R=60A/s 0.8 R=50A/s 0.6 R=40A/s 0.4 R=30A/s R=20A/s 0.2 R=10A/s 0 4000 5000 6000 7000 8000 9000 10000 11000 Current [A] Standard Fourier analysis characterization Difference greater than 1 unit for a 10A/s linear ramp 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  12. Parabolic ramp Standard Fourier analysis characterization -5 B3 B1 -4 x 10 x 10 5 1 4 0.8 3 0.6 abs[(B1-B1avg) [T] abs[(B3-B3avg) [T] 2 0.4 1 0.2 0 0 0 10 20 30 40 0 10 20 30 40 Number of coil turns Number of coil turns 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  13. Exponential ramp B3 -4 x 10 B1 -4 3 x 10 1.2 2.5 1 2 0.8 1.5 0.6 abs[(B3-B3avg) [T] abs[(B1-B1avg) [T] 1 0.4 0.5 0.2 0 0 0 10 20 30 40 0 10 20 30 40 Number of coil turns Number of coil turns Standard Fourier analysis characterization 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  14. Residual C1 evaluation: digital bucking sin(2πft) Phase FIR tg-1 Unwrap Modulus FIR x2 cos(2πft) Proposal 1: quadrature demodulation-based method Ф(t) Quadrature demodulation scheme 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  15. Proposal 1: quadrature demodulation-based method Sliding window FFT Overlap ratio: 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  16. Proposal 1: typical results Comparison of the nominal evolution of B3 (green) to those obtained through STFT (red) and demodulation+STFT (violet). Difference (D) between estimated and nominal evolution of B1. 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  17. Proposal 2 : extrapolation-based method For each angular position, the flux samples (red dots) acquired in the last four coil turns are used to extrapolate the flux samples related to the next turn for different sampling times (black dots). 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  18. Proposal 2 : extrapolation-based method 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  19. B1 1,00E-02 1,00E-03 Absolute RMS error [T] 1,00E-04 1,00E-05 50 40 Standard analysis 30 20 STFT 10 Ramp Rate [A/s] Extrapolation Performance comparison: linear ramp 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  20. B3 B5 Performance comparison: linear ramp 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  21. Performance comparison: parabolic ramp B1-B7 A1-A8 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  22. Performance comparison: exponential ramp B1-B7 A1-A8 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  23. Proposal 2: experimental results • Some measurements have been carried out on a reference, resistive magnetic dipole. • Continuous coil rotation has been assured. • Coil speed has been equal to 1 turn/s. • Different ramp rates have been considered: 5A/s, 10A/s, 20A/s. 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  24. Proposal 2: experimental results • As expected for the reference magnet measured, the first results seem to highlight that harmonic coefficients are independent of ramp rate. 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  25. Comparison • The evolution versus time of harmonic coefficients gained from proposal 2 result smoother than those from proposal 1. Blue trace: proposal 1 Black trace: proposal 2 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  26. Conclusions • Characterization of the standard Fourier analysis when applied to compensated magnetic fluxes in non-stationary conditions. • A quadrature demodulation-based method for a reliable digital bucking has been proposed (proposal 1). • Harmonic coefficients are gained from the application of the standard Fourier analysis to digitally compensated flux samples. • An alternative method that extrapolates, for a given time instant, the flux value for each angular position in a coil turn has also been presented (proposal 2). 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

  27. Conclusions • Many tests in simulated dynamic conditions have been carried out to assess and compare the performance of the proposed methods. • Proposal 1 allows more accurate estimate of harmonic coefficients, but B1, than that granted by standard Fourier analysis. • Proposal 2 performs much better even in the presence of high ramp rates. • The reduced computational burden of proposal 2 make real-time tracking of harmonic coefficients feasible. • The first results obtained in actual experiments seem to confirm the reliability of proposal 2. 14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland

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