Digital method and apparatus for sensing position with a linear variable differential transformer

1. An apparatus for determining a linear position of a movable component of a linear variable differential transformer (LVDT), which includes a primary coil driven by an excitation signal at an excitation frequency, a first positional output, and a second positional output, the apparatus comprising:

a first signal analyzer including an analog input operably coupled to the first positional output and a second signal analyzer including an analog input operably coupled to the second positional output, each of the first signal analyzer and the second signal analyzer comprising:

a feedback loop configured to generate a digital estimate that substantially tracks an amplitude of the analog input, the feedback loop comprising:

a comparator configured for comparing the analog input to an analog feedback signal and generating a comparison result;

a digital estimator, operating at an estimation frequency and configured to sample the comparison result and modify the digital estimate by an incremental adjustment amount responsive to the comparison result to reduce a difference between the amplitude of the analog input signal and an amplitude of the analog feedback signal; and

a digital-to-analog converter configured to convert the digital estimate to the analog feedback signal; and

an amplitude analyzer configured to collect a digital estimate history by sampling the digital estimate at a sample frequency that is a binary multiple of the excitation frequency and analyze the digital estimate history to determine an amplitude of the digital estimate substantially near the excitation frequency; and

a result calculator configured to evaluate the amplitude of the digital estimate from the first signal analyzer and the amplitude of the digital estimate from the second signal analyzer to generate a numerical representation of the linear position of the movable component.

2. The apparatus of claim 1 , further comprising a digital filter configured for filtering the linear position to generate a filtered linear position.

3. The apparatus of claim 1 , wherein the result calculator comprises an arithmetic unit configured for calculating the equation (A−B)/(A+B) wherein A represents the amplitude of the first signal analyzer, B represents the amplitude of the second signal analyzer, and the calculation result represents the linear position.

4. The apparatus of claim 1 , wherein the result calculator comprises:

a first adder configured for adding the amplitude of the first signal analyzer to the amplitude of the second signal analyzer to generate a first term;

a second adder configured for subtracting the amplitude of the second signal analyzer from the amplitude of the first signal analyzer to generate a second term; and

a divider configured for dividing the second term by the first term to generate the linear position.

5. The apparatus of claim 1 , wherein the digital-to-analog converter comprises:

a pulse-width modulator configured for converting the digital estimate to a digital pulse with a duty cycle correlated to the digital estimate to generate a pulse-width modulated estimate; and

a low pass filter configured for filtering the pulse-width modulated estimate to generate the analog feedback signal.

6. The apparatus of claim 1 , wherein the incremental adjustment amount is selected from the group consisting of no change, a positive increment, and a negative increment.

7. The apparatus of claim 1 , wherein the binary multiple for the sample frequency is at a frequency of 2 N times the sample frequency wherein N is in a range from 2 to 10.

8. The apparatus of claim 1 , wherein the amplitude analyzer further comprises a frequency analyzer configured to determine the amplitude of the digital estimate substantially near the excitation frequency by performing an operation selected from the group consisting of a fast Fourier transform, a discrete Fourier transform, and a limited discrete Fourier transform.

9. The apparatus of claim 1 , further comprising an excitation generator configured for generating the excitation signal as substantially a sine wave at the excitation frequency.

10. The apparatus of claim 9 , wherein the excitation generator comprises:

an amplitude generator configured for generating a digital representation of the excitation signal at each time period of a generation frequency;

a pulse-width modulator configured for converting the digital representation to a digital pulse with a duty cycle correlated to the digital representation to generate a pulse-width modulated signal; and

a low pass filter configured for filtering the pulse-width modulated signal to generate the excitation signal.

11. The apparatus of claim 10 , wherein the amplitude generator is selected from the group consisting of a look-up table and a trigonometric calculator.

12. A method for determining a linear position, comprising:

generating at least two correlated signals from a Linear Variable Differential Transformer (LVDT) by stimulating an excitation input with an excitation signal, wherein the at least two correlated signals are responsive to a linear position of a movable component of the LVDT and the excitation signal;

converting the at least two correlated signals to a digital estimate for each of the at least two correlated signals, the converting comprising:

comparing the correlated signal to an analog feedback signal to generate a comparison result;

incrementally adjusting the digital estimate at an estimation frequency in response to sampling the comparison result such that the incremental adjusting reduces a difference between the correlated signal and the analog feedback signal;

converting the digital estimate to the analog feedback signal;

collecting a digital estimate history by sampling the digital estimate at a sample frequency that is a binary multiple of an excitation frequency of the excitation signal; and

analyzing the digital estimate history to determine an amplitude of the digital estimate substantially near the excitation frequency; and

evaluating the amplitude of the digital estimate substantially near the excitation frequency of the at least two correlated signals to determine a numerical representation of the linear position of the movable component.

13. The method of claim 12 , further comprising digitally filtering the linear position to generate a filtered linear position.

14. The method of claim 12 , wherein evaluating the amplitude of the digital estimate of the at least two correlated signals comprises calculating the equation (A−B)/(A+B) wherein A represents the amplitude of a first of the at least two correlated signals, B represents the amplitude of a second of the at least two correlated signals, and the calculation result represents the linear position.

15. The method of claim 12 , wherein converting the digital estimate to the analog feedback signal comprises:

converting the digital estimate to a digital pulse with a duty cycle correlated to the digital estimate to generate a pulse-width modulated estimate; and

filtering the pulse-width modulated estimate to generate the analog feedback signal.

16. The method of claim 12 , wherein incrementally adjusting the digital estimate is a process selected from the group consisting of no change, a positive increment, and a negative increment.

17. The method of claim 12 , wherein the binary multiple for the sample frequency is at a frequency of 2 N times the sample frequency wherein N is in a range from 2 to 10.

18. The method of claim 12 , wherein analyzing the digital estimate history comprises performing an operation selected from the group consisting of a fast Fourier transform, a discrete Fourier transform, and a limited discrete Fourier transform.

19. The method of claim 12 , further comprising generating the excitation signal as substantially a sine wave at the excitation frequency.

20. The method of claim 19 , wherein generating the excitation signal comprises:

generating a digital representation of the excitation signal at each time period of a generation frequency;

converting the digital representation to a digital pulse with a duty cycle correlated to the digital representation to generate a pulse-width modulated signal; and

filtering the pulse-width modulated signal to generate the excitation signal.

21. The method of claim 20 , wherein generating the digital representation is a process selected from the group consisting of calculating the digital representation and retrieving the digital representation from a look-up table.

22. A method for determining a linear position of a movable component of a linear variable differential transformer (LVDT), which includes a primary coil driven by an excitation signal at an excitation frequency, a first signal from a first secondary coil, and a second signal from a second secondary coil, comprising:

converting the first signal to a first digital estimate, the converting comprising:

comparing the first signal to a first analog feedback signal to generate a first comparison result;

incrementally adjusting the first digital estimate at an estimation frequency in response to sampling the first comparison result to reduce a difference between an amplitude of the first signal and an amplitude of the first analog feedback signal;

converting the first digital estimate to the first analog feedback signal;

sampling the first digital estimate at the sample frequency to generate a first digital estimate history; and

analyzing the first digital estimate history to determine a first amplitude of the first signal substantially near the excitation frequency;

converting the second signal to a second digital estimate, the converting comprising:

comparing the second signal to a second analog feedback signal to generate a second comparison result;

incrementally adjusting the second digital estimate at an estimation frequency in response to sampling the second comparison result to reduce a difference between an amplitude of the second signal and an amplitude of the second analog feedback signal;

converting the second digital estimate to the second analog feedback signal;

sampling the second digital estimate at a sample frequency to generate a second digital estimate history; and

analyzing the second digital estimate history to determine a second amplitude of the second signal substantially near the excitation frequency; and

evaluating the first amplitude and the second amplitude to determine a numerical representation of the linear position of the movable component.

23. The method of claim 22 , further comprising digitally filtering the linear position to generate a filtered linear position.

24. The method of claim 22 , wherein evaluating the first amplitude and the second amplitude comprises:

adding the first amplitude to the second amplitude to generate a first term;

subtracting the second amplitude from the first amplitude to generate a second term;

dividing the second term by the first term to generate the linear position.

25. The method of claim 22 , wherein converting the digital estimate to the analog feedback signal comprises:

converting the digital estimate to a digital pulse with a duty cycle correlated to the digital estimate to generate a pulse-width modulated estimate; and

filtering the pulse-width modulated estimate to generate the analog feedback signal.

26. The method of claim 22 , wherein incrementally adjusting the first digital estimate and incrementally adjusting the second digital estimate are processes selected from the group consisting of no change, a positive increment, and a negative increment.

27. The method of claim 22 , wherein analyzing the first digital estimate and analyzing the second digital estimate each comprises performing an operation selected from the group consisting of a fast Fourier transform, a discrete Fourier transform, and a limited discrete Fourier transform.

28. The method of claim 22 , wherein:

analyzing the first digital estimate comprises:

collecting a first digital estimate history at a sample frequency that is a binary multiple of the excitation frequency of the excitation signal; and

analyzing the first digital estimate history to determine the first amplitude; and

analyzing the second digital estimate comprises:

collecting a second digital estimate history at the sample frequency that is the binary multiple of the excitation frequency of the excitation signal; and

analyzing the second digital estimate history to determine the second amplitude.

29. The method of claim 28 , wherein the binary multiple for the sample frequency is at a frequency of 2 N times the sample frequency wherein N is in a range from 2 to 10.

30. The method of claim 22 , further comprising generating the excitation signal as substantially a sine wave at the excitation frequency.

31. The method of claim 30 , wherein generating the excitation signal comprises:

generating a digital representation of the excitation signal at each time period of a generation frequency;

converting the digital representation to a digital pulse with a duty cycle correlated to the digital representation to generate a pulse-width modulated signal; and

filtering the pulse-width modulated signal to generate the excitation signal.

32. The method of claim 31 , wherein generating the digital representation is a process selected from the group consisting of calculating the digital representation and retrieving the digital representation from a look-up table.