Patent Publication Number: US-6982538-B2

Title: Methods and apparatus for generating a sinusoidal motor drive signal for a MEMS gyroscope

Description:
BACKGROUND OF THE INVENTION 
   This invention relates generally to digital signal processing (DSP) and, more specifically, to methods and apparatus for generating motor drive signals for micro-electromechanical system (MEMS) gyroscopes. 
   To provide a motor drive signal for MEMS gyroscopes, a digital sinusoidal signal of frequency f o  is generated by a numerically controlled dual-frequency oscillator (NCDFO). A command input to the oscillator is β o =cos(2πf o T), where f s =1/T is a clock frequency of the oscillator. The frequency f o  varies with changes in β o . The digital sinusoidal signal serves as the input to a drive circuit which, in turn, provides an analog signal to a gyroscope drive motor. Because the above described gyroscope motor drive configuration is within a closed-loop control system, the destabilizing effect of time delay, and an attendant phase shift resulting from the time delay, will cause an operational issue to result. 
   One known attempted solution is to pass the NCDFO output signal through a digital-to-analog converter (DAC), whose output is passed through a low pass, anti-aliasing filter to smooth the analog gyro-drive signal. Unfortunately, the time delay introduced by the combination of these operations is too long to permit solid closed-loop operation. A digital-to-analog-conversion scheme with lower phase shift is clearly needed. 
   BRIEF SUMMARY OF THE INVENTION 
   In one aspect, an apparatus to reduce a time delay and a resultant phase shift in a gyroscope motor drive signal is provided. The motor drive signal originates from a numerically controlled oscillator, the oscillator output being sampled at a predetermined rate. The apparatus comprises a first element which upsamples the oscillator output signal samples, a band pass filter configured to receive an output from the first element and remove spectral components of the output of the first element, a third element which generates a tuning parameter, β′ o , to tune the band pass filter, and a scaling multiplier configured to normalize an output of the filter. 
   In another aspect, a method for reducing a time delay and a resultant phase shift in a gyroscope motor drive signal which originates from a numerically controlled oscillator is provided. The method comprises placing I−1 zero value samples between each pair of oscillator output samples, filtering spectral components from the combined oscillator output samples and zero value samples, generating a tuning parameter, β′ o , for use in filtering, and scaling a filter ouput. 
   In still another aspect, an angular rate measurement system is provided. The system comprises a gyroscope configured to sense an angular rate input and provide a modulated angular rate information signal and a sinusoidal demodulation reference signal. The system also comprises a numerically controlled oscillator (NCO) configured to receive as an input a tuning parameter β, which is a digitized signal derived from the sinusoidal demodulation reference signal. The NCO is further configured to provide output samples. The system also comprises an automatic gain control (AGC) circuit configured to amplify the output samples of the NCO, an interpolator, and a digital-to-analog converter and filter configured to produce a motor drive signal from an output of the interpolator. The interpolator is configured to place I−1 zero value samples between each pair of amplified output samples, and the interpolator comprises a filter configured to filter spectral components from the combined amplified output samples and zero value samples. The interpolator further generates a tuning parameter, β′ o , for the filter, and scales the filtered samples to be output from the interpolator. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  illustrates a gyroscope angular rate sensing system including an interpolator circuit for reducing a time delay in generating a gyro motor drive signal. 
       FIG. 2  illustrates an embodiment of an interpolator circuit used in the angular rate sensing system of FIG.  1 . 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Referring to  FIG. 1 , an angular rate measurement system  10  as shown is built around gyroscope  20  which senses input angular rate  22 . A first output  24  of gyroscope  20  is an electrical signal which is a double side band suppressed carrier (DSSC) modulated representation, at a fundamental frequency 2f o , of the input angular rate  22 . First output  24  is input to an analog-to-digital conversion (ADC) system  26  including an internal analog anti-alias filter, a sampler, and a digitizer (none shown). An output  28  from ADC system  26  is input to and demodulated by demodulator  30  which, as further described below, receives demodulating signals from numerically controlled dual frequency oscillator (NCDFO)  32 . An output  34  from demodulator  30  is filtered with filter  36  whose output  38  is a base band digitized representation of angular input rate  22 . 
   Gyroscope  20  provides a second output  40 , which is a sinusoidal demodulation reference signal at a frequency 2f o . Second output  40  is connected to a second ADC system  42 , functionally identical to ADC system  26 . An output  44  from ADC  42  is then input to both a phase detector/servo equalizer  46  and an automatic gain control (AGC)  48 . Phase detector/servo equalizer  46  is a combination fast-acting automatic gain control, phase shifter, phase detector, and servo equalizer. An output  50  of phase detector/servo equalizer  46  is a tuning parameter β o =cos(2πf o T) which determines the frequency of oscillation of NCDFO  32  (NCDFO  32  has a clock rate of 1/T) and is connected to a first input  52  of NCDFO  32 . NCDFO  32  provides two outputs  54  and  56  in quadrature at frequency 2f o  and another pair of outputs in quadrature at frequency f o . In the embodiment shown, only one output  60  is connected to an input  62  of automatic-gain control (AGC)  48 . 
   As stated above, output signal  44  from ADC  42  is connected to a second input  64  of AGC  48 . Output signal  66  from AGC  48  is an amplified version of oscillator output  60 , and is automatically adjusted in amplitude until the amplitude of signal  64  reaches a predetermined level. Signal  66  is connected to an input  68  of interpolator  70 , which is described in further detail below. Output  72  of NCDFO  32  is the square of tuning parameters β o  and is connected to a second input  74  of interpolator  70 . Input signal  68  to interpolator  70  is a sinusoid of prescribed amplitude, frequency f o , and sampling frequency f s . Output signal  76  from interpolator  70  is a sinusoid of the same amplitude and frequency as input signal  68 , but at a sampling frequency of I·f s , as interpolator  70  increases a sampling rate of input signal  68  by a factor of I. Output signal  76  from interpolator  70  is connected to an input  78  of a signal conditioning element  80 , whose output  82  is input to a digital-to-analog converter (DAC) and filter  84 . An output  86  of DAC and filter  84  is input to an analog driver  88  which produces a motor-drive signal  90  for gyroscope  20 . 
     FIG. 2  is a block diagram of interpolator  70  including four elements. A first element upsamples an output signal from oscillator  32  (shown in  FIG. 1 ) by placing I−1 values of zero between each pair of samples from oscillator  32 . The upsampled signal drives the second element, a Gray-Markel, lattice-based, second order, band pass interpolation filter, which is clocked at a frequency of I/T to remove all extraneous spectral components of the upsampled signal. As further described below, a passband-width parameter, α, in a preferred embodiment, is set to 0.999 and a tuning parameter of the filter is set to 
         β   o   ′     =       cos   ⁡     (     2   ⁢   π   ⁢           ⁢     f   o     ⁢     T   /   I       )       =       cos   ⁡     [       1   I     ⁢       cos     -   1       ⁡     (     β   o     )         ]       .             
The third element tunes the filter by generating the filter tuning parameter β′ o , via a three term power series where, β′ o ≈a 0 +a 1 β o   2 +a 2 β o   4 . The term β 0   2 , is provided by oscillator  32 . A fourth element of interpolator  70  is a scaling multiplier which renormalizes the signal amplitude by a factor of I/2.
 
   Referring specifically to  FIG. 2 , interpolator  70  includes a three-input second-order band pass filter  100  and a power series calculation section  102 . In the embodiment shown, band pass filter  100  is a Gray-Markel single-multiplier per order all pass structure whose output  104  is subtracted from an input  106  to provide band pass filtering. Input  106  is delivered to band pass filter  100  by sampling function  108 . Output  110  from band pass filter  100  is scaled by I/2 in multiplier  112  to generate output signal  76 . 
   Input  106  is connected to an additive input  114  of a first subtraction element  116 , an additive input  118  of a second subtraction element  120 , and a first input  122  of a first adder  124 . Output  126  of first adder  124  is connected to a first input  128  of a first multiplier  130 . A second input  132  to first multiplier  130  is α, an externally supplied parameter. In a specific embodiment, α is set to a value of 0.999. An output  134  of first multiplier  130  is connected to a subtractive input  136  of first subtraction element  116  and a first input  138  of second adder  140 . Output  104  of second adder  140  is connected to a subtractive input  142  of second subtraction element  120 . 
   Output  150  of first subtraction element  116  is connected to an additive input  152  of third subtraction element  154  and to an additive input  156  of fourth subtraction element  158 . A first input  160  of second multiplier  162  is connected to an output  164  of third subtraction element  154 . A second input  166  to second multiplier  162  is β′ o , which is a tuning parameter for band pass filter  100 . An output  168  of second multiplier  162  is connected to a subtractive input  170  of third subtraction element  158  and a subtractive input  172  of a fifth subtraction element  174 . 
   An output  176  of fourth subtraction element  158  is connected to a first delay element  178 . An output  180  of first delay element  178  is connected to a subtractive input  182  of third subtraction element  154  and to an additive input  184  of fifth subtraction element  174 . An output  186  of fifth subtraction element  174  is connected to an input  188  of second delay element  190 . Output  192  of second delay element  190  is connected to a second input  194  of first adder  124  and a second input  196  of second adder  140 . 
   In operation, a sinusoid at a frequency f o , is provided at input  68  at a sampling frequency of f s , to sampling function  108 . The sinusoid at input  68  is modified at sampling function  108  by insertion of I−1 values of zero being input between each pair of input samples of the sinusoid. A new signal is created at a sampling rate of I·f s . As described above, band pass filter  100  has as its second input  132  the parameter α, that determines a bandwidth for band pass filter  100 . The bandwidth parameter, α, has, in one embodiment, a nominal value of 0.999, where α is determined as α=tan(πf BW T/I), and where f BW  is the 3 dB bandwidth (in Hz) of the pass band. A center of the pass band is tuned by input  166 , the parameter β′ o , where 
           β   o   ′     =       cos   ⁡     (     2   ⁢   π   ⁢           ⁢     f   o     ⁢     T   /   I       )       =     cos   ⁡     [       1   I     ⁢       cos     -   1       ⁡     (     β   o     )         ]           ,       
 
where β o  is the input to NCDFO  32 .
 
   Direct calculation of β′ o , from β o  is difficult, but a Chebychev approximation can be obtained, in one embodiment, by a three-term power series, for example, β′ o ≈a 0 +a 1 β o   2 +a 2 β o   4 . This power series is mechanized in power series calculation section  102  whose input  74 , β 0   2 , is obtained directly from NCDFO  32 . Input  74  is connected as a first input to third multiplier  200  and fourth multiplier  202 . A second input  204  of third multiplier  200  is coefficient a 2 . An output  206  of third multiplier  200  is summed with coefficient a 1 , in third adder  208 , whose output  210  is connected to a second input  212  of fourth multiplier  202 . Fourth adder  214  sums an output  216  of multiplier  202  with coefficient a 0 . An output  218  of adder  214  is the tuning parameter β′ o . In one embodiment, a 0 , a 1 , and a 2 , are computed utilizing a Chebychev approximation program as illustrated in Appendix A. In a specific embodiment, and as outlined in Appendix A, a 0  is 0.9967032511, a 1  is 0.00526891, and a 2  is −0.0021640344. 
   Numerically controlled, dual frequency oscillators (NCDFO) implemented in MEMS gyroscope motor drive systems, typically produce a sinusoid, whose frequency may not be constant, and which is sparsely sampled. Such a motor drive system can introduce an unacceptable amount of time delay and phase shift, as above described. One way to improve performance of such motor drive systems is to increase the sampling frequency of the NCDFO output signal through the use of interpolator  70 . Implementation of system  10 , including interpolator  70  allows an increase in the sampling frequency of the NCDFO output signal by a factor of I, where I is greater than one, and typically eight or more. The combined time delay of interpolator  70 , a higher frequency DAC, and a simple low pass, anti-aliasing filter (DAC and filter  84 ) is less than the time delays in known gyroscope motor drive systems. 
   While the invention has been described in terms of various specific embodiments, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the claims.