United States Patent [191
`Hulsing et al.
`
`[11]
`[45]
`
`Patent Number:
`Date of Patent:
`
`4,799,385
`Jan. 24, 1989
`
`Attorney, Agent, or Firm-Christensen, O’Connor,
`Johnson & Kindness
`[57]
`ABSTRACT
`A Coriolis rate sensor comprising ?rst and second ac
`celerometers mounted with their force sensing axes
`parallel to a common sensing axis. The accelerometers
`are vibrated along arcs in response to a periodic drive
`signal at a ?rst frequency, each are being tangent to a
`vibration axis normal to the sensing axis. The acceler
`ometer output signals are demodulated to determine
`angular rate, as well as to detect the phase shift between
`the drive signal and the periodic compounds of the
`output signals. In one arrangement, the detected phase
`shifts are used to drive a phase servo that tends to re
`duce the bias error caused by interaction between the
`phase shifts and misalignments of the accelerometers
`with respect to the sensing axis. In another arrange
`ment, the phase shifts are used to calculate a bias term
`for correcting the measured angular rate. A single ac
`-
`'
`'
`celerometer embodiment 1s also descnbed.
`
`19 Claims, 3 Drawing Sheets
`
`_ mule/came“ {0
`
`[54]
`
`[75]
`
`[73]
`
`[21]
`[22]
`[51]
`[52]
`[53]
`
`[56]
`
`ANGULAR RATE SENSOR WITH PHASE
`SHIFI‘ CORRECI'ION
`Inventors: Rand H. Hulsing, Redmond; Rex B.
`Peters, Woodinville, both of Wash.
`Assignee: Sundstrand Data Control, Inc.,
`Redmond, Wash.
`Appl'. No.: 72,235
`Filed:
`Jul. 10, 1987
`
`Int. Cl.4 ................................... .. G01P 9/04
`U.S. Cl. ......................... .. 73/505; 73/510
`Field of Search ................... .. 73/505, 510, 517 R;
`364/453
`
`References Cited
`U.S. PATENT DOCUMENTS
`
`
`
`4,445,376 5/1984 Merhav 4,510,802 4/1985 Peters ...... ..
`
`73/510
`73/505
`73/510
`.
`4,590,801 5/ 1986 Merhav
`4,665,748 5/ 1987 Peters .................................. .. 73/505
`Primary Examiner—-John Chapman
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`1
`
`ANGULAR RATE SENSOR WITH PHASE SHIFT
`CORRECTION
`
`TECHNICAL FIELD
`The present invention relates to an apparatus for
`determining angular rate of rotation utilizing acceler
`ometers.
`
`4,799,385
`2
`and phase shift is the largest source of bias error in an
`angular rate sensor of this type.
`An approach to eliminating the above-described rate
`bias is set forth in US. Pat. No. 4,665,748. In the system
`described in that patent, the angular rate output of the
`accelerometers is demodulated by a signal in phase with
`the accelerometer motion, to produce a feedback signal
`that is used to drive the components of the accelerome
`ter output signal that are synchronous with the acceler
`ometer motion toward a null value. The present inven
`tion relates to an improved technique for reducing the
`bias error caused by interaction between misalignment .
`and phase shift of the accelerometers.
`
`SUMMARY OF THE INVENTION
`The present invention provides an angular rate sensor
`with an improved bias reduction technique. In a pre
`ferred embodiment, the angular rate sensor includes a
`phase servo that operates to reduce the phase shift be
`tween the accelerometer output signal and the demodu
`lation time reference.
`In one preferred embodiment, the angular rate sensor
`comprises an accelerometer assembly, timing/control
`means, ?rst and second demodulation means, rate chan
`nel means, and delay control means. The accelerometer
`assembly comprises ?rst and second accelerometers
`mounted such that their force sensing axes are parallel
`to a common sensing axis, and means for vibrating the
`accelerometers along arcs, each of which is tangent to a
`vibration axis normal to the sensing axis. In this context,
`the term “parallel” should be understood to include
`“antiparallel.” In a preferred embodiment, the force
`sensing axes of the accelerometers are antiparallel to
`one another. The accelerometer assembly also includes
`drive means for vibrating the accelerometers along
`their respective arcs at a ?rst frequency in response to a
`periodic drive signal at the ?rst frequency. Thus the
`output signal of each accelerometer includes a compo
`nent at a second frequency equal to twice the ?rst fre
`quency.
`The timing/control means generates a periodic mas
`ter timing signal from which the drive signal is derived.
`The master timing signal is also used to generate ?rst
`and second timing signals. The ?rst timing signal repre
`sents a ?rst rate component at the ?rst frequency in
`quadrature phase with respect to the drive signal, and a
`?rst phase shift component at the second frequency in
`phase with the drive signal, the ?rst timing signal being
`delayed by a ?rst time delay that is a predetermined
`function of a ?rst delay signal. In a similar manner, the
`timing/control means generates a second timing signal
`that represents second rate and phase servo compo
`nents, and that is delayed by a second time delay that is
`a predetermined function of a second delay signal. The
`first demodulation means demodulates the ?rst output
`signal using the ?rst rate component to produce a ?rst
`rate signal, and demodulates the ?rst output signal using
`the first phase shift component to produce a ?rst phase
`shift signal. Similarly, the second demodulation means
`demodulates the second output signal using the second
`rate component to produce a second rate signal, and
`demodulates the second output signal using the second
`phase shift component to produce a second phase shift
`signal. The rate signals are used by the rate channel
`means to provide a measure of angular rate about an
`axis normal to the sensitive vibration axes.
`The delay control means receives the ?rst and second
`phase shift signals, and produces the ?rst and second
`
`BACKGROUND OF THE INVENTION
`Angular rate of rotation about a given coordinate axis
`may be measured by moving (e. g., vibrating) an acceler
`ometer along an axis normal to the accelerometer’s
`sensitive axis and normal to the rate axis about which
`rotation is to be measured. For example, consider a set
`of X, Y, Z coordinate axes ?xed in a body whose rota
`tion rate is to be measured, and an accelerometer also
`?xed in the body with its sensitive axis aligned along the
`Z axis. If the angular rotation vector of the body in
`cludes a component along the X axis, then periodic
`motion of the accelerometer along the Y axis will result
`in a periodic Coriolis acceleration acting in the Z direc
`tion that will be sensed by the accelerometer. The mag
`nitude of the Coriolis acceleration is proportional to the
`velocity along the Y axis and the rotation rate about the
`X axis. As a result, the output of the accelerometer
`includes a DC or slowly changing component that rep
`resents the linear acceleration of the body along the Z
`axis, and a periodic component that represents the rota
`30
`tion of the body about the X axis. The accelerometer
`output can be processed, along with the outputs of
`accelerometers that have their sensitive axes in the X
`and Y directions and that are moved along the Z and X
`axes, respectively, to yield linear acceleration and angu
`lar rate about the X, Y and Z axes. Such signal process
`ing is described in US. Pat. Nos. 4,445,375 and
`4,590,801.
`As described in U.S. Pat. No. 4,590,801, one pre
`ferred embodiment of a rotation rate sensor comprises,
`for each axis, two accelerometers oriented with their
`sensitive axes parallel or antiparallel to one another, and
`means for vibrating the accelerometers along an axis
`normal to their sensitive axes. A suitable method for
`vibrating such accelerometer pairs is described in US.
`45
`Pat. No. 4,510,802. In the system described in that pa
`tent, a parallelogram structure is used to vibrate the
`accelerometers along a common vibration axis. In such
`an arrangement, it may be demonstrated that a bias
`error is produced by interaction between misalignment
`of the accelerometers with respect to the desired sensi
`tive axis, and the phase shift between the motion of the
`accelerometers and their resulting output signals. This
`bias error results from the fact that the misalignment
`causes the accelerometer to sense a component of the
`acceleration used to vibrate the accelerometers. In the
`absence of any phase shift, thiscomponent is synchro
`nous with the acceleration caused by the vibration, and
`therefore 90° out of phase with the vibration velocity
`and therefore with the Coriolis acceleration. The vibra
`tion acceleration therefore would be cancelled in the
`rate channel. However because of the phase shift intro
`duced by the accelerometer between its vibration veloc
`ity and the Coriolis component of its output signal, the
`vibration acceleration component is phase shifted so
`that it includes a subcomponent that is in phase with the
`vibration velocity, and that therefore shows up in the
`rate channel. This interaction between misalignment
`
`40
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`50
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`55
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`5
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`

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`4,799,385
`4
`3
`delay signals. In a preferred embodiment, the delay
`phase offset control described in U.S. Pat. No.
`control means produces a ?rst offset signal representing
`4,510,802, or by the phase servo of the present inven
`the estimated difference, at the second frequency, be
`tion, Equation (1) can be written as:
`tween the phase shift corresponding to the ?rst time
`delay and the phase shift between the drive signal and
`the periodic components of the ?rst output signal. The
`delay control means compares the ?rst offset signal to
`the ?rst phase shift signal, to produce a ?rst error signal
`representing the difference therebetween. In a similar
`manner, the delay control means produces a second
`offset signal representing the estimated difference, at
`the second frequency, between the phase shift corre
`sponding to the second time delay and the phase shift
`between the drive signal and the periodic components
`of the second output signal. The second offset signal is
`compared to the second phase shift signal to produce a
`second error signal representing the difference therebe
`tween. The ?rst and second error signals are used to
`produce the ?rst and second delay signals, such that the
`difference between the ?rst and second error signals is
`driven towards a null value.
`In a preferred embodiment, the delay control means
`produces the ?rst and second delay signals so as to
`reduce the magnitude of the larger of the two error
`signals. In a further embodiment, means are provided
`enabling the rate channel means to calculate a correc
`tion term for correcting the measure of angular rate, the
`correction term being a function of the ?rst and second
`error signals and of signals representing the angular
`misalignments of the accelerometers with respect to the
`sensing axis. An embodiment of the invention compris
`ing a single accelerometer is also disclosed.
`
`15
`
`20
`
`25
`
`The nulling system described in U.S. Pat. No. 4,665,748
`tends to make (11 equal to —a.;, to thereby drive the ?rst
`term of Equation (2) to zero. However, the second term
`of Equation (2) will still produce a bias error, unless the
`accelerometer phase shifts are equal to one another. In
`one embodiment, the present invention provides a phase
`servo that attempts to set (in equal to (in, and/or to drive
`each of ¢1 and 4:2 to zero. In a second aspect of the
`invention, the quantities a1, a2, 4n and (152 are deter
`mined, and the second term of Equation (2) is evaluated
`and subtracted from the calculated angular rate, in ef
`fect subtracting out a known bias error. In a preferred
`embodiment, both techniques are used to minimize bias
`error. In a second preferred embodiment, Equation (2)
`is used to subtract out the known bias error, and a ?xed
`offset is set during laboratory calibration, as described
`in U.S. Pat. No. 4,510,802.
`The present invention is preferably implemented in a
`rate sensor in which a pair of accelerometers having
`antiparallel sensitive axes are vibrated 180 degrees out
`of phase with one another along a common vibration
`axis, in the manner described in U.S. Pat. No. 4,590,801.
`However, for ease of description, the phase servo as~
`pect of the present invention will initially be described
`in the context of the single accelerometer embodiment
`shown in FIG. 1. This embodiment includes accelerom
`eter assembly 12, timing/control circuit 30, demodula
`tor 32, angular rate channel 34, and phase shift estimator
`36. Accelerometer assembly 12 includes linear acceler
`ometer 14 that produces an output signal on line 22, the
`output signal being a function of the acceleration of
`accelerometer 14 along sensitive axis S that is aligned
`parallel to the Z axis. Accelerometer 14 is vibrated
`along arcuate path 16 that is tangent to vibration axis V
`that in turn is parallel to the Y axis and normal to the
`sensitive axis. The vibration is performed in a manner
`such that sensitive axis S remains parallel to the Z axis
`during the vibration motion. The accelerometer assem
`bly vibrates the accelerometer in response to (and syn
`chronously with) a drive signal proportional to sinwt on
`line 20. The designation sinmt for the drive signal indi
`cates that accelerometer 14 is at its vibration midpoint
`at time t=0.
`As set forth in U.S. Pat. No. 4,510,802, the accelera
`tion experienced by accelerometer 14 along its sensitive
`axis, due to vibration along path 16, is given by:
`
`30
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`FIG. 1 is a schematic block diagram of a preferred
`embodiment of the angular rate sensor and phase servo
`of the present invention;
`FIG. 2 is a block diagram of a preferred embodiment
`of the phase shift estimator;
`FIG. 3 is a block diagram of an angular rate sensor of
`40
`the present invention comprising a pair of accelerome
`ters;
`FIG. 4 is a block diagram of a preferred embodiment
`of the delay control circuit of FIG. 3.
`
`DETAILED DESCRIPTION OF THE
`INVENTION
`In an angular rate sensor of the type described in U.S.
`Pat. Nos. 4,590,801 and 4,665,748, the rate bias caused
`by the interaction of misalignment and phase shift is
`proportional to:
`
`45
`
`50
`
`2(a1 sin¢1+ a2 sinrbz)
`
`(1)
`
`where (11 and a; are the misalignments of the acceler
`ometers, and 4n and ¢2 are the corresponding net phase
`shifts between the accelerometer output signals and the
`demodulation time reference. In general, each phase
`shift will be equal to the phase shift between the acceler
`ometer vibration motion and the accelerometer output
`signal caused by such vibration, plus the phase shift
`between the drive signal and the actual accelerometer
`motion, less the phase correction introduced by the
`present invention, as described below. In general, the
`phase shift between the accelerometer motion and the
`accelerometer output signal will be much greater than
`the phase shift between the drive signal and the acceler
`ometer motion. For the normal case in which (in and d);
`are small angles, either by design, by adjustment of the
`
`55
`
`w2R0siml|sinmt+ m2R02 costllcosZmt
`
`(3)
`
`60
`
`65
`
`where m is the angular frequency of vibration, R is the
`radius of curvature of path 16, ti: is the initial- offset of
`the vibration, and 0 is the amplitude of vibration. Thus
`the output signal produced by accelerometer 14 on line
`22 will include four components: a linear acceleration
`component AZ due to linear acceleration along the Z
`axis; a Coriolis component proportional to 9,, coswt,
`where 0,, is the angular rate of accelerometer assembly
`12 about an X axis that is directed out of the plane of the
`?gure in FIG. 1; and components proportional to sinmt
`and cos2mt as per Equation (3) above. As described in
`U.S. Pat. No. 4,665,748, the output signal from acceler
`
`6
`
`

`

`4,799,385
`5
`6
`ometer 14 may be processed, together with the output
`spectively, the amount of the delay being controlled by
`signal of a second accelerometer that is vibrated in an
`a delay signal on line 58. The delayed versions of the
`opposite direction with its sensitive axis antiparallel to
`signals on lines 44 and 46 may comprise a single peri
`that of accelerometer 14, to produce a signal propor
`odic signal at frequency 40) that includes a rate compo
`tional to angular rate 0.x.
`nent representing cosmt and a phase shift component
`Operation of the signal processing elements illus
`representing sin 2wt. The delayed SGN cosmt signal on
`trated in FIG. 1 will now be described. To simplify the
`line 54 (i.e., the rate component) is used by angular rate
`discussion, it will be assumed that the AZ and sinmt
`channel 34 to demodulate the output signal on line 22, in
`components can be ignored. The purpose of the signal
`order to determine angular rate 0x about an X axis
`processing elements is to process the output signal on
`perpendicular to the Y and Z axes. The purpose of the
`line 22 to produce a signal indicative of angular rate 9,‘.
`delay introduced by delay circuit 52 is to phase shift the
`In general, this can be accomplished by demodulating
`demodulation signal on line 54 by an amount equal to
`the output signal with a periodic signal synchronous
`the phase shift of accelerometer assembly 12. In accor
`with coswt. However, in an actual system, there will be
`dance with the present invention, the delay introduced
`a phase shift between the periodic components of the
`by delay circuit 52 is determined by the delay signal on
`output signal and the drive signal on line 20. Thus ide
`line 58 that, in turn, is determined by demodulator 32
`ally, the demodulation of the output signal should be
`and phase shift estimator 36.
`performed by a signal synchronous with cosmt that has
`Demodulator 32 demodulates the output signal using
`the SGN sin2wt demodulation signal (i.e., the phase
`been time delayed or phase shifted by an amount corre
`sponding to the phase shift ¢.,, introduced by the accel
`shift component) on line 56. The resulting phase shift
`erometer assembly at frequency w. The phase shift of a
`signal produced by demodulator 32 on line 60 repre
`periodic signal produced by a time delay Td is equal to
`sents the difference, at twice the drive signal frequency,
`mTd, where w is the angular frequency of the signal. As
`between the phase shift of accelerometer assembly 12
`previously described, the phase shift gba, is the sum of a
`and the phase shift corresponding to time delay Td. This
`comparatively large phase shift between the accelerom
`phase shift signal is input to phase shift estimator 36.
`eter motion and the periodic output signal components,
`Phase shift estimator 36 compares the phase shift signal
`and a comparatively small phase shift between the drive
`to an offset signal generated by the phase shift estimator
`signal and the accelerometer motion.
`based upon the current delay signal. The offset signal
`A phase servo technique for delaying the coswt de
`represents an estimate of the difference, at twice the
`modulation signal by the required amount is described
`drive signal frequency, between” the phase shift pro
`below. This system can be most readily understood by
`duced by accelerometer assembly 12 and the phase shift
`first describing an open loop version of the system,
`corresponding to the present time delay T4. The phase
`without the phase servo closed. In this formulation, the
`shift estimator subtracts the offset signal from the phase
`required time delay of the cosmt demodulation signal is
`shift signal, and produces an error signal corresponding
`determined by ?rst measuring the phase shift of the
`to the difference therebetween. The phase shift estima
`output signal component proportional to cosZmt, thus
`tor then updates the delay signal based on the error
`determining the phase shift (bzm 0f the accelerometer
`signal, such that the error signal is driven towards a null
`assembly at frequency 21». The phase shift of the output
`value. The error signal may also be input to angular rate
`signal component proportional to cos2mt is determined
`channel 34 via line 70, and used by the angular rate
`by demodulating the output signal with a signal syn
`channel to re?ne the calculation of angular rate.
`40
`chronous with sin2wt. Once the phase shift d120, has been
`A preferred embodiment for phase shift estimator 36
`determined, it is used to estimate the phase shift 4),, at
`is illustrated in FIG. 2. The phase shift estimator may be
`frequency a). The estimated phase shift (be, is then con
`implemented in the digital domain by a programmed
`verted to the required time delay Td, using the relation
`data processor, or by analog signal processing compo
`Td=¢w/m.
`nents. In general, a digital implementation will be pre
`In an actual phase servo according to the present
`ferred, for higher accuracy. Thus use, for example, of
`invention, time delay Tdis used to delay both the sin2wt
`the term “signal” herein should be understood to in
`and cosmt demodulation signals. This is accomplished
`clude digital words produced by a data processor, as
`by a phase servo loop comprising timing/control circuit
`well as analog signals. The phase shift estimator com~
`30, demodulator 32, and phase shift estimator 36. Ti
`prises summation point 80, scaler 82, summing block 84,
`ming/control circuit 30 receives an appropriate clock
`and estimation model 86, and temperature sensor 90.
`signal on line 40, and uses the clock signal to generate
`The delay signal produced by summing block 84 on line
`the timing signals SGN sinmt, SGN coswt, and SGN
`58 is an estimate of the phase shift (bu, of the accelerome
`sin2mt on lines 42, 44 and 46, respectively. The symbol
`ter output signal with respect to the drive signal at
`“SGN” represents “sign off’, and the signals on lines
`frequency w. Estimation model 86 receives the signal
`42, 44 and 46 may comprise any signals that encode the
`4),,» and produces an offset signal (home; on line 88 that is
`sign of the corresponding periodic functions. It will be
`an estimate of the difference between the phase shift of
`appreciated by those skilled in the art that these signals
`the output signal at frequency 2:» and the phase shift
`on lines 42, 44 and 46 may comprise a single periodic
`corresponding to the current delay signal at frequency
`signal at frequency 4c». The SGN sinmt signal on line 42
`2w. In the simplest case, estimation model 86 could
`is input to drive signal generator 50, and is used by the
`simply assume that the phase shift at frequency 2:» is
`drive signal generator to generate a sinusoidal drive
`equal to twice the phase shift at frequency to, so that
`signal sinwt on line 20. Accelerometer assembly 12
`dag/Se; is equal to zero. This corresponds to the case of
`responds to the drive signal by vibrating accelerometer
`equal time delays at frequencies a) and 2:». However, if
`14 along path 16, as described above.
`it is assumed that accelerometer assembly 12 can be
`The SGN cosmt and SGN sin2wt signals on lines 44
`modeled as a second order system, then a more accurate
`and 46 are input to delay circuit 52 that produces de
`estimate of phase shift at 20) can be determined as fol
`layed versions of these signals on lines 54 and 56, re
`lows.
`
`50
`
`55
`
`65
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`
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`
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`
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`¢offset =
`
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`
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`
`41-02 hm
`
`_ 24):» + 43c
`
`where a)” is the natural frequency of the accelerometer
`assembly, and ¢c is a calibration value. As indicated by
`line 92 in FIG. 2, estimation model 86 can also provide
`for temperature modeling of the phase relationship.
`Thus, in the most general case, (120mg; can be modeled as
`a polynomial function only of d)", and temperature. In
`general, the estimation model will be a function of 4%,,
`which is generated by the system, and of quantities such
`as w and a)” that are either constants or repeatable func
`tions of temperature. It is this characteristic that makes
`the estimation process practical. For moderately
`damped second order systems, as well as for many other
`common low order dynamic systems, the phase shift at
`219 is nearly equal to twice the phase shift at a), so that
`¢,,ff,., is considerably less than (1%,. Thus the re?nement
`provided by Equation (4) is comparatively small, and
`the exact form of the estimation model will not be criti
`cal for many applications.
`Summing junction 80 determines the difference be
`tween the phase shift signal on line 60 and the (home;
`signal on line 88, and scaler 82 then converts this differ
`ence to the to (rather than 2:») domain by multiplying
`the difference signal by one-half. The result is the error
`signal on line 70 that represents the difference between
`the phase shift signal and the current estimate ¢ojyset of
`35
`the phase shift signal. The error signal is integrated by
`summing block 84 to produce the delay signal on line
`58, an arrangement that operates to continuously drive
`the error signal towards a null value.
`A preferred embodiment of an angular rate sensor
`with a phase servo, in accordance with the present
`invention, is illustrated in FIGS. 3 and 4. This angular
`rate sensor includes accelerometer assembly 100, ti
`ming/ control circuit 102, demodulators 104 and 106,
`delay control circuit 108, angular rate channel 110, and
`misalignment channel 112. Accelerometer assembly 100
`includes accelerometers 120 and 122 that are mounted
`in a parallelogram assembly 124, such as the one de
`scribed in U.S. Pat. No. 4,590,801. Accelerometers 120
`and 122 are positioned with their sensitive axes antipar
`50
`allel, and are vibrated along a vibration axis 180° out of
`phase with one another. The vibration axis is normal to
`the sensitive axes of the accelerometers. Accelerome
`ters 120 and 122 produce output signals on lines 130 and
`132, respectively.
`The output signal from accelerometer 120, on line
`130, is processed by demodulator 104, and the output
`signal of accelerometer 122, on line 132, is processed by
`demodulator 106. Demodulators 104 and 106 are con
`trolled by timing signals for timing/control circuit 102
`on lines 134 and 136, respectively. The timing/control
`circuit includes clock circuit 140, drive signal generator
`142, and delay circuits 144 and 146. Clock circuit 140
`produces a master timing signal on line 148 that defines
`the vibration cycle at frequency a). By way of example,
`the master timing signal on line 148 could comprise a
`series of pulses or edges spaced at intervals of 1r/2m.
`The master timing signal is received by drive signal
`generator 142, and is used by the drive signal generator
`
`10
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`25
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`4,799,385
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`to produce a drive signal on line 150 that is synchronous
`with sinwt.
`Delay circuit 144 receives the master timing signal,
`and produces a delayed timing signal on line 134, the
`amount of the delay being controlled by a delay signal
`received on line 150. In a similar manner, delay circuit
`146 receives the master timing signal, and produces a
`delayed timing signal on line 136, the amount of the
`delay being controlled by a delay signal on line 152.
`Each delayed timing signal includes a phase shift com
`ponent representing sin Zwt, a rate component repre
`senting cosmt, and an alignment component represent
`ing sinmt. Demodulator 104 uses the delayed timing
`signal on line 134 to demodulate the output signal of
`accelerometer 120 by the functions sin2wt, cosmt and
`sinwt, to produce, respectively, a phase shift signal P1
`on line 160, a rate signal C1 on line 162, and an align
`ment signal S1 on line 164. Similarly, demodulator 106
`demodulates the output signal from accelerometer 122,
`using the delayed timing signal on line 136, to produce
`a phase shift signal P2 on line 170, a rate signal C2 on
`line 172, and an alignment signal S2 on line 174.
`The phase shift signals P1 and P2 on lines 160 and 170
`are input to delay control circuit 108. The delay control
`signal compares the phase shift signals on lines 160 and
`170 to the current delay signals on lines 150 and 152
`respectively, and generates error signals ¢e1 and ¢e2 On
`lines 180 and 182 respectively, corresponding to the
`differences between the phase shift and current delay
`signals. Delay control circuit 108 adjusts the delay sig
`nals on lines 150 and 152, such that the difference be
`tween the error signals ibel and (be; is driven towards
`zero. In general, this may be accomplished by making
`the error signals equal to one another, and/or by mak
`ing both error signals equal to zero.
`The error signals are input to angular rate channel
`110, together with the signals C1, C2, S1 and S2 from
`demodulators 104 and 106. For an accelerometer assem
`bly of the type described, it may be shown that the
`angular change about the X axis A6,; during a vibration
`period T is given by:
`
`‘bell
`
`(5)
`
`In this equation, a, b, c and d are temperature modeled
`coefficients. The ?rst bracketed term in Equation (5)
`corresponds to Equation (7) in U.S. Pat. No. 4,665,748,
`while the second bracketed term in Equation (5) corre
`sponds to the second term in Equation (2) above. Angu
`lar rate channel 110 implements Equation (5), to deter
`mine A0,, for each vibration period, and thus measure
`angular rate about the X axis. Angular rate channel 110
`may also utilize the S1 and S2 values to generate a
`misalignment command \I/ on line 178 that is input to
`misalignment channel 112. Misalignment channel 112 is
`described in'greater detail in U.S. Pat. No. 4,665,748.
`The misalignment command is preferably generated as
`indicated in block 110, with f, g and h being temperature
`modeled coefficients.
`For a system in which delay control circuit 108 seeks
`only to drive each error signal 4M and 4:82 to zero, the
`delay control circuit may simply comprise two uncon
`nected circuits similar to phase shift estimator 36 shown
`in FIG. 2. However, referring to Equation (2), it can be
`seen that even if ¢e1 and (be; have nonzero values, the
`second term of Equation (2) can be driven to zero by
`
`60
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`8
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`

`

`5
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`25
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`30
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`4,799,385
`10
`making ¢e1 equal to cbez. Thus in a preferred embodi
`thereby produce a delayed ?rst timing signal, and
`ment, the delay control circuit also seeks to set the error
`means for generating a second timing signal such
`signals the; and qbez equal to one another, as well as to set
`that the second timing signal represents a second
`each error signal to zero. A preferred embodiment of
`rate component at the ?rst frequency in quadrature
`such a delay circuit is shown in FIG. 4. The delay con
`phase with respect to the drive signal and a second
`trol circuit comprises phase shift estimators 190 and 192,
`phase shift component at the second frequency in
`logic circuit 194, and summing blocks 196 and 198.
`phase with the drive signal, and means for delaying
`Each of phase shift estimators 190 and 192 may be iden
`the second timing signal by a second time delay
`tical to phase shift estimator 36 shown in FIG. 2. Phase
`that is a predetermined function of a second delay
`shift estimators 190 and 192 produce error signals 11:81
`signal to thereby produce a delayed second timing
`and ¢ez on lines 200 and 202 respectively. Logic block
`signal;
`194 examines the signals 4:21 and M, and determines
`?rst demodulation means connected to receive the
`which is the larger of the two. If (#81 is larger, then logic
`?rst output signal and the delayed ?rst timing sig
`block 194 decrements the count stored in summing
`nal, and including means for demodulating the ?rst
`block 196,