1 PPM PRECISIONMEMS C

A.A. Trusov1,2*, I.P.1 MicroSystems La

2 Northrop Grumman Electronic S ABSTRACT

We report a scale factor self-calibCoriolis vibratory gyroscopes enabled byof the sense-mode closed loop gain. closed loop scale factor employed in tResonator Gyroscope (HRG), we meascale factor changes by injecting a kn(virtual input rate) into the sense-modethe normal operation of the gyroscope. Tvalidated using an in-house developedMEMS Quad Mass Gyroscope (QMGstructural symmetry and low demonstrated a 350 ppm accuracy (limand a 1 ppm precision by simultaneoustrue and self-calibrated scale factors ovetemperature range. KEYWORDS

Self-calibration, scale factor, MEMS INTRODUCTION

Accuracy of MEMS inertial sensoaffected by the drifts in scale factopotential application in navigational-graa 1 ppm stability requirement. Temperon the order of 1000 ppm/°C are a majorachieving 1 ppm overall stability in MDrifts of analog front end gains acontribute to further degradation of scaWe propose to tackle the issue of scale by continuous self-calibration of the mode gain during its normal operatioperiodic offline physical re-calibrationusing sophisticated inertial characterizthe new approach eliminates the need foabsolute rotation reference or any other p

Similarly to the Closed Loop Scale approach employed in the macro-scnavigational-grade Hemispherical Reso(HRG), the method relies on a virtual into continuously observe and compensata gyroscope is operated in force-to-rebalof operation, the key factor enabling 1self-calibration is the whole-angle (Wprovides a stable in-situ reference (angterm stable down to ppb). An in-house dsilicon MEMS Quadruple Mass Gyrosccapable of both WA [5] and FTR-modeschosen for the approach validation duestructural parameters (operational anti-p2 to 3 kHz, measured Q-factors above 1 frequency and damping symmetry).

N SELF-CALIBRATION OF SCALE FACORIOLIS VIBRATORY GYROSCOPES

Prikhodko1, D.M. Rozelle2, A.D. Meyer2, A.Maboratory, University of California, Irvine, CASystems − Navigation Systems Division, Woo

bration in MEMS y real time control

Similarly to the the Hemispherical asure and remove own dither signal

e dynamics during The approach was d sub-°/hr silicon

G) with HRG-like dissipation. We ited by the setup) sly measuring the r a 10 °C dynamic

S gyroscope.

ors is significantly or, limiting their ade missions with rature sensitivities r limiting factor in

MEMS sensors [1]. and other effects ale factor stability.

factor uncertainty gyroscope sense-

on. In contrast to n of rate sensors zation equipment, or a high accuracy physical stimulus. Factor (CLSF) [2]

cale fused quartz onator Gyroscope nput rate injection te drifts. Although lance (FTR)-mode ppm scale factor

WA)-mode, which gular gain is long-developed sub-°/hr cope (QMG) [3,4] s of operation was e to its HRG-like

phase frequency of million, complete

FORCE-TO-REBALANCEThis section reviews FTR

provide framework for the CLS Principle of Operation

FTR operation [6] is usedof-mode-matched high-Q gadvantage of their inherently noise. As shown in Fig. 1, the operated at mechanical resonLocked Loop (PLL). The amplis stabilized by an Automatic sense-mode amplitude is maintrebalancing force which inquadrature signals. This allowof the mode-matched gyroscopthe sense-mode.

The rate (FTR) and qsimilarly to the drive-mode awith a zero set point. The ratio channel rebalancing force fy tocontrol force fx is used to measu ( zxxy kQff 2 Δ+Ω=where Qx is the drive-mode Q-factor, Δ(1/τ) is the decay time drive- and sense-modes, and θτ axis of damping. Eq. (1) higmismatch Δ(1/τ) is a major sour

Figure 1: QMG control loops:and closed loop scale factor (Cinjected to observe and correct

CTOR IN

M. Shkel1 A, USA odland Hills, CA, USA

E ANALYSIS rate gyroscope operation to

SF self-calibration.

d to improve the bandwidth gyroscopes while taking y high sensitivity and low

gyroscope’s drive-mode is nance ωx using a Phase-itude of drive-mode motion Gain Control (AGC). The

tained at zero by applying a ncludes the Coriolis and s increasing the bandwidth

pe using feedback control of

quadrature loops operate mplitude control loop, but of the sense-mode Coriolis

o the drive-mode amplitude ure the input rate [6]:

) xωθτ τ2sin)/1(Δ , (1) factor, k is the angular gain constant mismatch between is the angle of the principal ghlights that the damping rce of drift in the gyroscope.

: force-to-rebalance (FTR)CLSF). Virtual input rate ist for scale factor drifts.

Th1A.005

978-1-4673-5983-2/13/$31.00 ©2013 IEEE 2531 Transducers 2013, Barcelona, SPAIN, 16-20 June 2013

Bandwidth Bandwidth of the FTR rate loop is a critical

parameter since it must not interfere with the operation of the CLSF dither signal. Otherwise, the frequency domain based separation of the true inertial input from the virtual input (dither signal) introduced by the CLSF calibration loop is impossible. The bandwidth analysis assumes the gyroscope dynamics is governed by: ( ) ( )xkfyyQy zyyyy τθτωω 2sin)/1(22 Δ+Ω−=++ , (2) where y, ωy and Qy are the sense-mode displacement, frequency and Q-factor, respectively. Here, the drive-mode motion x is controlled by AGC and PLL loops to sustain an oscillation with a stable amplitude a0, x = a0 cosωxt.

FTR control laws are formulated in terms of the in-phase cy and quadrature sy components of the y signal: )sin()cos( φωφω +++= tstcy yy , (3) where cos(ωt+φ) and sin(ωt+φ) are the reference signals generated by PLL operating at the frequency ω = ωx +φ . The cy component proportional to the input rate is always rebalanced (zeroed) by the proportional-integral (PI) controller with the gain Kcy and integral time τcy [7]: ( ) )sin()(2/1

0φωτττ +⎥⎦

⎤⎢⎣⎡ += ∫ tdccKf

t

ycyycyy. (4)

Substituting (3) and (4) into (2), we obtain equation ( ) 22sin)/1(22 00

2 akdccc z

t

yyy τθττωτ Δ+Ω−=++ ∫ΩΩ, (5)

which can be used to analyze the transient response and bandwidth [7]. Here τΩ=4ω/Kcy and ωΩ=Kcy/(4ωτcy) are the values of settling time and the rate-loop bandwidth.

Similarly to Eq. (2), the derivative of Eq. (5) is an equation of damped, linear, second order system with bandwidth ωΩ and settling time τΩ defined by controller's proportional (P) and integral (I) gains Kcy and Kcy/τcy. In contrast to the open-loop operation, the closed-loop FTR bandwidth and settling time can be adjusted without sacrificing the low noise of the sense-mode. This is critical for high-Q rate sensors since the-mode-matching in open loop operation limits their measurement bandwidth. The open-loop settling time is given by the energy decay time constant τ=2Qy/ω, which for Q values greater than 1 million and frequencies below few kHz reaches several minutes, making it practically impossible to measure fast changes of the input rotation. The closed loop FTR operation resolves the gain-bandwidth tradeoff while preserving low noise operation of high-Q devices.

CLOSED LOOP SCALE FACTOR

This section presents adaptation of the CLSF approach [2] to mode-matched high-Q MEMS gyroscopes

Principle of Operation

Fig. 1 shows FTR and CLSF control loops, which continuously observe and adjust the sense-mode gain (scale factor). CLSF relies on adding a square-wave modulation signal to the FTR command (feedback signal, fy) and observing the output angle precession of the gyroscope. The self-calibration closed-loop is added to the four existing loops without interrupting the gyroscope normal FTR operation. This is possible because the frequency of the modulation signal is chosen to be outside

of the gyroscope bandwidth. It also allows separating the inertial input information from the modulated signal in frequency domain.

The injected modulation signal acts as a virtual input rate Ωr-mod and deviates the vibration pattern angle of the gyroscope from its nominal null position through the use of WA-mode. By comparing the angle output relative to the integrated virtual input, the scale factor change is made observable. The scale factor estimate is fed to the PI controller to form the CLSF feedback command. A notch filter is employed to remove the self-calibration dither signal from the sensor output. This way the CLSF loop does not interfere with the FTR operation. To perform an active self-calibration, the CLSF feedback signal is used to continuously regulate the loop gain by changing the forcer gain Kfy. Dynamics

Dynamics of a FTR gyroscope operated with CLSF can be described as: ( ) ( ) xxkfKyyQy rzyfyyyy mod

2 2 −Ω+Ω−=++ ωω , (6) with two inputs (true rate Ω z and virtual rate Ωr-mod). Here, the Δ(1/τ) term is omitted for clarity. The cy component of the gyroscope output contains responses to both inputs, which are separated by using a notch filter. While the filtered cy component is used in the FTR rate-loop controller to rebalance the term (Kcyfy−2kΩz) to zero, the raw cy signal is used to form the scale-factor error estimate for the CLSF controller and adjust its gain K c y .

When FTR loops are in place, the dynamics simplifies to: ( ) xyyQy ryyy mod

2−Ω=++ ωω , (7)

and the steady-state solution in terms of cy is given by [6]: ∫ −− Θ=Ω=

τττ

0 mod0mod0 )( rry adac . (8)

which is the WA output. Eq. (8) shows that for ideal case, the measured output angle Θ is exactly the integral of the virtual input rate Θr-mod. In reality, however, errors such as analog front-end gain drift lead to the output change. The angle difference is used to observe the scale factor error: ( )mod00 mod0 )( −− Θ−Θ=Ω− ∫ rry adac

τττ . (9)

Alternatively, scale factor change can be observed by demodulating the raw cy output with the Θr-mod reference input. This approach is implemented in the current paper. EXPERIMENTAL RESULTS

This section experimentally validates the CLSF self-calibration using the Quadruple Mass Gyroscope (QMG). Sensor and Electronics

To investigate the feasibility of CLSF for MEMS, we performed a series of experiments using a first generation silicon MEMS QMG [3] with natural frequencies of 2.2 kHz and measured Q-factors of 1.2 million with ΔQ/Q of ±1%. This gyroscope previously demonstrated an angle random walk (ARW) of 0.02 °/√hr and in-run bias instability of 0.2 °/hr [4]. The vacuum packaged QMG was mounted on a PCB with front-end electronics and mounted on a 1291 Ideal Aerosmith precision rate table equipped with a thermally controlled chamber.

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Electrostatic actuation and capacitiemployed along with the EAM techniqufeed-through elimination. All contprocessing were realized using a LabViHF2LI Zurich Instruments unit and a hDS345 signal generator square-wave mo

Force-to-Rebalance Characterizati

Fig. 2 shows the measured responsrates in a ±5°/s range using an FTR insThe data confirms that the sense-mode szero in presence of applied rotations,required to rebalance the motion fy was papplied rate with a 0.5% full scale RMSfull scale rate range of 150 °/s was achultra-high Q-factor and was only limitedavailable forcer voltage of 10 V.

For the proof of concept demonstrcalibration, the PI gains in Eq. (5) wer2 Hz FTR loop bandwidth, while the mfor the CLSF loop was set at 7 Hz. TAGC, PLL and quadrature loops was 15 Hz, and 2 Hz, respectively. Despitdown time constant of 172 s and a fast acceleration, the measured settling timewas in a good agreement with the 2 H

Figure 2: Rate response in 5°/s range, shlinearity and no interference of CLSF an

Figure 3: FTR rate-loop bandwidth meaby applying sinusoidal rotation with diffe

ive detection were ue for the parasitic trol and signal ew programmable high-stability SRS odulation.

ion e to input rotation strumented QMG. signal cy remained , while the force proportional to the S linearity. A wide hieved despite the d by the maximum

ration of the self-re chosen to set a modulation signal

The bandwidths of set to be 0.5 Hz, te the QMG ring 300 °/s2 rate table e of 0.5 s (Fig. 2) Hz FTR rate-loop

bandwidth, Fig. 3. Further charate noise performance of FTapproach that of the open-loop

Closed Loop Scale Factor C

While the nominal scale initially obtained using the ratchange or drift was observed demodulation of the QMG angfrequency of the injected moduFig. 4. The square-wave movirtual rate input, and accordinof the gyroscope is equal to which is the triangular wave sig

To analyze CLSF accuracyQMG was continuously obser±5 °/s physical rotations while 25 °C to 35 °C, Fig. 5. At tprovided an estimate of scale fan experimental comparison scale factor change over the 1range, demonstrating a close mRMS accuracy (difference betwvalues) was measured to confirming that CLSF output ccorrect the gyroscope’s true

howing 0.5% RMS nd FTR loops.

asured to be 2 Hzferent frequencies.

Figure 4: Measured input and self-calibration loop used to est

Figure 5: QMG rate output in input rotations, used to charact

aracterization revealed that TR-operated gyroscope can

high-Q sensor.

Characterization factor of 0.06 (°/s)/V was

te table (Fig. 2), its relative in real-time by amplitude

gle output (CLSF output) at ulation signal (CLSF input), dulation signal acts as a

ng to Eq. (8) the WA output the integral of this signal, gnal. y, a true scale factor of the rved by applying constant changing temperature from

the same time, the CLSF factor drift. Fig. 6(a) shows of the true and estimated

10 °C dynamic temperature match between values. The ween the true and estimated

be 350 ppm, Fig. 6(b), can be used to observe and e scale factor drift. The

output signals of the CLSF timate scale factor change.

response to physical ±5°/s terize the true scale factor.

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accuracy of the experiment was limited(0.01 %) rate table accuracy specified by

To perform an active self-calibrfeedback command was used to continuloop gain of the QMG using a PI constable scale factor. Allan deviation analloop scale factor showed that 30 pachieved after 1 minute of self-calibrat30 minutes of operation, 1 ppm precidemonstrating potential of MEMS calibration for inertial-grade performanc CONCLUSIONS

Scale-factor self-calibration was iman in-house developed sub-°/hr Quadr capable of both whole angle and fmodes of operation. The self-calibrationinjected modulation signal (virtual ratethe gyroscope dynamics and analog froin the same manner as does the true signal. We demonstrated 350 ppmsimultaneously measuring the true anscale factors over 10 °C dynamic tempeprecision of self-calibration was 1 ppmaveraging. The ongoing work on ra

(a) A close match between the measuredand CLSF estimate demonstrates feasibi

(b) Demonstration of a 350 ppm CLSF aby subtracting estimated CLSF from the

Figure 6: Experimental comparison of terrors over a 10 °C dynamic temperatur

d by the 100 ppm y the datasheet. ration, the CLSF uously regulate the ntroller, yielding a lysis of the closed ppm precision is tion, Fig. 7. Upon ision is achieved,

gyroscope self-ce.

mplemented using Mass Gyroscope

force-to-rebalance-n works since the e) passes through

ont-end electronics inertial input rate

m accuracy by nd self-calibrated erature range. The m after 2000 s of ate table encoder

synchronization is deemed to better than 100 ppm scale-factoWe believe that our initialintriguing new approach to theinertial MEMS performance anand development of self-calibra ACKNOWLEDGEMEN

This work was supported under Contract N66001-12-C-4William Chappell. The deviceat the MicroSystems Laborator

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[4] I.P. Prikhodko, S.A. ZoShkel, "Sub-degree-per-hsensor with 1 million QPapers Transducers‘11 CJune 5–9, 2011, pp. 2809–

[5] I.P. Prikhodko, S.A. Zotov"Foucault pendulum on a cMEMS gyroscope," SenPhysical, Vol. 177, pp. 67–

[6] D. Lynch, "Coriolis vibratGyro Technology 1998, ppAnnex B, Coriolis VibratIEEE Std. 1431-2004).

[7] D. Lynch, "Vibratory gyroaveraging," Proc. 2nd St.Gyroscopic Technology a1995.

CONTACT

*A.A. Trusov, alex.trusov@

d true scale factorility of the scheme.

accuracy obtainedtrue scale factor.

the true and CLSFre range.

Figure 7: Allan deviation anprecision of CLSF is achieved u

result in demonstration of or self-calibration accuracy. l results demonstrate an

e next level improvement in nd motivate future research ation techniques.

NTS by the DARPA/SPAWAR

4035, program manager Dr. s were designed and tested

ry, UC Irvine.

penis, "Error sources in in-k MEMS gyroscopes," J. vol. 15, no. 3, pp. 479–491,

op scale factor estimation," 8, 2009. Schofield, A.M. Shkel,

fork gyroscopes with ultra-ock rejection," US Patent

otov, A.A. Trusov, A.M. hour silicon MEMS rate Q-factor," in Digest Tech. Conference, Beijing, China, –2812. v, A.A. Trusov, A.M. Shkel, chip: rate integrating silicon nsors and Actuators A: –78, April 2012. tory gyros," in: Symposium p. 1.0–1.14. (Reproduced as tory Gyros, pp. 56–66 of

o analysis by the method of . Petersburg Int. Conf. on and Navigation, pp. 26–34.

@gmail.com

nalysis shows that 1 ppm upon 2000 s of averaging.

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