Navigation Grade MEMS IMU for a Satellite

micromachines

Article Navigation Grade MEMS IMU for A Satellite

Wanliang Zhao, Yuxiang Cheng *, Sihan Zhao, Xiaomao Hu, Yijie Rong, Jie Duan and Jiawei Chen

Shanghai Aerospace Control Technology Institute, 1555 Zhongchun Road, Shanghai 201109, China; [email protected] (W.Z.); [email protected] (S.Z.); [email protected] (X.H.); [email protected] (Y.R.); [email protected] (J.D.); [email protected] (J.C.) * Correspondence: [email protected]

Abstract: This paper presents a navigation grade micro-electromechanical system (MEMS) inertial measurement unit (IMU) that was successfully applied for the ﬁrst time in the Lobster-Eye X-ray Satellite in July 2020. A six-axis MEMS gyroscope redundant conﬁguration is adopted in the unit to improve the performance through mutual calibration of a set of two-axis gyroscopes in the same direction. In the paper, a satisfactory precision of the gyroscope is achieved by customized and self- calibration gyroscopes whose parameters are adjusted at the expense of bandwidth and dynamics. According to the in-orbit measured data, the MEMS IMU provides an outstanding precision of better than 0.02 ◦/h (1σ) with excellent bias instability of 0.006 ◦/h and angle random walk (ARW) of around 0.003 ◦/h1/2. It is the highest precision MEMS IMU for commercial aerospace use ever publicly reported in the world to date.

Keywords: IMU; MEMS gyroscopes; satellite; navigation grade; commercial aerospace

1. Introduction In the past decades, considerable attention has been paid to micro-electromechanical system (MEMS) inertial devices, including gyroscopes and accelerometers owing to their Citation: Zhao, W.; Cheng, Y.; Zhao, small sizes, low cost, and high sensitivity [1]. After decades of technology development, S.; Hu, X.; Rong, Y.; Duan, J.; Chen, J. MEMS gyroscopes with mid–low-end consumer grade and industrial grade precisions Navigation Grade MEMS IMU for A have been widely applied in automobiles, mobile phones, consumer electronics, and other Satellite. Micromachines 2021, 12, 151. ﬁelds [2–6]. https://doi.org/10.3390/mi12020151 However, in the high-end inertial application market, it is challenging for the current MEMS gyroscopes to compete with the fiber optic gyroscope in precision [7,8]. The precision Academic Editor: Ha Duong Ngo of mainstream high-precision MEMS gyroscope on today’s market is usually around 0.5 ◦/h, Received: 30 December 2020 such as Sensonor’s typical products STIM202 [9] and STIM210 [10]. The highest precision of Accepted: 29 January 2021 ◦ ◦ 1/2 Published: 4 February 2021 Honeywell’s HG4930 [11] can reach 0.25 /h, with angle random walk (ARW) of 0.04 /h , representing the top level of MEMS inertial measurement unit (IMU) commercial applications

Publisher’s Note: MDPI stays neutral worldwide at the moment. with regard to jurisdictional claims in On 25 July 2020, the Lobster-Eye X-ray Satellite (Einstein Probe Satellite), developed published maps and institutional afﬁl- by China, for dark matter signal detection, was successfully launched [12]. A new high- iations. precision MEMS IMU is carried out in the satellite’s attitude control system for the ﬁrst time, as shown in Figure1. This product has the bias stability of 0.02 ◦/h (1σ), bias instability of 0.006 ◦/h, AWR of about 0.003 ◦/h1/2, weight of less than 210 g, and power consumption of lower than 1.5 W, being the highest precision MEMS IMU product for the commercial aerospace application so far. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. The MEMS IMU consists of six independent MEMS gyroscopes, processors for data This article is an open access article acquisition and signal fusion processing, stress isolation support structure, lead layer distributed under the terms and for electromagnetic shielding and other parts, as schematically described in Figure2. conditions of the Creative Commons Each of the three orthogonal sensitive axes is equipped with two independent MEMS Attribution (CC BY) license (https:// gyroscopes, which enhance the reliability and precision. In an effort to boost the product’s creativecommons.org/licenses/by/ performance, the research mainly focused on the following three aspects of gyroscope 4.0/). design, combination environmental protection, and system-level calibration:

Micromachines 2021, 12, 151. https://doi.org/10.3390/mi12020151 https://www.mdpi.com/journal/micromachines Micromachines 2021, 12, x 2 of 12

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Figure 1. The navigation grade MEMS gyroscope unit product.

The MEMS IMU consists of six independent MEMS gyroscopes, processors for data acquisition and signal fusion processing, stress isolation support structure, lead layer for electromagnetic shielding and other parts, as schematically described in Figure 2. Each of the three orthogonal sensitive axes is equipped with two independent MEMS gyroscopes, which enhance the reliability and precision. In an effort to boost the product’s perfor-

mance, the research mainly focused on the following three aspects of gyroscope design, Figure 1. The navigation grade MEMS gyroscope unit product. combinationFigure 1. The navigationenvironmental grade protection micro-electromechanical, and system-level system calibration: (MEMS) gyroscope unit product. The MEMS IMU consists of six independent MEMS gyroscopes, processors for data acquisition and signal fusion processing, stress isolation support structure, lead layer for electromagnetic shielding and other parts, as schematically described in Figure 2. Each of the three orthogonal sensitive axes is equipped with two independent MEMS gyroscopes, which enhance the reliability and precision. In an effort to boost the product’s performance, the research mainly focused on the following three aspects of gyroscope design, combination environmental protection, and system-level calibration:

FigureFigure 2. 2. TheThe structure structure diagram diagram of of the the six-axis six-axis inertial inertial measurement unit (IMU). (1) For gyroscope design, the MEMS gyroscopes are manufactured using silicon- (1) For gyroscope design, the MEMS gyroscopes are manufactured using silicon-on- on-insulator (SOI) silicon technology, wafer-level stress isolation vacuum packaging, and insulator (SOI) silicon technology, wafer-level stress isolation vacuum packaging, and matched with the self-calibrated application-specific integrated (ASIC) circuit. Furthermore, matched with the self-calibrated application-specific integrated (ASIC) circuit. Further- on account of the special environment of micro-nano satellite applications, the accuracy more, on account of the special environment of micro-nano satellite applications, the ac- and noise index of MEMS gyroscopes are further promoted on the basis of meeting the curacy and noise index of MEMS gyroscopes are further promoted on the basis of meeting requirements of satellite applications by sacrificing the bandwidth and measurement range. the requirements of satellite applications by sacrificing the bandwidth and measurement Figure(2) 2. ForThe MEMSstructure IMU diagram design, of the the six-axis external inertial environment measurement interference unit (IMU). is largely investi- range. gated. Since the structure gap of the MEMS gyroscopes is very sensitive to stress variation, (2) For MEMS IMU design, the external environment interference is largely investi- we exploit(1) For a gyroscope dedicated design, support the for MEMS gyroscope gyroscopes installation are manufactured and implement using a special silicon-on- low gated. Since the structure gap of the MEMS gyroscopes is very sensitive to stress variation, stressinsulator device (SOI) installation silicon technology, method to wafer-level reduce the stress influence isolation of environmental vacuum packaging, stress such and we exploit a dedicated support for gyroscope installation and implement a special low asmatched vibration with and the temperature self-calibrated on application-specific the performance of integrated gyroscopes (ASIC) [13]. In circuit. order Further- to meet stress device installation method to reduce the influence of environmental stress such as themore, radiation on account resistance of the requirementsspecial environment in space of application, micro-nano asatellite protective applications, lead layer the is de-ac- vibration and temperature on the performance of gyroscopes [13]. In order to meet the signedcuracy outsideand noise the index gyroscope of MEMS structure gyroscopes to isolate are thefurther gyroscopes promoted device on the from basis the of impact meeting of radiation resistance requirements in space application, a protective lead layer is designed spacethe requirements ions. of satellite applications by sacrificing the bandwidth and measurement outside the gyroscope structure to isolate the gyroscopes device from the impact of space range.(3) For system-level calibration, the gyroscope noise can be lowered by the mutual ions. calibration(2) For ofMEMS two-axis IMU MEMS design, gyroscopes the external with environment parallel redundant interference configuration is largely investi- in the (3) For system-level calibration, the gyroscope noise can be lowered by the mutual samegated. direction, Since the andstructure the information gap of the MEMS fusion ofgyro gyroscopescopes is angularvery sensitive rate output to stress based variation, on the calibration of two-axis MEMS gyroscopes with parallel redundant configuration in the Kalmanwe exploit filter. a dedicated support for gyroscope installation and implement a special low stress device installation method to reduce the influence of environmental stress such as 2. Error Analysis vibration and temperature on the performance of gyroscopes [13]. In order to meet the radiationThe high-precisionresistance requirements MEMS gyroscope in space application, is the key point a protective to the implementation lead layer is designed of this IMU.outside In the general, gyroscope there structure are some to factors isolate in the improving gyroscopes the MEMSdevice from gyroscope the impact performance: of space (1)ions. the stability of the resonator’s vibration amplitude, which could affect the scale factor of the gyroscope; (2) the orthogonality of the driving direction X and the sensitive direction Y, (3) For system-level calibration, the gyroscope noise can be lowered by the mutual whose non-orthogonal term will lead to the drift of the gyroscope signal; (3) the asymmetry calibration of two-axis MEMS gyroscopes with parallel redundant configuration in the

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effect on the gyroscope arising from frequency split and damping split; (4) the change of resonator structure parameters caused by the environmental stress. After adding the control term, the dynamical model of the MEMS gyroscope with the non-idealities of frequency split and damping the split is as follows [14–17]:

 .. . 2 1 . 1 . x − 2KΩy + ( τ + ∆( τ ) cos 2θτ)x + ∆( τ ) sin 2θτy  2  +(ω − ω∆ω cos 2θω)x − ω∆ω sin 2θωy = fx .. . 2 1 . 1 . (1)  y+2KΩx + ( τ − ∆( τ ) cos 2θτ)y + ∆( τ ) sin 2θτ x  2 +(ω + ω∆ω cos 2θω)y − ω∆ω sin 2θω x = fy

where fx, and fy as the electrode forces imposed on the driving axis and the sensitive axis, which are controlled by driving direction and sensitive direction separately; x and y as the vibration displacements on the two vibration axes of the resonator; τ as the vibration attenuation constant of the resonator; K as the precession factor; Ω as the rotational speed; ω as the resonant frequency of the resonator; θτ as the damping principal axis azimuth; and θω as the stiffness principal axis azimuth. When the gyroscope is in the force feedback mode, we have:

x = A sin ω t 0 x (2) y = 0

That is to say, the driving direction x exhibits sinusoidal vibration with constant amplitude A0 and vibration frequency ωx of the principal mode with the action of amplitude (AMP) control loop and the frequency tracking loop; The node amplitude of the sensing direction Y remains at 0 under the control of force to rebalance (FTR) loop. Putting the above solution into the dynamical model, it was extended to the following form: 2 2 1 2 −A0ωx sin ωxt + ( τ + ∆( τ ) cos 2θτ)A0ωx cos ωxt + (ω − ω∆ω cos 2θω)A0 sin ωxt = fx 1 (3) 2KΩA0ωx cos ωxt + ∆( τ ) sin 2θτ A0ωx cos ωxt − ω∆ω sin 2θω A0 sin ωxt = fy By solving the above equation, it obtains:

 p 2  ωx = ω − ω∆ω cos 2θω 2 1 fx = ( τ + ∆( τ ) cos 2θτ)A0ωx cos ωxt (4)  1 fy = 2KΩA0ωx cos ωxt + ∆( τ ) sin 2θτ A0ωx cos ωxt − ω∆ω sin 2θω A0 sin ωxt

2 1 1 where ( τ + ∆( τ ) cos 2θτ)A0ωx represents the amplitude control term; 2KΩA0ωx + ∆( τ ) sin 2θτ A0ωx is the force equilibrium control term, which is also the gyroscope signal output; and −ω∆ω sin 2θω A0 denotes the orthogonal control term. Then, we could state the output of the gyroscope signal:

Ωout = K1·Ω + B0 1 (5) = 2KA0ωx·Ω + ∆( τ ) sin 2θτ A0ωx To sum up, the scale factor of MEMS gyroscope is related to the resonant frequency. The slow drift of the resonant frequency would result in the drift of the scale factor, which would lower to the performance level of the gyroscope. Furthermore, the frequency split directly gives rise to the random drift of gyroscope, thus reducing the gyroscope precision. The existence of a frequency split would generate orthogonal errors on the resonator, causing the periodic traveling wave component to appear alternately in the standing wave. At this time, the standing wave position will swing periodically. Hence, for high-precision gyroscopes, the errors caused by frequency split should be restrained. In addition, as the MEMS chip is light in weight, the structure gap is very sensitive to the change of stress. Of course, the damping, noise and other environmental interference could also risk the gyroscope precision. Micromachines 2021, 12, x 4 of 12

21+ Δθω Ωω+ Δ1 θ ω (()cos2)τ A0 x 2()sin2KA00xxτ A where ττ represents the amplitude control term; τ is the force equilibrium control term, which is also the gyroscope signal output; and −ωΔωsin 2 θ A ω 0 denotes the orthogonal control term. Then, we could state the output of the gyroscope signal: ΩΩ out =KB 1 + 0 1 (5) =2KAωΩ + Δ ( )sin 2 θ A ω 00x τ τ x

To sum up, the scale factor of MEMS gyroscope is related to the resonant frequency. The slow drift of the resonant frequency would result in the drift of the scale factor, which would lower to the performance level of the gyroscope. Furthermore, the frequency split directly gives rise to the random drift of gyroscope, thus reducing the gyroscope precision. The existence of a frequency split would generate orthogonal errors on the resonator, causing the periodic traveling wave component to appear alternately in the standing wave. At this time, the standing wave position will swing periodically. Hence, for high- precision gyroscopes, the errors caused by frequency split should be restrained. In addition, as the MEMS chip is light in weight, the structure gap is very sensitive to the change Micromachines 2021, 12, 151 of stress. Of course, the damping, noise and other environmental interference could4 also of 12 risk the gyroscope precision.

3. Design 3. Design 3.1.3.1. Frequency Frequency Stabilization Stabilization and and Frequency Frequency Split Split Mitigation Mitigation ItIt is is known known that that the the real-time real-time tracking tracking of of resonant resonant frequency frequency could could be be realized realized by by a a phase-lockedphase-locked loop circuit [[18],18], which,which, however,however, would would still still lead lead to to the the scale scale factor factor variation varia- tionof the of gyroscopethe gyroscope [19]. [19]. In an In effort an effort to overcome to overcome this challenge, this challenge, two movable two movable massblocks mass blocksof the MEMSof the MEMS gyroscope gyroscope are connected are connected to the massto the block mass anchor block anchor points ofpoints the twoof the groups two groupsof driving of driving frequency frequency adjustment adjustment structures stru throughctures through the driving the driving spring spring assembly assembly in this inpaper. this paper. Taking Taking advantage advantage of the of electrostatic the electrostatic negative negative stiffness stiffness effect, effect, we form we form the driv- the drivinging frequency frequency regulating regulating capacitance capacitance through through the movablethe movable electrode electrode and and ﬁxed fixed electrode elec- trodestructure, structure, and undertakeand undertake the closed-loop the closed-loop control control of the of gyroscopethe gyroscope resonator’s resonator’s stiffness, stiffness,allowing allowing the MEMSthe MEMS gyroscope gyroscope resonant resonant frequency frequency to achieveto achieve closed-loop closed-loop stability, stability, as asdepicted depicted in in Figure Figure3. 3.

FigureFigure 3. 3. TheThe structural structural design design of of the the MEMS MEMS gyroscope. gyroscope.

In accordance with Formula (4), when the frequency split of the resonant frequencies occurs in the X and Y directions due to the structure asymmetry, the output of the gyroscope would drift. The larger the frequency split is, the greater the introduced drift is. In order to reduce the impact of frequency split on the gyroscope, we perform the frequency split compensation of gyroscope resonator through electrostatic negative stiffness effect mentioned above. The resonant frequencies of the gyroscope in the X and Y directions are extracted by two separate phase-locked loops, and closed controlled to keep the frequencies same. The residual frequency split of resonator is suppressed by applying appropriate direct current (DC) voltage to the excitation electrode. It is observed from the results that the frequency split of the resonator can be completely suppressed to zero, as shown in Figure4.

3.2. Anti-Interference Design of External Environment The external environment disturbance can be conducted into the gyroscope chip through the IMU, and then into the resonator, which brings the change of the internal physical structure of the resonator. The structure change possesses some randomness, which causes the nonlinear and unpredictable variation of installation error, scale factor error and ZERO error of the MEMS gyroscope. It directly leads to the loss of the MEMS IMU precision. This paper proposes to set the bottom of the MEMS chip as a prismatic structure, as exhibited in Figure5. This prismatic structure can decrease the effect of packaging stress, by reducing the contact area between the MEMS chip and substrate. At the same time, the Micromachines 2021, 12, x 5 of 12

In accordance with Formula (4), when the frequency split of the resonant frequencies occurs in the X and Y directions due to the structure asymmetry, the output of the gyroscope would drift. The larger the frequency split is, the greater the introduced drift is. In order to reduce the impact of frequency split on the gyroscope, we perform the frequency split compensation of gyroscope resonator through electrostatic negative stiffness effect mentioned above. The resonant frequencies of the gyroscope in the X and Y directions are extracted by two separate phase-locked loops, and closed controlled to keep the frequencies same. The residual frequency split of resonator is suppressed by applying appropriate direct current (DC) voltage to the excitation electrode. It is observed from the results that the frequency split of the resonator can be completely suppressed to zero, as shown in Figure 4.

Micromachines 2021, 12, x 5 of 12

In accordance with Formula (4), when the frequency split of the resonant frequencies occurs in the X and Y directions due to the structure asymmetry, the output of the gyroscope would drift. The larger the frequency split is, the greater the introduced drift is. In order to reduce the impact of frequency split on the gyroscope, we perform the frequency split compensation of gyroscope resonator through electrostatic negative stiff- Micromachines 2021, 12, 151 ness effect mentioned above. The resonant frequencies of the gyroscope in the X and5 of 12Y directions are extracted by two separate phase-locked loops, and closed controlled to keep the frequencies same. The residual frequency split of resonator is suppressed by applying appropriate direct current (DC) voltage to the excitation electrode. It is observed from the vacuumresults that cavity the offrequency the gyroscope split of chip the is resonator separated can from be thecompletely prismatic suppressed structure to to limit zero, the as conductionshown in Figure path of4. external stress.

Figure 4. The result of multi-electrode electrical stiffness compensation.

3.2. Anti-Interference Design of External Environment The external environment disturbance can be conducted into the gyroscope chip through the IMU, and then into the resonator, which brings the change of the internal physical structure of the resonator. The structure change possesses some randomness, which causes the nonlinear and unpredictable variation of installation error, scale factor error and ZERO error of the MEMS gyroscope. It directly leads to the loss of the MEMS IMU precision. This paper proposes to set the bottom of the MEMS chip as a prismatic structure, as exhibited in Figure 5. This prismatic structure can decrease the effect of packaging stress, by reducing the contact area between the MEMS chip and substrate. At the same time, the vacuum cavity of the gyroscope chip is separated from the prismatic structure to limit the

conduction path of external stress. FigureFigure 4.4. TheThe resultresult ofof multi-electrodemulti-electrode electricalelectrical stiffnessstiffness compensation.compensation.

IMU precision.

FigureThis 5. Structural paper proposes design of to the set MEMS the bottom chip. of the MEMS chip as a prismatic structure, as FigureexhibitedThe 5. Structuralsimulation in Figure 5.designresults This prismatic stateof the that MEMS structurethis prismatic chip. can decrease structure the at effectthe bottom of packaging of the MEMS stress, chipby reducing Thesufficiently simulation the contactlessens results areathe stateconduction between that thisthe path MEMS prismatic from chip the structure andexternal substrate. at environment the bottomAt the same of to the the time, MEMS inside the sensingchipvacuum sufﬁciently structure cavity of lessens theon thegyroscope the resonator, conduction chip enabling is separated path fromthe fromequivalent the external the prismatic stress environment of structure the resonator to to the limit inside fine the structuresensingconduction structure from path external of on external the thermal resonator, stress. environment enabling theto decline equivalent by more stress than of the90%, resonator as shown ﬁne in Figurestructure 6. from external thermal environment to decline by more than 90%, as shown in Figure6.

Equivalent stress:stress： EquivalentEquivalent stress stress:：： Equivalent stress:：： 2 EquivalentEquivalentEquivalent stress stress:stress:：： Equivalent stress 9.5331 N/m 2 0.977160.97716N/m2 N/m2 1.2484 N/m22 9.5331N/m 20.86320.86320.863N/m N/mN/m222 1.2484N/m 89.7%89.7% reductionreduction 94%94% reduction reduction

Figure 5. Structural design of the MEMS chip.

(a) (b)

Figure 6. The simulation resultsFigure of the6. The equivalent simulation stress results between of the two equivalent kinds of chips:stress between (a) the traditional two kinds MEMS of chips: chip; (a) ( bthe) the tradi- MEMS chip proposed in thistional paper. MEMS chip; (b) the MEMS chip proposed in this paper.

4. Self-Calibration Because of the adverse impacts of working environment and machining error, the zero position and scale factor of the MEMS gyroscope would be unstable. The traditional control mode could only calibrate and bind the zero position and scale factor of the gyroscope initially, while the real-time online calibration cannot be realized as time changes, which is severely detrimental to the precision and storage life of the gyroscope. This paper explores a real-time self-calibration method of MEMS gyroscope bias offset and scale factor based on dual control path, by which the resonance signal and high- frequency harmonic information of the gyroscope could be measured and controlled respectively with two controller modules with the same structure and function, thus obtaining the angle output information, zero position and scale factor information of the gyroscope in real time. Then, after the compensation for the data fusion of above information, the MEMS gyroscope can attain real-time online self-calibration. The digital circuit mainly consists of the main control path and the auxiliary control path. Among them, the main control path is composed of the main controller, the orthogonal demodulation, and the orthogonal modulation module; the auxiliary control path includes the auxiliary controller, the auxiliary demodulation, and the auxiliary modulation module. Each control path contains an amplitude control loop, a phase-locked loop, an orthogonal control loop, a force equilibrium control loop, and so on, as indicated in Figure 7.

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4. Self-Calibration Because of the adverse impacts of working environment and machining error, the zero position and scale factor of the MEMS gyroscope would be unstable. The traditional control mode could only calibrate and bind the zero position and scale factor of the gyroscope initially, while the real-time online calibration cannot be realized as time changes, which is severely detrimental to the precision and storage life of the gyroscope. This paper explores a real-time self-calibration method of MEMS gyroscope bias offset and scale factor based on dual control path, by which the resonance signal and high-frequency harmonic information of the gyroscope could be measured and controlled respectively with two controller modules with the same structure and function, thus obtaining the angle output information, zero position and scale factor information of the gyroscope in real time. Then, after the compensation for the data fusion of above information, the MEMS gyroscope can attain real-time online self-calibration. The digital circuit mainly consists of the main control path and the auxiliary control path. Among them, the main control path is composed of the main controller, the orthogonal demodulation, and the orthogonal modulation module; the auxiliary control path includes the auxiliary controller, the auxiliary demodulation, and the auxiliary modulation module. Micromachines 2021, 12, x Each control path contains an amplitude control loop, a phase-locked loop, an orthogonal7 of 12

control loop, a force equilibrium control loop, and so on, as indicated in Figure7.

FigureFigure 7. 7.Schematic Schematic diagram diagram of of self-calibration self-calibration algorithm.

TheThe signal signal processing processing circuit circuit structurestructure of the X-path and and YY-path-path is is identical identical (but (but the the parametersparameters can can be be different),different), so so it it can can be be reus reuseded to reduce to reduce the thechip chip area. area. Nevertheless, Nevertheless, the thetwo two paths paths are are not not simply simply corresponding corresponding to the to driving the driving and sensitive and sensitive pathways pathways of the oftra- the traditionalditional gyroscope gyroscope chips. chips. TheThe working working condition condition of of the the wholewhole systemsystem (such as as working working mode mode selection, selection, on-off on-off naturenature of of the the module, module, signal signal path path selective selective switch, switch, etc.) etc.) isis controlledcontrolled byby thethe main controller.control- Theler. auxiliary The auxiliary control control path haspath the has same the same circuit circuit structure structure as the as main the main control control path, path, in which in allwhich the main all the modules main modules are turned are onturned or off on depending or off depending on the workingon the working mode mode of the of system. the Forsystem. example, For example, when only when the only function the function of traditional of traditional gyroscope gyroscope chip ischip needed, is needed, we could we solelycould use solely the mainuse the control main control path, and path, the and auxiliary the auxiliary control control path can path be can turned be turned off to off ensure to a lowerensure power a lower consumption power consumption level of thelevel system. of the system. TheThe main main controller controller andand the auxiliary auxiliary controller controller can can work work in different in different modes: modes: for in- for instance,stance, the main controller is is in in closed-loop closed-loop mode, mode, though though the the auxiliary auxiliary controller controller is isin in open-loopopen-loop mode mode (or (or test test mode, mode, self-calibration self-calibration mode, etc.). For For example, example, for for traditional traditional asymmetricasymmetric rate rate gyroscope, gyroscope, only only one one axisaxis isis suitablesuitable to be be selected selected as as the the driving driving axis, axis, and and thethe other other axis axis is is taken taken as as the the sensitive sensitive axis,axis, whichwhich is difficult difﬁcult to to construct construct two two gyroscopes gyroscopes withwith same same working working mode mode that that have have practicalpractical application value. value. At At this this moment, moment, the the main main controller works in the traditional rate gyroscope mode (open-loop or closed-loop), while the auxiliary controller measures (open-loop) or controls (closed-loop) the harmonics of the drive shaft and sensitive shaft, whose harmonic information can be considered as a measurement of the nonlinearity degree of the system for self-calibration of scale factor or bias offset, or for nonlinear correction of the system. In other words, the main controller can be utilized to control and measure a MEMS gyroscope working on the resonant frequency, yet the auxiliary controller to control and measure a “virtual” gyroscope working on the resonant frequency of Nth harmonic. Afterwards, the information fusion of the two gyroscopes output could result in self-calibration, or improvement of some performance indexes (such as stability and repeatability). The main controller and the auxiliary controller can exchange necessary information with each other. In fact, they can be regarded as the same controller. The parameters of the controller can be self-adapted to increase the adaptability of the system to external environment changes including the vibration, impact, pressure, humidity, and internal environment changes including temperature, stress, etc. The simultaneous information output from the main and auxiliary controller, which reflects the changes of external environment and internal parameters, can be combined and compensated to realize the self- calibration function, can be combined and compensated, so as to improve the repeatability and stability of the output.

Micromachines 2021, 12, 151 7 of 12

controller works in the traditional rate gyroscope mode (open-loop or closed-loop), while the auxiliary controller measures (open-loop) or controls (closed-loop) the harmonics of the drive shaft and sensitive shaft, whose harmonic information can be considered as a measurement of the nonlinearity degree of the system for self-calibration of scale factor or bias offset, or for nonlinear correction of the system. In other words, the main controller can be utilized to control and measure a MEMS gyroscope working on the resonant frequency, yet the auxiliary controller to control and measure a “virtual” gyroscope working on the resonant frequency of Nth harmonic. Afterwards, the information fusion of the two gyroscopes output could result in self-calibration, or improvement of some performance indexes (such as stability and repeatability). The main controller and the auxiliary controller can exchange necessary information with each other. In fact, they can be regarded as the same controller. The parameters of the controller can be self-adapted to increase the adaptability of the system to external environment changes including the vibration, impact, pressure, humidity, and internal environment changes including temperature, stress, etc. The simultaneous information output from the main and auxiliary controller, which reﬂects the changes of external environment and internal parameters, can be combined and compensated to realize the self- calibration function, can be combined and compensated, so as to improve the repeatability and stability of the output.

5. Results The actual size of the six-axis MEMS gyroscope unit is 72 × 72 × 35 mm3 and the weight is 210 g. Impressively, in the design of the IMU, the precision of the closed-loop controlled gyroscope could be further promoted by sacrificing the range and bandwidth for specific application situations. The research ideas are as follows: (1) To reduce the gain of the driving circuit: the proportional increase of digital control quantity when keeping the control objective unchanged could bring about the proportional increase of the scale factor. This way, however, would hamper the measurement range of the closed-loop gyroscope. (2) To lower the Proportion parameter of the Proportion Integration Differentiation (PID) controller: keeping the detection signal noise consistent could reduce the control quantity error, resulting in less error of digital control quantity, which, actually, is the gyroscope output signal. Nonetheless, this way would impair the gyroscope bandwidth. When the application environment needs of micro satellite have been satisfied, by the above methods (lifting the scale factor and lowering noise level), the gyroscope precision could be enhanced significantly at the acceptable expense of measurement range and bandwidth. In our study, the measurement range of the IMU is limited to 20 ◦/s, and the bandwidth to 12 Hz, to improve the precision index of the gyroscope. During the ground test, the IMU data were analyzed after continuous sampling for 24 h. It is summarized in Table1 that the bias stability of the six gyroscopes in the MEMS IMU is between 0.01 and 0.02 ◦/h, with ARW of approximately 0.003 ◦/h1/2, and bias instability of about 0.006 ◦/h. Figure8 shows the Allen variance of the six MEMS gyroscopes in the same unit.

Table 1. Ground test results of the inertial measurement unit (IMU).

Performance Index Unit X1 X2 Y1 Y2 Z1 Z2 Bias offset ◦/h −13.49 −4.28 3.85 −12.35 −10.06 11.05 ARW ◦/h1/2 3.59 × 10−3 2.39 × 10−3 2.22 × 10−3 3.03 × 10−3 2.89 × 10−3 2.61 × 10−3 Bias stability (1σ) ◦/h 2.15 × 10−2 1.47 × 10−2 1.39 × 10−2 1.80 × 10−2 1.78 × 10−2 1.63 × 10−2 Bias instability ◦/h 6.06 × 10−3 5.53 × 10−3 4.91 × 10−3 6.22 × 10−3 9.19 × 10−3 6.27 × 10−3 Micromachines 2021, 12, x 8 of 12

5. Results The actual size of the six-axis MEMS gyroscope unit is 72 × 72 × 35 mm3 and the weight is 210 g. Impressively, in the design of the IMU, the precision of the closed-loop controlled gyroscope could be further promoted by sacrificing the range and bandwidth for specific application situations. The research ideas are as follows: (1) To reduce the gain of the driving circuit: the proportional increase of digital control quantity when keeping the control objective unchanged could bring about the proportional increase of the scale factor. This way, however, would hamper the measurement range of the closed-loop gyroscope. (2) To lower the Proportion parameter of the Proportion Integration Differentia- tion (PID) controller: keeping the detection signal noise consistent could reduce the control quantity error, resulting in less error of digital control quantity, which, actually, is the gyroscope output signal. Nonetheless, this way would impair the gyroscope bandwidth. When the application environment needs of micro satellite have been satisfied, by the above methods (lifting the scale factor and lowering noise level), the gyroscope precision could be enhanced significantly at the acceptable expense of measurement range and bandwidth. In our study, the measurement range of the IMU is limited to 20 °/s, and the bandwidth to 12 Hz, to improve the precision index of the gyroscope. During the ground test, the IMU data were analyzed after continuous sampling for 24 h. It is summarized in Table 1 that the bias stability of the six gyroscopes in the MEMS IMU is between 0.01 and 0.02 °/h, with ARW of approximately 0.003 °/h1/2, and bias instability of about 0.006 °/h. Figure 8 shows the Allen variance of the six MEMS gyroscopes in the same unit.

Table 1. Ground test results of the IMU.

Performance Index Unit X1 X2 Y1 Y2 Z1 Z2 Bias offset °/h −13.49 −4.28 3.85 −12.35 −10.06 11.05 ARW °/h1/2 3.59 × 10−3 2.39 × 10−3 2.22 × 10−3 3.03 × 10−3 2.89 × 10−3 2.61 × 10−3 Bias stabil- °/h 2.15 × 10−2 1.47 × 10−2 1.39 × 10−2 1.80 × 10−2 1.78 × 10−2 1.63 × 10−2 ity(1σ) Micromachines 2021 12 Bias instability, , 151 °/h 6.06 × 10−3 5.53 × 10−3 4.91 × 10−3 6.22 × 10−3 9.19 × 10−3 6.27 ×8 of10 12−3

100 − Bias Stablity : 2.15× 102 / h Bias Stablity : 1.47× 10−2 / h − Bias Instablity : 6.06× 103 / h Bias Instablity : 5.53× 10−3 / h − ARW :3.59× 103 / h ARW : 2.39× 10−3 / h ） -1 °/h 10 （

10-2 Allan Variance Allan

10-3 0 1 2 3 4 5 Micromachines 2021, 12, x 10 10 10 10 10 109 of 12

time（s）

(a) X1 (b) X2

− Bias Stablity : 1.39× 10−2 / h Bias Stablity : 1.80× 102 / h − Bias Instablity : 4.91× 10−3 / h Bias Instablity : 6.22× 103 / h − ARW : 2.22× 10−3 / h ARW :3.03× 103 / h

Bias Stablity : 1.78× 10−2 / h Bias Stablity : 1.63× 10−2 / h Bias Instablity : 9.19× 10−3 / h Bias Instablity : 6.27× 10−3 / h ARW : 2.89× 10−3 / h ARW : 2.61× 10−3 / h

(e) Z1 (f) Z2

Figure 8. AllanFigure variance 8. Allan curves variance of the curves six MEMS of the gyroscopes six MEMS in gyroscopes the inertial in measurement the IMU. unit (IMU).

TheThe same same MEMS MEMS IMU IMU was was tested tested for for anothe anotherr 24 24 h, h, about about 4 4 months months later. later. The The data data showshow that that the the bias bias offset offset of of the the gyroscopes gyroscopes were were changed changed a alittle, little, as as shown shown in in Table Table 2,2, and and thethe Allen Allen variance variance of of the the six six MEMS MEMS gyroscopes gyroscopes are are shown shown in in Figure Figure 9.9.

Table 2. Ground test results of the IMU 4 months later.

Performance Index Unit X1 X2 Y1 Y2 Z1 Z2

Bias offset °/h −14.87 −2.01 3.79 −13.62 −9.34 11.03 3.07 × 3.75 × 2.66 × 2.75 × 2.53 × 3.06 × ARW °/h1/2 10−3 10−3 10−3 10−3 10−3 10−3 Bias stabil- 1.76 × 2.30 × 1.57 × 1.57 × 1.67 × 1.78 × °/h ity(1σ) 10−2 10−2 10−2 10−2 10−2 10−2 Bias insta- 5.90 × 6.49 × 4.63 × 4.31 × 7.33 × 5.21 × °/h bility 10−3 10−3 10−3 10−3 10−3 10−3

Micromachines 2021, 12, x 10 of 12 Micromachines 2021, 12, 151 9 of 12

− − × 2 Bias Stablity : 1.76× 102 / h Bias Stablity : 2.30 10 / h − − × 3 Bias Instablity : 5.90× 103 / h Bias Instablity : 6.49 10 / h − − × 3 ARW :3.07× 103 / h ARW :3.75 10 / h

(a) X1 (b) X2

Bias Stablity : 1.57× 10−2 / h Bias Stablity : 1.57× 10−2 / h Bias Instablity : 4.63× 10−3 / h Bias Instablity : 4.31× 10−3 / h ARW : 2.66× 10−3 / h ARW : 2.75× 10−3 / h

− Bias Stablity : 1.67× 102 / h Bias Stablity : 1.78× 10−2 / h Bias Instablity : 7.33× 10−3 / h Bias Instablity : 5.21× 10−3 / h − ARW : 2.53× 10−3 / h ARW :3.06× 103 / h ） °/h （ Allan Variance

(e) Z1 (f) Z2

FigureFigure 9. Allan 9. Allan variance variance curves curves of the of the six six MEMS MEMS gyro gyroscopesscopes in the IMUIMU tested tested 4 months4 months later. later.

The Lobster-Eye X-ray Satellite employed a MEMS IMU and a navigation grade fiber optic gyroscope (FOG) unit weighing 430 g. The in-orbit data of the MEMS unit transmitted from the satellite and the FOG unit almost completely overlap each other, as displayed in Figure 10, which means that the output and control effect of the MEMS IMU is similar

Micromachines 2021, 12, 151 10 of 12

Table 2. Ground test results of the IMU 4 months later.

Performance Index Unit X1 X2 Y1 Y2 Z1 Z2 Bias offset ◦/h −14.87 −2.01 3.79 −13.62 −9.34 11.03 ARW ◦/h1/2 3.07 × 10−3 3.75 × 10−3 2.66 × 10−3 2.75 × 10−3 2.53 × 10−3 3.06 × 10−3 Bias stability(1σ) ◦/h 1.76 × 10−2 2.30 × 10−2 1.57 × 10−2 1.57 × 10−2 1.67 × 10−2 1.78 × 10−2 Bias instability ◦/h 5.90 × 10−3 6.49 × 10−3 4.63 × 10−3 4.31 × 10−3 7.33 × 10−3 5.21 × 10−3

Micromachines 2021, 12, x The Lobster-Eye X-ray Satellite employed a MEMS IMU and a navigation grade ﬁber 11 of 12

optic gyroscope (FOG) unit weighing 430 g. The in-orbit data of the MEMS unit transmitted from the satellite and the FOG unit almost completely overlap each other, as displayed in Figure 10, which means that the output and control effect of the MEMS IMU is similar toto that that ofof thethe FOG FOG unit unit on on the the same same satellite. satellite. Meanwhile, Meanwhile, the weight the weight and volume and volume of the of the MEMSMEMS unitunit areare only only about about 1/2 1/2 of of the the FOG FOG unit. unit.

FOG X

FOG Y

FOG Z

MEMS X1

MEMS Y1

MEMS Z1 ROTATE STABLE PERIOD PERIOD

FigureFigure 10. In-orbitIn-orbit data data comparison comparison between between MEMS MEMS IMU IMU and ﬁber and opticFOG gyroscope unit. (FOG) unit. 6. Discussion 6. Discussion By sacriﬁcing the range and bandwidth, the mechanical scale factor of the gyroscope couldBy be sacrificing promoted, the which range would and further bandwidth, weaken the the mechanical MEMS gyroscope scale factor noise. Aof six-axisthe gyroscope couldMEMS be gyroscope promoted, redundant which IMU, would that further adopts doubleweaken gyroscopes the MEMS at one gyroscope coaxial direction, noise. A is six-axis MEMSdeveloped. gyroscope Therefore, redundant the performance IMU, that of this adopts MEMS double unit can gyroscopes be further improved at one coaxial through direction, isdata developed. processing Therefore, between the the two performance gyroscopes at of one this coaxial MEMS direction. unit Thecan performancebe further improved of throughthis six-axis data MEMS processing gyroscope between unit is the shown two in gyroscopes Table3. at one coaxial direction. The perfor- Furthermore, this product can directly replace the three MEMS gyroscopes in situ with mance of this six-axis MEMS gyroscope unit is shown in Table 3. three MEMS accelerometers, to turn it into a MEMS IMU with three MEMS gyroscopes and three MEMS accelerometers, which could be used for the high precise navigation. Table 3. The IMU performance index.

Index Unit Performance Range °/s ±20 Bias Stability(1σ) °/h 0.02 Bias Instability °/h 0.006 ARW °/h1/2 0.003 Bandwidth Hz 12 Power W <1.5 Weight g 210

Furthermore, this product can directly replace the three MEMS gyroscopes in situ with three MEMS accelerometers, to turn it into a MEMS IMU with three MEMS gyroscopes and three MEMS accelerometers, which could be used for the high precise navigation.

7. Conclusions The paper describes a new six-axis MEMS IMU with the bias stability of 0.02 °/h, bias instability of 0.006 °/h, and ARW of 0.003 °/h1/2, attaining the navigation grade, by means of customized gyroscope design and unique gyroscope self-calibration method. This product has been successfully put into use in the Lobster-Eye X-ray Satellite, which is the MEMS gyroscope commercial aerospace application with highest precision that has ever been reported worldwide. From the in-orbit data transmitted from the satellite, the performance of the MEMS IMU is competitive to the small FOG unit on the same satellite.

Micromachines 2021, 12, 151 11 of 12

Table 3. The IMU performance index.

Index Unit Performance Range ◦/s ±20 Bias Stability (1σ) ◦/h 0.02 Bias Instability ◦/h 0.006 ARW ◦/h1/2 0.003 Bandwidth Hz 12 Power W <1.5 Weight g 210

7. Conclusions The paper describes a new six-axis MEMS IMU with the bias stability of 0.02 ◦/h, bias instability of 0.006 ◦/h, and ARW of 0.003 ◦/h1/2, attaining the navigation grade, by means of customized gyroscope design and unique gyroscope self-calibration method. This product has been successfully put into use in the Lobster-Eye X-ray Satellite, which is the MEMS gyroscope commercial aerospace application with highest precision that has ever been reported worldwide. From the in-orbit data transmitted from the satellite, the performance of the MEMS IMU is competitive to the small FOG unit on the same satellite.

8. Patents The following patents are resulted from the work reported in this manuscript: CN201310497005.5, CN201720895640.2

Author Contributions: Conceptualization, W.Z.; design for gyroscope, Y.C.; design for unit, J.D. and X.H.; validation, J.C.; data curation, Y.R.; writing, Y.C. and S.Z. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Key Research and Development Program of China, grant number 2017YFB1104700, the Program of Shanghai Academic/Technology Re- search Leader, grant number 18XD1421700, and the Shanghai Rising Star Program, grant number 20QA1404300. Data Availability Statement: No New data were created or analyzed in this study. Data sharing is not applicable to this article. Conﬂicts of Interest: The authors declare no conﬂict of interest, and the funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

References 1. Cheng, Y.X.; Zhang, W.P.; Guan, R.; Zhang, G.; Xu, Z.X.; Chen, W.Y. MEMS-based piezoelectric BAW resonator based on out-of-plane degenerate mode for micro angular detector. Electron. Lett. 2013, 49, 406–407. [CrossRef] 2. Liu, K.; Zhang, W.; Chen, W.; Li, K.; Dai, F.; Cui, F.; Wu, X.; Ma, G.; Xiao, Q. TOPICAL REVIEW: The development of micro-gyroscope technology. J. Micromechanics Microengineering 2009, 19, 113001. [CrossRef] 3. Minin, O. Chapter 12—MEMS Gyroscopes for Consumers and Industrial Applications. In Microsensors; Books on Demand: Norderstedt, Germany, 2011. 4. Dunzhu, X.; Cheng, Y.; Kong, L. The Development of Micromachined Gyroscope Structure and Circuitry Technology. Sensors 2014, 14, 1394–1473. [CrossRef] 5. Passaro, V.M.N.; Cuccovillo, A.; Vaiani, L.; De Carlo, M.; Campanella, C.E. Gyroscope Technology and Applications: A Review in the Industrial Perspective. Sensors 2017, 17, 2284. [CrossRef][PubMed] 6. Zhanshe, G.; Fucheng, C.; Boyu, L.; Le, C.; Chao, L.; Ke, S. Research development of silicon MEMS gyroscopes: A review. Microsyst. Technol. 2015, 21, 2053–2066. [CrossRef] 7. Mordor Intelligence. High-End Inertial Systems Market—Growth, Trends, And Forecasts (2020–2025); Mordor Intelligence: Telangana, India, 2020. Micromachines 2021, 12, 151 12 of 12

8. Damianos, D.; Girardin, G. High-End Inertial Sensors For Defense, Aerospace And Industrial Applications 2020; Yole Développement: Villeurbanne, France, 2020. 9. TS1439r16-Datasheet-stim202 [EB/OL]. Available online: https://www.sensonor.com/products/gyroscope-modules/stim202/# (accessed on 16 August 2020). 10. Stim300-Datasheet [EB/OL]. Available online: https://www.sensonor.com/products/inertial-measurement-units/stim300/# (accessed on 16 August 2020). 11. HG4930 Mems Inertial Measurement Unit [EB/OL]. Available online: https://aerospace.honeywell.com/en/learn/products/ sensors/hg4930-mems-inertial-measurement-unit (accessed on 16 August 2020). 12. Launch of the World’s First Soft X-ray Satellite with ‘Lobster-Eye’ Imaging Technology [EB/OL]. Available online: https: //phys.org/news/2020-07-world-soft-x-ray-satellite-lobster-eye.html (accessed on 27 July 2020). 13. Zhao, W.; Sun, X.; Rong, Y.; Duan, J.; Chen, J.; Song, L.; Pan, Q. Optimization on the Precision of the MEMS-Redundant IMU Based on Adhesive Joint Assembly. Math. Probl. Eng. 2020, 2020, 8855141. [CrossRef] 14. Liu, F.; Zhao, W.; Song, L. Space Hemispherical Resonator Gyro Inertial Sensor and Its Application; China Aerospace Publishing House: Beijing, China, 2019. 15. IEEE. IEEE Standard Speciﬁcation Format Guide and Test Procedure for Coriolis Vibratory Gyros; IEEE: Piscataway, NJ, USA, 2004. 16. Wang, X. Study on Error Modeling Compensation and Force Balance Control for Hemispherical Resonator Gyro; National University of Defense Technology: Changsha, China, 2012. 17. Chen, H.; Zhong, Y.; Meng, Z. A Practical Pll-Based Drive Circuit with Ultra-Low-Noise Tia for Mems Gyroscope. Chin. J. Sci. Instrum. 2017, 2.[CrossRef] 18. Jia, J.; Ding, X.; Gao, Y.; Li, H. Automatic Frequency Tuning Technology for Dual-Mass MEMS Gyroscope Based on a Quadrature Modulation Signal. Micromachines 2018, 9, 511. [CrossRef][PubMed] 19. Wang, M.; Cao, H.; Shen, C.; Chai, J. A Novel Self-Calibration Method and Experiment of MEMS Gyroscope Based on Virtual Coriolis Force. Micromachines 2018, 9, 328. [CrossRef][PubMed]