ZHANG Yinqiang，JI Xunsheng，YANG Bo，LI Jing，WANG Shourong*

(1．Key Laboratory of Micro－Inertial Instrument and Advanced Navigation Technology，Ministry of Education，Southeast University，Nanjing 210096，China;2．College of Automation and Electronic Engineering，Nanjing University of technology，Nanjing 210009，China;3．School of Communication and Control Engineering，Jiangnan University，Wuxi Jiangsu 214122，China)

Recently，MEMS gyroscope(MMG)has been widely used in high-precision measurement applications such as inertial navigation，and automotive and platform stabilization，due to its high sensitivity，small size，mass production and low cost．In fact， the achieved performance level of MMG is rate-grade as a result of developments over the last decade[1]．However，the tactical-grade and inertial-grade devices are needed．Therefore，how to improve the performance of MEMS gyroscope hasbecome amain targetpursued by designers．Several methods have been developed to improve the performance of MEMS gyroscope in the past years．These methods include new structural design[2－3]，error modeling and filtering[4]，and close-loop adaptive control[5]．Particularly，a novel virtual gyroscope technology using multiple sensor fusion improves the accuracy effectively．Bayard create a virtual sensor by combining four individual gyros into a single gyroscope，the simulation results showed that the drifts is reduced from 8．66 °/h to 0．062 °/h．A silicon MEMS gyroscope array(SMGA)with individualgyroscopesis also studied in[6－9]．

In this paper，a novel quad-cell gyroscope array is proposed，which inherently improves the accuracy of the gyroscope．Therest of the paperis organized as followed．Section 1 introduces the new structural design and simulation results of the quad-cell gyroscope array．Symmetric mechanical structure is utilized in both drive mode and sense-mode．Section 2 presents the dynamics analysis theoretically in terms of the architecture of the proposed gyroscope array．Section 3 reports the design of digital control system of the gyroscope array．Signal processing of the virtual gyroscope is analyzed in Section 4．Finally，Section 5 concludes the paper with a summary of obtained results．

1 Design Concept

In this section，we describe the mechanical architectures and the modal simulations of the quadruple mass gyroscope array．

Fig．1 shows the quad-cell gyroscope array with a symmetrical structure．The gyroscope array utilizes quadmass topology structure and differential sensing mechanism todecreasecommon modeerror．The gyroscope array keeps the symmetry of suspension beams and mass in both drive and sense direction．The mechanical structure of the quad-cell gyroscope array consists of anchors，driving electrodes，driving combs，sensing electrodes，sensing combs，and four identical proof mass．The whole structure is fixed on the substrate through the eight anchors．The driving combs are linked with the mass by U-Type beam which can provide the decoupling effect from drive mode and sense mode．The comb-drive electrodes are employed to establish the vibrations in the drive-mode．A collection of sensing electrodes is distributed around the proof mass．The sensing-combs are set in the proof mass，and the Coriolis force is applied to the mass in y axis．

Fig．1 Schematic structure of the gyroscope array

The Proof mass are electrostatically excited in the drive direction(x axis)using driving voltages imposed across the driving electrodes．If there is an external rotation around the z axis，the Coriolis force applied to the proof mass induces sense-mode vibrations which are capacitively detected by the differential sensingcapacitors．

To validate the mechanical design and obtain the characteristics of the gyroscope array，finite element simulationsusing ANSYS are performed and the simulation results are presented in Fig．2．The simulated results show nine mode shapes of the gyroscope array．The drive and sense mode resonance frequencies are summarized in Table 1．

Table 1 The resonant frequency of the gyroscope array

Fig．2 Modal shapes of the gyroscope array

Along the x axis and the second mode shape causes the proof mass to parallelly move in the ydirection．This response occurs at 3．338 kHz and is defined as the corresponding sensing mode of the first mode．The third mode occurs at 3．364 8 kHz where the upper parallel dual mass and the lower dual mass moves in anti-phase mode along the x-direction．The corresponding sensing mode is the fourth mode shape which occurs at 3．393 2 kHz．There is an Interference mode at 3．3941kHz．The eighth mode shape，which occurs at 3．558 4 kHz，is an anti-phase driving mode and the seventh mode shape is the corresponding reverse-phase sensing mode．At the ninth mode shape，the left dual mass and the right dual mass move in antiphase mode while the upper dual mass and the lower dual mass move in in-phase mode．The corresponding sensing mode is the sixth mode shape．

2 Sensor Dynamics Analysis

the gyroscope system can be treated as a classical second-order oscillating system with multi degree of freedom．Conventionally，the gyroscope is continuously driven by a force Fdsin(ωdt)in the drive direction．Without considering the quadrature error，dynamic equations can be expressed as:

where Fdsin(ωdt)is the driving force applied to mass m at the driving frequency ωd;Ωzrefers to the angular velocity applied to the gyroscope about the z axis;dx，kxand dy，kyare the damping coefficients and the stiffness coefficient in the x and y directions，respectively．

3 Design of Digital Control System

Fig．3 Structure diagram of the Closed-Loop Control System

A schematic of the closed-loop control system can be seen in Fig．3．The whole system includes the drive control and the angular detection．In the drive control mode，a digital phase-locked loop(PLL)is utilized in frequency control and an automatic gain control(AGC)method is used in amplitude control．To improve the stability in the steady state resonant motion，a PI controller is introduced．The direct digital synthesizer(DDS)is used to generate the cosine and sine signals．In the detection mode，the phase sensitive demodulation algorithm is adopted in open-loop detection scheme．

Fig．4 illustrates the block-diagram of the analog and digital control systems．The key circuit elements include the Digital to Analog Converter，8 channel Analog to Digital Converters(ADCs)，and the Digital Signal Processor(DSP)functionality integrated into a Altera CycloneⅢFPGA．

Fig．4 A block-diagram of the control system

Fig．5 shows the circuit board，we used in the closed-loop controlexperiment．In the closed-loop control experiment，the gyroscope array could achieve at a stable frequency with the control-loop circuit and the relative deviation of the oscillating amplitude is 9×10－5．

Fig．5 Photograph of closed-loop driving circuit

4 Signal Processing oftheVirtual Gyroscope

Fig．6 shows the structure diagram of the proposed virtual gyroscope system．The gyroscope array is composed of four gyroscope，and the measure data of a same angular rate are fed into the data fusion system where Allan variance estimation is adopt to determine the covariance matrix Rkof the measurement noises and the covariance matrix Qkof the system noises．Then the Kalman filter is used to obtain the virtual gyroscope’s output．

Fig．6 Structure diagram of the virtual gyroscope

After eliminating the tread term，the corresponding bias drift of the four gyroscopes are plotted in Fig．7．From Fig．7，we can see that the random drift is very large．

Fig．7 Drift before filtering

Using the discrete-time KF depicted in Fig．6，the filtering result of virtual gyroscope are obtained as shown in Figs．8．The Fig．8 shows that the significant noise components are eliminated by the method．By the data fusion，the bias stability of the virtual gyroscope is decreased from 129．6 °/h to 10．54 °/h．

Fig．8 Drift of the virtual gyroscope

5 Conclusion

We reported a novel quadruplemass silicon MEMS gyroscope array based on multi-sensor fusion which utilizes symmetrically decoupled structure．Simulations and tests were carried out．A digital control circuit using PLL and AGC method with the FPGA was designed．In order to improve the overall accuracy，the Allan variace estimation and the Kalman filter was used for fusing multiple MEMS gyroscopes．It was proved that the virtual gyroscope is efficient to improve the system overall performance．

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