Elsevier

Measurement

Volume 62, February 2015, Pages 197-204
Measurement

A novel narrow-band force rebalance control method for the sense mode of MEMS vibratory gyroscopes

https://doi.org/10.1016/j.measurement.2014.11.009Get rights and content

Highlights

  • •

    We present a novel narrow-band force rebalance control method for MEMS gyroscopes.

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    There is no demodulation and modulation components in the control loop.

  • •

    Coriolis and quadrature forces are rebalanced simultaneously in one control loop.

  • •

    A BPF is adopted as a feedback controller, and the system is stable and robust.

  • •

    The bias instability is 5.1 deg/h, bandwidth is 97.2 Hz and nonlinearity is 0.06%.

Abstract

In this paper, a novel narrow-band force rebalance control method for the sense mode of a MEMS vibratory gyroscope is presented in detail. There is no demodulation and modulation components in the control loop, and a band pass filter is applied as a controller to accomplish the feedback control. The proposed approach possesses the following advantages: (1) the Coriolis force and quadrature force are rebalanced simultaneously in only one control loop; (2) the loop’s noise is suppressed much by the band pass filter; (3) the control system is linear and very simple to realize. Detailed theoretical analyses are performed to acquire the frequency response models of the closed loop system. Experimental results in the frequency domain of force demonstrate that the phase margins approximate to 60 deg, gain margins are larger than 43 dB, sensitivity margins are smaller than 2.5 dB, and the bandwidth is about 97.2 Hz, which accord with those of simulation. Besides, the overshoot of step response is smaller than 10%, and settling time is less than 15 ms. All these stability indexes in frequency domain and time domain verify that the control system is actually feasible and very robust. The scale factor of the MEMS gyroscope with closed loop controlled sense mode is measured to be 71.9 mV/deg/s with nonlinearity of 0.06%, and the bias instability and angle random walk are evaluated to be 5.1 deg/h and 0.21 deg/√h, respectively.

Graphical abstract

Force rebalance control schematic for the sense.

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Introduction

MEMS vibratory gyroscopes are widely used in various fields such as automotive industry, consumer electronics and navigation systems owing to their merits of low power, low cost and so on, which makes it significant to further advance the performances [1], [2]. Closed loop control for the sense mode can adjust the bandwidth, improve the nonlinearity, extend the measure range and so on, so that it is widely applied in the high-performance gyroscopes. Band-pass and low-pass sigma-delta modulator loops are widely used to realize the force feedback control [3], [4], [5], [6], [7], [8], but the robustness and stability are still problems since the signal–noise-ratio and stability may decrease due to the nonlinearity of the quantizer as the input amplitude increases [9], [10]. Adaptive controller and the adaptive laws based on a Lyapunov approach can be applied to closed loop control of the two modes [11], [12], [13]. However, bandwidth and non-smooth time-varying signals following performance are difficult issues to be solved. Automatic gain control (AGC) method can be utilized to set the vibration amplitude of the sense mode to a certain value according to Refs. [14], [15], but the input force cannot be balanced completely.

On the other hand, there are some closed loop control methods based on demodulation and modulation [16], [17], [18], [19], [20], [21], that is to say, two similar closed loops can be applied to balance the Coriolis force and quadrature force, respectively, due to demodulation and modulation. These methods are proved effective, but still a little complex because the signals’ phases should be control precisely in the demodulation and modulation components. Therefore, in this work, a simple and novel closed loop control method for the sense mode will be proposed after making a comparison and combination of the control methods above. There is no demodulation and modulation components in the control loop and the Coriolis force and quadrature force are balanced together in the same loop. Detailed theoretical analysis and experimental tests will be conducted in the following sections.

Section snippets

Theoretical analysis

The simplified schematic of a Z-axis doubly decoupled MEMS tuning fork gyroscope is shown in Fig. 1, and the design aims to make a gyroscope achieve a sub 10 deg/h bias instability, as well as a bandwidth larger than 90 Hz. The two groups of combs, namely slide-film drive combs and slide-film drive-sensing combs, are used for closed loop control of the drive mode. Similarly, another two groups of combs, namely squeeze-film sense combs and slide-film force feedback combs, are applied to closed

Simulation analysis

For the sake of comparison, the MEMS gyroscope applied to this research is identical to that used in literature [21], the key parameters of the gyroscope are depicted in Table 1. Qd represents the quality factor of the drive mode. Thus, the frequency responses of D(s), T(s), S(s) and Tr(s) can be simulated by Matlab with theoretical Eqs. (1), (2), (3), (4), (5), (6), (7), (8), (9), (10) in f domain and fr domain, respectively, as shown in Fig. 5, Fig. 6, Fig. 7. The expected control goals are

Experimental tests

After tuning with simulation by Matlab, the relevant parameters of the control loop can be confirmed finally, and the theoretical control schematic can be converted to a practical circuit, as shown in Fig. 8. The circuit mainly comprises a vacuum sealed gyroscope, a closed loop for the drive mode and a closed loop for the sense mode. Fig. 9 illustrates the typical differential force-generating circuit and the circuit of HPF and BPF, which are simple to be realized.

The test circuit is mounted on

Conclusion

This work presents a novel closed loop control method for the sense mode of a MEMS gyroscope. There is no demodulation and modulation components in the control loop, and the Coriolis force and quadrature force are rebalanced simultaneously in only one control loop. Moreover, a band pass filter is adopted as a controller to accomplish the feedback control, which simplifies the closed loop system much. Detailed theoretical analyses are performed to acquire the frequency response models of the

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