# A Quick Start Method for MEMS Disk Resonant Gyroscope

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## Abstract

**:**

## 1. Introduction

## 2. Architecture and Motion Model of Disk Gyroscope

#### 2.1. Basic Structure of Mems Disk Resonator Gyroscope

_{g}is the angular gain; τ = 2Q/ω, Q is the quality factor.

#### 2.2. Analysis of Frequency Locking Characteristics

_{d}is the gain of the phase detector, K

_{u}/s is the frequency domain model of DDS, and K

_{u}is the gain of DDS. K

_{d}can be written as Equation (3)

_{d}

_{1}is the amplitude of the input signal and K

_{d}

_{2}is the amplitude of the reference signal. The loop gain can be written as:

_{d}

_{1}of the input signal and the gain K

_{u}of the DDS module. It can be represented as shown in Figure 5.

_{4}to ω

_{3}determines the loop damping. When the ratio is 2, the damping is about 0.7. The bandwidth of PLL is:

_{d}

_{1}is small. At this time, the frequency locking range is small. Due to the small loop gain, the frequency locking time is also long.

#### 2.3. Analysis of Step Response Characteristics

_{n}is the undamped oscillation frequency and ω

_{d}is the damped oscillation frequency. The peak time is related to the gyro damping ratio. With the increasing quality factor of high-precision gyroscope, the start-up time of gyroscope will inevitably increase. As shown in Figure 6, the step response time of MEMS disk resonator gyroscope used in this paper is shown.

## 3. Design of Control System for Quick Start of Driving Mode

#### 3.1. Design of Quick Frequency Locking Control System

_{1}(t) is transformed into a square wave signal as shown in Figure 8. The square wave is used as the input of the phase detector to realize the quick locking of the phase control loop. After the frequency is approximately locked, the output signal of the gyro driving mode x

_{1}(t) is used as the input of the phase detector to achieve more accurate locking and tracking.

#### 3.2. Design of Quick Step Response Control System

_{0}is the initial plate spacing and x is the moving distance. As shown in Figure 1 and Figure 9, for the vibration mode n = 2, capacitors with an angle difference of 90° have opposite displacements to each other. The capacitance can be written as:

_{0}, the variation of capacitance can be obtained as Equation (18).

_{1}is applied to the excitation electrode and a voltage of V

_{p}is applied to the mass block, so that the voltage difference between the electrode and the mass block is:

_{dc}+ V

_{ac}sinω

_{d}t and V

_{dc}− V

_{ac}sinω

_{d}t are applied to the electrodes respectively, and the resulting driving force is:

_{dc}and AC amplitude V

_{ac}. V

_{dc}is mainly used for amplitude adjustment. The increase or decrease of the value is limited. As the digital control circuit is used in this paper, sinusoidal digital signal is mainly generated by DDS module, and then it converts to corresponding analog signal through DAC. Therefore, it can easily realize the multiplication change of V

_{ac}by shift operation. As shown in Figure 10, quick step response is realized by changing the value of V

_{ac}.

_{ac}in M5 is the same as that in M1, so it has the same upward slope in the initial stage. After reaching the predetermined value, the value of V

_{ac}is reduced to make it stable quickly.

_{d2}. In the design of quick step response, V

_{ac}is increased at the initial stage of start-up, which will inevitably lead to the increase of K

_{d}

_{2}in the same proportion, resulting in the increase of loop gain G(s). There will be a certain margin in the design of phase loop. The increase of V

_{ac}leads to insufficient margin. This will result in the instability of phase control loop. Therefore, at the initial stage of step response, the relative invariance of G(s) must be guaranteed while increasing V

_{ac}. Therefore, it is necessary to reduce the value of E at this stage. After switching to a smaller V

_{ac}, E can be restored to its original size. Therefore, the quick locking circuit in Section 3.1 is improved and the structure diagram is shown in Figure 11. Figure 11 is the final version of the quick start method in this paper. It can realize fast frequency locking and fast step response. Compared with Section 3.1, the control of the amplitude of the signal input to the DAC is increased, and the E value is changed synchronously. The test results of this circuit will be given in Section 4.

#### 3.3. Control System of Amplitude Stable Loop

_{dc}+V

_{ac}sinωt and V

_{dc}− V

_{ac}sinωt are applied to the electrodes of the gyro driving mode. The amplitude of gyro output signal is controlled by PI controller.

## 4. Circuit Realization and Test

_{ac}also brings frequency jitter. At 9 s, the frequency and phase stability have been realized. Figure 6 has shown the variation of amplitude when using the traditional method. It can be seen that when using the traditional method, the start-up time is greater than 80 s. Comparing Figure 6 and Figure 20, the fast start-up method in this paper reduces the start-up time by more than 80%. The time domain waveform observed by the oscilloscope is shown in Figure 21, where T3 is the time of frequency locking and T4 is the time of step response.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Xu, X.; Liu, X.; Zhang, Y.
A Quick Start Method for MEMS Disk Resonant Gyroscope. *Sensors* **2021**, *21*, 7986.
https://doi.org/10.3390/s21237986

**AMA Style**

Xu X, Liu X, Zhang Y.
A Quick Start Method for MEMS Disk Resonant Gyroscope. *Sensors*. 2021; 21(23):7986.
https://doi.org/10.3390/s21237986

**Chicago/Turabian Style**

Xu, Xiaodong, Xiaowei Liu, and Yufeng Zhang.
2021. "A Quick Start Method for MEMS Disk Resonant Gyroscope" *Sensors* 21, no. 23: 7986.
https://doi.org/10.3390/s21237986