Preface

**Section 4 Novel Applications of MEMS-Sensors 147**

**Turbine Generator 171**

**Test Systems 189**

**VI** Contents

Chapter 7 **MEMS Devices for Miniaturized Gas Chromatography 149** Imadeddine Azzouz and Khaldoun Bachari

Chapter 8 **Milliwatt-Level Electromagnetic Induction-Type MEMS Air**

Minami Kaneko, Ken Saito and Fumio Uchikoba

Chapter 9 **MEMS Technologies Enabling the Future Wafer**

Bahadir Tunaboylu and Ali M. Soydan

MEMS as a part of various applications ranging from smartphones to automobiles has be‐ come an integral part of our everyday life. MEMS is building synergy between previously unrelated fields such as biology, microelectronics, optics and communications, to improve the quality of human life and open up new applications previously unimagined. Many new MEMS applications will emerge beyond what they are currently identified as or known for. The sensors in MEMS gather information from the surroundings, which are then processed by the electronics for decision-making to control the environment. MEMS offers opportuni‐ ties to miniaturize devices, integrate them with electronics and realize cost savings through batch fabrication. MEMS technology has enhanced many important applications in domains such as automotive, consumer electronics, industrial automation, military applications, bio‐ technology and communication, and it holds great promise for continued contributions in the future.

This book focuses on understanding the design, development and applications in which the MEMS sensors can be used. The book is divided into four sections. The first section focuses on the design and development techniques for MEMS gyroscope and electret electrostatic harvesting for MEMS. The second and third sections focus on BioMEMS and RF MEMS sen‐ sors and the fourth section focuses on new areas of applications for MEMS sensors.

#### **Section I: MEMS Design and Implementation**

#### *Chapter 1. Dual-Mass MEMS Gyroscope Structure Design and Electrostatic Compensation*

In this chapter, the structure design and electrostatic compensation technology for dualmass MEMS gyroscope are introduced. First, a classical dual-mass MEMS gyroscope struc‐ ture is proposed; it works as a tuning fork (drive antiphase mode) and the structure dynamical model and the monitoring system are presented. Second, the imperfection ele‐ ments during the structure manufacture process are analyzed and the quadrature error cou‐ pling stiffness model for dual-mass structure is proposed. After that, the quadrature error correction system based on coupling stiffness electrostatic compensation method is designed and evaluated. Third, the dual-mass structure sensing mode modal is proposed and the force rebalancing comb stimulation method is utilized to achieve sensing mode transform function precisely.

#### *Chapter 2.Integrated Power Supply for MEMS Sensor*

In this chapter, the electret electrostatic harvesting structure is presented and analyzed to conclude that electret electrostatic harvesting structure is a kind of ideal energy harvesting method using ambient vibration and can be easily integrated with the MEMS system be‐ cause of its compatibility with MEMS technology.

#### **Section II: BioMEMS**

#### *Chapter 3. Enzyme Biosensors for Point-of-Care Testing*

This chapter outlines the recent advances of biosensors. Biosensors are classified based on immobilization method of biorecognition layers and fabrication of amperometric biosensors, as well as the applications on POCT. A summary of glucose biosensor development and in‐ tegrated setups is also included. The latest applications of enzyme biosensors in diagnostic applications focusing on POCT of biomarkers in real samples were described.

The fabricated MEMS air turbine and the multilayer ceramic magnetic circuit were com‐

This chapter explores the application of MEMS-based technologies on manufacturing of ad‐

I would like to thank the authors of the chapters of this book for their excellent contributions and for the efforts placed in the publication of their work. I would like to thank all and also

> **Dr. Siva Yellampalli** VTU Extension Centre UTL Technologies Ltd Bangalore, Karnataka

> > India

Preface IX

bined and the miniature electromagnetic induction-type generator was achieved.

vanced probe cards for probing dies with various new pad or bump structures.

my wife, Suma, and son, Gangadhar, for their patience and understanding.

*Chapter 9. MEMS Technologies Enabling the Future Wafer Test Systems*

**Acknowledgments**

#### *Chapter 4. Micropatterning in BioMEMS for the Separation of Cells/Bioparticles*

This chapter reviews the techniques, which have been substantiated and proven helpful for the separation of particles depending on mass and size with some constraints of highthroughput. The first part of the chapter focuses on the designing of the pattern for issues of the network like clogging and theoretical experiments by both hydrodynamic and other pas‐ sive methods for sorting/separation. The second part of the chapter focuses on the simula‐ tions for the separation of smaller and larger bioparticles depending on mass and size, samples of the blood, and other *Klebsiella*-infected fluidic samples for the experiment.

#### **Section III: RF-MEMS**

#### *Chapter 5. Study and Design of Reconfigurable Wireless and Radiofrequency Components Based on RF-MEMS for Low-Power Applications*

This chapter focuses on the study and design of reconfigurable components based on RF-MEMS for different applications. This chapter is subdivided into three parts. In the first part, the chapter highlights the attractive properties of the RF-MEMS structures and then uses these properties for design and modeling of RF-MEMS switches. The second part is about the design and the simulation study of nonradiating reconfigurable components: phase shifter and resonator. The last aspect includes the study and the evaluation of different ar‐ chitectures to realize frequency reconfigurable antenna for the radar applications.

#### *Chapter 6. RF-MEMS Switches Designed for High-Performance Uniplanar Microwave and mm-Wave Circuits*

In this chapter, electrostatically actuated RF-MEMS switch configurations that can be easily integrated in uniplanar circuits are presented. The design procedure and fabrication process of RF-MEMS switch topologies able to control the propagating modes of multimodal unipla‐ nar structures (those based on a combination of coplanar waveguide [CPW], coplanar stri‐ pline [CPS], and slotline) are described in detail.

#### **Section IV: Novel Applications of MEMS Sensors**

#### *Chapter 7. MEMS Devices for Miniaturized Gas Chromatography*

This chapter focuses on the recent development in the field of miniaturized gas chromatog‐ raphy and its component up to the present in various fields of analyses.

#### *Chapter 8. Milliwatt-Level Electromagnetic Induction-Type MEMS Air Turbine Generator*

In this chapter, an electromagnetic induction-type MEMS air turbine generator that com‐ bined with the MEMS technology and the multilayer ceramic technology is proposed. Three types of MEMS air turbine generator that included the different bearing systems, shape of the rotor and shape of the magnetic circuits are discussed to achieve the high-output power. The fabricated MEMS air turbine and the multilayer ceramic magnetic circuit were com‐ bined and the miniature electromagnetic induction-type generator was achieved.

*Chapter 9. MEMS Technologies Enabling the Future Wafer Test Systems*

This chapter explores the application of MEMS-based technologies on manufacturing of ad‐ vanced probe cards for probing dies with various new pad or bump structures.

#### **Acknowledgments**

**Section II: BioMEMS**

VIII Preface

**Section III: RF-MEMS**

*Wave Circuits*

*RF-MEMS for Low-Power Applications*

pline [CPS], and slotline) are described in detail. **Section IV: Novel Applications of MEMS Sensors**

*Chapter 7. MEMS Devices for Miniaturized Gas Chromatography*

raphy and its component up to the present in various fields of analyses.

*Chapter 3. Enzyme Biosensors for Point-of-Care Testing*

This chapter outlines the recent advances of biosensors. Biosensors are classified based on immobilization method of biorecognition layers and fabrication of amperometric biosensors, as well as the applications on POCT. A summary of glucose biosensor development and in‐ tegrated setups is also included. The latest applications of enzyme biosensors in diagnostic

This chapter reviews the techniques, which have been substantiated and proven helpful for the separation of particles depending on mass and size with some constraints of highthroughput. The first part of the chapter focuses on the designing of the pattern for issues of the network like clogging and theoretical experiments by both hydrodynamic and other pas‐ sive methods for sorting/separation. The second part of the chapter focuses on the simula‐ tions for the separation of smaller and larger bioparticles depending on mass and size,

*Chapter 5. Study and Design of Reconfigurable Wireless and Radiofrequency Components Based on*

This chapter focuses on the study and design of reconfigurable components based on RF-MEMS for different applications. This chapter is subdivided into three parts. In the first part, the chapter highlights the attractive properties of the RF-MEMS structures and then uses these properties for design and modeling of RF-MEMS switches. The second part is about the design and the simulation study of nonradiating reconfigurable components: phase shifter and resonator. The last aspect includes the study and the evaluation of different ar‐

*Chapter 6. RF-MEMS Switches Designed for High-Performance Uniplanar Microwave and mm-*

In this chapter, electrostatically actuated RF-MEMS switch configurations that can be easily integrated in uniplanar circuits are presented. The design procedure and fabrication process of RF-MEMS switch topologies able to control the propagating modes of multimodal unipla‐ nar structures (those based on a combination of coplanar waveguide [CPW], coplanar stri‐

This chapter focuses on the recent development in the field of miniaturized gas chromatog‐

In this chapter, an electromagnetic induction-type MEMS air turbine generator that com‐ bined with the MEMS technology and the multilayer ceramic technology is proposed. Three types of MEMS air turbine generator that included the different bearing systems, shape of the rotor and shape of the magnetic circuits are discussed to achieve the high-output power.

*Chapter 8. Milliwatt-Level Electromagnetic Induction-Type MEMS Air Turbine Generator*

samples of the blood, and other *Klebsiella*-infected fluidic samples for the experiment.

chitectures to realize frequency reconfigurable antenna for the radar applications.

applications focusing on POCT of biomarkers in real samples were described. *Chapter 4. Micropatterning in BioMEMS for the Separation of Cells/Bioparticles*

I would like to thank the authors of the chapters of this book for their excellent contributions and for the efforts placed in the publication of their work. I would like to thank all and also my wife, Suma, and son, Gangadhar, for their patience and understanding.

> **Dr. Siva Yellampalli** VTU Extension Centre UTL Technologies Ltd Bangalore, Karnataka India

**Section 1**

**MEMS Design and Implementation**

**MEMS Design and Implementation**

**Chapter 1**

Provisional chapter

**Dual-Mass MEMS Gyroscope Structure, Design, and**

DOI: 10.5772/intechopen.74364

Dual-mass MEMS gyroscope is one of the most popular inertial sensors. In this chapter, the structure design and electrostatic compensation technology for dual-mass MEMS gyroscope is introduced. Firstly, a classical dual-mass MEMS gyroscope structure is proposed, how it works as a tuning fork (drive anti-phase mode), and the structure dynamical model together with the monitoring system are presented. Secondly, the imperfect elements during the structure manufacture process are analyzed, and the quadrature error coupling stiffness model for dual-mass structure is proposed. After that, the quadrature error correction system based on coupling stiffness electrostatic compensation method is designed and evaluated. Thirdly, the dual-mass structure sensing mode modal is proposed, and the force rebalancing combs stimulation method is utilized to achieve sensing mode transform function precisely. The bandwidth of sensing open loop is calculated and experimentally proved as 0.54 times with the resonant frequency difference between sensing and drive modes. Then, proportional-integral-phase-leading controller is presented in sensing close loop to expand the bandwidth, and the experiment shows that the bandwidth is improved from 13 to 104 Hz. Finally, the results are concluded and

Keywords: MEMS gyroscope, dual-mass structure, mode analysis, quadrature error,

The precision of micro-electro-mechanical system (MEMS) gyroscope improves a lot in this decade, and achieves the tactical grade level. On the benefits of the small size, low costs, and light weight the MEMS gyro is applied in more and more areas, such as inertial navigation, roller detection, automotive safety, industrial controlling, railway siding detection, consumer

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

bandwidth expansion, electrostatic compensation

Dual-Mass MEMS Gyroscope Structure, Design, and

**Electrostatic Compensation**

Electrostatic Compensation

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Huiliang Cao and Jianhua Li

Huiliang Cao and Jianhua Li

Abstract

summarized.

1. Introduction

http://dx.doi.org/10.5772/intechopen.74364

#### **Dual-Mass MEMS Gyroscope Structure, Design, and Electrostatic Compensation** Dual-Mass MEMS Gyroscope Structure, Design, and Electrostatic Compensation

DOI: 10.5772/intechopen.74364

Huiliang Cao and Jianhua Li Huiliang Cao and Jianhua Li

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.74364

#### Abstract

Dual-mass MEMS gyroscope is one of the most popular inertial sensors. In this chapter, the structure design and electrostatic compensation technology for dual-mass MEMS gyroscope is introduced. Firstly, a classical dual-mass MEMS gyroscope structure is proposed, how it works as a tuning fork (drive anti-phase mode), and the structure dynamical model together with the monitoring system are presented. Secondly, the imperfect elements during the structure manufacture process are analyzed, and the quadrature error coupling stiffness model for dual-mass structure is proposed. After that, the quadrature error correction system based on coupling stiffness electrostatic compensation method is designed and evaluated. Thirdly, the dual-mass structure sensing mode modal is proposed, and the force rebalancing combs stimulation method is utilized to achieve sensing mode transform function precisely. The bandwidth of sensing open loop is calculated and experimentally proved as 0.54 times with the resonant frequency difference between sensing and drive modes. Then, proportional-integral-phase-leading controller is presented in sensing close loop to expand the bandwidth, and the experiment shows that the bandwidth is improved from 13 to 104 Hz. Finally, the results are concluded and summarized.

Keywords: MEMS gyroscope, dual-mass structure, mode analysis, quadrature error, bandwidth expansion, electrostatic compensation

#### 1. Introduction

The precision of micro-electro-mechanical system (MEMS) gyroscope improves a lot in this decade, and achieves the tactical grade level. On the benefits of the small size, low costs, and light weight the MEMS gyro is applied in more and more areas, such as inertial navigation, roller detection, automotive safety, industrial controlling, railway siding detection, consumer

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

electronics and stability controlling system [1–5]. During use, the acceleration along the sense axis causes great error in MEMS gyroscope output signal, and dual-mass gyroscope structure restrains this phenomenon well by employing differential detection technology; so, a lot of research institutes are interested in this structure [6–8].

together. A novel quadrature compensation method is proposed in literature [17] based on sigma-delta-modulators (ΣΔM), the quadrature error is detected by utilizing a pure digital pattern recognition algorithm and is compensated by using DC bias voltages, and the system works beyond the full-scale limits of the analog ΣΔM hardware. The quadrature error is compensated by open-loop charge injecting circuit in Ref. [18], the circuit is implemented on application specific integrated circuits (ASIC) and the experimental results show that the quadrature

Dual-Mass MEMS Gyroscope Structure, Design, and Electrostatic Compensation

http://dx.doi.org/10.5772/intechopen.74364

5

High precision MEMS gyros are reported in literatures, and the bias drift parameters are even better than the tactical grade requirement. But the bandwidth performance always restrains the MEMS gyro application (100 Hz bandwidth is required in both Tactical and Inertial Grade) [4]. For most linear vibrating MEMS gyro, the mechanical sensitivity is determined by the difference between drive and sensing modes' resonant frequencies Δf. It means smaller difference achieves higher mechanical sensitivity (such as higher scale factor, higher resolution and smaller output noise) [19]. It is also proved that the mechanical bandwidth of the gyro is about 0.54Δf [20], so smaller Δf causes worse bandwidth characteristic. Some works employ modematching technology to make Δf ≈ 0 Hz, and the best mechanical sensitivity can be acquired but bandwidth is sacrificed. It seems like that the bargain should be made between mechanical sensitivity and bandwidth in sensing open loop. So the sensing closed loop is required to improve MEMS gyro dynamic characteristics and bandwidth. The work in [21] employs a ΣΔ closed loop to reduce the frequency difference between the drive and sensing mode to less than 50 Hz. The research in work [22] utilizes PI controlling technology to make Δf tunable, and the bandwidth is optimized to 50 Hz. The sensing closed loop for single mass MEMS gyroscope based on automatic generation control (AGC) technology is proposed in paper [23]. The force rebalance controller extends the bandwidth, but it only contains a pure integral section which makes sensing closed loop with high Q value structure unstable. The bandwidth for another single mass MEMS gyroscope is introduced in work [24]; the bandwidth is improved from 30 to 98 Hz with notch filter and lead–lag compensator. The notch filter is designed for the "peak response" caused by the conjugate complex poles at Δf. But the resonant frequencies of the drive and sensing modes usually drift with temperature [6], so the notch filter method cannot satisfy the temperature-changing environment. The work in [25] proposes a method to avoid problems caused by notch filter and expands the bandwidth from 2.3 to 94.8 Hz. However, its left and right sensing modes are not coupled, and the bandwidth is only determined by the low pass filter (different with left and right sensing modes coupled structure). Its dual-mass structure can be considered as two independent gyroscopes with different Δfs, and two sensing loops should be designed separately to expand the bandwidth. The left and right sensing modes coupled structures are investigated in [26, 27, 28]. The work in Ref. [26] illustrates the vibration characteristics of dual-mass and spring structure. The work in Ref. [27] analyzes the energy of gyroscope under in-phase and anti-phase modes. And literature [28] proposes that the real working sensing mode of gyroscope is formed by sensing in-phase and anti-phase modes. However, these works do not focus on the bandwidth method of this kind of sensing loop. The gyro bandwidth optimized by mechanical method is proposed in Ref. [29], but the bandwidth varies with the temperature. Literature [30] employs eight drive mode units to

1.2. Development of dual-mass MEMS gyroscope bandwidth expansion

error component is effectively rejected.

#### 1.1. Development of dual-mass MEMS gyroscope structure quadrature error compensation

Most of the literature informs that the dominate signal component in output signal is quadrature error, which is generated in the structure manufacture process, and brings over several 100 S<sup>1</sup> equivalent input angular [9–14]. The original source of quadrature is the coupling stiffness, which is modulated by drive mode movement and generates quadrature error force. The force has same frequency but has a 90 phase difference with Coriolis force and stimulates sense mode [11]. Most previous works utilize phase-sensitivity demodulation method to pick Coriolis signal from sense channel [9, 13], which requires accurate phase information and longterm, full-temperature range stability. However, the demodulation phase error and noise usually exist (sometimes more than 1 [9, 12]), which bring undesirable bias. The coupling stiffness drift (the drive and sense modes' equivalent stiffness vary with temperature and generate the drift of coupling stiffness [6, 11]) causes the quadrature error force drift, which is considered to be one of the most important reasons leading to bias long-term drift, and is proved by [11, 14] experimental work.

The previous works provide several effective ways to reduce quadrature error and are concluded into three aspects after the structure is manufactured [9, 11]: the quadrature signal compensation, the quadrature force correction and coupling stiffness correction. In work [9], the quadrature error is reduced by dc voltage based on synchronous demodulation and electrostatic quadrature compensation method, and the sigma-delta technology is employed in ADC and DAC. The research in Ref. [14] also employs coupling stiffness correction method to improve the performance of "butterfly" MEMS gyroscope. The bias stability and scale factor temperature stability enhance from 89/h and 662 ppm/C to 17/h and 231 ppm/C, respectively, which achieves the correction goal. The quadrature error correction in dual-mass tuning fork MEMS gyro structure is investigated in literature [11], and this work also proves the quadrature stiffness are different in left and right masses. A quadrature error correction closed loop is proposed in the work, and utilizing the coupling stiffness correction method, the masses are corrected separately. The stiffness correction combs utilize unequal gap method with dc voltages [15]. The bias stability improves from 2.06 to 0.64/h with Allan Deviation analysis method, and the noise characteristic is also optimized [11]. Another coupling stiffness correction work is proposed in literature [7]; in this work, coupling stiffness correction controller uses PI technology, and the quadrature error equivalent input angular rate is measured as 450/s. The experiment in the work shows that the bias stability and ARW improve from 7.1/h and 0.36/√h to 0.91/h and 0.034/√h, respectively. In Ref. [16], quadrature signal is compensated based on charge injecting technology in the sense loop, the compensation signal has same frequency, amplitude and anti-phase with quadrature error signal. The quadrature error correction method proposed in literature [8] employs both the quadrature force and stiffness correction methods, the modulation reference signal is generated by PLL technology and the correction loop uses PI regulator; the two masses are controlled together. A novel quadrature compensation method is proposed in literature [17] based on sigma-delta-modulators (ΣΔM), the quadrature error is detected by utilizing a pure digital pattern recognition algorithm and is compensated by using DC bias voltages, and the system works beyond the full-scale limits of the analog ΣΔM hardware. The quadrature error is compensated by open-loop charge injecting circuit in Ref. [18], the circuit is implemented on application specific integrated circuits (ASIC) and the experimental results show that the quadrature error component is effectively rejected.

#### 1.2. Development of dual-mass MEMS gyroscope bandwidth expansion

electronics and stability controlling system [1–5]. During use, the acceleration along the sense axis causes great error in MEMS gyroscope output signal, and dual-mass gyroscope structure restrains this phenomenon well by employing differential detection technology; so, a lot of

Most of the literature informs that the dominate signal component in output signal is quadrature error, which is generated in the structure manufacture process, and brings over several 100 S<sup>1</sup> equivalent input angular [9–14]. The original source of quadrature is the coupling stiffness, which is modulated by drive mode movement and generates quadrature error force. The force has same frequency but has a 90 phase difference with Coriolis force and stimulates sense mode [11]. Most previous works utilize phase-sensitivity demodulation method to pick Coriolis signal from sense channel [9, 13], which requires accurate phase information and longterm, full-temperature range stability. However, the demodulation phase error and noise usually exist (sometimes more than 1 [9, 12]), which bring undesirable bias. The coupling stiffness drift (the drive and sense modes' equivalent stiffness vary with temperature and generate the drift of coupling stiffness [6, 11]) causes the quadrature error force drift, which is considered to be one of the most important reasons leading to bias long-term drift, and is

The previous works provide several effective ways to reduce quadrature error and are concluded into three aspects after the structure is manufactured [9, 11]: the quadrature signal compensation, the quadrature force correction and coupling stiffness correction. In work [9], the quadrature error is reduced by dc voltage based on synchronous demodulation and electrostatic quadrature compensation method, and the sigma-delta technology is employed in ADC and DAC. The research in Ref. [14] also employs coupling stiffness correction method to improve the performance of "butterfly" MEMS gyroscope. The bias stability and scale factor temperature stability enhance from 89/h and 662 ppm/C to 17/h and 231 ppm/C, respectively, which achieves the correction goal. The quadrature error correction in dual-mass tuning fork MEMS gyro structure is investigated in literature [11], and this work also proves the quadrature stiffness are different in left and right masses. A quadrature error correction closed loop is proposed in the work, and utilizing the coupling stiffness correction method, the masses are corrected separately. The stiffness correction combs utilize unequal gap method with dc voltages [15]. The bias stability improves from 2.06 to 0.64/h with Allan Deviation analysis method, and the noise characteristic is also optimized [11]. Another coupling stiffness correction work is proposed in literature [7]; in this work, coupling stiffness correction controller uses PI technology, and the quadrature error equivalent input angular rate is measured as 450/s. The experiment in the work shows that the bias stability and ARW improve from 7.1/h and 0.36/√h to 0.91/h and 0.034/√h, respectively. In Ref. [16], quadrature signal is compensated based on charge injecting technology in the sense loop, the compensation signal has same frequency, amplitude and anti-phase with quadrature error signal. The quadrature error correction method proposed in literature [8] employs both the quadrature force and stiffness correction methods, the modulation reference signal is generated by PLL technology and the correction loop uses PI regulator; the two masses are controlled

1.1. Development of dual-mass MEMS gyroscope structure quadrature error

research institutes are interested in this structure [6–8].

proved by [11, 14] experimental work.

compensation

4 MEMS Sensors - Design and Application

High precision MEMS gyros are reported in literatures, and the bias drift parameters are even better than the tactical grade requirement. But the bandwidth performance always restrains the MEMS gyro application (100 Hz bandwidth is required in both Tactical and Inertial Grade) [4]. For most linear vibrating MEMS gyro, the mechanical sensitivity is determined by the difference between drive and sensing modes' resonant frequencies Δf. It means smaller difference achieves higher mechanical sensitivity (such as higher scale factor, higher resolution and smaller output noise) [19]. It is also proved that the mechanical bandwidth of the gyro is about 0.54Δf [20], so smaller Δf causes worse bandwidth characteristic. Some works employ modematching technology to make Δf ≈ 0 Hz, and the best mechanical sensitivity can be acquired but bandwidth is sacrificed. It seems like that the bargain should be made between mechanical sensitivity and bandwidth in sensing open loop. So the sensing closed loop is required to improve MEMS gyro dynamic characteristics and bandwidth. The work in [21] employs a ΣΔ closed loop to reduce the frequency difference between the drive and sensing mode to less than 50 Hz. The research in work [22] utilizes PI controlling technology to make Δf tunable, and the bandwidth is optimized to 50 Hz. The sensing closed loop for single mass MEMS gyroscope based on automatic generation control (AGC) technology is proposed in paper [23]. The force rebalance controller extends the bandwidth, but it only contains a pure integral section which makes sensing closed loop with high Q value structure unstable. The bandwidth for another single mass MEMS gyroscope is introduced in work [24]; the bandwidth is improved from 30 to 98 Hz with notch filter and lead–lag compensator. The notch filter is designed for the "peak response" caused by the conjugate complex poles at Δf. But the resonant frequencies of the drive and sensing modes usually drift with temperature [6], so the notch filter method cannot satisfy the temperature-changing environment. The work in [25] proposes a method to avoid problems caused by notch filter and expands the bandwidth from 2.3 to 94.8 Hz. However, its left and right sensing modes are not coupled, and the bandwidth is only determined by the low pass filter (different with left and right sensing modes coupled structure). Its dual-mass structure can be considered as two independent gyroscopes with different Δfs, and two sensing loops should be designed separately to expand the bandwidth. The left and right sensing modes coupled structures are investigated in [26, 27, 28]. The work in Ref. [26] illustrates the vibration characteristics of dual-mass and spring structure. The work in Ref. [27] analyzes the energy of gyroscope under in-phase and anti-phase modes. And literature [28] proposes that the real working sensing mode of gyroscope is formed by sensing in-phase and anti-phase modes. However, these works do not focus on the bandwidth method of this kind of sensing loop. The gyro bandwidth optimized by mechanical method is proposed in Ref. [29], but the bandwidth varies with the temperature. Literature [30] employs eight drive mode units to form a drive band (not a single frequency). It provides a high mechanical sensitivity band for the gyroscope, but the bandwidth is determined by sensing mode frequency. And the phase margin of the closed loop is difficult to design. In Ref. [31], the bandwidth estimation methods of MEMS gyroscope in open loop and closed loop are proposed, but the bandwidth expanding method is not discussed clearly. The precise test method of bandwidth is introduced in Ref. [32]. The method uses vibration velocity of virtual drive mode multiplied by virtual angular rate to generate Coriolis force and substitutes angular turntable. The vibration velocity of drive mode is produced by signal source, not by drive mode, which ignores the frequency drift of drive mode and the mechanical coupling between drive and sensing mode.

structure is shown in Figure 2. This structure model is constituted by two symmetrical parts, which are connected by two center U-shaped connect springs whose parameters are the same with drive U-shaped spring. The left and right Coriolis mass are sustained by 2 drive U-shaped springs (DS-A,B) and 4 sense U-shaped springs (SS-C,D,E,F), respectively, and these springs are linked by drive and sensing frames. The moving comb fingers are combined with frames while the static ones are fixed with the substrate. The whole structure is suspended and supported by 8 drive (DS-C,D,E,F for left part) and 4 sense (SS-A,B) U-shaped springs [6].

Dual-Mass MEMS Gyroscope Structure, Design, and Electrostatic Compensation

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7

The drive U-shaped springs' stiffness coefficients are large along y-axis and very small in x direction while sense springs have the adverse characteristic. When the structure works, the drive combs support the electrostatic force to stimulate the drive frame and the Coriolis mass (together with SS-C,D,E,F) to move along x direction, and no displacement is generated in sense direction because of SS-A,B. When there is an angular rate Ω<sup>z</sup> input around the z-axis, the Coriolis mass together with sense frame and DS-A, B will have a component motion in y orientation under the influence of Coriolis force (the drive frame will not move in y-axis because of the effect of DS-C,D,E,F), and then this displacement involved with Ω<sup>z</sup> is detected

The drive mode of the structure bases on tuning for k theory. The left and right masses are coupled by connect U-shaped spring, when two sensing masses are coupled by the x-axis warp of drive springs. The mode analyses of the first four order modes are shown in Figure 3 [34]. The first-order mode is drive in-phase mode, the left and right masses together with drive frames vibrate toward same direction along drive axis (x direction in Figure 2), as shown in Figure 3(a). The second- and third-order modes are sensing in-phase and antiphase modes, as shown in Figure 3(b) and (c). The left and right masses together with sense frames vibrate in same and inverse directions along sensing axis (y direction in Figure 2), respectively. And sensing anti-phase mode is the expected working mode. Drive anti-phase

by the sense combs.

Figure 2. Schematic of the structure.

This chapter focuses on the investigation of the dual-mass MEMS gyroscope structure, and the electrostatic compensation method for the structure, including quadrature error correction and bandwidth expansion technology. Through these technologies, the static and dynamic performance of the MEMS gyroscope is improved.

## 2. Dual-mass MEMS gyroscope structure design and analysis

#### 2.1. Dual-mass MEMS gyroscope structure design

The fully decoupled linear vibrating gyroscope structure's ideal movement model can be found in many papers; the model can be described as two "spring-mass-damping" systems: drive mode and sense mode. In x-axis direction, drive frame is connected with Coriolis mass which is linked by sense frame in y direction. The drive frame and sense frame can be stimulated by their own mode's effective stiffness and damping, as shown in Figure 1. This chapter employs a dual-mass fully decoupled structure as mentioned in [6, 33], and it works in linear vibrating principle, with slide-film combs in both drive and sense modes. The whole

Figure 1. Schematic of ideal gyroscope fully decoupled model.

structure is shown in Figure 2. This structure model is constituted by two symmetrical parts, which are connected by two center U-shaped connect springs whose parameters are the same with drive U-shaped spring. The left and right Coriolis mass are sustained by 2 drive U-shaped springs (DS-A,B) and 4 sense U-shaped springs (SS-C,D,E,F), respectively, and these springs are linked by drive and sensing frames. The moving comb fingers are combined with frames while the static ones are fixed with the substrate. The whole structure is suspended and supported by 8 drive (DS-C,D,E,F for left part) and 4 sense (SS-A,B) U-shaped springs [6].

The drive U-shaped springs' stiffness coefficients are large along y-axis and very small in x direction while sense springs have the adverse characteristic. When the structure works, the drive combs support the electrostatic force to stimulate the drive frame and the Coriolis mass (together with SS-C,D,E,F) to move along x direction, and no displacement is generated in sense direction because of SS-A,B. When there is an angular rate Ω<sup>z</sup> input around the z-axis, the Coriolis mass together with sense frame and DS-A, B will have a component motion in y orientation under the influence of Coriolis force (the drive frame will not move in y-axis because of the effect of DS-C,D,E,F), and then this displacement involved with Ω<sup>z</sup> is detected by the sense combs.

The drive mode of the structure bases on tuning for k theory. The left and right masses are coupled by connect U-shaped spring, when two sensing masses are coupled by the x-axis warp of drive springs. The mode analyses of the first four order modes are shown in Figure 3 [34]. The first-order mode is drive in-phase mode, the left and right masses together with drive frames vibrate toward same direction along drive axis (x direction in Figure 2), as shown in Figure 3(a). The second- and third-order modes are sensing in-phase and antiphase modes, as shown in Figure 3(b) and (c). The left and right masses together with sense frames vibrate in same and inverse directions along sensing axis (y direction in Figure 2), respectively. And sensing anti-phase mode is the expected working mode. Drive anti-phase

Figure 2. Schematic of the structure.

form a drive band (not a single frequency). It provides a high mechanical sensitivity band for the gyroscope, but the bandwidth is determined by sensing mode frequency. And the phase margin of the closed loop is difficult to design. In Ref. [31], the bandwidth estimation methods of MEMS gyroscope in open loop and closed loop are proposed, but the bandwidth expanding method is not discussed clearly. The precise test method of bandwidth is introduced in Ref. [32]. The method uses vibration velocity of virtual drive mode multiplied by virtual angular rate to generate Coriolis force and substitutes angular turntable. The vibration velocity of drive mode is produced by signal source, not by drive mode, which ignores the frequency drift of

This chapter focuses on the investigation of the dual-mass MEMS gyroscope structure, and the electrostatic compensation method for the structure, including quadrature error correction and bandwidth expansion technology. Through these technologies, the static and dynamic perfor-

The fully decoupled linear vibrating gyroscope structure's ideal movement model can be found in many papers; the model can be described as two "spring-mass-damping" systems: drive mode and sense mode. In x-axis direction, drive frame is connected with Coriolis mass which is linked by sense frame in y direction. The drive frame and sense frame can be stimulated by their own mode's effective stiffness and damping, as shown in Figure 1. This chapter employs a dual-mass fully decoupled structure as mentioned in [6, 33], and it works in linear vibrating principle, with slide-film combs in both drive and sense modes. The whole

drive mode and the mechanical coupling between drive and sensing mode.

2. Dual-mass MEMS gyroscope structure design and analysis

mance of the MEMS gyroscope is improved.

6 MEMS Sensors - Design and Application

2.1. Dual-mass MEMS gyroscope structure design

Figure 1. Schematic of ideal gyroscope fully decoupled model.

where m ¼

mx my my

cy2y2=ωy2my/Qy2 and kxx=ωx22

3 7 <sup>5</sup>,<sup>D</sup> <sup>¼</sup>

x y1 y2 3 7 <sup>5</sup>,<sup>k</sup> <sup>¼</sup> 2 6 4

mx, ky1y1=ωy12

x2ω<sup>2</sup> d=Q<sup>2</sup> x2

x2ω<sup>2</sup> d=Q<sup>2</sup> x2 e � <sup>ω</sup>x<sup>2</sup> <sup>2</sup>Qx<sup>2</sup> t cos

ω2 <sup>x</sup><sup>2</sup> � <sup>ω</sup><sup>2</sup> d � �<sup>2</sup> <sup>þ</sup> <sup>ω</sup><sup>2</sup>

<sup>x</sup><sup>2</sup> <sup>þ</sup> <sup>ω</sup><sup>2</sup>

<sup>r</sup> sin <sup>ω</sup>dt <sup>þ</sup> <sup>φ</sup>x<sup>2</sup> <sup>þ</sup>

h i

<sup>þ</sup> <sup>ω</sup><sup>2</sup> y1,2ω<sup>2</sup> d=Q<sup>2</sup> y1, 2

y1,2

<sup>d</sup> ð Þ � �,Fc <sup>¼</sup> �2ΩzωdFd mx

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � <sup>1</sup>=4Q<sup>2</sup>

ωy1,2t

� �=mx

<sup>d</sup> � <sup>ω</sup><sup>2</sup> x2

h i

<sup>y</sup>1,<sup>2</sup> � <sup>ω</sup><sup>2</sup> d � � cosφx<sup>2</sup>

y1, 2

ω2 x2�ω<sup>2</sup> <sup>d</sup> ð Þ<sup>2</sup>

The abovementioned equations indicate that the movement of drive and sensing modes are the compound motion of stable vibration and attenuation vibration. Since drive mode closed loop

x2=Q<sup>2</sup>

x2

<sup>þ</sup> <sup>ω</sup><sup>2</sup> <sup>y</sup>1, <sup>2</sup>ω<sup>2</sup> d=Q<sup>2</sup> y1,2

<sup>q</sup> sin <sup>ω</sup>dt <sup>þ</sup> <sup>φ</sup>x<sup>2</sup>

kxx kxy<sup>1</sup> kxy<sup>2</sup> ky1<sup>x</sup> ky1y<sup>1</sup> 0 ky2<sup>x</sup> 0 ky2y<sup>2</sup> 3 7 <sup>5</sup>,<sup>c</sup> <sup>¼</sup>

are the mass, displacement, stiffness, damping and external force matrix, respectively; mx is equivalent mass of drive mode; x is displacement of drive mode; y1 and y2 are displacements of sensing in-phase and anti-phase modes, respectively; Qy1 and Qy2 are quality factors; Ω<sup>z</sup> is angular rate input; sensing mode mass my approximates to Coriolis mass mc; Fd and ω<sup>d</sup> are stimulating magnitude and frequency of drive mode; cxx=ωx2mx/Qx2, cy1y1=ωy1my/Qy1,

my, ky2y2=ωy22

drive and sensing in-phase and anti-phase modes; cxy1, cxy2 and cy1x, cy2x are coupling damping, kxy1, kxy2 and ky1x, ky2x are coupling stiffness (caused by machining error) between drive and sensing in-phase and anti-phase modes, respectively; sensing mode displacement y = y1 + y2, and for ideal gyro structure model (ignoring the coupling stiffness and damping), we get [35]:

� �

q

x2ω<sup>2</sup> d=Q<sup>2</sup> x2

� � <sup>þ</sup> <sup>ω</sup><sup>d</sup> <sup>ω</sup><sup>2</sup>

ω2 <sup>y</sup>1, <sup>2</sup> � <sup>ω</sup><sup>2</sup> d � �<sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>þ</sup>ω<sup>2</sup> x2ω<sup>2</sup> d=Q<sup>2</sup> x2

h i

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � <sup>1</sup>=4Q<sup>2</sup>

> e � <sup>ω</sup>x<sup>2</sup> <sup>2</sup>Qx<sup>2</sup> t sin

� �

x2

π <sup>2</sup> <sup>þ</sup> <sup>φ</sup>y1,<sup>2</sup>

� ��

e � <sup>ω</sup>y1,<sup>2</sup> <sup>2</sup>Qy1,<sup>2</sup> t cos

<sup>y</sup>1,2<sup>=</sup> <sup>2</sup>Q<sup>2</sup>

� �

<sup>þ</sup> <sup>ω</sup><sup>2</sup> <sup>y</sup>1, <sup>2</sup>ω<sup>2</sup> d=Q<sup>2</sup> y1,2

<sup>q</sup> ,φy1, <sup>2</sup> ¼ � tg �<sup>1</sup> <sup>ω</sup>y1,2ω<sup>d</sup>

ωx2t

q

q

� � sinφx<sup>2</sup>

y1, 2 � � <sup>þ</sup> <sup>ω</sup><sup>2</sup>

2 6 4

cxx cxy<sup>1</sup> cxy<sup>2</sup> cy1<sup>x</sup> cy1y<sup>1</sup> 0 cy2<sup>x</sup> 0 cy2y<sup>2</sup>

Dual-Mass MEMS Gyroscope Structure, Design, and Electrostatic Compensation

3 7 <sup>5</sup>,<sup>F</sup> <sup>¼</sup>

my are effective damping and stiffness of

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � <sup>1</sup>=4Q<sup>2</sup>

� �

x2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � <sup>1</sup>=4Q<sup>2</sup>

> <sup>y</sup>1,<sup>2</sup> � <sup>ω</sup><sup>2</sup> d

Qy1,<sup>2</sup> ω<sup>2</sup>

0 @

<sup>y</sup>1, <sup>2</sup>�ω<sup>2</sup> d � �

ωx2t

y1,2

� �<sup>þ</sup>

ωy1, <sup>2</sup>t

(3)

1 A.

(2)

2 6 4

http://dx.doi.org/10.5772/intechopen.74364

Fd sin ð Þ ωdt �2mcΩzx\_ �2mcΩzx\_

3 7 5. 9

2 6 4

x tðÞ¼ Fd=mx ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Fdωx2ωd=mxQx

Fdω<sup>d</sup> ω<sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � <sup>1</sup>=4Q<sup>2</sup>

Fc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Fc <sup>ω</sup>y1, <sup>2</sup>ω<sup>d</sup> sinφx2=Qy1, <sup>2</sup> <sup>þ</sup> <sup>ω</sup><sup>2</sup>

<sup>y</sup>1,<sup>2</sup> � <sup>3</sup>ω<sup>2</sup> d � � cosφx2<sup>=</sup> <sup>2</sup>Qy1, <sup>2</sup>

ωy1,<sup>2</sup>

q

� �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � <sup>1</sup>=4Q<sup>2</sup>

ω2 <sup>y</sup>1,<sup>2</sup> � <sup>ω</sup><sup>2</sup> d � �<sup>2</sup>

q

Qx<sup>2</sup> ω<sup>2</sup> x2�ω<sup>2</sup>

ω2 <sup>x</sup><sup>2</sup> � <sup>ω</sup><sup>2</sup> d � �<sup>2</sup> <sup>þ</sup> <sup>ω</sup><sup>2</sup>

ω2 <sup>x</sup><sup>2</sup> � <sup>ω</sup><sup>2</sup> d � �<sup>2</sup> <sup>þ</sup> <sup>ω</sup><sup>2</sup>

ωx<sup>2</sup>

ω2 <sup>y</sup>1, <sup>2</sup> � <sup>ω</sup><sup>2</sup> d � �<sup>2</sup>

Fc ωy1, <sup>2</sup> ω<sup>2</sup>

e � <sup>ω</sup>y1, <sup>2</sup> <sup>2</sup>Qy1, <sup>2</sup> t sin

where <sup>φ</sup>x<sup>2</sup> ¼ � tg �<sup>1</sup> <sup>ω</sup>x2ω<sup>d</sup>

q

þ

þ

y1,2ðÞ¼ t

2 6 4

Figure 3. (a) Drive in-phase mode (first mode) with frequency ωx1 = 2623 � 2π rad/s; (b) sensing in-phase mode (second mode) with frequency ωy1 = 3342 � 2π rad/s; (c) sensing anti-phase mode (third mode) with frequency ωy2 = 3468 � 2π rad/s; (d) drive anti-phase mode (fourth mode) with frequency ωx2 = 3484 � 2π rad/s.

mode is the fourth order, in which mode, the left and right masses move in inverse directions along drive axis as Figure 3(d) shows. The drive anti-phase is another expected working mode.

#### 2.2. Dual-mass MEMS gyroscope structure working principle analysis

Due to a large difference (>1000 Hz) between the in-phase (the first mode) and anti-phase drive modes frequencies, the quality factor of drive anti-phase mode is Qx2 > 2000 and the stimulating method of the drive mode. The real working drive mode is considered to be pure antiphase drive mode (the fourth mode). Considering the real working sensing mode is formed by second and third modes, the motion equation of gyroscope structure can be expressed as (ideal condition) [35]:

$$
\dot{m}\ddot{D} + c\dot{D} + kD = F \tag{1}
$$

Dual-Mass MEMS Gyroscope Structure, Design, and Electrostatic Compensation http://dx.doi.org/10.5772/intechopen.74364 9

$$\text{where } \mathfrak{m} = \begin{bmatrix} m\_x \\ m\_y \\ m\_\sharp \end{bmatrix}, \mathbf{D} = \begin{bmatrix} \mathbf{x} \\ \mathbf{y}\_1 \\ \mathbf{y}\_2 \end{bmatrix}, \mathbf{k} = \begin{bmatrix} k\_{\text{xx}} & k\_{\text{xy1}} & k\_{\text{xy2}} \\ k\_{\text{y1x}} & k\_{\text{y1y1}} & 0 \\ k\_{\text{y2x}} & 0 & k\_{\text{y2y2}} \end{bmatrix}, \mathbf{c} = \begin{bmatrix} c\_{\text{xx}} & c\_{\text{xy1}} & c\_{\text{xy2}} \\ c\_{\text{y1x}} & c\_{\text{y1y1}} & 0 \\ c\_{\text{y2x}} & 0 & c\_{\text{y2y2}} \end{bmatrix}, \mathbf{F} = \begin{bmatrix} F\_d \sin(\omega\_d t) \\ -2m\_i \Omega\_z \dot{\mathbf{x}} \\ -2m\_i \Omega\_z \dot{\mathbf{x}} \end{bmatrix}.$$

are the mass, displacement, stiffness, damping and external force matrix, respectively; mx is equivalent mass of drive mode; x is displacement of drive mode; y1 and y2 are displacements of sensing in-phase and anti-phase modes, respectively; Qy1 and Qy2 are quality factors; Ω<sup>z</sup> is angular rate input; sensing mode mass my approximates to Coriolis mass mc; Fd and ω<sup>d</sup> are stimulating magnitude and frequency of drive mode; cxx=ωx2mx/Qx2, cy1y1=ωy1my/Qy1, cy2y2=ωy2my/Qy2 and kxx=ωx22 mx, ky1y1=ωy12 my, ky2y2=ωy22 my are effective damping and stiffness of drive and sensing in-phase and anti-phase modes; cxy1, cxy2 and cy1x, cy2x are coupling damping, kxy1, kxy2 and ky1x, ky2x are coupling stiffness (caused by machining error) between drive and sensing in-phase and anti-phase modes, respectively; sensing mode displacement y = y1 + y2, and for ideal gyro structure model (ignoring the coupling stiffness and damping), we get [35]:

x tðÞ¼ Fd=mx ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ω2 <sup>x</sup><sup>2</sup> � <sup>ω</sup><sup>2</sup> d � �<sup>2</sup> <sup>þ</sup> <sup>ω</sup><sup>2</sup> x2ω<sup>2</sup> d=Q<sup>2</sup> x2 <sup>q</sup> sin <sup>ω</sup>dt <sup>þ</sup> <sup>φ</sup>x<sup>2</sup> � � þ Fdωx2ωd=mxQx ω2 <sup>x</sup><sup>2</sup> � <sup>ω</sup><sup>2</sup> d � �<sup>2</sup> <sup>þ</sup> <sup>ω</sup><sup>2</sup> x2ω<sup>2</sup> d=Q<sup>2</sup> x2 e � <sup>ω</sup>x<sup>2</sup> <sup>2</sup>Qx<sup>2</sup> t cos ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � <sup>1</sup>=4Q<sup>2</sup> x2 q ωx2t � � þ Fdω<sup>d</sup> ω<sup>2</sup> x2=Q<sup>2</sup> <sup>x</sup><sup>2</sup> <sup>þ</sup> <sup>ω</sup><sup>2</sup> <sup>d</sup> � <sup>ω</sup><sup>2</sup> x2 � �=mx ωx<sup>2</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � <sup>1</sup>=4Q<sup>2</sup> x2 q ω2 <sup>x</sup><sup>2</sup> � <sup>ω</sup><sup>2</sup> d � �<sup>2</sup> <sup>þ</sup> <sup>ω</sup><sup>2</sup> x2ω<sup>2</sup> d=Q<sup>2</sup> x2 h i e � <sup>ω</sup>x<sup>2</sup> <sup>2</sup>Qx<sup>2</sup> t sin ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � <sup>1</sup>=4Q<sup>2</sup> x2 q ωx2t � � (2) y1,2ðÞ¼ t Fc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ω2 <sup>y</sup>1, <sup>2</sup> � <sup>ω</sup><sup>2</sup> d � �<sup>2</sup> <sup>þ</sup> <sup>ω</sup><sup>2</sup> <sup>y</sup>1, <sup>2</sup>ω<sup>2</sup> d=Q<sup>2</sup> y1,2 <sup>r</sup> sin <sup>ω</sup>dt <sup>þ</sup> <sup>φ</sup>x<sup>2</sup> <sup>þ</sup> π <sup>2</sup> <sup>þ</sup> <sup>φ</sup>y1,<sup>2</sup> � �� Fc <sup>ω</sup>y1, <sup>2</sup>ω<sup>d</sup> sinφx2=Qy1, <sup>2</sup> <sup>þ</sup> <sup>ω</sup><sup>2</sup> <sup>y</sup>1,<sup>2</sup> � <sup>ω</sup><sup>2</sup> d � � cosφx<sup>2</sup> h i ω2 <sup>y</sup>1,<sup>2</sup> � <sup>ω</sup><sup>2</sup> d � �<sup>2</sup> <sup>þ</sup> <sup>ω</sup><sup>2</sup> y1,2ω<sup>2</sup> d=Q<sup>2</sup> y1, 2 e � <sup>ω</sup>y1,<sup>2</sup> <sup>2</sup>Qy1,<sup>2</sup> t cos ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � <sup>1</sup>=4Q<sup>2</sup> y1,2 q ωy1, <sup>2</sup>t � �<sup>þ</sup> Fc ωy1, <sup>2</sup> ω<sup>2</sup> <sup>y</sup>1,<sup>2</sup> � <sup>3</sup>ω<sup>2</sup> d � � cosφx2<sup>=</sup> <sup>2</sup>Qy1, <sup>2</sup> � � <sup>þ</sup> <sup>ω</sup><sup>d</sup> <sup>ω</sup><sup>2</sup> <sup>y</sup>1,2<sup>=</sup> <sup>2</sup>Q<sup>2</sup> y1, 2 � � <sup>þ</sup> <sup>ω</sup><sup>2</sup> <sup>y</sup>1,<sup>2</sup> � <sup>ω</sup><sup>2</sup> d � � sinφx<sup>2</sup> h i ωy1,<sup>2</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � <sup>1</sup>=4Q<sup>2</sup> y1, 2 q ω2 <sup>y</sup>1, <sup>2</sup> � <sup>ω</sup><sup>2</sup> d � �<sup>2</sup> <sup>þ</sup> <sup>ω</sup><sup>2</sup> <sup>y</sup>1, <sup>2</sup>ω<sup>2</sup> d=Q<sup>2</sup> y1,2 � � e � <sup>ω</sup>y1, <sup>2</sup> <sup>2</sup>Qy1, <sup>2</sup> t sin ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � <sup>1</sup>=4Q<sup>2</sup> y1,2 q ωy1,2t � � (3)

mode is the fourth order, in which mode, the left and right masses move in inverse directions along drive axis as Figure 3(d) shows. The drive anti-phase is another expected working

Figure 3. (a) Drive in-phase mode (first mode) with frequency ωx1 = 2623 � 2π rad/s; (b) sensing in-phase mode (second mode) with frequency ωy1 = 3342 � 2π rad/s; (c) sensing anti-phase mode (third mode) with frequency ωy2 = 3468 � 2π

Due to a large difference (>1000 Hz) between the in-phase (the first mode) and anti-phase drive modes frequencies, the quality factor of drive anti-phase mode is Qx2 > 2000 and the stimulating method of the drive mode. The real working drive mode is considered to be pure antiphase drive mode (the fourth mode). Considering the real working sensing mode is formed by second and third modes, the motion equation of gyroscope structure can be expressed as (ideal

mD€ <sup>þ</sup> cD\_ <sup>þ</sup> kD <sup>¼</sup> <sup>F</sup> (1)

2.2. Dual-mass MEMS gyroscope structure working principle analysis

rad/s; (d) drive anti-phase mode (fourth mode) with frequency ωx2 = 3484 � 2π rad/s.

mode.

8 MEMS Sensors - Design and Application

condition) [35]:

$$\text{where } \wp\_{x2} = -\text{tg}^{-1}\left(\frac{\omega\_{x2}\omega\_{d}}{Q\_{\text{2}}\left(\omega\_{z2}^{2} - \omega\_{d}^{2}\right)}\right) \\ F\_{c} = \frac{-2\Omega\_{z}\omega\_{d}F\_{d}}{\mathfrak{w}\_{z}\sqrt{\left(\omega\_{z2}^{2} - \omega\_{d}^{2}\right)^{2} + \omega\_{z2}^{2}\omega\_{d}^{2}/Q\_{\text{2}}^{2}}} \\ \wp\_{y1,2} = -\text{tg}^{-1}\left(\frac{\omega\_{y1,2}\omega\_{d}}{Q\_{\text{2}}\left(\omega\_{y1,2}^{2} - \omega\_{d}^{2}\right)}\right).$$

The abovementioned equations indicate that the movement of drive and sensing modes are the compound motion of stable vibration and attenuation vibration. Since drive mode closed loop is employed, drive mode is stimulated with stable amplitude (ω<sup>d</sup> = ωx2). Then (2) can be simplified as [20]:

$$\mathbf{x}(t) = \frac{F\_d Q\_{x2}}{m\_x \omega\_d^2} \cos \left(\omega\_d t\right) = A\_x \cos \left(\omega\_d t\right) \tag{4}$$

The sensing in-phase and anti-phase modes movement equation can be got from (3):

$$y\_{1,2}(t) = \frac{-2\Omega\_z F\_d Q\_{z2} \sin\left(\omega\_d t\right)}{m\_x \omega\_d \sqrt{\left(\omega\_{y1,2}^2 - \omega\_d^2\right)^2 + \omega\_{y1,2}^2 \omega\_d^2 / Q\_{y1,2}^2}} \tag{5}$$

Then, the mechanical sensitivity can be expressed as:

$$S\_{\rm net} = \frac{A\_{y1} + A\_{y2}}{\Omega\_z} \approx \frac{-F\_d Q\_\mathbf{x}}{m\_\text{x} \omega\_d^2} \left(\frac{1}{\omega\_{y1} - \omega\_{\mathbf{x}2}} + \frac{1}{\omega\_{y2} - \omega\_{\mathbf{x}2}}\right) = -A\_\mathbf{x} \left(\frac{1}{\Delta \omega\_1} + \frac{1}{\Delta \omega\_2}\right) \tag{6}$$

The mechanical sensitivity of dual-mass sensing mode coupled structure is determined by vibration amplitude of drive mode and frequency differences between drive working mode and sensing modes (including the second and third modes). Furthermore, the one near the fourth mode is the dominant element. Therefore, the sensing anti-phase mode determines the gyro structure mechanical sensitivity. The schematic diagram of gyro sensing mode is shown in Figure 4. Ginphase and Ganphase are transform functions of in-phase and anti-phase sensing modes; Kinyv and Kanyv are displace-voltage transform parameters of sensing in-phase and anti-phase modes; Kpre is the preamplifier; Vstotal is sensing mode output and GsV/F can be expressed as:

$$\mathbf{G}\_{\rm sV/F} = \left(\mathbf{G}\_{\rm imphase}\mathbf{K}\_{\rm invy} + \mathbf{G}\_{\rm amphase}\mathbf{K}\_{\rm amyv}\right)\mathbf{K}\_{\rm pre} \tag{7}$$

2.3. Dual-mass MEMS gyroscope monitoring system

Figure 5. Dual-mass gyroscope monitoring system schematic.

The gyro control and detection system is shown in Figure 5. In drive loop, the drive frame displacement x(t) is detected by drive sensing combs and picked up by differential amplifier ①. Then, the signal phase is delayed by 90 (through ②) to satisfy the phase requirement of AC drive signal VdacSin(ωdt). After that, VdacSin(ωdt) is processed by a full-wave rectifier ③ and a low pass filter ④. Afterwards, Vdac is compared (in ⑤) with the reference voltage Vref ⑥. Next, drive PI controller ⑦ generates the control signal, which is modulated by VdacSin(ωdt), and then the signal is superposed (through ⑩) by VDC ⑨ to stimulation drive mode. The sensing system employs a closed loop, which utilizes the same interface as drive circuit. First, the left and right masses' sensing signals are detected separately with differential detection amplifier⑪. And the output signals VRQS (from right mass) and VLQS (from left mass) are processed by second differential amplifier⑫ to generate signal Vstotal. Then, Vstotal is demodulated by signal VdacSin(ωdt) (in ⑬). After that, the demodulated signal Vdem passes through the low pass filter ⑭; so, the sensing mode's movement signal VOopen can be got. For sense closed loop ("pink" section in Figure 5), VOopen is first sent in proportional-integral-phase-leading controller (PIPLC) ⑮ to calculate the control signal superposed (through ⑯) with test signal VTes ⑰. Then the signal is modulated with VdacSin(ωdt) (in ⑱). Finally, DC voltage VFDC ⑳ is superposed with the modulated signal in ⑲ to generate the feedback signal. In quadrature error compensation system, VRQS and VLQS are demodulated by drive frame displacement signal VQEDCos(ωdt) separately in?21. The quadrature

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where Ginphase <sup>¼</sup> <sup>1</sup> my 1 <sup>s</sup>2þωy<sup>1</sup> Qy1 <sup>s</sup>þω<sup>2</sup> y1 and Ganphase <sup>¼</sup> <sup>1</sup> my 1 <sup>s</sup>2þωy<sup>2</sup> Qy2 <sup>s</sup>þω<sup>2</sup> y2 are the sensing in-phase and anti-phase mode transform functions, respectively.

Figure 4. Schematic diagram of sensing mode real working mode.

Dual-Mass MEMS Gyroscope Structure, Design, and Electrostatic Compensation http://dx.doi.org/10.5772/intechopen.74364 11

Figure 5. Dual-mass gyroscope monitoring system schematic.

is employed, drive mode is stimulated with stable amplitude (ω<sup>d</sup> = ωx2). Then (2) can be

The sensing in-phase and anti-phase modes movement equation can be got from (3):

1 ωy<sup>1</sup> � ωx<sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>þ</sup> <sup>ω</sup><sup>2</sup> y1,2ω<sup>2</sup> d=Q<sup>2</sup> y1, 2 <sup>r</sup> <sup>¼</sup> Ay1,<sup>2</sup> sin ð Þ <sup>ω</sup>dt (5)

þ

The mechanical sensitivity of dual-mass sensing mode coupled structure is determined by vibration amplitude of drive mode and frequency differences between drive working mode and sensing modes (including the second and third modes). Furthermore, the one near the fourth mode is the dominant element. Therefore, the sensing anti-phase mode determines the gyro structure mechanical sensitivity. The schematic diagram of gyro sensing mode is shown in Figure 4. Ginphase and Ganphase are transform functions of in-phase and anti-phase sensing modes; Kinyv and Kanyv are displace-voltage transform parameters of sensing in-phase and anti-phase modes; Kpre is the preamplifier; Vstotal is sensing mode output and GsV/F can be

GsV=<sup>F</sup> ¼ GinphaseKinyv þ GanphaseKanyv

1 <sup>s</sup>2þωy<sup>2</sup> Qy2 <sup>s</sup>þω<sup>2</sup> y2

my

and Ganphase <sup>¼</sup> <sup>1</sup>

� �

1 ωy<sup>2</sup> � ωx<sup>2</sup>

cos ð Þ¼ ωdt Ax cos ð Þ ωdt (4)

¼ �Ax

� �Kpre (7)

are the sensing in-phase and anti-phase

1 Δω<sup>1</sup> þ 1 Δω<sup>2</sup>

� �

(6)

x tðÞ¼ FdQx<sup>2</sup> mxω<sup>2</sup> d

<sup>y</sup>1, <sup>2</sup>ðÞ¼ <sup>t</sup> �2ΩzFdQx<sup>2</sup> sin ð Þ <sup>ω</sup>dt

ω2 <sup>y</sup>1,<sup>2</sup> � <sup>ω</sup><sup>2</sup> d � �<sup>2</sup>

<sup>≈</sup> �FdQx mxω<sup>2</sup> d

mxω<sup>d</sup>

Then, the mechanical sensitivity can be expressed as:

Sme <sup>¼</sup> Ay<sup>1</sup> <sup>þ</sup> Ay<sup>2</sup> Ω<sup>z</sup>

simplified as [20]:

10 MEMS Sensors - Design and Application

expressed as:

where Ginphase <sup>¼</sup> <sup>1</sup>

my

mode transform functions, respectively.

1 <sup>s</sup>2þωy<sup>1</sup> Qy1 <sup>s</sup>þω<sup>2</sup> y1

Figure 4. Schematic diagram of sensing mode real working mode.

#### 2.3. Dual-mass MEMS gyroscope monitoring system

The gyro control and detection system is shown in Figure 5. In drive loop, the drive frame displacement x(t) is detected by drive sensing combs and picked up by differential amplifier ①. Then, the signal phase is delayed by 90 (through ②) to satisfy the phase requirement of AC drive signal VdacSin(ωdt). After that, VdacSin(ωdt) is processed by a full-wave rectifier ③ and a low pass filter ④. Afterwards, Vdac is compared (in ⑤) with the reference voltage Vref ⑥. Next, drive PI controller ⑦ generates the control signal, which is modulated by VdacSin(ωdt), and then the signal is superposed (through ⑩) by VDC ⑨ to stimulation drive mode. The sensing system employs a closed loop, which utilizes the same interface as drive circuit. First, the left and right masses' sensing signals are detected separately with differential detection amplifier⑪. And the output signals VRQS (from right mass) and VLQS (from left mass) are processed by second differential amplifier⑫ to generate signal Vstotal. Then, Vstotal is demodulated by signal VdacSin(ωdt) (in ⑬). After that, the demodulated signal Vdem passes through the low pass filter ⑭; so, the sensing mode's movement signal VOopen can be got. For sense closed loop ("pink" section in Figure 5), VOopen is first sent in proportional-integral-phase-leading controller (PIPLC) ⑮ to calculate the control signal superposed (through ⑯) with test signal VTes ⑰. Then the signal is modulated with VdacSin(ωdt) (in ⑱). Finally, DC voltage VFDC ⑳ is superposed with the modulated signal in ⑲ to generate the feedback signal. In quadrature error compensation system, VRQS and VLQS are demodulated by drive frame displacement signal VQEDCos(ωdt) separately in?21. The quadrature error compensation reference is provided in ?<sup>22</sup> and is compared with quadrature error amplitude in ?23; the results are sent to coupling stiffness compensation (CSC) controller?24.

#### 3. Dual-mass MEMS gyroscope quadrature error compensation

#### 3.1. Dual-mass MEMS gyroscope structure quadrature error model

The quadrature error is caused by coupling stiffness, which is generated in structure processing stage, and the stiffness elements in Eq. (1) can be calculated by:

$$\begin{cases} k\_{\rm xx} = k\_{\rm x} \cos^2 \beta\_{Q\rm x} + k\_{\rm y} \sin^2 \beta\_{Q\rm y} \\ k\_{\rm xy} = k\_{\rm yx} = k\_{\rm x} \sin \beta\_{Q\rm x} \cos \beta\_{Q\rm x} - k\_{\rm y} \cos \beta\_{Q\rm y} \sin \beta\_{Q\rm y} \\ k\_{\rm yy} = k\_{\rm x} \sin^2 \beta\_{Q\rm x} + k\_{\rm y} \cos^2 \beta\_{Q\rm y} \end{cases} \tag{8}$$

Figure 6. (a) Stiffness system of ideal dual-mass gyro structure; (b) ideal structure movement without angular rate input; (c) ideal structure movement with steady angular rate input; (d) stiffness system with in-phase quadrature error angular; (e) the movement of in-phase quadrature error angular structure without angular rate input; (f) the movement of in-phase quadrature error angular structure with steady angular rate input; (g) stiffness system with anti-phase quadrature error angular; (h) the movement of anti-phase quadrature error angular structure without angular rate input; (i) the movement

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of anti-phase quadrature error angular structure with steady angular rate input.

Figure 7. Right mass SCS system.

where kx and ky are the design stiffness along designed axis x and y; βQx and βQy are the quadrature error angle and they are the angles between practical axis and designed axis [11, 35], and usually it is assumed that βQx = βQy.

The equivalent stiffness and masses system and structure motion of dual-mass gyro structure is shown in Figure 6. The design drive and sense stiffness axis are x and y (gray); the real drive and sense axis of left and right masses after manufacture are xl', xr' (with light blue) and yl', yr' (with light yellow), respectively; the stiffness of drive and sense modes of left and right masses after manufacture are klx, krx (with dark blue) and kly, kry (with dark yellow), respectively; the projections of klx on –x- and y-axis are klxx and klxy; the projections of krx on x- and y-axis are krxx and krxy; the projections of kly on –x- and y-axis are klyx and klyy; the projections of kry on x- and y-axis are kryx and kryy; the quadrature error angular of left and right masses are βly and βry. In design stage, |klx|=|krx|, |kly|=|kry|, and βly = βry = 0, but after the manufacture process, the parameters change and they do not meet the equal equations, so the coupling stiffness of two masses are different.

#### 3.2. Dual-mass MEMS gyroscope structure coupling stiffness compensation

The CSC method utilizes quadrature error correction combs to generate negative electrostatic stiffness and correct quadrature error coupling stiffness. This special comb is unequal gap style, and is introduced in [11]; its stiffness is expressed as:

$$k\_{qxy} = k\_{qyx} = k\_{qcup} V\_{qD} V\_{qc} = -\frac{4n\_{q}\varepsilon\_{0}\hbar}{\mathcal{Y}\_{q0}{}^{2}} \left(1 - \frac{1}{\lambda^{2}}\right) V\_{qD} V\_{qc} \tag{9}$$

where kqxy and kqyx are the quadrature error correction comb stiffness along designed axes x and y; VqD and Vqc are correction fixed voltage and controlling voltage; nq is the number of comb; ε<sup>0</sup> is the permittivity of vacuum; h is the thickness of the comb; yq0 and x0 are the parallel capacitance's gap and overlap length, respectively; λ is a constant. Figure 7 shows the right mass CSC system which is same with left mass CSC system, GRsV/F is the transform function of

Dual-Mass MEMS Gyroscope Structure, Design, and Electrostatic Compensation http://dx.doi.org/10.5772/intechopen.74364 13

Figure 6. (a) Stiffness system of ideal dual-mass gyro structure; (b) ideal structure movement without angular rate input; (c) ideal structure movement with steady angular rate input; (d) stiffness system with in-phase quadrature error angular; (e) the movement of in-phase quadrature error angular structure without angular rate input; (f) the movement of in-phase quadrature error angular structure with steady angular rate input; (g) stiffness system with anti-phase quadrature error angular; (h) the movement of anti-phase quadrature error angular structure without angular rate input; (i) the movement of anti-phase quadrature error angular structure with steady angular rate input.

Figure 7. Right mass SCS system.

error compensation reference is provided in ?<sup>22</sup> and is compared with quadrature error ampli-

The quadrature error is caused by coupling stiffness, which is generated in structure

kxy ¼ kyx ¼ kx sin βQx cos βQx � ky cos βQy sin βQy

where kx and ky are the design stiffness along designed axis x and y; βQx and βQy are the quadrature error angle and they are the angles between practical axis and designed axis [11,

The equivalent stiffness and masses system and structure motion of dual-mass gyro structure is shown in Figure 6. The design drive and sense stiffness axis are x and y (gray); the real drive and sense axis of left and right masses after manufacture are xl', xr' (with light blue) and yl', yr' (with light yellow), respectively; the stiffness of drive and sense modes of left and right masses after manufacture are klx, krx (with dark blue) and kly, kry (with dark yellow), respectively; the projections of klx on –x- and y-axis are klxx and klxy; the projections of krx on x- and y-axis are krxx and krxy; the projections of kly on –x- and y-axis are klyx and klyy; the projections of kry on x- and y-axis are kryx and kryy; the quadrature error angular of left and right masses are βly and βry. In design stage, |klx|=|krx|, |kly|=|kry|, and βly = βry = 0, but after the manufacture process, the parameters change and they do not meet the equal equations, so the coupling stiffness of two

The CSC method utilizes quadrature error correction combs to generate negative electrostatic stiffness and correct quadrature error coupling stiffness. This special comb is unequal gap

where kqxy and kqyx are the quadrature error correction comb stiffness along designed axes x and y; VqD and Vqc are correction fixed voltage and controlling voltage; nq is the number of comb; ε<sup>0</sup> is the permittivity of vacuum; h is the thickness of the comb; yq0 and x0 are the parallel capacitance's gap and overlap length, respectively; λ is a constant. Figure 7 shows the right mass CSC system which is same with left mass CSC system, GRsV/F is the transform function of

yq0

<sup>2</sup> <sup>1</sup> � <sup>1</sup> λ2 � �

VqDVqc (9)

(8)

tude in ?23; the results are sent to coupling stiffness compensation (CSC) controller?24.

3. Dual-mass MEMS gyroscope quadrature error compensation

3.1. Dual-mass MEMS gyroscope structure quadrature error model

8 >><

12 MEMS Sensors - Design and Application

>>:

35], and usually it is assumed that βQx = βQy.

masses are different.

processing stage, and the stiffness elements in Eq. (1) can be calculated by:

kxx <sup>¼</sup> kx cos <sup>2</sup>βQx <sup>þ</sup> ky sin <sup>2</sup>βQy

kyy <sup>¼</sup> kx sin <sup>2</sup>βQx <sup>þ</sup> ky cos <sup>2</sup>βQy

3.2. Dual-mass MEMS gyroscope structure coupling stiffness compensation

kqxy <sup>¼</sup> kqyx <sup>¼</sup> kqcoupVqDVqc ¼ � <sup>4</sup>nqε0<sup>h</sup>

style, and is introduced in [11]; its stiffness is expressed as:

right mass. In Figure 7, the coupling stiffness kyx is modulated by drive-mode movement, and the controller employs PI controlling technology. The correction stiffness does not need to be modulated by quadrature error in-phase signal, which is better for circuit simplification and power consumption. We can get the following equations:

$$V\_{RQS} = F\_{Q\overline{E}} G\_{RsV/F} = \mathfrak{x} \{ k\_{yx} + k\_{qyx} \} G\_{RsV/F} \tag{10}$$

Then, combining (9), (11) and (12), we have:

is basically corrected which proves (15).

<sup>2</sup> kqcoupVqDVQEDFRLPF2ð Þs GRsV=<sup>F</sup>ð Þþ s þ jω<sup>d</sup> GRsV=<sup>F</sup>ð Þ s � jω<sup>d</sup>

When the system is under stable state, s = 0, and the above equation has:

4. Dual-mass MEMS gyroscope bandwidth expansion

4.1. Dual-mass MEMS gyroscope structure sense mode model

<sup>2</sup> kqcoupVqDVQEDFLPF2ð Þ<sup>s</sup> GRsV=<sup>F</sup>ð Þþ <sup>s</sup> <sup>þ</sup> <sup>j</sup>ω<sup>d</sup> GRsV=<sup>F</sup>ð Þ <sup>s</sup> � <sup>j</sup>ω<sup>d</sup>

<sup>2</sup> kqcoupVqDVQEDFRLPF2ð Þs GRsV=<sup>F</sup>ð Þþ s þ jω<sup>d</sup> GRsV=<sup>F</sup>ð Þ s � jω<sup>d</sup>

The coupling stiffness is corrected. The CSC system is simulated and the curves are shown in Figure 8. The Pole-Zero Map is shown in Figure 8(a), no pole is in the positive real axis and Figure 8(b) is the Nyquist Diagram, the curve does not contain (�1,0j) point, which proves the system's stability. The time-domain simulation curves are shown in Figure 8(c)–(e), and the curves indicate that the CSC system is under stable state after about 0.7 s. It is obvious that in start-up stage, the sense channel signal mainly consists of quadrature error signal. But, in stable state, the dominate element is Coriolis in-phase signal. Furthermore, the overall coupling stiffness kyxs is suppressed from original value (about 0.18 N/m) to �0.00016 N/m, and kyx

The force rebalancing combs stimulation method (FRCSM) is employed to test the sense mode. Force rebalancing combs are slide-film form (does not vary ωy1 and ωy2). And they are arranged to generate electrostatic force and rebalance the Coriolis force applied on sense frame. The movement of sensing frame is restricted, which improves the dynamic performance of gyro. Therefore, Coriolis simulation signal is designed to be produced through force rebalancing combs, and this method can be further applied to scale factor and bandwidth tests. The FRCSM

schematic diagram is shown in Figure 9, and the equivalent input angular rate of VTes is:

<sup>Ω</sup>VTes <sup>¼</sup> KFByVTesVdac 2mcAxω<sup>d</sup>

where KFBy is voltage-force interface transform coefficient of force rebalances combs; Vdac is modulate signal amplitude, which is picked up after 90� shifter in drive loop and is considered to be constant when gyro works. KFBy can be got either from the calculation of structure parameter or turntable test, and it is determined by force rebalancing combs number,

kpqS <sup>þ</sup> kIqS

Dual-Mass MEMS Gyroscope Structure, Design, and Electrostatic Compensation

kpqS <sup>þ</sup>

kpqS <sup>þ</sup> kIqS

kqyx ≈ � kyx (15)

s 

kIqS s 

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 s¼0

s (13)

(14)

15

(16)

Ax

<sup>1</sup> � Ax

kqyxð Þs kyxð Þ<sup>s</sup> <sup>¼</sup>

<sup>1</sup> <sup>¼</sup> Ax

Then:

$$V\_{q\text{c}} = \left(V\_{Q\text{ES}} - V\_{r\text{effQES}}\right) \left(k\_{pq\text{S}} + \frac{k\_{lq\text{S}}}{\text{s}}\right) \tag{11}$$

We have x=Axcos(ωdt) and VrefQES = 0, after the low pass filter, VQES can be expressed as:

$$V\_{QES} = \frac{1}{2} A\_x \left( k\_{yx} + k\_{qyx} \right) G\_{RsV/F} V\_{QED} \tag{12}$$

Figure 8. (a) CSC system pole-zero map; (b) CSC system Nyquist diagram; (c) CSC system simulation curves; (d) CSC system start-up stage enlarge curves; (e) CSC system stable stage enlarge curves.

Then, combining (9), (11) and (12), we have:

$$\frac{k\_{qyx}(s)}{k\_{yx}(s)} = \frac{\frac{A\_x}{2}k\_{qapop}V\_{qD}V\_{qD}F\_{RLPF2}(s)\left[G\_{RSV/F}(s+j\omega\_d) + G\_{RSV/F}(s-j\omega\_d)\right]\left(k\_{pqS} + \frac{k\_{q\delta}}{s}\right)}{1 - \frac{A\_x}{2}k\_{qapop}V\_{qD}V\_{qD}F\_{QED}F\_{RLPF2}(s)\left[G\_{RSV/F}(s+j\omega\_d) + G\_{RSV/F}(s-j\omega\_d)\right]\left(k\_{pqS} + \frac{k\_{k\delta}}{s}\right)}\tag{13}$$

When the system is under stable state, s = 0, and the above equation has:

$$1 = \frac{A\_x}{2} k\_{qcop} V\_{qD} V\_{QED} F\_{LP2}(\mathbf{s}) \left[ \mathbf{G}\_{\text{RV}/F}(\mathbf{s} + j\omega\_d) + \mathbf{G}\_{\text{RV}/F}(\mathbf{s} - j\omega\_d) \right] \left( k\_{pqS} + \frac{k\_{lqS}}{s} \right) \bigg|\_{s=0} \tag{14}$$

Then:

right mass. In Figure 7, the coupling stiffness kyx is modulated by drive-mode movement, and the controller employs PI controlling technology. The correction stiffness does not need to be modulated by quadrature error in-phase signal, which is better for circuit simplification and

kpqS <sup>þ</sup>

GRsV=<sup>F</sup> (10)

GRsV=FVQED (12)

(11)

kIqS s 

VRQS ¼ FQEGRsV=<sup>F</sup> ¼ x kyx þ kqyx

We have x=Axcos(ωdt) and VrefQES = 0, after the low pass filter, VQES can be expressed as:

Ax kyx þ kqyx

Figure 8. (a) CSC system pole-zero map; (b) CSC system Nyquist diagram; (c) CSC system simulation curves; (d) CSC

system start-up stage enlarge curves; (e) CSC system stable stage enlarge curves.

Vqc ¼ VQES � VrefQES

VQES <sup>¼</sup> <sup>1</sup> 2

power consumption. We can get the following equations:

14 MEMS Sensors - Design and Application

$$k\_{\!\!\!\!\!y} \approx -k\_{\!\!\!y} \tag{15}$$

The coupling stiffness is corrected. The CSC system is simulated and the curves are shown in Figure 8. The Pole-Zero Map is shown in Figure 8(a), no pole is in the positive real axis and Figure 8(b) is the Nyquist Diagram, the curve does not contain (�1,0j) point, which proves the system's stability. The time-domain simulation curves are shown in Figure 8(c)–(e), and the curves indicate that the CSC system is under stable state after about 0.7 s. It is obvious that in start-up stage, the sense channel signal mainly consists of quadrature error signal. But, in stable state, the dominate element is Coriolis in-phase signal. Furthermore, the overall coupling stiffness kyxs is suppressed from original value (about 0.18 N/m) to �0.00016 N/m, and kyx is basically corrected which proves (15).

#### 4. Dual-mass MEMS gyroscope bandwidth expansion

#### 4.1. Dual-mass MEMS gyroscope structure sense mode model

The force rebalancing combs stimulation method (FRCSM) is employed to test the sense mode. Force rebalancing combs are slide-film form (does not vary ωy1 and ωy2). And they are arranged to generate electrostatic force and rebalance the Coriolis force applied on sense frame. The movement of sensing frame is restricted, which improves the dynamic performance of gyro. Therefore, Coriolis simulation signal is designed to be produced through force rebalancing combs, and this method can be further applied to scale factor and bandwidth tests. The FRCSM schematic diagram is shown in Figure 9, and the equivalent input angular rate of VTes is:

$$
\Omega\_{VTest} = \frac{K\_{FBy} V\_{Tes} V\_{dac}}{2m\_c A\_x \omega\_d} \tag{16}
$$

where KFBy is voltage-force interface transform coefficient of force rebalances combs; Vdac is modulate signal amplitude, which is picked up after 90� shifter in drive loop and is considered to be constant when gyro works. KFBy can be got either from the calculation of structure parameter or turntable test, and it is determined by force rebalancing combs number,

Figure 9. FRCSM schematic in sensing loop.

parameters and feedback direct voltage VFDC. The system diagram of sense open loop is shown in Figure 9, and the equations below can be derived from Figure 9:

$$\begin{cases} F\_{ct}(t) = 2\Omega\_z(t) m\_y A\_x \omega\_d \sin\left(\omega\_d t\right) + K\_{FBy} V\_{Tes}(t) V\_{dac} \sin\left(\omega\_d t\right) \\ V\_{Open} = F\_{ct}(t) G\_{sV/F} V\_{dac} \sin\left(\omega\_d t\right) F\_{LPF} \end{cases} \tag{17}$$

After Laplace transformation, we can get [35]:

$$V\_{\rm Open}(\mathbf{s}) = K\_{\rm pre} \left[ \frac{A\_{\rm x} \omega\_d V\_{\rm dic} \Omega\_{\rm z}(\mathbf{s}) F\_{\rm LPF}(\mathbf{s})}{2} + \frac{K\_{\rm FBy} V\_{\rm dic}^2 V\_{\rm Test}(\mathbf{s}) F\_{\rm LPF}(\mathbf{s})}{4m\_{\rm y}} \right] \mathbf{G}\_{\rm sV/F}(\mathbf{s}) \tag{18}$$

$$\begin{array}{ll} \text{where} & G\_{\theta V/\Gamma}(\mathbf{s}) = \left[ \frac{\text{K}\_{\text{uyr}} \left( s^2 + \frac{\omega\_{\text{d}1}}{\text{Q}\_{\text{g1}}} \mathbf{s} + \omega\_{\text{g1}}^2 - \omega\_{\text{d}}^2 \right)}{\left( s^2 + \frac{\omega\_{\text{d}1}}{\text{Q}\_{\text{g1}}} \mathbf{s} + \omega\_{\text{g1}}^2 - \omega\_{\text{d}}^2 \right)^2 + \left( 2s\omega\_{\text{d}} + \frac{\omega\_{\text{d}1}}{\text{Q}\_{\text{g1}}} \omega\_{\text{d}} \right)^2} + \frac{\text{K}\_{\text{uyr}} \left( s^2 + \frac{\omega\_{\text{d}2}}{\text{Q}\_{\text{g2}}} \mathbf{s} + \omega\_{\text{g2}}^2 - \omega\_{\text{d}}^2 \right)}{\left( s^2 + \frac{\omega\_{\text{d}2}}{\text{Q}\_{\text{g2}}} + \omega\_{\text{g2}}^2 - \omega\_{\text{d}}^2 \right)^2 + \left( 2s\omega\_{\text{d}} + \frac{\omega\_{\text{d}2}}{\text{Q}\_{\text{g2}}} \omega\_{\text{d}} \right)^2} \right], \qquad \text{and} \quad \mathbf{s} \in \{ \text{R}\_{\text{u}}, \text{f} \}$$

ω<sup>d</sup> = 3488.9\*2π rad/s, ωy1 = 3360.1\*2π rad/s, ωy2 = 3464.1\*2π rad/s, Qy1 = 1051 and Qy2 = 1224, then the Bode Diagram map is shown in Figure 10, and the bandwidth of the mechanical system is [20, 35]:

$$
\omega\_b = 0.54 \Delta a\_2 \tag{19}
$$

rate VTes is employed to test the closed system frequency response. From Figure 8, the equa-

<sup>4</sup>my � KpreKFByV<sup>2</sup>

point B, so bandwidth range is considered before point B), Eq. (22) can be expressed as:

 

The above equation means that the scale factor in closed loop is constant value and is not

Generally speaking, the open-loop Bode diagram of sensing closed-loop is expected to have the following characteristics: (a) In low frequency range, a first-order pure integral element is configured to achieve enough gain and reduce the steady state error of the system, (b) In

 <sup>¼</sup> <sup>2</sup>mcAxω<sup>d</sup> KFByVdac

VOclose ΩVTes

 

FyfðÞ¼ t KFBy½ � VOcloseð Þþ t VTesð Þt Vdac sin ð Þ ωdt (20)

<sup>¼</sup> <sup>2</sup>mcAxωdKpreGseVdacFLPFð Þ<sup>s</sup> FPIPLCð Þ<sup>s</sup>

VOcloseð Þ¼ s Vdemð Þs FLPFð Þs FPIPLCð Þs (21)

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dacGseFLPFð Þs FPIPLCð Þs

dacGseFLPFð Þs FPIPLCð Þs within bandwidth range (Gse reduces a lot at

(22)

(23)

tions can be derived:

Because 4my ≪ KpreKFByV<sup>2</sup>

Combining Eq. (20) with (21), we have:

 

restricted by resonant peak (A point).

VOclose ωopen ΩVTes ωopen

 

Figure 10. Simulation and FRCSM test results of dual-mass gyroscope structure bode diagram.

In Figure 10, point A (frequency is Δω2) and C (frequency is Δω1) peak points are generated by two conjugate poles, respectively; B valley point (ΔωB) is caused by conjugate zeros shown in Eq. (18). The bandwidth obtained from the simulation curve is 12.9 Hz and from FRCSM test curve is 13 Hz, which verifies the theory calculation result in Eq. (19). In addition, the FRCSM test curve matches simulation curve well and proves the theory analysis conclusion proposed in Section 2.2.

#### 4.2. Dual-mass MEMS gyroscope bandwidth expanding

Sensing closed-loop control method provides electrostatic force to rebalance the Coriolis force applied on sensing mode, which is one of the most effective ways to improve gyro dynamic performance. When sensing closed-loop works, the sensing frame's displacement is restricted and the Coriolis force is transformed into electronic signal directly. And it also avoids the nonlinearity of sensing mode displacement. Meanwhile, closed loop provides better antivibration and anti-shock characteristics to the gyroscope. The sensing closed-loop schematic is shown in Figure 9, where the real input angular rate Ω<sup>z</sup> = 0�/s and the simulation angular Dual-Mass MEMS Gyroscope Structure, Design, and Electrostatic Compensation http://dx.doi.org/10.5772/intechopen.74364 17

Figure 10. Simulation and FRCSM test results of dual-mass gyroscope structure bode diagram.

rate VTes is employed to test the closed system frequency response. From Figure 8, the equations can be derived:

$$F\_{\mathcal{Y}}(t) = K\_{\text{FBy}}[V\_{\text{Oclese}}(t) + V\_{\text{Tes}}(t)]V\_{\text{date}}\sin\left(\omega\_d t\right) \tag{20}$$

$$V\_{\text{Oclse}}(\mathbf{s}) = V\_{\text{dem}}(\mathbf{s}) F\_{\text{LPF}}(\mathbf{s}) F\_{\text{IPPLC}}(\mathbf{s}) \tag{21}$$

Combining Eq. (20) with (21), we have:

parameters and feedback direct voltage VFDC. The system diagram of sense open loop is shown

FctðÞ¼ t 2Ωzð Þt myAxω<sup>d</sup> sin ð Þþ ωdt KFByVTesð Þt Vdac sin ð Þ ωdt

KFByV<sup>2</sup>

<sup>s</sup>2þωy<sup>2</sup> Qy2 <sup>s</sup>þω<sup>2</sup> y2�ω<sup>2</sup> d

" #

dacVTesð Þs FLPFð Þs 4my

> Kanyv <sup>s</sup>2þωy<sup>2</sup> Qy2 <sup>s</sup>þω<sup>2</sup> y2�ω<sup>2</sup> d

ω<sup>b</sup> ¼ 0:54Δω<sup>2</sup> (19)

� �<sup>2</sup>

� �

<sup>þ</sup> <sup>2</sup>sωdþωy<sup>2</sup> Qy2 ωd � �<sup>2</sup> (17)

GsV=<sup>F</sup>ð Þs (18)

3 7 <sup>5</sup>, and

in Figure 9, and the equations below can be derived from Figure 9:

Kinyv <sup>s</sup>2þωy<sup>1</sup> Qy1 <sup>s</sup>þω<sup>2</sup> y1�ω<sup>2</sup> d

� �<sup>2</sup>

<sup>s</sup>2þωy<sup>1</sup> Qy1 <sup>s</sup>þω<sup>2</sup> y1�ω<sup>2</sup> d

4.2. Dual-mass MEMS gyroscope bandwidth expanding

(

Figure 9. FRCSM schematic in sensing loop.

16 MEMS Sensors - Design and Application

VOopenð Þ¼ s Kpre

where, GsV=<sup>F</sup>ð Þ¼ s

system is [20, 35]:

in Section 2.2.

After Laplace transformation, we can get [35]:

2 6 4

VOopen ¼ Fctð Þt GsV=FVdac sin ð Þ ωdt FLPF

AxωdVdacΩzð Þs FLPFð Þs

� �

2 þ

<sup>þ</sup> <sup>2</sup>sωdþωy<sup>1</sup> Qy1 ωd � �<sup>2</sup> þ

ω<sup>d</sup> = 3488.9\*2π rad/s, ωy1 = 3360.1\*2π rad/s, ωy2 = 3464.1\*2π rad/s, Qy1 = 1051 and Qy2 = 1224, then the Bode Diagram map is shown in Figure 10, and the bandwidth of the mechanical

In Figure 10, point A (frequency is Δω2) and C (frequency is Δω1) peak points are generated by two conjugate poles, respectively; B valley point (ΔωB) is caused by conjugate zeros shown in Eq. (18). The bandwidth obtained from the simulation curve is 12.9 Hz and from FRCSM test curve is 13 Hz, which verifies the theory calculation result in Eq. (19). In addition, the FRCSM test curve matches simulation curve well and proves the theory analysis conclusion proposed

Sensing closed-loop control method provides electrostatic force to rebalance the Coriolis force applied on sensing mode, which is one of the most effective ways to improve gyro dynamic performance. When sensing closed-loop works, the sensing frame's displacement is restricted and the Coriolis force is transformed into electronic signal directly. And it also avoids the nonlinearity of sensing mode displacement. Meanwhile, closed loop provides better antivibration and anti-shock characteristics to the gyroscope. The sensing closed-loop schematic is shown in Figure 9, where the real input angular rate Ω<sup>z</sup> = 0�/s and the simulation angular

$$\left| \frac{V\_{\text{Oclese}}(\omega\_{\text{open}})}{\Omega\_{\text{VTS}}(\omega\_{\text{open}})} \right| = \frac{2m\_{\text{c}}A\_{\text{x}}\omega\_{\text{d}}K\_{\text{pre}}G\_{\text{se}}V\_{\text{dac}}F\_{\text{LPF}}(\mathbf{s})F\_{\text{PIPLC}}(\mathbf{s})}{4m\_{\text{y}} - K\_{\text{pre}}K\_{\text{FBy}}V\_{\text{dac}}^2G\_{\text{se}}F\_{\text{LPF}}(\mathbf{s})F\_{\text{PIPLC}}(\mathbf{s})} \tag{22}$$

Because 4my ≪ KpreKFByV<sup>2</sup> dacGseFLPFð Þs FPIPLCð Þs within bandwidth range (Gse reduces a lot at point B, so bandwidth range is considered before point B), Eq. (22) can be expressed as:

$$\left|\frac{V\_{\text{Oclose}}}{\Omega\_{VT\text{es}}}\right| = \frac{2m\_c A\_x \omega\_d}{K\_{FBy} V\_{\text{dac}}}\tag{23}$$

The above equation means that the scale factor in closed loop is constant value and is not restricted by resonant peak (A point).

Generally speaking, the open-loop Bode diagram of sensing closed-loop is expected to have the following characteristics: (a) In low frequency range, a first-order pure integral element is configured to achieve enough gain and reduce the steady state error of the system, (b) In middle frequency range, the slope of magnitude line is designed to be �20 dB/dec at 0 dB crossing frequency point. The cut off frequency is ωcut, which provides enough phase margin (more than 30�), (c) At Δω<sup>2</sup> frequency point (A point), the phase lags 180� acutely, so two firstorder differential elements are utilized to compensate the system phase before Δω2. After the phase compensation, the �180� crossing frequency is improved and optimizes the magnitude margin (expected more than 5 dB), (d) Since a pair of conjugate zero is at ΔωB, which provides +20 dB/dec magnitude curve, cut off frequency ωcut is arranged before ΔωB, (e) In high frequency range, the magnitude curve is designed to be �60 dB/dec to reduce magnitude rapidly, which restrains high frequency noise and white noise effectively. FLPF element is second-order type and generates �40 dB/dec, and a pair of conjugate pole is at Δω1, providing �20 dB/dec slope, (f) An inertial element is required to match the phase compensation elements and its frequency should be arranged outside the bandwidth. Meanwhile, the inertial element also provides another �20 dB/dec slope in high frequency range, which is better to restrain high frequency noise and (g) Temperature compensation module is required to ensure the widetemperature range characteristic of PIPLC. So, the PIPLC is expressed as:

$$F\_{\rm PlPLC}(\mathbf{s}) = k\_{\rm pi}(t\_{\rm tem}) \frac{\mathbf{s} + \omega\_{\rm pi1}}{\mathbf{s}} \frac{\mathbf{s} + \omega\_{\rm pi1}}{\mathbf{s} + \omega\_{\rm pi2}(t\_{\rm tem})} \tag{24}$$

Figure 12. (a) Open-loop bode diagram of sensing close loop; (b) pole-zero map of sensing close loop; (c) Nyquist map of

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sense close loop; (d) sense close loop simulation bode diagram.

Figure 13. Dual-mass gyroscope bandwidth test.

According to the analysis, we make kpi = 32 (experience value, over high value brings instability), ωpi1 = 10π rad/s and ωpi2 = 400π rad/s. In addition, the kpi and ωpi2 can be adjusted by temperature ttem. The PIPLC circuit diagram is shown in Figure 11. The transform function can be written as following:

The open-loop Bode Diagram of the sensing closed-loop is simulated in Simulink software and shown in Figure 12(a). Figure 12 indicates that the minimum phase margin of the loop is 34.6� and the magnitude margin is 7.21 dB, which satisfy the design requests. The Pole-Zero Map and Nyquist Map of sensing closed-loop are shown in Figure 12(b) and (c). The poles distribute in negative side of real axis and the Nyquist curve does not contain (�1, 0j) point. These two criterions both illustrate the closed system is pretty stable. The Bode Diagram of sensing closed-loop simulation is shown in Figure 12(d), whose curves indicate that the bandwidth of the gyro is 100 Hz, the lowest point within the bandwidth range is �13.8 dB, the DC magnitude is �12.3 dB and the highest point is �10.4 dB. The resonant peak point A (shown in Figure 10) is compensated, and the new bandwidth bottleneck point is valley B. Therefore, one of the best methods to expand the bandwidth under this condition is to enlarge the frequency

Figure 11. PIPLC circuit diagram.

Dual-Mass MEMS Gyroscope Structure, Design, and Electrostatic Compensation http://dx.doi.org/10.5772/intechopen.74364 19

Figure 12. (a) Open-loop bode diagram of sensing close loop; (b) pole-zero map of sensing close loop; (c) Nyquist map of sense close loop; (d) sense close loop simulation bode diagram.

Figure 13. Dual-mass gyroscope bandwidth test.

middle frequency range, the slope of magnitude line is designed to be �20 dB/dec at 0 dB crossing frequency point. The cut off frequency is ωcut, which provides enough phase margin (more than 30�), (c) At Δω<sup>2</sup> frequency point (A point), the phase lags 180� acutely, so two firstorder differential elements are utilized to compensate the system phase before Δω2. After the phase compensation, the �180� crossing frequency is improved and optimizes the magnitude margin (expected more than 5 dB), (d) Since a pair of conjugate zero is at ΔωB, which provides +20 dB/dec magnitude curve, cut off frequency ωcut is arranged before ΔωB, (e) In high frequency range, the magnitude curve is designed to be �60 dB/dec to reduce magnitude rapidly, which restrains high frequency noise and white noise effectively. FLPF element is second-order type and generates �40 dB/dec, and a pair of conjugate pole is at Δω1, providing �20 dB/dec slope, (f) An inertial element is required to match the phase compensation elements and its frequency should be arranged outside the bandwidth. Meanwhile, the inertial element also provides another �20 dB/dec slope in high frequency range, which is better to restrain high frequency noise and (g) Temperature compensation module is required to ensure the wide-

> s þ ωpi<sup>1</sup> s

According to the analysis, we make kpi = 32 (experience value, over high value brings instability), ωpi1 = 10π rad/s and ωpi2 = 400π rad/s. In addition, the kpi and ωpi2 can be adjusted by temperature ttem. The PIPLC circuit diagram is shown in Figure 11. The transform function can

The open-loop Bode Diagram of the sensing closed-loop is simulated in Simulink software and shown in Figure 12(a). Figure 12 indicates that the minimum phase margin of the loop is 34.6� and the magnitude margin is 7.21 dB, which satisfy the design requests. The Pole-Zero Map and Nyquist Map of sensing closed-loop are shown in Figure 12(b) and (c). The poles distribute in negative side of real axis and the Nyquist curve does not contain (�1, 0j) point. These two criterions both illustrate the closed system is pretty stable. The Bode Diagram of sensing closed-loop simulation is shown in Figure 12(d), whose curves indicate that the bandwidth of the gyro is 100 Hz, the lowest point within the bandwidth range is �13.8 dB, the DC magnitude is �12.3 dB and the highest point is �10.4 dB. The resonant peak point A (shown in Figure 10) is compensated, and the new bandwidth bottleneck point is valley B. Therefore, one of the best methods to expand the bandwidth under this condition is to enlarge the frequency

s þ ωpi<sup>1</sup> s þ ωpi2ð Þ ttem

(24)

temperature range characteristic of PIPLC. So, the PIPLC is expressed as:

FPIPLCð Þ¼ s kpið Þ ttem

be written as following:

18 MEMS Sensors - Design and Application

Figure 11. PIPLC circuit diagram.

difference between ωy1 and ωy2. The gyro is fixed on the turntable and tested under room temperature (about 20C) with FRCSM. More specifically, the employed method is a step-bystep test and step length is 1 Hz. First, the result is shown as Figure 13 with red stars, where the bandwidth is about 104 Hz (as the simulation value is 102 Hz in Figure 13) [23]. Since the scale factor can be adjusted with the output level amplifier, the 3 dB point is the key, not the absolute value of the magnitude. After the turntable test is done, since the turntable's swing frequency value is hard to get accurately, we mainly focus on the bandwidth, not each frequency point's value. Within the bandwidth range, the step-by-step test (step length is 10 Hz) is carried out, and the bandwidth is found to be 102 Hz, which verifies the FRCSM result.

References

[1] Zaman M, Sharma A, Hao Z, et al. A mode-matched silicon-yaw tuning-fork gyroscope with subdegree-per-hour Allan deviation bias instability. Journal of Microelectrome-

Dual-Mass MEMS Gyroscope Structure, Design, and Electrostatic Compensation

http://dx.doi.org/10.5772/intechopen.74364

21

[2] Xu Y, Chen XY, Wang Y. Two-mode navigation method for low-cost inertial measurement unit-based indoor pedestrian navigation. Journal of Chemical Information & Computer

[3] Huang H, Chen X, Zhang B, et al. High accuracy navigation information estimation for inertial system using the multi-model EKF fusing Adams explicit formula applied to underwater gliders. ISA TRANSACTIONS. 2017;66:414-424. DOI: 10.1016/j.isatra.2016.10.020

[4] Antonello R, Oboe R. Exploring the potential of MEMS gyroscopes. IEEE Industrial

[5] Xia DZ, Yu C, Kong L. The development of micromachined gyroscope structure and

[6] Cao HL, Li HS. Investigation of a vacuum packaged MEMS gyroscope structure's temperature robustness. International Journal of Applied Electromagnetics & Mechanics. 2013;4:

[7] Tatar E, Alper S, Akin T. Quadrature- error compensation and corresponding effects on the performance of fully decoupled MEMS gyroscopes. Journal of Microelectromechanical

[8] Chaumet B, Leverrier B, Rougeot C, et al. A new silicon tuning fork gyroscope for aerospace applications. In: Proceedings of Symposium Gyro Technology. 2009, 1.1-1.13

[9] Saukski M, Aaltonen L, Halonen K. Zero-rate output and quadrature compensation in vibratory MEMS gyroscopes. IEEE Sensors Journal. 2007;(12):1639-1652. DOI: 10.1109/

[10] Tally C, Waters R, Swanson P. Simulation of a MEMS Coriolis gyroscope with closed-loop control for arbitrary inertial force, angular rate, and quadrature inputs. Proceedings of

[11] Li HS, Cao HL, Ni YF. Electrostatic stiffness correction for quadrature error in decoupled dual-mass MEMS gyroscope. Journal of Micro-Nanolithography Mems And Moems.

[12] Walther A, Blanc CL, Delorme N, Deimerly Y, Anciant R, Willemin J. Bias contributions in a MEMS tuning fork gyroscope. Journal of Microelectromechanical Systems. 2013;22(2):

[13] Cao HL, Li HS, Liu J et al. An improved interface and noise analysis of a turning fork microgyroscope structure. Mechanical Systems and Signal Processing. 2016;s 70–71:1209-1220. DOI:

chanical Systems. 2008;(6):1526-1536. DOI: 10.1109/jmems.2008.2004794

Sciences. 2016;44(5):1840-1848. DOI: 10.1177/0037549716655220

Electronics Magazine. 2012;3:14-24. DOI: 10.1109/mie.2012.2182832

Systems. 2012;(3):656-667. DOI: 10.1109/jmems.2012.2189356

2014;13(3): 033003. DOI: 10.1117/1.jmm.13.3.033003

303-308. DOI: 10.1109/jmems.2012.2221158

495-506. DOI: 10.3233/jae-131668

jsen.2007.908921

IEEE Sensors. 2011:1681-1684

10.1016/j.ymssp.2015.08.002

circuitry technology. Sensors. 2014;14:1394-1473. DOI: 10.3390/s140101394

## 5. Conclusion

In this chapter, the recent achievements in our research group for dual-mass MEMS gyroscope are proposed. Three main parts are discussed: dual-mass gyroscope structure design, quadrature error electrostatic compensation and bandwidth expansion. First, dual-mass MEMS gyroscope structure is designed and simulated in ANSYS soft and dual-mass structure movement function is derived. Second, quadrature error is traced to the source, and the coupling stiffness electrostatic compensation method is employed to reduce the quadrature error. Finally, proportional-integral-phase-leading controller is presented in sensing close loop to expand the bandwidth from 13 to 104 Hz.

#### Acknowledgements

This work was supported by National Natural Science Foundation of China No.51705477. The research was also supported by Research Project Supported by Shanxi Scholarship Council of China No. 2016-083, Fund of North University of China, Science and Technology on Electronic Test and Measurement Laboratory No. ZDSYSJ2015004, and The Open Fund of State Key Laboratory of Deep Buried Target Damage No. DXMBJJ2017-15. The authors deliver their special gratitude to Prof. Hongsheng Li (Southeast University, Nanjing, China) and his group for the guidance, discussions and help.
