Presents the mathematical framework, technical language, and control systems know-how needed to design, develop, and instrument micro-scale whole-angle gyroscopes

This comprehensive reference covers the technical fundamentals, mathematical framework, and common control strategies for degenerate mode gyroscopes, which are used in high-precision navigation applications. It explores various energy loss mechanisms and the effect of structural imperfections, along with requirements for continuous rate integrating gyroscope operation. It also provides information on the fabrication of MEMS whole-angle gyroscopes and the best methods of sustaining oscillations.

Whole-Angle Gyroscopes: Challenges and Opportunities begins with a brief overview of the two main types of Coriolis Vibratory Gyroscopes (CVGs): non-degenerate mode gyroscopes and degenerate mode gyroscopes. It then introduces readers to the Foucault Pendulum analogy and a review of MEMS whole angle mode gyroscope development. Chapters cover: dynamics of whole-angle coriolis vibratory gyroscopes; fabrication of whole-angle coriolis vibratory gyroscopes; energy loss mechanisms of coriolis vibratory gyroscopes; and control strategies for whole-angle coriolis vibratory gyro- scopes. The book finishes with a chapter on conventionally machined micro-machined gyroscopes, followed by one on micro-wineglass gyroscopes. In addition, the book:

* Lowers barrier to entry for aspiring scientists and engineers by providing a solid understanding of the fundamentals and control strategies of degenerate mode gyroscopes

* Organizes mode-matched mechanical gyroscopes based on three classifications: wine-glass, ring/disk, and mass spring mechanical elements

* Includes case studies on conventionally micro-machined and 3-D micro-machined gyroscopes

Whole-Angle Gyroscopes is an ideal book for researchers, scientists, engineers, and college/graduate students involved in the technology. It will also be of great benefit to engineers in control systems, MEMS production, electronics, and semi-conductors who work with inertial sensors.

Doruk Senkal, PhD, has been working on the development of Inertial Navigation Technologies for Augmented and Virtual Reality applications at Facebook since 2018. Before joining Facebook, he was developing MEMS Inertial Sensors for mobile devices at TDK Invensense. He received his Ph.D. degree in 2015 from University of California, Irvine, with a focus on MEMS Coriolis Vibratory Gyroscopes. Dr. Senkal 's research interests, represented in over 20 international conference papers, 9 peer-reviewed journal papers, and 16 patent applications, encompass all aspects of MEMS inertial sensor development, including sensor design, device fabrication, algorithms, and control.

Andrei M. Shkel, PhD, has been on faculty at the University of California, Irvine since 2000, and served as a Program Manager in the Microsystems Technology Office of DARPA. His research interests are reflected in over 250 publications, 40 patents, and 2 books. Dr. Shkel has been on a number of editorial boards, including Editor of IEEE/ASME JMEMS and the founding chair of the IEEE Inertial Sensors. He was awarded the Office of the Secretary of Defense Medal for Exceptional Public Service in 2013, and the 2009 IEEE Sensors Council Technical Achievement Award. He is the IEEE Fellow.

Inhalt

List of Abbreviations ix

Preface xi

About the Authors xiii

Part I Fundamentals of Whole-Angle Gyroscopes 1

1 Introduction 3

1.1 Types of Coriolis Vibratory Gyroscopes 3

1.1.1 Nondegenerate Mode Gyroscopes 4

1.1.2 Degenerate Mode Gyroscopes 5

1.2 Generalized CVG Errors 5

1.2.1 Scale Factor Errors 7

1.2.2 Bias Errors 7

1.2.3 Noise Processes 7

1.2.3.1 Allan Variance 7

1.3 Overview 9

2 Dynamics 11

2.1 Introduction to Whole-Angle Gyroscopes 11

2.2 Foucault Pendulum Analogy 11

2.2.1 Damping and Q-factor 12

2.2.1.1 Viscous Damping 13

2.2.1.2 Anchor Losses 14

2.2.1.3 Material Losses 15

2.2.1.4 Surface Losses 16

2.2.1.5 Mode Coupling Losses 16

2.2.1.6 Additional Dissipation Mechanisms 16

2.2.2 Principal Axes of Elasticity and Damping 16

2.3 Canonical Variables 18

2.4 Effect of Structural Imperfections 18

2.5 Challenges of Whole-Angle Gyroscopes 20

3 Control Strategies 23

3.1 Quadrature and Coriolis Duality 23

3.2 Rate Gyroscope Mechanization 24

3.2.1 Open-loop Mechanization 24

3.2.1.1 Drive Mode Oscillator 24

3.2.1.2 Amplitude Gain Control 26

3.2.1.3 Phase Locked Loop/Demodulation 26

3.2.1.4 Quadrature Cancellation 26

3.2.2 Force-to-rebalance Mechanization 27

3.2.2.1 Force-to-rebalance Loop 27

3.2.2.2 Quadrature Null Loop 29

3.3 Whole-Angle Mechanization 29

3.3.1 Control System Overview 30

3.3.2 Amplitude Gain Control 32

3.3.2.1 Vector Drive 32

3.3.2.2 Parametric Drive 33

3.3.3 Quadrature Null Loop 34

3.3.3.1 AC Quadrature Null 34

3.3.3.2 DC Quadrature Null 34

3.3.4 Force-to-rebalance and Virtual Carouseling 35

3.4 Conclusions 35

Part II 2-D Micro-Machined Whole-Angle Gyroscope Architectures 37

4 Overview of 2-D Micro-Machined Whole-Angle Gyroscopes 39

4.1 2-D Micro-Machined Whole-Angle Gyroscope Architectures 39

4.1.1 Lumped Mass Systems 39

4.1.2 Ring/Disk Systems 40

4.1.2.1 Ring Gyroscopes 40

4.1.2.2 Concentric Ring Systems 41

4.1.2.3 Disk Gyroscopes 42

4.2 2-D Micro-Machining Processes 42

4.2.1 Traditional Silicon MEMS Process 43

4.2.2 Integrated MEMS/CMOS Fabrication Process 43

4.2.3 Epitaxial Silicon Encapsulation Process 44

5 Example 2-D Micro-Machined Whole-Angle Gyroscopes 47

5.1 A Distributed Mass MEMS Gyroscope Toroidal Ring Gyroscope 47

5.1.1 Architecture 48

5.1.1.1 Electrode Architecture 49

5.1.2 Experimental Demonstration of the Concept 49

5.1.2.1 Fabrication 49

5.1.2.2 Experimental Setup 50

5.1.2.3 Mechanical Characterization 51

5.1.2.4 Rate Gyroscope Operation 52

5.1.2.5 Comparison of Vector Drive and Parametric Drive 53

5.2 A Lumped Mass MEMS Gyroscope Dual Foucault Pendulum Gyroscope 54

5.2.1 Architecture 56

5.2.1.1 Electrode Architecture 57

5.2.2 Experimental Demonstration of the Concept 57

5.2.2.1 Fabrication 57

5.2.2.2 Experimental Setup 58

5.2.2.3 Mechanical Characterization 60

5.2.2.4 Rate Gyroscope Operation 60

5.2.2.5 Parameter Identification 60

Part III 3-D Micro-Machined Whole-Angle Gyroscope Architectures 65

6 Overview of 3-D Shell Implementations 67

6.1 Macro-scale Hemispherical Resonator Gyroscopes 67

6.2 3-D Micro-Shell Fabrication Processes 69

6.2.1 B...