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This paper presents a novel micro dynamically tuned gyroscope (MDTG) with adjustable static capacitance. First, the principle of MDTG is theoretically analyzed. Next, some simulations under the optimized structure parameters are given as a reference for the mask design of the rotor wafer and electrode plates. As two key components, the process flows of the rotor wafer and electrode plates are described in detail. All the scanning electron microscopy (SEM) photos show that the fabrication process is effective and optimized. Then, an assembly model is designed for the static capacitance adjustable MDTG, whose static capacitance can be changed by rotating the lower electrode plate support and substituting gasket rings of different thicknesses. Thus, the scale factor is easily changeable. Afterwards, the digitalized closed-loop measurement circuit is simulated. The discrete correction and decoupling modules are designed to make the closed-loop stable and cross-coupling effect small. The dual axis closed-loop system bandwidths can reach more than 60 Hz and the dual axis scale factors are completely symmetrical. All the simulation results demonstrate the proposed fabrication of the MDTG can meet the application requirements. Finally, the paper presents the test results of static and dynamic capacitance values which are consistent with the simulation values.

As a traditional high precision gyroscope (the bias stability is usually around 0.001–1 °/h), the dynamically tuned gyroscope (DTG) has been widely applied in the fields of inertial navigation and accurate positioning. The DTG signals contain noise and random drift due to the influence of the rebalance loop, driving motor and the structural thermal deformation,

The research on the MDTG was first proposed by Jenkins

Regardless of the difference between the DTG and MDTG, normally we can adopt the circuitry and signal processing methods in the tradional DTG as a key reference of the MDTG concerning the rebalance loop. In recent years, the rebalance loop has been designed for the DTG using analog or digital circuits, where a lot of control and signal processing approaches are investigated to improve the performance of the DTG [

The rotor wafer of the MDTG in _{p}_{n}_{p}_{n}_{C}_{x}_{y}_{x} and φ̇_{y} are respectively the input rotational rate along y-axis and x-axis. λ, δ and

The MDTG structure adopted here is shown in

During this process, the equilibrium ring always do a rocking motion at twice the frequency of the rotation rate. To make the rotor ring work in a stable and limited area, the closed-loop force rebalance mechanism is adopted to offset its rotation in the centre position. Here the negative electrical stiffness and the feedback torque will simultaneously be generated from a higher servo voltage originated by the correction and decoupling operation of two angle signals of the rotor rings around x and y axes. To make sure that all the modes are effectively away from the second and third harmonic frequencies of the motor rotation rate, we need to select optimized geometry parameters to get more proper modes.

The meshing method of the torsional spring and other parts are adopted by 1 μm fine and 5 μm normal tetrahedron meshing elements, respectively. The center inner cylinder of the inner ring is fixed as a boundary condition.Through modal simulation in

The MDTG mechanical simulation is necessary for optimizing the structure parameters in

According to the field

The rotor ring of MDTG should have some load capacity especially used in reality. The deformation when a pressure of 1 Pa to 10 Pa is applied on the upside of the rotor ring while the inner ring is constant can be seen in

The miniature motor used in the MDTG can spin from 6,000 rpm up to 20,000 rpm. When the MDTG rotates around the z-axis quickly, the rotor wafer will be subject to the force in the xy planes caused by the centrifugal force. As the rotation speed ranges from 6,000 rpm to 20,000 rpm, the maximum deformation can reach from 0.0041 μm at 6,000 rpm to 0.0457 μm at 20,000 rpm in

The assembly distance between the electrode plates and the MDTG is very vital to the capacitance signal extraction shown in

The fabrication process starts with a double side polished boron doped low resistivity silicon wafer shown as ^{2} is conducted to pattern the opening for selective etching bulk silicon. MF-319 is used to develop the UV exposed photoresist. The shallow trench is etched in high aspect ratio Bosch ICP etching to ensure straight sidewalls as seen in

The same recipe is used for the photoresist on the back side of the wafer in ^{2} light intensity at 405 nm can pattern the photoresist in

After AZ 4620 photoresist is developed, the thermally grown silicon dioxide masking layer is etched in C_{4}F_{8} plasma. The remaining photoresist and silicon dioxide are the masking layers for the through silicon wafer etch. Then the bulk silicon is etched by Bosch process to ensure straight sidewalls in

During the above process, some key characteristics are recorded by microscope diagrams.

A novel assembly model shown in

The base board is connected to the motor support through a chute. Thus, the base board could rotate freely to ensure that the coordinates of the base board are in accordance with the coordinates of the electrode plates for the purpose of convenient adjustment. The lower electrode support and the motor support are assembled together through the screw thread so that the gap between the rotor wafer and the lower electrode plate can be adjusted by screwing. There are total 120 even scales on the lower electrode support. When the scale reference 1 and the scale reference 2 are aligned, the assembly gap is zero. Then, the adjustable gap increases 4.167 μm by rotating a scale. The capacitance values are changeable with the gap shown in _{1}, D_{2} are the thicknesses of gasket ring and C/V converter board, respectively. H_{1}, H_{2} are the gaps of the lower and upper electrode plates, respectively. The rotor wafer is fixed by the lower rotor support and upper rotor support. The signals such as carrier signal and bias voltage can be applied on the rotor wafer through upper bearing even though the rotor wafer rotates at a high speed. Besides, the C/V converter board can be embedded in the assembly and all the interface leads are symmetrically distributed by two layers beneficial for soldering, which can greatly eliminate the parasitic effect to improve the anti-interference capability between the signals. The adjustable capacitance assembly obviously has the advantage of adjusting the scale factor easily, avoiding pull in effect and so on.

As seen from _{C}_{C} can be written as:
_{r} is the outer radius of the rotor ring, r_{F} is the inner radius of the feedback electrode plate, V_{F} is the bias voltage and d is the assembly gap between the electrode plates and the rotor wafer. Therefore, the bias voltage is:

The digital circuit of MDTG can be seen in

The sensing electrode plates and feedback electrode plates are upper and lower electrode plates in _{t11}_{t12}_{t21}_{t22}_{b11}_{b12}C_{b21}_{b22}_{0}_{s11}_{s12}_{s21}_{s22}_{3}=C_{4}=C_{0}_{s11}+C_{s12}=C_{s21}+C_{s22}_{0}_{D}_{s11}_{s12}C_{p}_{a}

When Δ_{C}

The decoupled transfer function matrix can be set as type II:

With a zero-order holder, a new Z transformation equation can be written as:

Considering the zero-order holder, we can obtain

Let

Solving the equation above, we can obtain the digital decoupling matrix

The digital block diagram of the decoupling system is shown in

The open-loop transfer function matrix of the gyro after decoupling can be expressed as:

By the bilinear transformation,

Similarly, through the correction, we can get the following correction transfer function:

Last, _{J}_{J}

The open-loop transfer function Bode plots can be seen in

As seen in

The simulation diagram of closed-loop system can be seen in _{11}_{12}_{21}_{22}_{J}_{J1}_{J2}_{J3}, G_{J4}_{J5}_{J6}_{11}_{12}_{21}_{22}_{bc}_{CV}_{VF}

The bandwiths and scale factors have been simulated in ^{o}/s and –0.1007 V/^{o}/s, respectively. According the above simulations, the designs of both x-axis and y-axis closed-loop systems are stable enough.

In

The adjustable effect of the static capacitance has been verified using various pieces of equipment, including an impedance analyzer, an oscilloscope, a multimeter and a power supply shown in

The experimental results of static capacitance between rotor wafer and the sensing electrode plates can be seen in

The experimental results of adjusting the dynamical capaticance between the rotor wafer and the sensing electrode plates can be seen in

A novel micro dynamically tuned gyroscope (MDTG) is described from the principle, simulation and fabrication, assembly, circuitry and experimental detail point of view, respectively. Through modal analysis, mechanical and static capacitance simulation, the optimized geometry parameters are derived. Then the fabrication process of rotor wafer, electrode plates and assembly model are investigated step by step. The SEM photos and even the electrical measurement results demonstrate that the proposed design is effective. The static capacitance adjustable assembly model is elaborated to easily tune the static capacitance. First, C/V conversion factors are adjustable because of the changeable static capacitances, which means the scale factors are adjustable conveniently. Second, the optimized gap between electrode plates and rotor wafer can be obtained by experiments. Last, the parallel level between the rotor wafer and electrode plates or the assembly working face can be tested compared with the simulation.

To realize a complete dual-axis gyroscope, a digitalized closed-loop measurement circuit is designed and analyzed. The simulation results can show a satisfactory effect compared with the previous analog design. The discrete correction and decoupling modules are designed to make the closed-loop stable and cross-coupling effect reduced. The system closed-loop bandwidths can reach more than 60 Hz and the dual axis scale factors are completely symmetrical. All the simulation results demonstrate the proposed fabrication of the MDTG can meet the application requirement. In the end, the assembled model is proved effective to achieve the adjustable static capacitance by experiments.

The authors gratefully acknowledge the financial supports from Chinese National Natural Science Foundation (Contract No. 61001048), Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, China (Project No. KL201102), Major Project Guidance Foundation of Basic Scientific Research Operation Expenses, Southeast University (No. 3222002107), and Natural Science Fund project in Jiangsu Province (BK2012739).

_{∞}robust rebalance loop controller design for a micromachined electrostatically suspended gyroscope

_{2}methodology

(

The deflection under gravity. (

The deformation under a load. (

The deformation under a rotation speed. (

The simulation of static capacitance values. (

Process flow for Rotor.

Views of fabrication. (

Process flow for electrode plate.

(

The assembly model of MDTG.

The digital MDTG circuitry system.

The interface circuit of MDTG. (

The digital block diagram of the decoupling system.

The digital Bode plots of open-loop system.

The simulation diagram of closed-loop system.

Simulation results diagrams. (

The output of system

Experimental setup for the adjustable static capacitance of MDTG.

The experimental results of static capacitance. (

The experimental results of dynamical capacitance under different rotation speed.

The simulation parameters.

Name | Outer radius (mm) | Inner radius (mm) | Thickness (μm) |
---|---|---|---|

Rotor ring | 10 | 7.0 | 400 |

Equilibrium ring | 6.9 | 5.0 | 400 |

Inner ring | 4.9 | 2.5 | 400 |

Name | Length (mm) | Width (μm) | Thickness (μm) |

Torsional spring | 1 | 50 | 350 |

Material | Density (kg/m^{3}) |
Young modulus (Pa) | Poisson's ratio |

Si | 2,329 | 1.7 × 10^{11} |
0.28 |

The parameter values of the closed-loop system.

Moment of Inertia (J) | 3.2173 × 10^{−9} kg·m^{2} |

Angular Momentum (H) | 6.7512 × 10^{−6} kg·m^{2}·rad/s |

Sample Time (T) | 1/1,000 s |

β/C Factor (K_{bc}) |
6.0478 × 10^{−9} F/rad |

C/V Factor (K_{CV}) |
3.4781 × 10^{10}V/F |

Power Amplification Factor (K_{D}) |
10 |

V/F Factor (K_{VF}) |
−8.0269 × 10^{−8} N·m/V |

Angle to Radian Conversion Factor (K) | π/180 |