• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.9
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• pp.1931-1942
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• 2002

In this paper a formulation of robust optimization is presented and illustrated by a design example of vibratory micro gyroscopes in order to reduce the effect of variations due to uncertainties in MEMS fabrication processes. For the vibratory micro gyroscope considered it is important to match the resonance frequencies of the vertical (sensing) and lateral (driving) modes as close as possible to attain a high sensing sensitivity. A deterministic optimization in which the difference of both the sensing and driving natural frequencies is minimized as an objective function results in highly enhanced performance but apt to be very sensitive to fabrication errors. The formulation proposed is to attain robustness of the performance by including the sensitivity of the response with respect to uncertain variables as a term of objective function to be minimized. This formulation is simple and practically applicable since no detail statistical information on fabrication errors is required. The geometric variables, beam width, length and thickness of vibratory micro gyroscopes are adopted as design variables and at the same time considered as uncertain variables because here occur the fabrication errors. A robustness test in terms of a percentage yield by using the Monte Carlo simulation has shown that the robust optimum produces twice more acceptable designs than the deterministic optimum. Improvement of robustness becomes bigger as the amount of fabrication errors is assumed larger. Considering that the magnitude of fabrication errors and uncertainties in a MEMS structure are comparatively large, the present method is illustrated to be a viable approach for a robust MEMS design.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.602-606
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• 2005

A systematic procedure of probability analysis for general distributions is developed based on the first four moments estimated from polynomial interpolation of the system response function and the Pearson system. The function approximation is based on a specially selected experimental region for accuracy and the number of function evaluations is taken equal to that of the unknown coefficient for efficiency. For this purpose, three error-minimizing conditions are proposed and corresponding canonical experimental regions are formed for popular probability. This approach is applied to study the stochastic properties of the performance functions of a MEMS structure, which has quite large fabrication errors compared to other structures. Especially, the vibratory micro-gyroscope is studied using the statistical moments and probability density function (PDF) of the performance function to be the difference between resonant frequencies corresponding to sensing and driving mode. The results show that it is very sensitive to the fabrication errors and that the types of PDF of each variable also affect the stochastic properties of the performance function although they have same the mean and variance.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.9
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• pp.1733-1740
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• 2011

In this research, a MEMS vibratory gyroscope with dual-mass system in the sensing mode has been proposed to increase the stability of the device using wide bandwidth. A wide flat region between the two resonance peaks of the dual-mass system removes the need for a frequency matching typically required for single mass vibratory gyroscopes. Bandwidth, mass ratio, spring constant, and frequency response of the dual-mass system have been analyzed with MATLAB and ANSYS simulation. Designed first and second peaks of sensing mode are 5,917 and 8,210Hz, respectively. Driving mode resonance frequency of 7,180Hz was located in the flat region between the two resonance peaks of the sensing mode. The device is fabricated with anodically bonded silicon-on-glass substrate. The chip size is 6mm x 6mm and the thickness of the silicon device layer is $50{\mu}m$. Despite the driving mode resonance frequency decrease of 2.8kHz and frequency shift of 176Hz from the sensing mode due to fabrication imperfections, measured driving frequency was located within the bandwidth of sensing part, which validates the utilized dual-mass concept. Measured bandwidth was 768Hz. Sensitivity calculated with measured displacement of driving and sensing parts was 22.4aF/deg/sec. Measured slope of the sensing point was 0.008dB/Hz.

• Journal of the Korea Institute of Military Science and Technology
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• v.12 no.1
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• pp.106-113
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• 2009

This paper presents a surface acoustic wave(SAW) micro-electro-mechanical-systems(MEMS) interdigital transducer (IDT) gyroscope with 80MHz central frequency on a $128^{\circ}\;YX\;LiNbO_3$, which is consisted of a two-port SAW resonator, metallic dots and dual delay lines for the sensor and reference oscillators. Reason for using two delay line oscillators is to extract the gyroscope effect by comparing the resonant frequencies between two oscillators and to compensate the temperature effect. Based on the coupling of modes(COM) simulation, an 80MHz two ports SAW resonator and dual delay line were fabricated and characterized by the network analyzer. Obtained sensitivity was $109Hz/deg{\cdot}s^{-1}$ in the angular rate range of $0{\sim}1000deg/s$. Good Linearity and superior directivity were observed.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.2
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• pp.125-130
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• 2011

This paper shows a method to design complementary filter using least square. The complementary filter is one of useful filters estimating angle. The basic concept of this filter is to enhance advantages of each sensor that angle detecting using a gyroscope has good accuracy at a high frequency and an accelerometer at a low frequency. When designing complementary filter, the most commonly used method is using cut-off frequency. However, it may be not easy to obtain a cut-off frequency. This paper presents a systematic method to determine the coefficients of the complementary filter using well-known linear least squares minimizing error between estimating angle and true angle.

• Journal of KSNVE
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• v.10 no.5
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• pp.880-885
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• 2000

In a verical type, vibratory gyroscope, the coupled motion between the reference and sensing vibrations causes the zero-point output which means non-zero sensing vibration without angular velocity. This structural coupling leaks to an inherent discrepancy between the natural frequencies of the reference and sensing oscillations, causing the degradation of the sensing performance and dynamic stability. In this paper, the dynamic characteristics associated the coupling phenomenon are theoretically analyzed. Effects of reference frequency and coupling factor on the rotational direction and amplitude of elliptic oscillation are studied. A technique to predict the existence of curve veering of crossing in frequency trajectories is introduced to apply the design of micro gyroscopes with decoupled structures.

• Journal of Navigation and Port Research
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• v.35 no.10
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• pp.785-791
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• 2011

This paper describes the evaluation and selection of MEMS(Micro-Elect Mechanical System) based inertial sensor to fit to implement the Inertial Measurement Unit(IMU) for a small-sized vessel at sea. At first, the error model and the noise model of the inertial sensors are defined with Euler's equations and then, the inertial sensor evaluation is carried out with Allan Variance techniques and Monte Carlo simulation. As evaluation results for the five sensors, ADIS16405, SAR10Z, SAR100Grade100, LIS344ALH and ADXL103, the combination of gyroscope and accelerometer of ADIS16405 is shown minimum error having around 160 m/s standard deviation of velocity error and around 35 km standard deviation of position error after 600 seconds. Thus, we select the ADIS16405 inertial sensor as a MEMS-based inertial sensor to implement IMU and, the error reducing method is also considered with the search for reference papers.

• International Journal of Control, Automation, and Systems
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• v.6 no.6
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• pp.873-883
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• 2008

This paper presents a parametric study on the controller design scheme for a gyro-accelerometer to have robust performance under some parameter variations. In particular, an integral and derivative based controller design method is suggested to achieve the desired performances of stability margin, bandwidth, and uniformity of scale for both gyroscopes and accelerometers with uncertainties of quality factor and resonant frequency. The simulation result shows that the control loop based on the suggested method gives satisfactory performance robustness under parameter variations, demonstrating the usefulness of the proposed design scheme.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.3
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• pp.555-564
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• 2017

In this paper, a new technique for attitude and heading reference system (AHRS) using low-cost MEMS sensors of the gyroscope, accelerometer, and magnetometer is addressed particularly in vibration environments. The motion of MEMS sensors interact with the scale factor and cross-coupling errors to produce random errors by the harsh environment. A new adaptive attitude estimation algorithm based on the Kalman filter is developed to overcome these undesirable side effects by analyzing windowed measurement error covariance. The key idea is that performance degradation of accelerometers, for example, due to linear vibrations can be reduced by the proposed measurement error covariance analysis. The computed error covariance is utilized to the measurement covariance of Kalman filters adaptively. Finally, the proposed approach is verified by using numerical simulations and experiments in an acceleration phase and/or vibrating environments.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.39C no.1
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• pp.82-89
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• 2014

Recently, inertial sensors are popularly used for the location and position recognition of small devices for M2M/IoT. In this paper, we designed low power, low noise, small sized 6-axis inertial sensor IC for mobile applications, which uses a 3-axis piezo-electric gyroscope sensor and a 3-axis piezo-resistive accelerometer sensor. Proposed IC is composed of 3-axis gyroscope readout circuit, two gyroscope sensor driving circuits, 3-axis accelerometer readout circuit, 16bit sigma-delta ADC, digital filter and control circuit and memory. TSMC $0.18{\mu}m$ mixed signal CMOS process was used. Proposed IC reduces 27% of the current consumption of LSM330.