• Journal of Institute of Control, Robotics and Systems
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• v.12 no.6
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• pp.608-613
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• 2006

Any input acceleration that bends RLG dithering axis causes flexure error, which is a source of the noncommutative error that can not be compensated by simply using integrated gyro sensor output. This paper introduces noncommutative error equations that define attitude errors caused by flexure errors. In this paper, flexure error is classified as sensor level error if the sensing axis coincides with the dithering axis and as system level error if the two axes do not coincide. The relationship between gyro output and the rotation vector is introduced and is used to define the coordinate transformation matrix and angular motion. Equations are derived for both sensor level and system level flexure error analysis. These equations show that RLG based INS attitude error caused by flexure is directly proportional to time, amount of input acceleration and the dynamic frequency of the vehicle.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1958-1961
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• 2004

Ring Laser Gyroscopes used as navigational sensors inherently experience a lock-in region, where very low rotational rates are not measurable. Most RLG manufacturers use a mechanical dither motor that applies a small oscillatory rotational motion larger than this region to resolve this problem. Any input acceleration that bends this dithering axis causes flexure error, which is a noncommutative error that can not be compensated by simply using integrated gyro sensor output. This paper introduces noncommutative error equations that define attitude errors caused by flexure errors. In this paper, flexure error is classified as sensor level error if the sensing axis coincides with the dithering axis and as system level error if the two axes do not coincide. The relationship between gyro output and the rotation vector is introduced and is used to define the coordinate transformation matrix and angular motion. Equations are derived for both sensor level and system level flexure error analysis. These equations show that RLG based INS attitude error caused by flexure is directly proportional to time, amount of input acceleration and the dynamic frequency of the vehicle.

• Korean Journal of Optics and Photonics
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• v.15 no.1
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• pp.68-73
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• 2004

Flexure measurement of ring laser gyro was investigated by using an interferometer. A two-beam interferometer of Fiezo-fringe pattern obtained the flexure angle in 1-gravity acceleration and the higher acceleration environments. These environments were made with the addition of dummy mass to the ring laser gyro axis. The flexure angle change for 1-gravity acceleration change was measured as 2.37 arcsec/g with low repeatability error of 0.01 arcsec/g. The laser navigation system consisting of 3 flexure-reduced ring laser gyros showed the improvement of flexure error.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.3
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• pp.626-637
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• 2014

On ship, especially on large ship, the flexure deformation between Master (M)/Slave (S) Inertial Navigation System (INS) is a key factor which determines the accuracy of the integrated system of M/S INS. In engineering this flexure deformation will be increased with the added ship size. In the M/S INS integrated system, the attitude error between MINS and SINS cannot really reflect the misalignment angle change of SINS due to the flexure deformation. At the same time, the flexure deformation will bring the change of the lever arm size, which further induces the uncertainty of lever arm velocity, resulting in the velocity matching error. To solve this problem, a $H_{\infty}$ algorithm is proposed, in which the attitude and velocity matching error caused by deformation is considered as measurement noise with limited energy, and measurement noise will be restrained by the robustness of $H_{\infty}$ filter. Based on the classical "attitude plus velocity" matching method, the progress of M/S INS information fusion is simulated and compared by using three kinds of schemes, which are known and unknown flexure deformation with standard Kalman filter, and unknown flexure deformation with $H_{\infty}$ filter, respectively. Simulation results indicate that $H_{\infty}$ filter can effectively improve the accuracy of information fusion when flexure deformation is unknown but non-ignorable.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.2
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• pp.178-184
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• 2002

This paper deals with the transfer alignment problem of SDINS(StrapDown Inertial Navigation System) subjected to roll and pitch motions of the ship. In order to reduce alignment errors induced by ship body flexure, a linearized error model for the velocity and attitude matching transfer alignment system is first derived by linearizing the nonlinear measurement equation with respect to the dominant y axis component and defining the flexure state of random constant type. And then a robust state estimation scheme is introduced to account for modeling uncertainty of the flexure. By interpreting the simulation results and comparing with the velocity and DCM(Direction Cosine Matrix) partial matching method, it is shown that the proposed method is effective enough to improve the azimuth alignment performance.

• Journal of the Korea Institute of Military Science and Technology
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• v.25 no.6
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• pp.561-571
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• 2022

An optical mirror assembly is an opto-mechanically coupled system as the optical and mechanical behaviors interact. In the assembly, a flexure mount attached to an optical mirror should be flexible in the radial direction, but rigid for the remaining degrees of freedom for supporting the mirror rigidly and suppressing the wavefront error of the optical mirror. This work presents an optimal design of the flexure mount using topology optimization with thermal stress constraint. By simplifying the optical mirror assembly into finite shell elements, topology optimization model was built for efficient design and good machinability. The stress at the boundary between the optical mirror and the mount together with the first natural frequency were applied as constraints for the optimization problem, while the objective function was set to minimize the strain energy. As a result, we obtained the optimal design of the flexure mount yielding the improved wavefront error, proper rigidity, and machinability.

• Journal of the Korea Institute of Military Science and Technology
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• v.4 no.1
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• pp.225-233
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• 2001

This paper deals with the transfer alignment problem of SDINS(StrapDown Inertial Navigation System) subjected to roll and pitch motions of the ship. Specifically, to reduce alignment errors induced by measurement time-delay and ship body flexure, an error compensation method is suggested based on delay state augmentation and DCM(Direction Cosine Matrix) partial matching. A linearized error model for the velocity and attitude matching transfer alignment system is first derived by linearizing the nonlinear measurement equation with respect to its time delay and augmenting the delay state into the conventional linear state equations. And then DCM partial matching is properly combined to reduce effects of a ship's Y axis flexure. The simulation results show that the suggested method is effective enough resulting in considerably less azimuth alignment errors.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.32 no.8
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• pp.693-700
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• 2008

The primary mirror system in a satellite camera is an opto-mechanically coupled system for a reason that optical and mechanical behaviors are intricately interactive. In order to enhance the opto-mechanical performance of the primary mirror system, opto-mechanical behaviors should be thoroughly investigated by using various analysis procedures such as elastic, thermo-elastic, optical and eigenvalue analysis. In this paper, optimal design of the bipod flexure mounts for high opto-mechanical performance is performed. Optomechanical performances considered in this paper are RMS wavefront error under the gravity and thermal loading conditions and 1st natural frequency of the mirror system. The procedures of the flexure mounts design based on design of experiments and statistics is as follows. The experiments for opto-mechanical analysis are constructed based on the tables of orthogonal arrays and analysis of each experiment is carried out. In order to deal with the multiple opto-mechanical properties, MADM (Multiple-attribute decision making) is employed. From the analysis results, the critical design variables of the flexure mounts which have dominant influences on opto-mechanical performance are determined through analysis of variance and F-test. The regression model in terms of the critical design variables is constructed based on the response surfaceanalysis. Then the critical design variables are optimized from the regression model by using SQP algorithm. Opto-mechanical performance of the optimal bipod flexure mounts is verified through analysis.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.1638-1642
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• 2003

Piezoactuator using a flexure hinge mechanism is often used in the precision stages. When the total size of the hinge mechanism become small compared with the deformation of the hinge mechanism, the geometrical nonlinearity makes a considerable error in the output displacement. In this research, the incremental method based on the matrix method is developed to model the effect of the geometrical nonlinearity. Developed modeling method is applied to derive the error of output displacement of the bridge-type hinge mechanism and its results are derived with respect to the design parameters. This method can be easily used to the design optimization of the hinge mechanism and analysis results show that the geometrical nonlinearity error should be considered to achieve a high accuracy to the piezoactuators.

• Journal of Institute of Control, Robotics and Systems
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• v.3 no.3
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• pp.238-243
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• 1997

A new transfer alignment algorithm using the velocity and the quaternion partial matching methods is proposed to reduce the effect of a ship's Y-axis flexure on the performance of azimuth error estimation of Kalman filter. The simulation results show that it can significantly reduce the effect of Y-axis flexure on error estimation by the transfer alignment algorithm. As its results, azimuth transfer alignment error is reached up to 3 mrad under proper roll and pitch attitude motion of the ship.