• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.56.1-56
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• 2001

Initial attitude error is one of the large error sources in the navigation errors of SDINS. And it is important to decide the initial attitude of SDINS. The method, like a self-alignment or a transfer alignment method, is required to a precise INS. If we do not have a precise INS, we should get large attitude error. After performing the initial alignment, a vehicle has the initial attitude error. Therefore, it results in navigation error due to the initial attitude error. But, if we use position information during flight, we could estimate and compensate a vehicle attitude error. So, we can maintain a precise attitude in spite of existing the initial attitude error. Using the uplinked position information from a land-based radar system, the new algorithm estimates the attitude of the SDINS during flight ...

• Journal of Ocean Engineering and Technology
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• v.19 no.6 s.67
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• pp.78-85
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• 2005

Initial alignment and localization are important topics in inertial navigation systems, since misalignment and initial position error wholly propagate into the navigation systems and deteriorate the performance of the systems. This paper presents the error convergence characteristics of the hybrid navigation system for underwater vehicles initial position, which is based on an inertial measurement unit (IMU) accompanying a range sensor. This paper demonstrates the improvement on the navigational performance oj the hybrid system with the range information, especially focused on the convergence of the estimation of underwater vehicles initial position error. Simulations are performed with experimental data obtained from a rotating ann test with a fish model. The convergence speed and condition of the initial error removal for random initial position errors are examined with Monte Carlo simulation. In addition, numerical simulation is conducted with an AUV model in lawn-mowing survey mode to illustrate the error convergence of the hybrid navigation System for initial position error.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.6
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• pp.524-532
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• 2002

This paper presents a new in-flight alignment method for an SDINS under large initial heading error. To handle large heading error, a new attitude error model is introduced. The attitude errors are divided into heading error and leveling errors using a newly defined horizontal frame. Some navigation error dynamic models are derived from the attitude error model for indirect feedback filtering of the in-flight alignment system. A Kalman filter with Position measurement is designed to estimate navigation errors as the indirect feedback filter Simulation results show that the proposed in-flight alignment method reduces the heading error very quickly from more than 40deg to about 5deg so as to apply a refined navigation filter. The total alignment process including leveling mode and navigation mode in addition to the proposed one allows large initial values not only in heading error but also in leveling errors.

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.167-177
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• 2012

In this article, we propose exponentially fitted error correction methods(EECM) which originate from the error correction methods recently developed by the authors (see [10, 11] for examples) for solving nonlinear stiff initial value problems. We reduce the computational cost of the error correction method by making a local approximation of exponential type. This exponential local approximation yields an EECM that is exponentially fitted, A-stable and L-stable, independent of the approximation scheme for the error correction. In particular, the classical explicit Runge-Kutta method for the error correction not only saves the computational cost that the error correction method requires but also gives the same convergence order as the error correction method does. Numerical evidence is provided to support the theoretical results.

• Transactions of the Korean Society of Automotive Engineers
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• v.25 no.2
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• pp.133-139
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• 2017

The timing chain system, which is a typical power transmission technology applied to a vehicle, has been widely used by the automotive industry because it is normally designed to last a car's lifetime. However, the timing chain system may cause some problems due to the shape of the chains and the polygonal behavior on contact between the chain and the sprocket. In addition, noise and vibration caused by transmission error are the most typical problems encountered by major automotive manufacturers and they are considered as the main source of customer complaint. The initial tension of the chain-sprocket system is thought to be the main cause of transmission error, and it is regarded as the source of engine vibration and noise. The initial tension of the chain system should be controlled carefully since a low initial tension can cause twisting, which may lead to a system malfunction, while a high initial tension can reduce the service life due to a worn down contact surface. In this paper, the kinematic analysis model is generated with various initial tensions, which are controlled by changing the shape of the fixed guide with the largest contact surface with chain. The results showed that the transmission error was minimized on a particular range of initial tension, and the tendency showed that the error changed with a higher sensitivity at a lower initial tension.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.311-327
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• 2016

In this paper, we propose an error embedded Runge-Kutta method to improve the traditional embedded Runge-Kutta method. The proposed scheme can be applied into most explicit embedded Runge-Kutta methods. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, the van der Pol equation and another one having a difficulty for the global error control are numerically solved. Finally, a two-body Kepler problem is also used to assess the efficiency of the proposed algorithm.

• The Transactions of the Korean Institute of Power Electronics
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• v.27 no.6
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• pp.481-488
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• 2022

This study proposes compensation methods for the initial position error and torque ripple in vector control of two-phase hybrid stepping motors. Stepping motors have an asymmetrical structure due to misalignment, such as the eccentricity generated by the manufacturing and assembly process. When vector control is applied using the position information measured by an incremental encoder attached to the rotor shaft of such stepping motors, the following problems occur. First, an initial position error occurs during the forced excitation process for the initial rotor position alignment. Second, torque ripple corresponding to the mechanical rotation frequency is generated. In this study, these non-ideal phenomena that occur in vector control of the stepping motor are analyzed, and compensation methods are proposed to eliminate them. The validity of the proposed initial position error and torque ripple compensation methods is verified through experiments on a two-phase hybrid stepping motor drive system.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1996.10a
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• pp.158-162
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• 1996

A split shaft device is commonly used to measure the radial force of lip seals. The radial force measured with this device includes some inevitable error. This error is caused by the fact that the split shafts cannot maintain a perfect circle when the interference becomes larger or smaller than some initial interference. In this study, a theoretical model for the calculation of the radial contact force has been carried out, and an explicit equation for the measurement error as a function of the initial interference and the interference to be measured has been obtained. The error when the interference is small is not dependent upon the material properties and the shape of the lip seal, but rather upon the amplitude of the initial interference and the interference to be measured. When the interference is larger or smaller than the initial interference, the measured contact force is always underestimated or overestimated.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.28 no.1
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• pp.33-58
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• 2024

This paper reviews basic concepts for Physics-Informed Neural Networks (PINN) applied to the initial value problems for ordinary differential equations. In particular, using only basic calculus, we derive the error estimates where the error functions (the differences between the true solution and the approximations expressed by neural networks) are dominated by training loss functions. Numerical experiments are conducted to validate our error estimates, visualizing the relationship between the error and the training loss for various first-order differential equations and a second-order linear equation.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.335-338
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• 1996

In this paper, we are going to design an iterative learning controller with the robust properties for initial error. For this purpose, the PID-type learning law will be considered and the design guide-line will be presented for the selection of the learning gain. Also, we are going to suggest a condition for the convergence of control input for a plant with input delay. Several simulation results are presented, which shows the effectiveness of the proposed algorithms.