• Journal of Power Electronics
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• v.9 no.2
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• pp.188-197
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• 2009

This paper presents an adaptive flux observer to estimate stator flux linkage and stator inductances of an interior permanent-magnet synchronous machine considering magnetic saturation. The concept of static and dynamic inductances due to saturation is introduced in the machine model to describe the relationship between current and flux linkage and the relationship between their time derivatives. A flux observer designed in the stationary reference frame with constant inductance is analyzed in the rotor reference frame by a frequency-response characteristic. An adaptive algorithm for an on-line inductance estimation is proposed and a Lyapunov-based analysis is given to discuss its stability. The dynamic inductances are estimated by using Taylor approximation based on the static inductances estimated by the adaptive method. The simulation and experimental results show the feasibility and performance of the proposed technique.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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• pp.317-335
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• 2014

In this work, we investigate the global stability analysis of a viral infection model with antibody immune response. The incidence rate is given by a general function of the populations of the uninfected target cells, infected cells and free viruses. The model has been incorporated with two types of intracellular distributed time delays to describe the time required for viral contacting an uninfected cell and releasing new infectious viruses. We have established a set of conditions on the general incidence rate function and determined two threshold parameters $R_0$ (the basic infection reproduction number) and $R_1$ (the antibody immune response activation number) which are sufficient to determine the global dynamics of the model. The global asymptotic stability of the equilibria of the model has been proven by using Lyapunov theory and applying LaSalle's invariance principle.

• International Journal of Control, Automation, and Systems
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• v.6 no.2
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• pp.263-268
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• 2008

An improved linear matrix inequality (LMI) representation of delay-independent $H_2$ performance analysis is introduced for linear delay systems with delays of any size. Based on this representation we propose a new $H_2$ memoryless state feedback design. By introducing a new matrix variable, the new LMI formulation enables us to parameterize memoryles s controllers without involving the Lyapunov variables in the formulations. By using a parameter-dependent Lyapunov function, this new representation proposed here provides us the results with less conservatism.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2525-2527
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• 2000

The analysis of distribution line faults is essential to the proper protection of power system. A high impedance fault(HIF) dose not make enough current to cause conventional protective device operating, so it is well known that undesirable operating conditions and certain types of faults on electric distribution feeders cannot be detected by using conventional protection system. In this paper, we prove that the nature of the high impedance faults is indeed a deterministic chaos, not a random motion. Algorithms for estimating Lyapunov spectrum and the largest Lyapunov exponent are applied to various fault currents detections in order to evaluate the orbital instability peculiar to deterministic chaos dynamically, and fractal dimensions of fault currents which represent geometrical self-similarity are calculated. Wavelet transform analysis is applied the time-scale information to fault signal. Time-scale representation of high impedance faults can detect easily and localize correctly the fault waveform.

• Journal of Mechanical Science and Technology
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• v.18 no.7
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• pp.1246-1257
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• 2004

The objective of this paper is to characterize dynamic pressure traces measured at self-excited combustion instabilities occurring in two combustion systems of different hardware. One system is a model lean premixed gas turbine combustor and the other a fullscale bipropellant liquid rocket thrust chamber. It is commonly observed in both systems that low frequency waves at around 300㎐ are first excited at the onset of combustion instabilities and after a short duration, the instability mode becomes coupled to the resonant acoustic modes of the combustion chamber, the first longitudinal mode for the lean premixed combustor and the first tangential mode for the rocket thrust chamber. Low frequency waves seem to get excited at first since flame shows the higher heat release response on the lower frequency perturbations with the smaller phase differences between heat release and pressure fluctuations. Nonlinear time series analysis of pressure traces reveals that even stable combustion might have chaotic behavior with the positive maximum Lyapunov exponent. Also, pressure fluctuations under combustion instabilities reach a limit cycle or quasi-periodic oscillations at the very similar run conditions, which manifest that a self-excited high frequency instability has strong nonlinear characteristics.

• Proceedings of the KOSOMBE Conference
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• v.1996 no.11
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• pp.258-262
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• 1996

The physiological systems have nonlinear complex phenomena. Expecially, the flow of capillary blood vessel has a nonlinear dynamic system. Thus, this study analyzes nonlinear characteristics of the flow of capillary blood vessel in physiological systems using chaotic tools(phase space reconstruction, correlation dimension, largest lyapunov exponent). Experimental data have been acquired from examining 10 rabbits. The results of chaotic analysis showed a decreasing largest lyapunov exponent and correlation dimension according to increasement glocose index. And we also know the chaotic behavior.

• Journal of the Korea Institute of Military Science and Technology
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• v.20 no.1
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• pp.108-118
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• 2017

In this paper, the path tracking controller for a surface vessel based on the sliding mode control (SMC) with the switching law is proposed. In order to have no restriction on movement and improved tracking performance, the proposed control system is developed as follows: First, the kinematic and dynamic models in Cartesian coordinates are considered to solve the singularity problem at the origin. Second, the new multiple sliding surfaces are designed with the SMC and approach angle concept to solve the under-actuated property. Third, the switching control system is designed to improve tracking performance. To prove the stability of the proposed switching system under the arbitrary switching, the Lyapunov stability analysis method with the common Lyapunov function is used. Finally, the computer simulations are performed to demonstrate the performance, effectiveness and stability of the proposed tracking controller of a surface vessel.

• Journal of Navigation and Port Research
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• v.31 no.6
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• pp.523-530
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• 2007

Crane systems are very important in industrial fields to carry heavy objects such that many investigations about control of the systems are actively conducted for enhancing its control performance. This paper presents an adaptive control approach using the model matching for a complex 3-DOF nonlinear crane system. First, the system model is linearized through feedback linearization method and then PD control is applied in the approximated model. This linear model is considered as nominal to derive corrective control law for a perturbed crane model using Lyapunov theory. This corrective control is primitively aimed to compensate real-time control deviation due to partially known perturbation. We additionally study stability analysis of the crane control system using Lyapunov perturbation theory. Evaluation of our control approach is numerically carried out through computer simulation and its superiority is demonstrated comparing with the classical control.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.10
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• pp.130-136
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• 2008

The purpose of this study was to investigate chaotic characteristics of major joint motions during treadmill walking. Gait experiments were carried out for 20 healthy young women. The subjects were asked to walk on a treadmill at their own natural speeds. The chaos analysis was used to quantify nonlinear motions of eleven major joints of each woman. The joints analyzed included the neck and the right and left shoulders, elbows, hips, knees and ankles. The recorded gait patterns were digitized and then coordinated by motion analysis software. Lyapunov exponent for every joint was calculated to evaluate joint characteristics from a state space created by time series and its embedding dimension. This study shows that differences in joint motion were statistically significant.

• Smart Structures and Systems
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• v.29 no.3
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• pp.485-498
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• 2022

In near-fault earthquake prone areas, the velocity pulse-like seismic waves often results in excessive horizontal displacement for structures, which may result in severe structural failure during large or near-fault earthquakes. The recently developed isolator-gap damper (IGD) systems provide a solution for the large horizontal displacement of long period base-isolated structures. However, the hysteresis characteristics of the IGD system are significantly different from the traditional hysteretic behavior. At present, the hysteretic behavior is difficult to be reflected in the structural analysis and performance evaluation especially under random earthquake excitations for lacking of effective analysis models which prevent the application of this kind of IGD system. In this paper, we propose a mathematical hysteretic model for the IGD system that presents its nonlinear hysteretic characteristics. The equivalent linearization is conducted on this nonlinear model, which requires the variances of the IGD responses. The covariance matrix for the responses of the structure and the IGD system is obtained for random earthquake excitations represented by the Kanai-Tajimi spectrum by solving the Lyapunov equation. The responses obtained by the equivalent linearization are verified in comparison with the nonlinear responses by the Monte Carlo simulation (MCS) analysis for random earthquake excitations.