• Journal of Power Electronics
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• v.19 no.3
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• pp.655-664
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• 2019

In order to analyze the nonlinear phenomena of the bifurcation and chaos caused by the switching of nonlinear switching devices in inductively coupled power transfer (ICPT) systems, a Jacobian matrix model, based on discrete mapping numerical modeling, is established to judge the system stability of the periodic closed orbit and to study the nonlinear behavior of Hopf bifurcation in a system under full resonance. The general flow of the parameter design, based on the stability principle for ICPT systems, is proposed to avoid the chaos and bifurcation phenomena caused by unreasonable parameter selection. Firstly, based on the state equation of SS-type compensation, a three-dimensional bifurcation diagram with the coupling coefficient as the bifurcation parameter is established with a numerical simulation to observe the nonlinear phenomena in the system. Then Filippov's method based on a Jacobian matrix model is adopted to deduce the boundary of stable operation and to judge the type of the bifurcation in the system. Then the general flow of the parameter design based on the stability principle for ICPT systems is proposed through the above analysis to realize stable operation under the conditions of weak coupling. Finally, an experimental platform is built to confirm the correctness of the numerical simulation and modeling.

• Journal of the Korean Society of Industry Convergence
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• v.18 no.2
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• pp.67-74
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• 2015

Two-wheeled driying mobild robots are precise controlled in terms of linear contol methods without considering the nonlinear dynamical characteristics. However, in the high maneuvering situations such as fast turn and abrupt start and stop, such neglected terms become dominant and heavy influence the overall driving performance. This study describes the nonlinear optimal control method to take advantage of the exact nonlinear dynamics of the balancing robot. Simulation results indicate that the optimal control outperforms in the respect of transient performance and required wheel torques. A design example is suggested for the state matrix that provides design flexibility in the control. It is shown that a well-planned state matrix by reflecting the physics of a balancing robot greatly conrtibutes to the driving performance and stability.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.5
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• pp.533-536
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• 2014

In this paper, a near optimal decentralized observer-controller design method is proposed for ramp metering systems based on SDRE (State Dependent Riccati Equation) approach. The optimal nonlinear observer gain is parameterized in terms of the solution matrix of an SDRE. This paper gives a simple algorithm to compute the near optimal observer gain. The optimal control design problem is also considered. Finally, numerical simulation results are given to illuminate the effectiveness and practicality of the proposed design method.

• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.3
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• pp.1-8
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• 1987

In this paper, the localized finite element method(LFEM) is applied to 3-dimensional ship motion problems in water of infinite depth. The LFEM used here is based on the functional constructed by Bai & Yeung(1974). To test the present numerical scheme, a few vertical axisymmetric bodies are treated by general 3-dimensional formulation. The computed results of hydrodynamic coefficients for a few vertical spheroids and vertical circular cylinders show good agreement with results obtained by others. The advantages of the present numerical method compared with the method of integral equation are as follows; (i) The cumbersome existence of irregular frequencies in the method of conventional integral equation is removed. (ii) The final matrix is banded and symmetric and the computation of the matrix elements is comparatively easier, whereas the size of the matrix in the present scheme is much larger. (iii) In the future research, it is possible to accommodate with the nonlinear exact free surface boundary condition in the localized finite element subdomain, whereas the linear solution is assumed in the truncated(far field) subdomain.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1529-1540
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• 2018

The matrix equation $X^p+A^*XA=Q$ has been studied to find the positive definite solution in several researches. In this paper, we consider fixed-point iteration and Newton's method for finding the matrix p-th root. From these two considerations, we will use the Newton-Schulz algorithm (N.S.A). We will show the residual relation and the local convergence of the fixed-point iteration. The local convergence guarantees the convergence of N.S.A. We also show numerical experiments and easily check that the N.S. algorithm reduce the CPU-time significantly.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.303-306
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• 2003

In radar tracking, since the sensor measures range, azimuth and elevation angle of a target, the measurement equation is nonlinear and the extended Kalman filter (EKF) is applied to nonlinear estimation. The conventional EKF has been widely used as a nonlinear filter for radar tracking, but the considerably large measurement error due to the linearization of nonlinear function in highly nonlinear situations may deteriorate the performance of the EKF To solve this problem, a fuzzy-model-based Kalman filter (FMBKF) is proposed for radar tracking. The FMBKF uses a local model approximation based on a TS fuzzy model instead of a Jacobian matrix to linearize nonlinear measurement equation. The hybrid GA and RLS method is used to identify the premise and the consequent parameters and the rule numbers of this TS fuzzy model. In two-dimensional radar tracking problem, the proposed method is compared with the conventional EKF.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.5
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• pp.561-566
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• 1998

This paper presents an algebraic approach to optimal control for time invariant continuous system using STWS(single term Walsh series). In optimal control, it is well known that the design problem with quadratic performance criteria often involves the determination of time-varying feedback gain matrix by solving the matrix nonlinear Riccati equation and of command signal by solving the integral equation, which makes design procedure quite difficult. Therefore, in order to resolve this problem, this paper is introduced to STWS. In this paper, the time-varying feedback gains and command signals are determined by piecewise constant gains which can be easily obtained from algebraic equation using STWS.

• Proceedings of the KIEE Conference
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• 2007.04a
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• pp.89-91
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• 2007

In this paper, a new approach for a sampled-data representation of nonlinear system that has time-delayed multi-input is proposed. That is largely devoid of illconditioning and is suitable for any nonlinear problem. The new scheme is applied to nonlinear systems with two or three inputs; and then the delayed multi-input general equation is derived. The method is based on thematrix exponential theory. Itdoes not require excessive computational resources and lends itself to a short and robust piece of software that can be easily inserted into large simulation packages. A performance of the proposed method is evaluated using a nonlinear system with time-delay: maneuvering an automobile.

• Structural Engineering and Mechanics
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• v.45 no.1
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• pp.95-110
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• 2013

In the recent decade, practical of wavelet technique is being utilized in various domain of science. Particularly, engineers are interested to the wavelet solution method in the time series analysis. Fundamentally, seismic responses of structures against time history loading such as an earthquake, illustrates optimum capability of systems. In this paper, a procedure using particularly discrete Haar wavelet basis functions is introduced, to solve dynamic equation of motion. In the proposed approach, a straightforward formulation in a fluent manner is derived from the approximation of the displacements. For this purpose, Haar operational matrix is derived and applied in the dynamic analysis. It's free-scaled matrix converts differential equation of motion to the algebraic equations. It is shown that accuracy of dynamic responses relies on, access of load in the first step, before piecewise analysis added to the technique of equation solver in the last step for large scale of wavelet. To demonstrate the effectiveness of this scheme, improved formulations are extended to the linear and nonlinear structural dynamic analysis. The validity and effectiveness of the developed method is verified with three examples. The results were compared with those from the numerical methods such as Duhamel integration, Runge-Kutta and Wilson-${\theta}$ method.

• Structural Engineering and Mechanics
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• v.4 no.2
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• pp.139-148
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• 1996

Vector algorithms and the relative importance of the four basic modules (computation of element stiffness matrices, assembly of the global stiffness matrix, solution of the system of linear simultaneous equations, and calculation of stresses and strains) of a finite element computer program for inelastic analysis of reinforced concrete shells are presented. Performance of the vector program is compared with a scalar program. For a cooling tower problem, the speedup factor from the scalar to the vector program is 34 for the element stiffness matrices calculation, 25.3 for the assembly of global stiffness matrix, 27.5 for the equation solver, and 37.8 for stresses, strains and nodal forces computations on a Gray Y-MP. The overall speedup factor is 30.9. When the equation solver alone is vectorized, which is computationally the most intensive part of a finite element program, a speedup factor of only 1.9 is achieved. When the rest of the program is also vectorized, a large additional speedup factor of 15.9 is attained. Therefore, it is very important that all the modules in a nonlinear program are vectorized to gain the full potential of the supercomputers. The vector finite element computer program for inelastic analysis of RC shells with layered elements developed in the present study enabled us to perform mesh convergence studies. The vector program can be used for studying the ultimate behavior of RC shells and used as a design tool.