• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1181-1199
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• 2023

For solving complex symmetric positive definite linear systems, we propose a single step real-valued (SSR) iterative method, which does not involve the complex arithmetic. The upper bound on the spectral radius of the iteration matrix of the SSR method is given and its convergence properties are analyzed. In addition, the quasi-optimal parameter which minimizes the upper bound for the spectral radius of the proposed method is computed. Finally, numerical experiments are given to demonstrate the effectiveness and robustness of the propose methods.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.9
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• pp.897-901
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• 2011

This paper presents a TS (Takagi-Sugeno) type FLC (Fuzzy Logic Controller) with only 3 rules. The choice of parameters of FLC is very difficult job on design FLC controller. Therefore, the choice of appropriate linguistic variable is an important part of the design of fuzzy controller. However, since fuzzy controller is nonlinear, it is difficult to analyze mathematically the affection of the linguistic variable. So this choice is depend on the expert's experience and trial and error method. In the design of the system, we use a variety of response characteristics like stability, rising time, overshoot, settling time, steady-state error. In particular, it is important for a stable system design to predict the steady-state error because the system's steady-state response of the system is related to the overall quality. In this paper, we propose the method to choose the consequence linear equation's parameter of T-S type FLC in the view of steady-state error. The parameters of consequence linear equations of FLC are tuned according to the system error that is the input of FLC. The full equation of T-S type FLC is presented and using this equation, the relation between output and parameters can represented. As well as the FLC parameters of consequence linear equations affect the stability of the system, it also affects the steady-state error. In this study, The system according to the parameter of consequence linear equations of FLC predict the steady-state error and the method to remove the system's steady-state error is proposed using the prediction error value. The simulation is carried out to determine the usefulness of the proposed method.

• Structural Engineering and Mechanics
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• v.33 no.1
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• pp.15-30
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• 2009

In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained by using Hamilton's principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Natural frequencies are calculated for different boundary conditions, stepped ratios and stepped locations by Newton-Raphson Method. The corresponding nonlinear correction coefficients are also calculated for the fundamental mode. At the second part, an alternative method is produced for the analysis. The calculated natural frequencies and nonlinear corrections are used for training an artificial neural network (ANN) program which has a multi-layer, feed-forward, back-propagation algorithm. The results of the algorithm produce errors less than 2.5% for linear case and 10.12% for nonlinear case. The errors are much lower for most cases except clamped-clamped end condition. By employing the ANN algorithm, the natural frequencies and nonlinear corrections are easily calculated by little errors, and the computational time is drastically reduced compared with the conventional numerical techniques.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.392-398
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• 1998

In order to check the validity of nonlinear normal modes of continuous, systems by means of the energy-based formulation, we consider a beam with a nonlinear boundary condition. The initial and boundary e c6nsl of a linear partial differential equation and a nonlinear boundary condition is reduced to a linear boundary value problem consisting of an 8th order ordinary differential equations and linear boundary conditions. After obtaining the asymptotic solution corresponding to each normal mode, we compare this with numerical results by the finite element method.

• 전기의세계
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• v.20 no.4
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• pp.12-16
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• 1971

The electrical detector and computer systems for traffic flow and speed measurement are demonstrated in this paper. For the best traffic control optimization, linear and non-linear equations in the transition state are dealing with the perturbation of the linear car-following. In the conclusions, we construct a realizable system for the central automatic traffic control with a computer. Furthermore, fixed periodic switching system by manual with the automatic traffic control system is recommended for emergency perturbation.

• Biomaterials and Biomechanics in Bioengineering
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• v.2 no.4
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• pp.207-223
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• 2015

In this paper a method for simultaneous swift non-linear analysis and optimal design/posture of mechanical/biomechanical systems is presented. The method is developed to get advantages of iterations in non-linear analysis and/or generations in genetic algorithm (GA) for the purpose of efficient analysis within the optimal design/posture. The method is applicable for both size and geometry optimizations wherein material and geometry non-linearity are present. In addition to established mechanical systems, the method can solve biomechanical models of human musculoskeletal system. Optimization-based procedures are popular methods for resolving the redundancy at joints wherein the number of unknown muscle forces is far more than the number of equilibrium equations. These procedures involve optimization of a cost function(s) which is assumed to be consistent with the central nervous system's strategy when activating muscles to assure equilibrium. However, because of the complexity of biomechanical problems (i.e., due to non-linear biomaterial, large deformation, redundancy of the problem and so on) efficient analysis are required within optimization procedures as suggested in this paper.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.5
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• pp.497-504
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• 2006

This paper presents a new technique that derives the dynamic acceleration bounds of multiple cooperating robot systems from given individual torque limits of robots. A set of linear algebraic homogeneous equation is derived from the dynamic equations of multiple robots with friction contacts. The mobility of the robot system is analyzed by the decomposition of the null space of the linear algebraic equation. The acceleration bounds of multiple robot systems are obtained from the joint torque constraints of robots by the medium of the decomposed null space. As the joint constraints of the robots are given in the infinite norm sense, the resultant acceleration bounds of the systems are described as polytopes. Several case studies are presented to validate the proposed method in this paper.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.455-460
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• 2000

Impact occurs when the vibration amplitude of a mechanical component exceeds a given clearance size. Examples of these mechanical systems include impact dampers, gears, link mechanism, rotor rub, and so on. The vibration due to impact has strong non-linear characteristics, which cannot be predicted by usual linear analysis. The designs of mechanical systems with impacts should be done on the basis of overall dynamic characteristics of the systems. In this paper, the nonlinear behaviors of a beam with a periodically moving support and a rigid stop are investigated numerically and experimentally. The beam vibration with impact is modeled by the equations of motion containing piecewise linear restoring forces and by the coefficient of restitution, respectively. Experimental and numerical results show jump phenomena and higher-harmonic vibrations. The effects between the increase of stiffness during impact and the coefficient of restitution are investigated through the comparison of the experimental and numerical results.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.10
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• pp.977-982
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• 2008

In this paper Haar functions are developed to approximate the solutions of continuous time linear system. Properties of Haar functions are first presented, and an explicit expression for the inverse of the Haar operational matrix is presented. Using the inverse of the Haar operational matrix the full order Stein equation should be solved in terms of the solutions of pure algebraic matrix equations, which reduces the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity of the proposed algorithm.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.9
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• pp.806-811
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• 2012

In this paper Hartley functions are used to approximate the solutions of continuous time linear dynamical system. The Hartley function and its integral operational matrix are first presented, an efficient algorithm to solve the Stein equation is proposed. The algorithm is based on the compound matrix and the inverse of sum of matrices. Using the structure of the Hartley's integral operational matrix, the full order Stein equation should be solved in terms of the solutions of pure algebraic matrix equations, which reduces the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity of the proposed algorithm.