• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.4
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• pp.53-61
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• 1998

This paper describes the stability analysis of TSK (Takagi-Sugeno-Kang) fuzzy systems which can represent a large class of nonlinear systems with good accuracy. A TSK fuzzy model consists of TSK fuzzy rules and the consequent of each fuzzy rule is a linear input-output equation with a constant term. There may exist equilibrium points more than one in the TSK fuzzy model and each equilibrium point rnay also have different nature of stability. The local stability of an equilibrium point is determined by eigenvalues of the Jacobian matrix of the linearized TSK fuzzy model around the equilibrium point. Stability of both the continuous-time and the discrete-time systems is analyzed in this paper.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1583-1602
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• 2011

A special system of partial differential equations (PDEs) occur in a natural way while studying a class of irrotational inviscid fluid flow problems involving infinite channels. Certain aspects of solutions of such PDEs are analyzed in the context of flow problems involving multiple layers of fluids of different constant densities in a channel associated with arbitrary bottom topography. The whole analysis is divided into two parts-part A and part B. In part A the linearized theory is employed along with the standard Fourier analysis to understand such flow problems and physical quantities of interest are derived analytically. In part B, the same set of problems handled in part A are examined in the light of a weakly non-linear theory involving perturbation in terms of a small parameter and it is shown that the original problems can be cast into KdV type of nonlinear PDEs involving the bottom topography occurring in one of the coefficients of these equations. Special cases of bottom topography are worked out in detail and expressions for quantities of physical importance are derived.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.26 no.1
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• pp.144-149
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• 2017

There have been lots of interest on service and entertainment robots. To ensure that robots work in harmony with humans, their stability and compactness are some of the key issues. Obviously, robots with fewer wheels occupy a smaller floor area compared to those with more wheels. In addition, robots with fewer wheels, whose posture stabilities are maintained by feedback control, are stable even under larger accelerations and/or higher locations of the center of mass. To facilitate controller design, it is assumed that both pitch and roll dynamics are decoupled. The dynamic equations of motion for the proposed robot are derived from the Euler-Lagrange equation. To obtain the optimal balancing control law, linear quadratic regulator control methods are applied to the linearized dynamic equations. Simulation and experimental results verify the effectiveness and performance of the proposed balancing control algorithm for a single-wheeled mobile robot.

• Journal of Mechanical Science and Technology
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• v.20 no.12
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• pp.2105-2114
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• 2006

In this paper, a simplified model is studied to predict analytically the vibration from the helical gear system due to an axial excitation of helical gears. The simplified model describes gear, shaft, bearing, and housing. In order to obtain the axial force of helical gears, the mesh stiffness is calculated in the load deflection relation. The axial force is obtained from the solution of the equation of motion, using the mesh stiffness. It is used as a longitudinal excitation of the shaft, which in turn drives the gear housing through the bearing. In this study, the shaft is modeled as a rod, while the bearing is modeled as a parallel spring and damper only supporting longitudinal forces. The gear housing is modeled as a clamped circular plate with viscous damping. For the modeling of this system, transfer matrices for the rod and bearing are used, using a spectral method with four pole parameters. The model is validated by finite element analysis. Using the model, parameter studies are carried out. As a result, the linearized dynamic shaft force due to the gear excitation in the frequency domain was proposed. Out-of-plan displacement from the forced vibrating circular plate and the renewed mode normalization constant of the circular plate were also proposed. In order to control the axial vibration of the helical gear system, the plate was more important than the shaft and the bearing. Finally, the effect of the dominant design parameters for the gear system can be investigated by this model.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.12
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• pp.128-141
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• 1998

We propose the robust nonlinear controller design methodology for the multivariable system which has hard nonlinearities (Coulomb friction, dead-zone, etc) and the structured real parameter uncertainty. The hard nonlinearity can be linearized by the RIDF technique and structured real parameter uncertainty can be modelled as the sense of Peterson-Hollot's quadratic Lyapunov bound. For this system, we apply the robust QLQG/H$_{\infty}$ control and then can obtain four Riccati equations. Because of the system's nonlinearity, however, one Riccati equation contains the nonlinear correction term that is very difficult to solve numerically, In order to treat this problem, using some transformations to Riccati equations, the nonlinear correction term can be eliminated. Then, only two Riccati equations need to design a controller. Finally, the robust nonlinear controller is synthesized via IRIDF techniques. To test this proposed control method, we consider the direct-drive robot manipulator system that has Coulomb frictions and varying inertia.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.11
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• pp.1860-1867
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• 2016

In this paper, first, a linearized modeling of a phase shift full-bridge converter used in chargers of electric vehicles is derived by using state-space approach and transfer functions from the duty ratio to output voltage and the inductor current are also verified. second, control systems for the output voltage and the inductor current are designed using the root locus technique. It is illustrated by experimental results that the control performance on the output variables is satisfied with the designed digital control system based on a automobile qualified 32-bit microcontroller.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.265-270
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• 2005

This paper presents a new attitude stabilization and control of an unmanned helicopter based on neural network compensation. A systematic derivation on the dynamics of an unmanned small-scale helicopter is performed. Combined rotor-fuselage-tail dynamics is derived in body-fixed reference frame with its origin at the C.G. of the helicopter. And the resulting nonlinear equation of motion consists of 6-DOF air vehicle dynamics as well as the rotor flapping and engine torque equations. A simulation model was modified using the existing simulator for an unmanned helicopter dynamic model, which reflects the unmanned test helicopter(CNUHELI). The dynamic response of the refined model was compared with the flight test data. It can be shown that a good coincidence was accomplished between the real unmanned helicopter system and the mathematical model. This dynamic model was linearized for classical controller design using small perturbation method. A Neuro-PD control system was designed for both longitudinal and lateral flight modes, and the results were compared with the PD-only control response. Simulation results show that the proposed Neuro-PD control system demonstrates better performance.

• Journal of the Korean earth science society
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• v.38 no.3
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• pp.173-181
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• 2017

The stability of the steady Rossby-Haurwitz wave (R-H wave) in the nondivergent barotropic model (NBM) on the sphere was investigated with the normal mode method. The linearized NBM equation with respect to the R-H wave was formulated into the eigenvalue-eigenvector problem consisting of the huge sparse matrix by expanding the variables with the spherical harmonic functions. It was shown that the definite threshold R-H wave amplitude for instability could be obtained by the normal mode method. It was revealed that some unstable modes were stationary, which tend to amplify without the time change of the spatial structure. The maximum growth rate of the most unstable mode turned out to be in almost linear proportion to the R-H wave amplitude. As a whole, the growth rate of the unstable mode was found to increase with the zonal- and total-wavenumber. The most unstable mode turned out to consist of more-than-one zonal wavenumber, and in some cases, the mode exhibited a discontinuity over the local domain of weak or vanishing flow. The normal mode method developed here could be readily extended to the basic state comprised of multiple zonalwavenumber components as far as the same total wavenumber is given.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.10
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• pp.34-43
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• 1990

An improved parameter adaptation and control law for robot manipulator are proposed based on a linearized parametric system equation and augmented error vectors. In view of the modeling error and parasitics with small time constants which inevitably introduced during modelling process, their effects on the robustness of the system performance are reviewed and as an conutermearsure, adaptation mechanism with low pass filter is proposed. Proposed parameter adaptation and control low assure the stability of the robot manipulator in the large without further assumption. Computer simulation shows its effectiveness of the proposed adaptation mechanism to improve the robustness of the system in presence of the parasitics in the system and superior performance for high speed operations make it an attractive option in application of the adaptive control field for robot manipulator.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2647-2655
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• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness i n a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time -varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i=1,2,3..).