• Journal of Power System Engineering
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• v.2 no.2
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• pp.55-59
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• 1998

In practice, the property of nonlinearity is contained in all physical systems. In other word, all physical systems are nonlinear to some degree. Therefore it is important that we acquires a facility for analyzing feedback control systems with varying degrees of nonlinearity. To operate the system linearly over wide range of variation of signal amplitude and frequency, the system requires components of an extremely high quality. Such a system would probably be impractical in the view points of cost, space and weight. In this context of view, it is worth noting that the nonlinearities may be intentionally introduced into a system in order to compensate for the effects of other undesirable nonlinearities or to obtain better performance than what could be achieved using linear element only. A simple example of an intentional nonlinearity is the use of a nonlinear damped system to optimize response in accordance with the magnitude of error. In this paper, an on-off type nonlinear controller is introduced and the applicability and validity of a simple on-off controller are presented by the experimental result.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1433-1451
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• 2014

In this paper we study the existence of multiple periodic solutions of second-order ordinary differential equations. New results of multiplicity of periodic solutions are obtained when the nonlinearity may cross multiple consecutive eigenvalues. The arguments are proceeded by a combination of variational and degree theoretic methods.

• Journal of Electrical Engineering and Technology
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• v.12 no.4
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• pp.1649-1656
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• 2017

This paper addresses the control problem of a laboratory-level 2 degree-of-freedom helicopter. The exact fuzzy model in a Takagi - Sugeno form is constructed by the sector nonlinearity technique, and is then represented as a set of uncertain linear systems. Output-tracking controller is designed in terms of linear matrix inequalities and the closed-loop stability is rigorously analyzed. Experimental evaluation shows that the proposed method is of benefit to many real industrial plants.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.233-242
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• 2011

We get a theorem that there exist at least two solutions for the piecewise linear suspension bridge equation with variable coefficient jumping nonlinearity and Dirichlet boundary condition when the variable coefficient of the nonlinear term crosses first two successive negative eigenvalues. We obtain this multiplicity result by applying Leray-Schauder degree theory.

• East Asian mathematical journal
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• v.35 no.1
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• pp.41-50
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• 2019

This paper is dealt with one-dimensional elliptic jumping problem with nonlinearities crossing n eigenvalues. We get one theorem which shows multiplicity results for solutions of one-dimensional elliptic boundary value problem with jumping nonlinearities. This theorem is that there exist at least two solutions when nonlinearities crossing odd eigenvalues, at least three solutions when nonlinearities crossing even eigenvalues, exactly one solutions and no solution depending on the source term. We obtain these results by the eigenvalues and the corresponding normalized eigenfunctions of the elliptic eigenvalue problem and Leray-Schauder degree theory.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.145-149
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• 1987

The input-output relation for nonlinear systems can be explicitly represented by the Voltera functional series and it is characterized by the Volterra Kernels. A block diagram reduction method is introduced to determine the Volterra Kernels for the nonlinear systems represented by nonlinear differential equations. Degree of nonlinearity is defined and analyzed for the analysis of nonlinear systems.

• Steel and Composite Structures
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• v.48 no.6
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• pp.693-708
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• 2023

Composite beams, two materials joined together, have become more common in structural engineering over the past few decades because they have better mechanical and structural properties. The shear connectors between their layers exhibit some deformability with finite stiffness, resulting in interfacial shear slip, a phenomenon known as partial shear interaction. Such a partial shear interaction contributes significantly to the composite beams. To provide precise predictions of the geometric nonlinear behavior shown by two-layered composite beams with interfacial shear slips, a robust analytical model has been developed that incorporates the influence of significant displacements. The application of a higher-order beam theory to the two material layers results in a third-order adjustment of the longitudinal displacement within each layer along the depth of the beam. Deformable shear connectors are employed at the interface to represent the partial shear interaction by means of a sequence of shear connectors that are evenly distributed throughout the beam's length. The Von-Karman theory of large deflection incorporates geometric nonlinearity into the governing equations, which are then solved analytically using the Navier solution technique. Suggested model exhibits a notable level of agreement with published findings, and numerical outputs derived from finite element (FE) model. Large displacement substantially reduces deflection, interfacial shear slip, and stress values. Geometric nonlinearity has a significant impact on beams with larger span-to-depth ratio and a greater degree of shear connector deformability. Potentially, the analytical model can accurately predict the geometric nonlinear responses of composite beams. The model has a high degree of generality, which might aid in the numerical solution of composite beams with varying configurations and shear criteria.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.7 no.1
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• pp.116-125
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• 1995

Higher order nonlinear transfer functions are applied to model the nonlinear responses obtained Inn dynamic analysis of single degree of freedom systems (SDOF) subjected to wave and current loadings. The structural systems are subjected to single harmonic, two wave combination and irregular wave loading. Three different sources of nonlinearities are examined for each of the wave loading condition and it is shown that the nonlinear response appear at the resonance frequencies of the SDOF even when virtually no wave energy exists at those resonance frequencies. Higher order nonlinear transfer functions based on Volterra series representation are used to model the nonlinear responses mainly f3r the flexible systems and clearly shows the degrees of nonlinearity either as quadratic or cubic.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.3
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• pp.267-272
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• 2012

This paper propose the implementation of robust fuzzy controller for controlling an active magnetic bearing (AMB) system with 6 degree of freedom (DOF). A basic model with 6 DOF rotor dynamics and electromagnetic force equations for conical magnetic bearings is proposed. The developed model has severe nonlinearity and uncertainty so that it is not easy to obtain the control objective. For solving this problem, we use the Takagi-Sugeno (T-S) fuzzy model which is suitable for designing fuzzy controller. The control object in the AMB system enables the rotor to rotate without any phsical contact by using magnetic force. In this paper, we analyze the nonlinearity of the active magnetic bearing system by using fuzzy control algorithm and desing the robust control algorithm for solving the parameter variation. Simulation results for AMB are demonstrated to visualize the feasibility of the proposed method.

• Smart Structures and Systems
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• v.18 no.1
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• pp.1-16
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• 2016

Model Order Reduction (MOR) denotes the theory by which one tries to catch a model of order lower than that of the real model. This is conveniently pursued in view of the design of an efficient structural control scheme, just passive within this paper. When the nonlinear response of the reference structural system affects the nature of the reduced model, making it dependent on the visited subset of the input-output space, standard MOR techniques do not apply. The mathematical theory offers some specific alternatives, which however involve a degree of sophistication unjustified in the presence of a few localized nonlinearities. This paper suggests applying standard MOR to the linear parts of the structural system, the interface remaining the original unreduced nonlinear components. A case study focused on the effects of a helicopter land crash is used to exemplify the proposal.