• Structural Engineering and Mechanics
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• v.61 no.1
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• pp.105-116
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• 2017

In this paper, the optimal extended homotopy analysis method (OEHAM) is introduced to deal with the damped Duffing resonator driven by a van der Pol oscillator, which can be described as a complex Multi-Degree-of-Freedom (MDOF) nonlinear coupling system. Ecumenically, the exact solutions of the MDOF nonlinear coupling systems are difficult to be obtained, thus the development of analytical approximation becomes an effective and meaningful approach to analyze these systems. Compared with traditional perturbation methods, HAM is more valid and available, and has been widely used for nonlinear problems in recent years. Hence, the method will be chosen to study the system in this article. In order to acquire more suitable solutions, we put forward HAM to the OEHAM. For the sake of verifying the accuracy of the above method, a series of comparisons are introduced between the results received by the OEHAM and the numerical integration method. The results in this article demonstrate that the OEHAM is an effective and robust technique for MDOF nonlinear coupling systems. Besides, the presented methods can also be broadly used for various strongly nonlinear MDOF dynamical systems.

• Journal of the Institute of Convergence Signal Processing
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• v.23 no.4
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• pp.185-193
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• 2022

This paper proposes an adaptive sliding mode control with radial basis function neural network(RBFNN) scheme to enhance the performance of position and attitude tracking control of quadrotor UAV. The RBFNN is utilized on the approximation of nonlinear function in the UAV dynmic model and the weights of the RBFNN are adjusted online according to adaptive law from the Lyapunov stability analysis to ensure the state hitting the sliding surface and sliding along it. In order to compensate the network approximation error and eliminate the existing chattering problems, the sliding mode control term is adjusted by adaptive laws, which can enhance the robust performance of the system. The simulation results of the proposed control method confirm the effectiveness of the proposed controller which applied for a nonlinear quadrotor UAV is presented. Form the results, it's shown that the developed control system is achieved satisfactory control performance and robustness.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.103-106
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• 1996

This paper presents an iterative fuzzy learning control scheme which is applicable to a broad class of nonlinear systems. The control scheme achieves system stability and boundedness by using the linear feedback plus adaptive fuzzy controller and achieves precise tracking by using the iterative learning rules. The switching mode control unit is added to the adaptive fuzzy controller in order to compensate for the error that has been inevitably introduced from the fuzzy approximation of the nonlinear part. It also obviates any supervisory control action in the adaptive fuzzy controller which normally requires high gain signal. The learning control algorithm obviates any output derivative terms which are vulnerable to noise.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.544-556
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• 1991

The optimization of many engineering design problems requires a nonlinear programming algorithm that is robust and efficient. A general-purpose nonlinear optimization program IDOL (Interactive Design Optimization Library) is developed based on the Augmented Lagrange Mulitiplier (ALM) method. The ideas of selecting a good initial design point, using resonable initial values for Lagrange multipliers, constraints scaling, descent vector restarting, and dynamic stopping criterion are employed for computational enhancement to the ALM method. A descent vector is determined by using the Broydon-Fletcher-Goldfarb-Shanno (BFGS) method. For line search, the Incremental-Search method is first used to find bounds on the solution, then the bounds are reduced by the Golden Section method, and finally a cubic polynomial approximation technique is applied to locate the next design point. Seven typical test problems are solved to show IDOL efficient and robust.

• The Journal of Korea Robotics Society
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• v.2 no.4
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• pp.327-333
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• 2007

We propose a navigation algorithm using image-based visual servoing utilizing a fixed camera. We define the mobile robot navigation problem as an unconstrained optimization problem to minimize the image error between the goal position and the position of a mobile robot. The residual function which is the image error between the position of a mobile robot and the goal position is generally large for this navigation problem. So, this navigation problem can be considered as the nonlinear least squares problem for the large residual case. For large residual, we propose a method to find the second-order term using the secant approximation method. The performance was evaluated using the simulation.

• Structural Engineering and Mechanics
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• v.44 no.2
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• pp.219-238
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• 2012

Objective of this paper is to compare linear buckling analysis formulations, available in commercial finite element programs. Modern steel design codes, including Eurocode 3, make abundant use of linear buckling loads for calculation of slenderness, and of linear buckling modes, used as shapes of imperfections for nonlinear analyses. Experience has shown that the buckling mode shapes and the magnitude of buckling loads may differ, sometimes significantly, from one algorithm to another. Thus, three characteristic examples have been used in order to assess the linear buckling formulations available in the finite element programs ADINA and ABAQUS. Useful conclusions are drawn for selecting the appropriate algorithm and the proper reference load in order to obtain either the classical linear buckling load or a good approximation of the actual geometrically nonlinear buckling load.

• Structural Engineering and Mechanics
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• v.26 no.5
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• pp.545-556
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• 2007

In this paper, a hybrid boundary element technique is implemented to analyze nonlinear transient pile soil interaction in Gibson type nonhomeogenous soil. Inelastic modeling of soil media is presented by introducing a rational approximation to the continuum with nonlinear interface springs along the piles. Modified $\ddot{O}$zdemir's nonlinear model is implemented and systems of equations are coupled at interfaces for piles and pile groups. Linear beam column finite elements are used to model the piles and the resulting governing equations are solved using an implicit integration scheme. By enforcing displacement equilibrium conditions at each time step, a system of equations is generated which yields the solution. A numerical example is performed to investigate the effects of nonlinearity on the pile soil interaction.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.631-644
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• 2008

In this paper, we present a new method for solving a nonlinear two-point boundary value problem with finitely many singularities. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximation $u_n(x)$ to the exact solution u(x) is obtained and is proved to converge to the exact solution. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other.

• International Journal of Control, Automation, and Systems
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• v.3 no.spc2
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• pp.270-277
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• 2005

In this paper, a decentralized control problem is considered for multimachine power systems with nonlinear interconnections and disturbances. A direct feedback linearization compensator is employed to cancel most of the nonlinearities, and then a backstepping procedure is applied to deal with the interconnections and to reduce the effects of a disturbance that does not satisfy the matching condition. In this procedure, the disturbance is handled by using a smooth approximation of the signum function. Practical stability is achieved under the assumption that the infinite norm of the disturbance is known. However, even in the case where the infinite norm of the disturbance is not known precisely, the proposed control system still guarantees $L_2$ stability. Furthermore, the origin is globally uniformly asymptotically stable in the absence of the disturbance. A three-machine power system is considered as an application example.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.32 no.12
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• pp.419-426
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• 1983

This study is to analyze the nonlinear characteristics of magnetic flux distribution of a transformer by Finite Element Method using 2-dimensional elements. To accomplish this, first a single phase shell-type transformer is selected a model to be analyzed, and the element equation is derived by the vriational approach. And then using the numerical approximation of a magnetization curve and the Direct Convergence Method which is presented in this study, the magnetic nonlinear characteristic is analyzed. In this consequence, the resultant values are converged within 10 iterations of calculation. And in the comparison with the case of linear analysis, these results are more accurate and reasonable.