• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.381-391
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• 2012

In this paper, the formal linearization method is used to construct multisoliton solutions for three model of shallow water waves equations. The three models are completely integrable. The formal linearization method is an efficient method for obtaining exact multisoliton solutions of nonlinear partial differential equations. The method can be applied to nonintegrable equations as well as to integrable ones.

• Structural Engineering and Mechanics
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• v.30 no.1
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• pp.67-76
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• 2008

Limit cycle oscillations of a two-dimensional airfoil with quadratic and cubic pitching nonlinearities are investigated. The equivalent stiffness of the pitching stiffness is obtained by combining the linearization and harmonic balance method. With the equivalent stiffness, the equivalent linearization method for nonlinear flutter analysis is generalized to address aeroelastic system with quadratic nonlinearity. Numerical example shows that good approximation of the limit cycle can be obtained by the generalized method. Furthermore, the proposed method is capable of revealing the unsymmetry of the limit cycle; however the ordinary equivalent linearization method fails to do so.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.207-214
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• 2011

The formal linearization method is an efficient method for constructing multisoliton solution of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. In this paper, we obtain multisoliton solution of generalization Burger's equation and the (3+1)-dimension Burger's equation and the Boussinesq equation by the formal linearization method.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.1
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• pp.37-41
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• 1995

In order to analyze the rolling motion of a ship in random beam waves we use the partial stochastic linearization method. The quadratic damping and the nonlinear restoring moments given by the odd polynomials up to the 11th order are added to a single degree of freedom linear equation of roll motion. The irregular excitation moment is assumed to be the Gaussian white noise. The statistical characteristics of the response by the partial stochastic linearization method is compared with results by the equivalent linearization method and Monte Carlo simulation. It is fecund that the partial stochastic linearization method is not necessarily superior to the equivalent linearization method.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.4
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• pp.377-384
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• 2007

This paper studies on the relation between linearization methods and controller gains in the looper ILQ(lnverse Linear Quadratic optimal control) system for hot strip finishing mills. Firstly, two linear models arc respectively derived by a linearization method using Taylor's series expansion and a static state feedback linearization method, respectively, and the linear models are compared with the nonlinear model. Secondly, the looper servo controllers are respectively designed on the basis of two linearization models. Finally, the relation between the performances of two ILQ servo controllers and the linearization methods, and the structures and control gains of two controllers are evaluated by a computer simulation.

• Journal of Electrical Engineering and Technology
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• v.9 no.4
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• pp.1437-1445
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• 2014

In this paper a novel method for angular position determination using sensors with sin/cos output and without an excitation signal, is presented. The linearization of the sensor transfer characteristic and digitalization of the measurement results are performed simultaneously with a goal to increase the measurement resolution. This improvement is particularly important for low angular velocities, and can be used to increase the resolution of incremental Hall, magnetic and optical sensors. This method includes two phases of sin/cos signal linearization. In the first linearization phase the pseudo-linear signal is generated. The second linearization phase, executed by the two-stage piecewise linear ADC, is an additional linearization of the pseudo-linear signal. Based on the LabVIEW software simulations of the proposed method, the contribution of each processing phase to a final measurement error is examined. After the proposed method is applied within $2{\pi}$ [rad] range, the maximal nonlinearity is reduced from 0.3307 [rad] ($18.9447^{\circ}$) to $3{\cdot}10^{-4}$ [rad] ($0.0172^{\circ}$).

• Proceedings of the KIEE Conference
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• 1999.07b
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• pp.936-938
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• 1999

In this Paper, the design of a feedback linearization controller using multilayer neural network is proposed. The Proposed feedback linearization control scheme is designed by finding Lie derivatives from an identified neural networks. Lie derivatives are expressed as a combination of weights and neuron outputs. The proposed method is applied to an antenna arm problem and the simulation results show performance comparisons between the ordinary feedback linearization and the Proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.198-198
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• 2000

In this paper, the linearization method of nonlinear systems via fuzzy controllers which can be the basic research for designing a systematic fuzzy controllers with singleton consequents is proposed. We regard a closed loop system as a canonical form and propose a methodology for linearization of nonlinear system which adjust the input at vertex using zero condition and affinity condition. Through some examples, we show the validity of the proposed method and it can be extended to the design problem of fuzzy controller.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.17 no.1
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• pp.71-76
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• 2008

Nonlinear dynamic system under random excitation was analyzed by using stochastic method. A linearization method was used in order to linearize non-linear structural characteristics but the parametric excitation was used as it was given. An equivalent energy method which equalizes the expectation value of energy of the original nonlinear system and that of quasi-linearized system was proposed. Ito's differential rule was applied to obtain steady state moments. Quasi-linearization coefficients can be obtained the iterative calculation of linearization scheme and steady state moments. Monte Carlo simulation was used to verify the results of the proposed method. Nonlinear vibration of a slender beam was analyzed in this research. The analysis results were compared with Monte Carlo simulation result and showed good agreement. As the spectral density of the given excitation increased, the analysis results showed the better agreement with Monte Carlo simulation.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.5
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• pp.819-832
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• 2017

We propose a new switching control scheme for a ball and beam system by utilizing two linearization methods. First, the Jacobian linearization is applied and state observer is developed afterward. Then, motivated [6], the approximate input-output linearization is carried out, and after that, the Jacobian linearization is applied along with the design of state observer. Since the second approach requires two linearizations, it is called a two-step linearization method. The state observer is needed for the estimation of the velocities of ball and motor movement. Since the Jacobian linearization based controller tends to provide faster response at the initial time, and after that, the two-step linearization based controller tends to provide better response in terms of output overshoot and convergence to the origin, it is natural to give a switching control scheme to provide the best overall control response. The validity of our control scheme is shown in both simulation and experimental results.