• Title/Summary/Keyword: Linearization Method

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THE FORMAL LINEARIZATION METHOD TO MULTISOLITON SOLUTIONS FOR THREE MODEL EQUATIONS OF SHALLOW WATER WAVES

  • Taghizadeh, N.;Mirzazadeh, M.;Paghaleh, A. Samiei
    • 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.

On the limit cycles of aeroelastic systems with quadratic nonlinearities

  • Chen, Y.M.;Liu, J.K.
    • 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.

THE MULTISOLITON SOLUTION OF GENERALIZED BURGER'S EQUATION BY THE FORMAL LINEARIZATION METHOD

  • Mirzazadeh, Mohammad;Taghizadeh, Nasir
    • 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.

Analysis of Random Ship Rolling Using Partial Stochastic Linearization (통계적 부분선형화 방법을 이용한 선체의 불규칙 횡동요 운동의 해석)

  • Dong-Soo Kim;Won-Kyoung Lee
    • 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.

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Controller Structure and Performance According to Linearization Methods in the Looper ILQ Control for Hot Strip Finishing Mills (열간사상압연기의 루퍼 ILQ 제어에 있어 선형화 기법에 따른 제어기 구조 및 성능)

  • Park, Cheol-Jae;Hwang, I-Cheol
    • 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.

A Novel Linearization Method of Sin/Cos Sensor Signals Used for Angular Position Determination

  • Zivanovi, Dragan;Lukic, Jelena;Denic, Dragan
    • 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] ($0.0172^{\circ}$).

Design of Input-Output Feedback Linearization Controller using Neural Network (신경회로망을 이용한 입력-출력 피드백 선형화 제어기 설계)

  • Cho, Gyu-Sang
    • 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.

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Linearization of Nonlinear System Using Fuzzy Controller with Singleton Consequents (싱글톤 후건부를 갖는 퍼지제어기에 의한 비선형시스템의 선형화)

  • 김응선;이상형;이창훈;박민용
    • 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.

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Linearization of Nonlinear Random Vibration Beam by Equivalent Energy Method (비선형 불규칙 진동 보의 등가에너지법에 의한 선형화)

  • Lee, Sin-Young;Cai, G.Q.
    • 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.

Switching Control of Ball and Beam System using Partial State Feedback: Jacobian and Two-Step Linearization Methods (자코비안 및 2단 선형화 기법과 부분 상태궤환을 이용한 볼-빔 시스템의 스위칭 제어)

  • Lee, Kyung-Tae;Choi, Ho-Lim
    • 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.