• Title/Summary/Keyword: linear approximation

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Dynamic Modeling Method for Beams Undergoing Overall Rigid Body Motion Considering Two Geometric Non-linear Effects (두 기하학적 비선형 효과들을 고려한 대변위 강체운동을 하는 보의 동적 모델링 방법)

  • Kim, Na-Eun;Yoo, Hong-Hee
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.27 no.6
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    • pp.1014-1019
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    • 2003
  • A dynamic modeling method for beams undergoing overall rigid body motion is presented in this paper. Two special deformation variables are introduced to represent the stretching and the curvature and are approximated by the assumed mode method. Geometric constraint equations that relate the two special deformation variables and the cartesian deformation variables are incorporated into the modeling method. By using the special deformation variables, all natural as well as geometric boundary conditions can be satisfied. It is shown that the geometric nonlinear effects of stretching and curvature play important roles to accurately predict the dynamic response when overall rigid body motion is involved.

A Study on the Linear System Simplification by Auxiliary Denominator Polynomial and Moment Matching (보조분모분수식과 모멘트 정합에 의한 선형 시스템 간략법에 관한 연구)

  • 황형수;이경근;양해권
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.24 no.6
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    • pp.948-955
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    • 1987
  • The model reduction method of the high order linear time invariant systems is proposed. The continuous fraction expansion of Auxiliary denominator polynomial is used to obtain denominator polynomial of the reduced order model, and the numerator polynomial of the reduced order model is obtained by equating the first some moments of the original and the reduced order model, using simplified moment function. This methiod does not require the calculation of the reciprocal transformation which should be calculated in Routh approximation, furthemore the stability of the reduced order model is guaranted if original system is stable. Responses of this method showed us good characteristics.

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A Design of Reconfigurable Neural Network Processor (재구성 가능한 신경망 프로세서의 설계)

  • 장영진;이현수
    • Proceedings of the IEEK Conference
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    • 1999.11a
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    • pp.368-371
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    • 1999
  • In this paper, we propose a neural network processor architecture with on-chip learning and with reconfigurability according to the data dependencies of the algorithm applied. For the neural network model applied, the proposed architecture can be configured into either SIMD or SRA(Systolic Ring Array) without my changing of on-chip configuration so as to obtain a high throughput. However, changing of system configuration can be controlled by user program. To process activation function, which needs amount of cycles to get its value, we design it by using PWL(Piece-Wise Linear) function approximation method. This unit has only single latency and the processing ability of non-linear function such as sigmoid gaussian function etc. And we verified the processing mechanism with EBP(Error Back-Propagation) model.

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Vibration of an Axially Moving String Coupled between Longitudinal and Transverse Deflections (종방향과 횡방향 변위가 연성된 축방향으로 움직이는 현의 진동)

  • Chung, J.T.;Shin, C.H.;Han, C.S.
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2000.06a
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    • pp.731-736
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    • 2000
  • The vibration of an axially moving string is studied when the string has geometric non-linearity and translating acceleration. Based upon the von karman strain theory, The equation for the longitudinal vibration is linear and uncoupled, while the equation for the transverse vibration is non-linear and coupled between the longitudinal and transverse deflections. The governing equations are discretized by using the Galerkin approximation. With the discretized nonlinear equations, the time responses are investigated by using the generalized-${\alpha}$ method.

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Solving Dynamic Equation Using Combination of Both Trigonometric and Hyperbolic Cosine Functions for Approximating Acceleration

  • Quoc Do Kien;Phuoc Nguyen Trong
    • Journal of Mechanical Science and Technology
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    • v.19 no.spc1
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    • pp.481-486
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    • 2005
  • This paper introduces a numerical method for integration of the linear and nonlinear differential dynamic equation of motion. The variation of acceleration in two time steps is approximated as a combination of both trigonometric cosine and hyperbolic cosine functions with weighted coefficient. From which all necessary formulae are elaborated for the direct integration of the governing equation. A number of linear and nonlinear dynamic problems with various degrees of freedom are analysed using both the suggested method and Newmark method for the comparison. The numerical results show high advantages and effectiveness of the new method.

Operators in L(X,Y) in which K(X,Y) is a semi M-ideal

  • Cho, Chong-Man
    • Bulletin of the Korean Mathematical Society
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    • v.29 no.2
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    • pp.257-264
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    • 1992
  • Since Alfsen and Effors [1] introduced the notion of an M-ideal, many authors [3,6,9,12] have worked on the problem of finding those Banach spaces X and Y for which K(X,Y), the space of all compact linear operators from X to Y, is an M-ideal in L(X,Y), the space of all bounded linear operators from X to Y. The M-ideal property of K(X,Y) in L(X,Y) gives some informations on X,Y and K(X,Y). If K(X) (=K(X,X)) is an M-ideal in L(X) (=L(X,X)), then X has the metric compact approximation property [5] and X is an M-ideal in $X^{**}$ [10]. If X is reflexive and K(X) is an M-ideal in L(X), then K(X)$^{**}$ is isometrically isomorphic to L(X)[5]. A weaker notion is a semi M-ideal. Studies on Banach spaces X and Y for which K(X,Y) is a semi M-ideal in L(X,Y) were done by Lima [9, 10].

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Large Displacement Dynamic Analysis with Frictional Contact by Linear Complementarity Formulation (선형 상보성 수식화를 이용한 마찰 접촉 대변형 동역학 문제의 해석)

  • Sung, Jae-Hyuk;Kwak, Byung-Man
    • Proceedings of the KSME Conference
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    • 2001.06a
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    • pp.674-679
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    • 2001
  • For a large deformation nonlinear dynamic analysis of two-dimensional frictional contact, the linear complementarity formulation combined with a linearization is used. The solution procedure is based on the total Lagrangian formulation with a predictor and corrector scheme. For contact searching, a hierarchical scheme with a circular territory is used. A second-order approximation of displacements is used to detect impact time and position. The formulation is illustrated by means of numerical examples.

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On-line parameter estimation of continuous-time systems using a genetic algorithm (유전알고리즘을 이용한 연속시스템의 온라인 퍼래미터 추정)

  • Lee, Hyeon-Sik;Jin, Gang-Gyu
    • Journal of Institute of Control, Robotics and Systems
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    • v.4 no.1
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    • pp.76-81
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    • 1998
  • This paper presents an on-line scheme for parameter estimation of continuous-time systems, based on the model adjustment technique and the genetic algorithm technique. To deal with the initialisation and unmeasurable signal problems in on-line parameter estimation of continuous-time systems, a discrete-time model is obtained for the linear differential equation model and approximations of unmeasurable states with the observable output and its time-delayed values are obtained for the nonlinear state space model. Noisy observations may affect these approximation processes and degrade the estimation performance. A digital prefilter is therefore incorporated to avoid direct approximations of system derivatives from possible noisy observations. The parameters of both the model and the designed filter are adjusted on-line by a genetic algorithm, A set of simulation works for linear and nonlinear systems is carried out to demonstrate the effectiveness of the proposed method.

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The Robust Control of Robot Manipulator using Adaptive-Neuro Control Method (적응-뉴럴 제어 기법에 의한 로보트 매니퓰레이터의 견실 제어)

  • 차보남;한성현;이만형;김성권
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1995.04b
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    • pp.262-266
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    • 1995
  • This paper presents a new adaptive-neuro control scheme to control the velocity and position of SCARA robot with parameter uncertainties. The adaptive control of linear system found wiedly in many areas of control application. While techniques for the adaptive control of linear systems have been well-established in the literature, there are a few corresponding techniques for nonlinear systems. In this paper an attempt is made to present a newcontrol scheme for theadaptive control of ponlinear robot based on a feedforward neural network. The proposed approach incorporates a neuro controller used within a reinforcement learning framework, which reduces the problem to one of learning a stochastic approximation of an unknown average error surface Emphasis is focused on the fact that the adaptive-neuro controoler dose not need any input/output information about the controlled system. The simulation result illustrates the effectiveness of the proposed adaptive-neuro control scheme.

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Elastic Stability of Thin-Walled Arches subjected to Uniform Bending - Linear Bending Normal Strain Distribution -

  • Ryu, Hyo-Jin;Lim, Nam-Hyoung;Lee, Chin-Ok
    • Journal of the Korean Society of Hazard Mitigation
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    • v.9 no.2
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    • pp.11-15
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    • 2009
  • This paper is concerned with the elastic buckling of thin-walled arches that are subjected to uniform bending. Nonlinear strain-displacement relations with the initial curvature are substituted into the second variation of the total potential energy to obtain the energy equation including initial curvature effects. The approximation for initial curvature effects that the bending normal strain distribution is linear across the cross section is applied consistently in the derivation process. The closed form solution is obtained for flexural-torsional buckling of arches under uniform bending and, it is compared with the previous theoretical results.