• Title/Summary/Keyword: Jacobian Matrix

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3-Dimensional Equilibrium Position Searching of HDD/Head System using Multi-Dimensional Newton-Raphson Method (다차원 뉴튼-랩슨 방법을 이용한 하드 디스크/헤드 시스템의 3차원 평형위치 검색)

  • Chang, In-Bae
    • Journal of Industrial Technology
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    • v.15
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    • pp.203-208
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    • 1995
  • This paper suggests the three dimensional steady state searching techniques of hard disk/head system, which has some skew angle with flexure. In order to analyze the steady state behaviors of magnetic head slider, the localized Knudsen number and the localized bearing numbers are sued. For finding the steady state of magnetic head slider under the pre-loaded condition, I proposed multi-dimensional Newton-Raphson method which traces the equilibrium position of magnetic head slider, which has 3-degrees of freedom, using Jacobian matrix. The multi-dimensional Newton-Raphson method is very efficient technique for finding the steady state position of magnetic head slider because it approaches to the equilibrium position with changing three parameters simultaneously.

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Voltage Stability Analysis of AC/DC Systems (AC/DC 계통의 전압안정도 해석)

  • Nam, Hae-Kon;Kim, Yong-Hak
    • Proceedings of the KIEE Conference
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    • 1995.11a
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    • pp.89-91
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    • 1995
  • This paper describes an extension or a pair or multiple load flow solutions and nose curve method developed for voltage stability analysis or AC power systems to AC/DC systems. In this approach the converters are regarded as voltage dependent loads. Assuming that the converters at the unstable (-mode) solution consume the same power equal to the power at the stable (+mode) solution, the unstable solutions or the nose curves arc determined. This method is very efficient since estimating voltage collapse point and voltage stability margin arc determined by a few iterations of multiple load flow solutions. Also the method has the advantages that since the structure or Jacobian matrix is same with that of AC load flow, modal analysis or voltage stability is readily applicable if desired.

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Turning Dynamics and Equilibrium of Two-Wheeled Vehicles

  • Chen Chih-Keng;Dao Thanh-Son;Yang Chih-Kai
    • Journal of Mechanical Science and Technology
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    • v.19 no.spc1
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    • pp.377-387
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    • 2005
  • The equations of motion of two-wheeled vehicles, e.g. bicycles or motorcycles, are developed by using Lagrange's equations for quasi-coordinates. The pure rolling constraints between the ground and the two wheels are considered in the dynamical equations of the system. For each wheel, two nonholonomic and two holonomic constraints are introduced in a set of differential-algebraic equations (DAE). The constraint Jacobian matrix is obtained by collecting all the constraint equations and converting them into the velocity form. Equilibrium, an algorithm for searching for equilibrium points of two-wheeled vehicles and the associated problems are discussed. Formulae for calculating the radii of curvatures of ground-wheel contact paths and the reference point are also given.

카메라 디포커싱을 이용한 로보트의 시각 서보

  • 신진우;고국현;조형석
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1994.10a
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    • pp.559-564
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    • 1994
  • Recently, a visual servoing for an eye-in-hand robot has become an interesting problem. A distance between a camera and a task object is very useful information for visual servoing. In the previous works for visual servoing, the distance can be obtained from the difference between a reference and a measured feature value of the object such as area on image plane. However, since this feature depends on the object, the reference feature value must be changed when other task object is taken. To overcome this difficulty, this paper presents a novel method for visual servoing. In the proposed method, a blur is used to obtain the distance. The blur, one of the most important features, depends on the focal length of camera. Since it is not affected by the change of object, the reference feature value is not changed although other task object is taken. In this paper, we show a relationship between the distance and the blur, and define the feature jacobian matrix based on camera defocusing to operate the robot. A series of experiments is performed to verify the proposed method.

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A Position Control for a Parallel Stage with 6 degrees of freedom Using Magnetic Actuators (전자기 구동장치를 이용한 병렬형 6자유도 스테이지의 위치제어)

  • Lee Se-Han
    • Journal of the Korean Society for Precision Engineering
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    • v.22 no.7 s.172
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    • pp.102-111
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    • 2005
  • In this paper, we address a position control for a parallel stage, which is levitated and driven by electric magnetic force. This consists of a levitating object (called platen) with 4 permanent magnetic linear synchronous motors in parallel. Each motor generates vertical force for suspension against gravity and propulsion force horizontally as well. This stage can generate six degrees of freedom motion by the vertical and horizontal force. A dynamic equation of the stage system is derived based on Newton-Euler method and it's special Jacobian matrix describing a relation between the limited velocity and Cartesian velocity is done. There are proposed two control methods for positioning which are Cartesian space controller and Actuator space controller. The control performance of the Cartesian space controller is better than the Actuator space controller in task space trajectory while the Actuator space controller is simpler than the Cartesian space controller in controller realization.

An Euler Parameter Updating Method for Multibody Kinematics and Dynamics (다물체의 기구해석 및 동적거동해석을 위한 오일러 매개변수의 교정방법)

  • 김성주;배대성;최창곤;양성모
    • Transactions of the Korean Society of Automotive Engineers
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    • v.4 no.4
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    • pp.9-17
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    • 1996
  • This paper develops a sequential updating method of the Euler parameter generalized coordinates for the machine kinematics and dynamics, The Newton's method is slightly modified so as to utilize the Jacobian matrix with respect to the virtual rotation instead of this with repect to the Euler parameters. An intermediate variable is introduced and the modified Newton's method solves for the variable first. Relational equation of the intermediate variable is then solved for the Euler parameters. The solution process is carried out efficiently by symoblic inversion of the relational equation of the intermediate variable and the iteration equation of the Euler parameter normalization constraint. The proposed method is applied to a kinematic and dynamic analysis with the Generalized Coordinate Partitioning method. Covergence analysis is performed to guarantee the local convergence of the proposed method. To demonstrate the validity and practicalism of the proposed method, kinematic analysis of a motion base system and dynamic analysis of a vehicle are carried out.

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Reflection travel time tomography using blocky parameterization

  • Kim Wonsik;Hong Soonduk;Shin Changsoo;Yang Seungjin
    • Proceedings of the KSEEG Conference
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    • 2002.04a
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    • pp.163-166
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    • 2002
  • Initial velocity model close to real velocity structure of the subsurface governs the quality of image of prestack depth migration. Geophysicists employ velocity estimation tools such as velocity analysis (curvature method, coherency inversion), tomography and waveform inversion. We present a reflection tomography that parameterizes the subsurface into the movable blocks. By interpreting the depth-migrated section or stacked section, we can design an initial constant velocity model having only impedance boundaries. We use shooting-raytracing method that allows us to calculate the Jacobian-matrix efficiently.

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The study on the Intelligent Control of Robot using Fuzzy Inverse Kinematics Mapping (Fuzzy Inverse Kinematics Mapping을 이용한 로봇의 지능제어에 관한 연구)

  • 김관형;이상배
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 1996.10a
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    • pp.166-171
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    • 1996
  • Generally, when we control the robot, we should calculate exactly Inverse Kinematics. However, Inverse Kinematics calculation is complex and it takes much time for the manipulator to control in real-time. Therefore, the calculation of Inverse Kinematics can result in significant control delay in real time. In this paper, we will present that Inverse Kinematics can be calculated through Fuzzy Logic Mapping, Based on an exact solution through fuzzy reasoning instead of Inverse Kinematics calculation Also, the result provides sufficient precision and transient tracking error can be controlled based on a fuzzy adaptive scheme proposed in this paper. Based on the Denavit-Hartenberg parameters specification, after the Jacobian matrix of arbitrary manipulator is calculated, we will construct Fuzzy Inverse Kinematics Mapping(FIKM) using fuzzy logic and represent a good control efficiency through simulation of 2-DOF manipulator.

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Development of Optimal Path Planning for Automated Excavator (자동화 굴삭기 최적경로 생성 알고리즘 개발)

  • Shin, Jin-Ok;Park, Hyong-Ju;Lee, Sang-Hak;Hong, Dae-Hee
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2007.04a
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    • pp.78-83
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    • 2007
  • The paper focuses on the establishment of optimized bucket path planning and trajectory control designated for force-reflecting backhoe reacting to excavation environment, such as potential obstacles and ground characteristics. The developed path planning method can be used for precise bucket control, and more importantly for obstacle avoidance which is directly related to safety issues. The platform of this research was based on conventional papers regarding the kinematic model of excavator. Jacobian matrix was constructed to find optimal joint angles and rotation angles of bucket from position and orientation data of excavator. By applying Newton-Raphson method optimal joint angles and bucket orientation were derived simultaneously in the way of minimizing positional errors of excavator. The model presented in this paper was intended to function as a cornerstone to build complete and advanced path planning of excavator by implementing soil mechanics and further study of excavator dynamics together.

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The New Load Flow Algorithm using Optimal Programming (최적화기법을 이용한 새로운 조류계산 알고리즘)

  • Jeon, Dong-Hoon;Kim, Kern-Joong;Choi, Jang-Hum;Eom, Jae-Sun;Huh, Hyung;Rhee, Byoung-Ill
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.49 no.11
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    • pp.542-548
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    • 2000
  • In this paper, we proposed a new load flow analysis algorithm. In order to develop it, we converted typical power flow problem into optimal problem. This problem has the objective function that minimize the difference between calculated values and specified values of bus powers and subject to bus power equations of P and Q. Using it, we solved the divergence by singularity of Jacobian matrix, the divergence by initial value in the typical power flow study. In the study of a sample system, we verified the superiority of proposed algorithm.

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