• Title/Summary/Keyword: jacobian matrix

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An Accelerated Iterative Method for the Dynamic Analysis of Multibody Systems (반복 계산법 및 계산 가속기법에 의한 다물체 동역학 해법)

  • 이기수;임철호
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.5
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    • pp.899-909
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    • 1992
  • An iterative solution technique is presented to analyze the dynamic systems of rigid bodies subjected to kinematic constraints. Lagrange multipliers associated with the constraints are iteratively computed by monotonically reducing an appropriately defined constraint error vector, and the resulting equation of motion is solved by a well-established ODE technique. Constraints on the velocity and acceleration as well as the position are made to be satisfied at joints at each time step. Time integration is efficiently performed because decomposition or orthonormalization of the large matrix is not required at all. An acceleration technique is suggested for the faster convergence of the iterative scheme.

Development of a New 6-DOF Parallel-type Motion Simulator (6자유도 병렬형 모션 시뮬레이터 개발)

  • Kim, Han-Sung
    • Journal of the Korean Society of Manufacturing Technology Engineers
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    • v.19 no.2
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    • pp.171-177
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    • 2010
  • This paper presents the development of a new 6-DOF parallel-kinematic motion simulator. The moving platform is connected to the fixed base by six P-S-U (Prismatic-Spherical-Universal) serial chains. Comparing with the well-known Gough-Stewart platform-type motion simulator, it uses commercialized linear actuators mounted at the fixed base whereas a 6-UPS manipulator uses telescopic linear ones. Therefore, the proposed motion simulator has the advantages of easier fabrication and lower inertia over a 6-UPS counterpart. Furthermore, since most forces acting along the legs are transmitted to the structure of linear actuators, smaller actuation forces are required. The inverse position and Jacobian matrix are analyzed. In order to further increase workspace, inclined arrangement of universal joints is introduced. The optimal design considering workspace and force transmission capability has been performed. The prototype motion simulator and PC-based real-time controller have been developed. Finally, position control experiment on the prototype has been performed.

2-D Periodic Unsteady Flow Analysis Using a Partially Implicit Harmonic Balance Method (부분 내재적 조화 균형법을 이용한 주기적인 2차원 비정상 유동 해석)

  • Im, Dong-Kyun;Park, Soo-Hyung;Kwon, Jang-Hyuk
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.38 no.12
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    • pp.1153-1161
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    • 2010
  • An efficient solution method for harmonic balance techniques with Fourier transform is presented for periodic unsteady flow problems. The present partially-implicit harmonic balance treats the flux terms implicitly and the harmonic source term is solved explicitly. The convergence of the partially Implicit method is much faster than the explicit Runge-Kutta harmonic balance method. The method does not need to compute the additional flux Jacobian matrix from the implicit harmonic source term. Compared with fully implicit harmonic balance method, this partial approach turns out to have good convergence property. Oscillating flows over NACA0012 airfoil are considered to verify the method and to compare with results of explicit R-K(Runge-Kutta) and dual time stepping methods.

Configuration Control of Vaiable-Geometry Truss Structures (가변형상 트러스구조물의 자세제어)

  • Roh, Tae-Hwan;Kim, Tae-Ik;Park, Hyun-Chul;Kwon, Young-Doo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.20 no.9
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    • pp.2854-2865
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    • 1996
  • The concept of variable-geometry truss structure(VGTS) is introduced as a class of actively controlled adaptive structure. VGTS can purposefully vary its geometric configurations by changing the lengths of some members of the structure. General kinematics and inverse kinematics of a statically determinate VGTS(variable geometry truss structure) are studied. The solution technique is based on the Jacobian matrix obtained via joint equilibrium equations. Pseudoinverse control method is applied to resolve the redundancy of a large VGTS. two types of actuator layout of octahedral type VGTS, VG truss and Stewart platform, are compared. Introducing the concept of performance index, Stewart platform based layout was found to has less consumption energy and manipulation time. A functional VGTS model with 3 octahedral modules is designed and manufactured for the labaratory demonstration. Six vertically located length-variable members are used to create general 6 d.o.f. motions.

Radar Tracking Using a Fuzzy-Model-Based Kalman Filter (퍼지모델 기반 칼만 필터를 이용한 레이다 표적 추적)

  • Lee, Bum-Jik;Joo, Young-Hoon;Park, Jin-Bae
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2003.05a
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    • pp.303-306
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    • 2003
  • In radar tracking, since the sensor measures range, azimuth and elevation angle of a target, the measurement equation is nonlinear and the extended Kalman filter (EKF) is applied to nonlinear estimation. The conventional EKF has been widely used as a nonlinear filter for radar tracking, but the considerably large measurement error due to the linearization of nonlinear function in highly nonlinear situations may deteriorate the performance of the EKF To solve this problem, a fuzzy-model-based Kalman filter (FMBKF) is proposed for radar tracking. The FMBKF uses a local model approximation based on a TS fuzzy model instead of a Jacobian matrix to linearize nonlinear measurement equation. The hybrid GA and RLS method is used to identify the premise and the consequent parameters and the rule numbers of this TS fuzzy model. In two-dimensional radar tracking problem, the proposed method is compared with the conventional EKF.

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Preliminary Test of Adaptive Neuro-Fuzzy Inference System Controller for Spacecraft Attitude Control

  • Kim, Sung-Woo;Park, Sang-Young;Park, Chan-Deok
    • Journal of Astronomy and Space Sciences
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    • v.29 no.4
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    • pp.389-395
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    • 2012
  • The problem of spacecraft attitude control is solved using an adaptive neuro-fuzzy inference system (ANFIS). An ANFIS produces a control signal for one of the three axes of a spacecraft's body frame, so in total three ANFISs are constructed for 3-axis attitude control. The fuzzy inference system of the ANFIS is initialized using a subtractive clustering method. The ANFIS is trained by a hybrid learning algorithm using the data obtained from attitude control simulations using state-dependent Riccati equation controller. The training data set for each axis is composed of state errors for 3 axes (roll, pitch, and yaw) and a control signal for one of the 3 axes. The stability region of the ANFIS controller is estimated numerically based on Lyapunov stability theory using a numerical method to calculate Jacobian matrix. To measure the performance of the ANFIS controller, root mean square error and correlation factor are used as performance indicators. The performance is tested on two ANFIS controllers trained in different conditions. The test results show that the performance indicators are proper in the sense that the ANFIS controller with the larger stability region provides better performance according to the performance indicators.

The Forward/Inverse Force Transmission Analyses of the Stewart Platform (스튜어트 플랫폼의 순방향/역방향 힘 전달 해석)

  • Kim, Han-Sung;Choi, Yong-Je
    • Journal of the Korean Society for Precision Engineering
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    • v.16 no.5 s.98
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    • pp.200-208
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    • 1999
  • The statics relation of the Stewart platform has been investigated from the viewpoint of the forward and inverse force transmission analyses. Two eigenvalue problems corresponding to the forward and inverse force transmission analyses have been formulated. The forward force transmission analysis is to determine the ranges of the magnitudes of the force and moment generated at the end-effector for the given magnitude of linear actuator forces. In reverse order, the inverse force transmission analysis is to find the range of the magnitude of actuator forces for the given ranges of the magnitudes of the force and moment at the end-effector. The inverse force transmission analysis is important since it can provide a designer with a valuable information about how to choose the linear actuators. It has been proved that two eigenvalue problems have a reciprocal relation, which implies that solving either of the eigenvalue problems may complete the forward/inverse force transmission analysis. A numerical example has been also presented.

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Dynamic analysis of multi-functional maintenance platform based on Newton-Euler method and improved virtual work principle

  • Li, Dongyi;Lu, Kun;Cheng, Yong;Zhao, Wenlong;Yang, Songzhu;Zhang, Yu;Li, Junwei;Shi, Shanshuang
    • Nuclear Engineering and Technology
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    • v.52 no.11
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    • pp.2630-2637
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    • 2020
  • The structure design of divertor Multi-Functional Maintenance Platform (MFMP) actuated by hydraulic system for China Fusion Engineering Test Reactor (CFETR) was introduced in this paper. The model of MFMP was established according to maintenance requirements. In this paper, Newton-Euler method and the improved virtual work principle were used, the equivalent driving force of each actuator was obtained through the equivalent Jacobian inverse matrix derived from velocity relationship among the components. The accuracy of the model was verified by ADAMS simulation. The stability control of the heavy-duty components driven by hydraulic cylinders based on Newton-Euler method and improved virtual work principle was established.

The Performance Verification of Optimal State Feedback Controllers via The Inverted Pendulum (도립진자 시스템을 통한 최적 상태 되먹임 제어기의 성능 검증)

  • Lee, Jong-Yeon;Lee, Bo-Ra;Hyun, Chang-Ho
    • Journal of the Korean Institute of Intelligent Systems
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    • v.20 no.6
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    • pp.768-773
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    • 2010
  • This paper presents the performance verification of the optimal state feedback controller via inverted pendulum systems. The proposed method generates the optimal control inputs satisfying both the constrained input and the performance specification. In addition, it reduces the steady-state error by adopting the integral control technique. In order to verify the performance of the proposed method, we apply both the proposed method and the general state feedback control to an inverted pendulum, CEM-IP-01 in the experiment.

Optimal Reactive Power and Voltage Control Using A New Matrix Decomposition Method (새로운 행렬 분할법을 이용한 최적 무효전력/전압제어)

  • 박영문;김두현;김재철
    • The Transactions of the Korean Institute of Electrical Engineers
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    • v.39 no.3
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    • pp.232-239
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    • 1990
  • A new algorithm is suggested to solve the optimal reactive power and voltage control (optimal VAR control) problem. The model minimizes the real power losses in the system. The constraints include the reactive power limits of the generators, limits on the bus voltages and the operating limits of control variables-the transformer tap positions generator terminal voltages and switchable reactive power sources. The method presented herein, using a newly developed Jacobian decomposition method, employs linearized sensitivity relationships of power systems to establish both the objective function for minimizing the system losses and the system performance sensitivities relating dependent and control variables. The algorithm consists of two modules, i.e. the Q-V module for reactive power-voltage control, and load flow module for computational error adjustments. In particular the acceleration factor technique is introduced to enhance the convergence property in Q-V module. The combined use of the afore-mentioned two modules ensures more effective and efficient solutions for optimal reactive power dispatch problems. Results of the application of the method to a sample system and other worst-case systems demonstrated that the algorithm suggested herein is compared favourably with conventional ones in terms of computation accuracy and convergence characteristics.

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