• Title/Summary/Keyword: Discretization Error

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Hardware-in-the-loop Simulation of CNC-controlled Feed Drives (CNC 제어 이송계의 Hardware-in-the-loop 시뮬레이션)

  • Lee, Wonkyun;Lee, Chan-Young;Kim, Joo-Yeong;Song, Chang Kyu;Min, Byung-Kwon
    • Journal of the Korean Society for Precision Engineering
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    • v.32 no.5
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    • pp.447-454
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    • 2015
  • Design and application of hardware-in-the-loop simulation (HILS) for design of CNC-controlled machine tool feed drives is discussed. The CNC machine tool is a complex mechatronics system where the complexity results from the software-based controller composed of a variety of functionalities and advanced control algorithms. Therefore, using a real CNC controller in the control simulation has merits considering the efforts and accuracy of the simulation modeling. In this paper challenges in HILS for a CNC controlled feed drive, such as minimization of time delay and transmission error that are caused by discretization of the feed drive model, is elaborated. Using an experimental HILS setup of a machine tool feed drive applications in controller gain selection and CNC diagnostics are presented.

Numerical analysis of the cooling effects for the first wall of fusion reactor (핵 융합로 제1벽의 냉각성능에 관한 수치해석적 연구)

  • Jeong, I.S.;Hwang, Y.K.
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.11 no.1
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    • pp.18-30
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    • 1999
  • A heat transfer analysis for the two-dimensional (2-D) steady state using finite difference method (FDM) is performed to predict the thermal behavior of the primary first-wall (FW) system of fusion reactor under various geometric and thermo-hydraulic conditions, such as the beryllium (Be) armor thickness, pitch of cooling tube, and coolant velocity. The FW consists of authentic steel (type 316 stainless steel solution annealed) for cooling tubes, Cu for cooling tubes embedding material, and Be for a protective armor, based on the International Thermonuclear Experiment Reactor (ITER) report. The present 2-D analysis, the control volume discretized with hybrid grid (rectangular grid and polar grid) and Gauss-Seidel iteration method are adapted to solve the governing equations. In the present study, geometric and thermo-hydraulic parameters are optimized with consideration of several limitations. Consequently, it is suggested that the adequate pitch of cooling tube is 22-32mm, the beryllium armor thickness is 10-12mm, and that the coolant velocity is 4.5m/s-6m/s for $100^{\circ}C$ of inlet coolant temperature. The cooling tube should locate near beryllium armor. But, it would be better for locating the center of Cu wall, considering problems of material and manufacturing. Also, 2-D analysis neglecting the axial temperature distribution of cooling tube is appropriate, regarding the discretization error in axial direction.

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An hp-angular adaptivity with the discrete ordinates method for Boltzmann transport equation

  • Ni Dai;Bin Zhang;Xinyu Wang;Daogang Lu;Yixue Chen
    • Nuclear Engineering and Technology
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    • v.55 no.2
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    • pp.769-779
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    • 2023
  • This paper describes an hp-angular adaptivity algorithm in the discrete ordinates method for Boltzmann transport applications with strong angular effects. This adaptivity uses discontinuous finite element quadrature sets with different degrees, which updates both angular mesh and the degree of the underlying discontinuous finite element basis functions, allowing different angular local refinement to be applied in space. The regular and goal-based error metrics are considered in this algorithm to locate some regions to be refined. A mapping algorithm derived by moment conservation is developed to pass the angular solution between spatial regions with different quadrature sets. The proposed method is applied to some test problems that demonstrate the ability of this hp-angular adaptivity to resolve complex fluxes with relatively few angular unknowns. Results illustrate that a reduction to approximately 1/50 in quadrature ordinates for a given accuracy compared with uniform angular discretization. This method therefore offers a highly efficient angular adaptivity for investigating difficult particle transport problems.

A discretization method of the three dimensional heat flow equation with excellent convergence characteristics (우수한 수렴특성을 갖는 3차원 열흐름 방정식의 이산화 방법)

  • Lee, Eun-Gu;Yun, Hyun-Min;Kim, Cheol-Seong
    • Journal of IKEEE
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    • v.6 no.2 s.11
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    • pp.136-145
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    • 2002
  • The simulator for the analysis of the lattice temperature under the steady-state condition is developed. The heat flow equation using the Slotboom variables is discretized and the integration method of the thermal conductivity without using the numerical analysis method is presented. The simulations are executed on the $N^+P$ junction diode and BJT to verify the proposed method. The average relative error of the lattice temperature of $N^+P$ diode compared with DAVINCI is 2% when 1.4[V] forward bias is applied and the average relative error of the lattice temperature of BJT compared with MEDICI is 3% when 5.0[V] is applied to the collector contact and 0.5[V] is applied to the base contact. BANDIS using the proposed method of integration of thermal conductivity needs 3.45 times of matrix solution to solve one bias step and DAVINCI needs 5.1 times of matrix solution MEDICI needs 4.3 times of matrix solution.

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Structural modal identification and MCMC-based model updating by a Bayesian approach

  • Zhang, F.L.;Yang, Y.P.;Ye, X.W.;Yang, J.H.;Han, B.K.
    • Smart Structures and Systems
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    • v.24 no.5
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    • pp.631-639
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    • 2019
  • Finite element analysis is one of the important methods to study the structural performance. Due to the simplification, discretization and error of structural parameters, numerical model errors always exist. Besides, structural characteristics may also change because of material aging, structural damage, etc., making the initial finite element model cannot simulate the operational response of the structure accurately. Based on Bayesian methods, the initial model can be updated to obtain a more accurate numerical model. This paper presents the work on the field test, modal identification and model updating of a Chinese reinforced concrete pagoda. Based on the ambient vibration test, the acceleration response of the structure under operational environment was collected. The first six translational modes of the structure were identified by the enhanced frequency domain decomposition method. The initial finite element model of the pagoda was established, and the elastic modulus of columns, beams and slabs were selected as model parameters to be updated. Assuming the error between the measured mode and the calculated one follows a Gaussian distribution, the posterior probability density function (PDF) of the parameter to be updated is obtained and the uncertainty is quantitatively evaluated based on the Bayesian statistical theory and the Metropolis-Hastings algorithm, and then the optimal values of model parameters can be obtained. The results show that the difference between the calculated frequency of the finite element model and the measured one is reduced, and the modal correlation of the mode shape is improved. The updated numerical model can be used to evaluate the safety of the structure as a benchmark model for structural health monitoring (SHM).

Linear decentralized learning control for the robot moving on the horizontal plane

  • Lee, Soo-Cheol
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 1995.04a
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    • pp.869-879
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    • 1995
  • The new field of learning control develops controllers that learn to improve their performance at executing a given task, based on experience performing this task. The simplest forms of learning control are based on the same concept as integral control, but operating in the domain of the repetitions of the task. In the previous paper, I had studied the use of such controllers in a decentralized system, such as a robot with the controller for each link acting independently. The basic result of the paper is to show that stability of the learning controllers for all subsystems when the coupling between subsystems is turned off, assures stability of the decentralized learning in the coupled system, provided that the sample time in the digital learning controller is sufficiently short. In this paper, we present two examples. The first illustrates the effect of coupling between subsystems in the system dynamics, and the second studies the application of decentralized learning control to robot problems. The latter example illustrates the application of decentralized learning control to nonlinear systems, and also studies the effect of the coupling between subsystems introduced in the input matrix by the discretization of the system equations. The conclusion is that for sufficiently small learning gain, and sufficiently small sample time, the simple learning control law based on integral control applied to each robot axis will produce zero tracking error in spite o the dynamic coupling in the robot equations. Of course, the results of this paper have much more general application than just to the robotics tracking problem. Convergence in decentralized systems is seen to depend only on the input and output matrices, provided the sample time is suffiently small.

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