• Title/Summary/Keyword: systems of ODE

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Improvement of Falling Motions for Humanoid Robot Using Injection PGA (주입형 PGA를 이용한 휴머노이드 로봇의 넘어짐 자세 개선)

  • An, Kwang-Chul;Cho, Young-Wan;Seo, Ki-Sung
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2008.04a
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    • pp.343-346
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    • 2008
  • 휴머노이드 로봇이 넘어질 경우, 충격에 의한 손상이 발생할수 있다. 이를 최소화하는 넘어짐 자세의 생성을 위하여 개선된 PGA 기반의 탐색기법을 제안한다. 다목적함수를 고려한 군집 간 이주방식의 효율적 조합을 통해 넘어짐 충격을 최소화하는 각 관절 궤적을 구할수 있도록 하였다. 제안된 기법의 검증을 위하여 Sony QRIO 로봇에 대해서 ODE 기반의 Webots 시뮬레이션을 이용하여 실험을 수행하였다.

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An efficient solution for multibody dynamics and application to satellite deployment mechanism (효율적인 다물체 동역학 해법 및 인공위성 전개장치에의 응용)

  • 이기수;김진철
    • 제어로봇시스템학회:학술대회논문집
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    • 1992.10a
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    • pp.680-685
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    • 1992
  • Solar arrays and antennas of the satellite are usually stowed within the dimensions of the launch-vehicle fairing and deployed in the orbit. To solve such multibody dynamic problems, differential equations and algebraic equations are simultaneously solved, and special solution techniques are required. In this paper, 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. Defomable bodies as well as rigid bodies are treated, and applications to satellite solar arrays are explained.

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A Historical Study on the Representations of Diffusion Phenomena in Mathematical Models for Population Changes of Biological Species (생물 종의 개체 수 변화를 기술하는 수학적 모델의 확산현상 표현에 대한 역사적 고찰)

  • Shim, Seong-A
    • Journal for History of Mathematics
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    • v.29 no.6
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    • pp.353-363
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    • 2016
  • In mathematical population ecology which is an academic field that studies how populations of biological species change as times flows at specific locations in their habitats, PDE models have been studied in many aspects and found to have different properties from the classical ODE models. And different approaches to PDE type models in mathematical biology are still being tried currently. This article investigate various forms to express diffusion effects and review the history of PDE models involving diffusion terms in mathematical ecology. Semi-linear systems representing the spatial movements of each individual as random simple diffusion and quasi-linear systems describing more complex diffusions reflecting interspecific interactions are studied. Also it introduce a few of important problems to be solved in this field.

Generation of Falling Motion for Humanoid Robot Using GA (GA를 이용한 휴머노이드 로봇의 넘어짐 자세 생성)

  • An, Kwang-Chul;Cho, Young-Wan;Seo, Ki-Sung
    • Journal of the Korean Institute of Intelligent Systems
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    • v.17 no.6
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    • pp.843-848
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    • 2007
  • This paper introduced an automatic generation method of falling motions for humanoid robots to minimize a damage. The proposed approach used a GA based optimization technique to find a set of joint trajectories which minimize a damage of the falling over and down. A couple of fitness functions are provided to generate various falling motions. To verify the proposed method, experiments for falling motions were executed for Sony QRIO robot in Webots simulation environments.

Opposition Based Differential Evolution Algorithm for Capacitor Placement on Radial Distribution System

  • Muthukumar, R.;Thanushkodi, K.
    • Journal of Electrical Engineering and Technology
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    • v.9 no.1
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    • pp.45-51
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    • 2014
  • Distribution system is a critical link between customer and utility. The control of power loss is the main factor which decides the performance of the distribution system. There are two methods such as (i) distribution system reconfiguration and (ii) inclusion of capacitor banks, used for controlling the real power loss. Considering the improvement in voltage profile with the power loss reduction, later method produces better performance than former method. This paper presents an advanced evolutionary algorithm for capacitor inclusion for loss reduction. The conventional sensitivity analysis is used to find the optimal location for the capacitors. In order to achieve a better approximation for the current candidate solution, Opposition based Differential Evolution (ODE) is introduced. The effectiveness of the proposed technique is validated through 10, 33, 34 and85-bus radial distribution systems.

Sensitivity Analysis with Optimal Input Design and Model Predictive Control for Microalgal Bioreactor Systems (미세조류 생물반응기 시스템의 민감도분석을 위한 최적입력설계 및 모델예측제어)

  • Yoo, Sung Jin;Oh, Se-Kyu;Lee, Jong Min
    • Korean Chemical Engineering Research
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    • v.51 no.1
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    • pp.87-92
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    • 2013
  • Microalgae have been suggested as a promising feedstock for producing biofuel because of their potential of lipid production. In this study, a first principles ODE model for microalgae growth and neutral lipid synthesis proposed by Surisetty et al. (2010) is investigated for the purpose of maximizing the rate of microalgae growth and the amount of neutral lipid. The model has 6 states and 12 parameters and follows the assumption of Droop model which explains the growth as a two-step phenomenon; the uptake of nutrients is first occurred in the cell, and then use of intra-cellular nutrient to support cells growth. In this study, optimal input design using D-optimality criterion is performed to compute the system input profile and sensitivity analysis is also performed to determine which parameters have a negligible effect on the model predictions. Furthermore, model predictive control based on successive linearization is implemented to maximize the amount of neutral lipid contents.

Closed Integral Form Expansion for the Highly Efficient Analysis of Fiber Raman Amplifier (라만증폭기의 효율적인 성능분석을 위한 라만방정식의 적분형 전개와 수치해석 알고리즘)

  • Choi, Lark-Kwon;Park, Jae-Hyoung;Kim, Pil-Han;Park, Jong-Han;Park, Nam-Kyoo
    • Korean Journal of Optics and Photonics
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    • v.16 no.3
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    • pp.182-190
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    • 2005
  • The fiber Raman amplifier(FRA) is a distinctly advantageous technology. Due to its wider, flexible gain bandwidth, and intrinsically lower noise characteristics, FRA has become an indispensable technology of today. Various FRA modeling methods, with different levels of convergence speed and accuracy, have been proposed in order to gain valuable insights for the FRA dynamics and optimum design before real implementation. Still, all these approaches share the common platform of coupled ordinary differential equations(ODE) for the Raman equation set that must be solved along the long length of fiber propagation axis. The ODE platform has classically set the bar for achievable convergence speed, resulting exhaustive calculation efforts. In this work, we propose an alternative, highly efficient framework for FRA analysis. In treating the Raman gain as the perturbation factor in an adiabatic process, we achieved implementation of the algorithm by deriving a recursive relation for the integrals of power inside fiber with the effective length and by constructing a matrix formalism for the solution of the given FRA problem. Finally, by adiabatically turning on the Raman process in the fiber as increasing the order of iterations, the FRA solution can be obtained along the iteration axis for the whole length of fiber rather than along the fiber propagation axis, enabling faster convergence speed, at the equivalent accuracy achievable with the methods based on coupled ODEs. Performance comparison in all co-, counter-, bi-directionally pumped multi-channel FRA shows more than 102 times faster with the convergence speed of the Average power method at the same level of accuracy(relative deviation < 0.03dB).

HIGH ORDER IMPLICIT METHOD FOR ODES STIFF SYSTEMS

  • Vasilyeva, Tatiana;Vasilev, Eugeny
    • Journal of applied mathematics & informatics
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    • v.8 no.1
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    • pp.165-180
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    • 2001
  • This paper presents a new difference scheme for numerical solution of stiff system of ODE’s. The present study is mainly motivated to develop an absolutely stable numerical method with a high order of approximation. In this work a double implicit A-stable difference scheme with the sixth order of approximation is suggested. Another purpose of this study is to introduce automatic choice of the integration step size of the difference scheme which is derived from the proposed scheme and the one step scheme of the fourth order of approximation. The algorithm was tested by means of solving the Kreiss problem and a chemical kinetics problem. The behavior of the gas explosive mixture (H₂+ O₂) in a closed space with a mobile piston is considered in test problem 2. It is our conclusion that a hydrogen-operated engine will permit to decrease the emitted levels of hazardous atmospheric pollutants.

A Practical Method for Identification of Nonlinear Chemical Processes by use of Volterra Kernel Model

  • Numata, Motoki;Kashiwagi, Hiroshi;Harada, Hiroshi
    • 제어로봇시스템학회:학술대회논문집
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    • 1999.10a
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    • pp.145-148
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    • 1999
  • It is known that Volterra kernel models can represent a wide variety of nonlinear chemical processes. Also, it is necessary for Volterra model identification to excite the process to be identified with a signal having wide range of frequency spectrum and high enough amplitude of input signals. Kashiwagi[4 ∼ 7] has recently shown a method for measuring Volterra kernels up to third order using pseudorandom M-sequence signals. However, in practice, since it is not always possible to apply such input sequences to the actual chemical plants. Even when we can apply such a pseudorandom signal to the process, it takes much time to obtain higher order Volterra kernels. Considering these problems, the authors propose here a new method for practical identification of Volterra kernels by use of approximate open differential equation (ODE) model and simple plant test. Simulation results are shown for verifying the usefulness of our method of identification of nonlinear chemical processes.

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ADAPTIVE SLICING ODE CONTROL USING FUZZY LOGIC SYSTEM

  • Yoo, Byungkook;Jeoung, Sacheul;Ham, Woonchul
    • 제어로봇시스템학회:학술대회논문집
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    • 1995.10a
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    • pp.26-30
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    • 1995
  • In this study, the fuzzy approximator and sliding mode control (SMC) scheme are considered. An adaptive sliding mode control is proposed based on the SMC theory. This proposed control scheme is that a adaptive law is utilized to approximate the unknown function f by fuzzy logic system in designing the sliding mode controller for the nonlinear system. In order to reduce the approximation errors, the differences of nonlinear function and fuzzy approximator, an adaptive law is also intoduced and the stability of proposed control scheme are proven with simple adaptive law and roburst adaptive law. This proposed control scheme is applied to a single link robot arm.

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