• 제목/요약/키워드: Quadratic form

검색결과 273건 처리시간 0.028초

미지 입력을 가진 기계 시스템을 위한 비선형 관측기 설계 (Design of a Nonlinear Observer for Mechanical Systems with Unknown Inputs)

  • 송봉섭;이지민
    • 제어로봇시스템학회논문지
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    • 제22권6호
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    • pp.411-416
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    • 2016
  • This paper presents the design methodology of an unknown input observer for Lipschitz nonlinear systems with unknown inputs in the framework of convex optimization. We use an unknown input observer (UIO) to consider both nonlinearity and disturbance. By deriving a sufficient condition for exponential stability in the linear matrix inequality (LMI) form, existence of a stabilizing observer gain matrix of UIO will be assured by checking whether the quadratic stability margin of the error dynamics is greater than the Lipschitz constant or not. If quadratic stability margin is less than a Lipschitz constant, the coordinate transformation may be used to reduce the Lipschitz constant in the new coordinates. Furthermore, to reduce the maximum singular value of the observer gain matrix elements, an object function to minimize it will be optimally designed by modifying its magnitude so that amplification of sensor measurement noise is minimized via multi-objective optimization algorithm. The performance of UIO is compared to a nonlinear observer (Luenberger-like) with an application to a flexible joint robot system considering a change of load and disturbance. Finally, it is validated via simulations that the estimated angular position and velocity provide true values even in the presence of unknown inputs.

State-Space Model Predictive Control Method for Core Power Control in Pressurized Water Reactor Nuclear Power Stations

  • Wang, Guoxu;Wu, Jie;Zeng, Bifan;Xu, Zhibin;Wu, Wanqiang;Ma, Xiaoqian
    • Nuclear Engineering and Technology
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    • 제49권1호
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    • pp.134-140
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    • 2017
  • A well-performed core power control to track load changes is crucial in pressurized water reactor (PWR) nuclear power stations. It is challenging to keep the core power stable at the desired value within acceptable error bands for the safety demands of the PWR due to the sensitivity of nuclear reactors. In this paper, a state-space model predictive control (MPC) method was applied to the control of the core power. The model for core power control was based on mathematical models of the reactor core, the MPC model, and quadratic programming (QP). The mathematical models of the reactor core were based on neutron dynamic models, thermal hydraulic models, and reactivity models. The MPC model was presented in state-space model form, and QP was introduced for optimization solution under system constraints. Simulations of the proposed state-space MPC control system in PWR were designed for control performance analysis, and the simulation results manifest the effectiveness and the good performance of the proposed control method for core power control.

이원 분산성분의 사영분석 (Projection analysis for two-way variance components)

  • 최재성
    • Journal of the Korean Data and Information Science Society
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    • 제25권3호
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    • pp.547-554
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    • 2014
  • 본 논문은 실험자료에 대한 분석모형으로 이원 분산분석모형을 가정한다. 확률효과 모형의 가정하에 분산성분의 추정량을 구하기 위한 방법으로 적률법을 가정하고 있다. 분산성분의 적률 추정방법인 Henderson의 방법 I과 방법 III을 다루고 있다. Henderson의 두 방법에서 소개되는 제곱합 대신에 벡터공간에서의 사영을 활용하는 방법을 제시하고 있다. 또한 제곱합의 기대값 계산을 위해 두 방법 모두 Hartley의 합성법을 제공하고 있으나 본 논문에서는 관련행렬의 고유근을 이용할 수 있음을 제시하고 있다. 분산성분의 해를 얻기 위한 방법의 차이에서 유도되는 연립방정식들은 같지 않으나 양수의 분산성분들에 대한 해는 유사함을 보여주고 있다.

자기구성 퍼지 다항식 뉴럴 네트워크 구조의 설계 (Design of Self-Organizing Fuzzy Polynomial Neural Networks Architecture)

  • 박호성;박건준;오성권
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 2003년도 하계학술대회 논문집 D
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    • pp.2519-2521
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    • 2003
  • In this paper, we propose Self-Organizing Fuzzy Polynomial Neural Networks(SOFPNN) architecture for optimal model identification and discuss a comprehensive design methodology supporting its development. It is shown that this network exhibits a dynamic structure as the number of its layers as well as the number of nodes in each layer of the SOFPNN are not predetermined (as this is the case in a popular topology of a multilayer perceptron). As the form of the conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as linear, quadratic, and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership function are studied and the number of the premise input variables used in the rules depends on that of the inputs of its node in each layer. We introduce two kinds of SOFPNN architectures, that is, the basic and modified one with both the generic and the advanced type. The superiority and effectiveness of the proposed SOFPNN architecture is demonstrated through nonlinear function numerical example.

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Active control of three-phase CNT/resin/fiber piezoelectric polymeric nanocomposite porous sandwich microbeam based on sinusoidal shear deformation theory

  • Navi, B. Rousta;Mohammadimehr, M.;Arani, A. Ghorbanpour
    • Steel and Composite Structures
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    • 제32권6호
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    • pp.753-767
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    • 2019
  • Vibration control in mechanical equipments is an important problem where unwanted vibrations are vanish or at least diminished. In this paper, free vibration active control of the porous sandwich piezoelectric polymeric nanocomposite microbeam with microsensor and microactuater layers are investigated. The aim of this research is to reduce amplitude of vibration in micro beam based on linear quadratic regulator (LQR). Modified couple stress theory (MCST) according to sinusoidal shear deformation theory is presented. The porous sandwich microbeam is rested on elastic foundation. The core and face sheet are made of porous and three-phase carbon nanotubes/resin/fiber nanocomposite materials. The equations of motion are extracted by Hamilton's principle and then Navier's type solution are employed for solving them. The governing equations of motion are written in space state form and linear quadratic regulator (LQR) is used for active control approach. The various parameters are conducted to investigate on the frequency response function (FRF) of the sandwich microbeam for vibration active control. The results indicate that the higher length scale to the thickness, the face sheet thickness to total thickness and the considering microsensor and microactutor significantly affect LQR and uncontrolled FRF. Also, the porosity coefficient increasing, Skempton coefficient and Winkler spring constant shift the frequency response to higher frequencies. The obtained results can be useful for micro-electro-mechanical (MEMS) and nano-electro-mechanical (NEMS) systems.

EXISTENCE OF THE CONTINUED FRACTIONS OF ${\sqrt{d}}$ AND ITS APPLICATIONS

  • Lee, Jun Ho
    • 대한수학회보
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    • 제59권3호
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    • pp.697-707
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    • 2022
  • It is well known that the continued fraction expansion of ${\sqrt{d}}$ has the form $[{\alpha}_0,\;{\bar{{\alpha}_1,\;{\ldots},\;{\alpha}_{l-1},\;2_{{\alpha}_0}}]$ and ${\alpha}_1,\;{\ldots},\;{\alpha}_{l-1}$ is a palindromic sequence of positive integers. For a given positive integer l and a palindromic sequence of positive integers ${\alpha}_1,\;{\ldots},\;{\alpha}_{l-1},$ we define the set $S(l;{\alpha}_1,\;{\ldots},\;{\alpha}_{l-1})\;:=\;\{d{\in}{\mathbb{Z}}{\mid}d>0,\;{\sqrt{d}}=[{\alpha}_0,\;{\bar{{\alpha}_1,\;{\ldots},\;{\alpha}_{l-1},\;2_{{\alpha}_0}}],\;where\;{\alpha}_0={\lfloor}{\sqrt{d}}{\rfloor}\}.$ In this paper, we completely determine when $S(l;{\alpha}_1,\;{\ldots},\;{\alpha}_{l-1})$ is not empty in the case that l is 4, 5, 6, or 7. We also give similar results for $(1+{\sqrt{d}})/2.$ For the case that l is 4, 5, or 6, we explicitly describe the fundamental units of the real quadratic field ${\mathbb{Q}}({\sqrt{d}}).$ Finally, we apply our results to the Mordell conjecture for the fundamental units of ${\mathbb{Q}}({\sqrt{d}}).$

Hull-form optimization of KSUEZMAX to enhance resistance performance

  • Park, Jong-Heon;Choi, Jung-Eun;Chun, Ho-Hwan
    • International Journal of Naval Architecture and Ocean Engineering
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    • 제7권1호
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    • pp.100-114
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    • 2015
  • This paper deploys optimization techniques to obtain the optimum hull form of KSUEZMAX at the conditions of full-load draft and design speed. The processes have been carried out using a RaPID-HOP program. The bow and the stern hull-forms are optimized separately without altering neither, and the resulting versions of the two are then combined. Objective functions are the minimum values of wave-making and viscous pressure resistance coefficients for the bow and stern. Parametric modification functions for the bow hull-form variation are SAC shape, section shape (U-V type, DLWL type), bulb shape (bulb height and size); and those for the stern are SAC and section shape (U-V type, DLWL type). WAVIS version 1.3 code is used for the potential and the viscous-flow solver. Prior to the optimization, a parametric study has been conducted to observe the effects of design parameters on the objective functions. SQP has been applied for the optimization algorithm. The model tests have been conducted at a towing tank to evaluate the resistance performance of the optimized hull-form. It has been noted that the optimized hull-form brings 2.4% and 6.8% reduction in total and residual resistance coefficients compared to those of the original hull-form. The propulsive efficiency increases by 2.0% and the delivered power is reduced 3.7%, whereas the propeller rotating speed increases slightly by 0.41 rpm.

수도(水稻) 적정시비량(適正施肥量) 결정(決定)에 대한 대체모형(代替模型) (An Alternative Model for Determining the Optimal Fertilizer Level)

  • 장석환
    • 한국토양비료학회지
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    • 제13권1호
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    • pp.21-32
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    • 1980
  • Linear models, with and without site variables, have been investigated in order to develop an alternative methodology for determining optimal fertilizer levels. The resultant models are : (1) Model I is an ordinary quadratic response function formed by combining the simple response function estimated at each site in block diagonal form, and has parameters [${\gamma}^{(1)}_{m{\ell}}$], for m=1, 2, ${\cdots}$, n sites and degrees of polynomial, ${\ell}$=0, 1, 2. (2) Mode II is a multiple regression model with a set of site variables (including an intercept) repeated for each fertilizer level and the linear and quadratic terms of the fertilizer variables arranged in block diagonal form as in Model I. The parameters are equal to [${\beta}_h\;{\gamma}^{(2)}_{m{\ell}}$] for h=0, 1, 2, ${\cdots}$, k site variable, m=1, 2, ${\cdots}$ and ${\ell}$=1, 2. (3) Model III is a classical response surface model, I. e., a common quadratic polynomial model for the fertilizer variables augmented with site variables and interactions between site variables and the linear fertilizer terms. The parameters are equal to [${\beta}_h\;{\gamma}_{\ell}\;{\theta}_h$], for h=0, 1, ${\cdots}$, k, ${\ell}$=1, 2, and h'=1, 2, ${\cdots}$, k. (4) Model IV has the same basic structure as Mode I, but estimation procedure involves two stages. In stage 1, yields for each fertilizer level are regressed on the site variables and the resulting predicted yields for each site are then regressed on the fertilizer variables in stage 2. Each model has been evaluated under the assumption that Model III is the postulated true response function. Under this assumption, Models I, II and IV give biased estimators of the linear fertilizer response parameter which depend on the interaction between site variables and applied fertilizer variables. When the interaction is significant, Model III is the most efficient for calculation of optimal fertilizer level. It has been found that Model IV is always more efficient than Models I and II, with efficiency depending on the magnitude of ${\lambda}m$, the mth diagonal element of X (X' X)' X' where X is the site variable matrix. When the site variable by linear fertilizer interaction parameters are zero or when the estimated interactions are not important, it is demonstrated that Model IV can be a reasonable alternative model for calculation of optimal fertilizer level. The efficiencies of the models are compared us ing data from 256 fertilizer trials on rice conducted in Korea. Although Model III is usually preferred, the empirical results from the data analysis support the feasibility of using Model IV in practice when the estimated interaction term between measured soil organic matter and applied nitrogen is not important.

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Effects of Dietary Chromium Methionine on Growth Performance, Carcass Composition, Meat Colour and Expression of the Colour-related Gene Myoglobin of Growing-finishing Pigs

  • Li, Y.S.;Zhu, N.H.;Niu, P.P.;Shi, F.X.;Hughes, C.L.;Tian, G.X.;Huang, R.H.
    • Asian-Australasian Journal of Animal Sciences
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    • 제26권7호
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    • pp.1021-1029
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    • 2013
  • To investigate the effect of dietary chromium (Cr) as Cr methionine (CrMet) on growth performance, carcass traits, pork quality, meat colour and expression of meat colour-related genes in growing-finishing pigs, 189 crossbred Duroc${\times}$(Landrace${\times}$Yorkshire) growing-finishing pigs (male, castrated, average initial BW $74.58{\pm}1.52$ kg) were selected and randomly allocated into four groups. Dietary treatments per kg of feed were as follows: 0 (CT), 0.3 mg/kg (T1), 0.6 mg/kg (T2) and 0.9 mg/kg (T3) Cr (in the form of CrMet; as-fed basis), and each treatment was replicated five times with 8 to 10 pigs per replicate pen. During the 28 d of the experiment, both the ADG and the ADFI increased linearly (p<0.05) as the level of dietary Cr increased. The F/G ratio decreased linearly (p<0.05). As dietary Cr increased, loin muscle areas (linear, p = 0.013) and average backfat thickness (linear, p = 0.072) decreased. Shear force (linear, p = 0.070) and Commission Internationale de I'$\acute{E}$clairage (CIE) redness (quadratic, p = 0.028) were increased. In addition, CIE Lightness (quadratic, p = 0.053) were decreased as dietary Cr increased. As dietary Cr increased, total myglobin (Mb) content (quadratic, p = 0.015) and the mb mRNA levels (quadratic, p = 0.046) in longissimus muscles of pigs were up-regulated. In conclusion, supplementation of dietary Cr improved growth and meat colour, but increased shear force and decreased IMF reduced palatability of longissimus muscles. Moreover, the increasing total Mb content and mb mRNA levels indicated that CrMet dietary supplementation may improve meat colour via up-regulating expression of the mb gene.

임의로 관측중단된 두 표본 자료에 대한 카이제곱 검정방법 (Two-sample chi-square test for randomly censored data)

  • 김주한;김정란
    • 응용통계연구
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    • 제8권2호
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    • pp.109-119
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    • 1995
  • 두 모집단에서 임의로 관측중단도니 두 표본을 얻었을 때, 두 모집단의 분포가 같다는 가설을 검정하기 위한 카이제곱 검정방법이 제안되었다. 여기서 제안된 통계량은 대립가설이 두 모집단의 분포가 같지 않다는 양측가설일 때 쓰일 수 있다. 귀무가설이 사실일 때 제안된 통계량의 극한분포는 카이제곱 분포가 된다. 두 가지 형태의 카이제곱 검정통계량이 제안되었는데, 하나는 product-limit 추정치로부터 얻은 관측된 칸(cell) 확률의 차이들의 벡터의 이차형식으로 표현된 것이고, 다른 하나는 간단한 합의 모양으로 표현된 것이다. 두 형태의 검정통계량을 사용하여 암치료를 위한 화학요법 실험으로부터 얻은 자료를 분석하여 보았다.

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