• 제목/요약/키워드: steady-state multiplicity

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연속식 MMA/MA 공중합 반응기의 정상상태 및 동특성 해석 (Analysis of steady-states and dynamic characteristics of a continuous MMA/MA copolymerization reactor)

  • 박명준;안성모;이현구
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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    • pp.309-312
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    • 1997
  • The dynamic characteristics of a continuous MMA/MA free-radical solution copolymerization reactor were studied. A mathematical model was developed and kinetic parameters which had been estimated in the previous work were used. With this model, bifurcation diagrams were constructed with various parameters as the bifurcation parameter to predict the region of stable operating conditions and to enhance the controller performance. It was shown that the steady-state multiplicity existed over wide ranges of residence time and jacket inlet temperature. Periodic solution branches were found to emanated from Hopf bifurcation points. Under certain conditions isola was also observed, which would result in poor performance of feedback controllers.

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점동특성시스템이 다중의 정상상태해를 갖기 위한 필요충분조건 (A Necessary and Sufficient Condition for Multiplicity of Steady-State Solutions of Point-Kinetics Reactor Feedback Svstems)

  • Yang, Chae-Yong
    • Nuclear Engineering and Technology
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    • 제27권4호
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    • pp.463-469
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    • 1995
  • 궤환효과의 지배를 받는 점동특성시스템은 특정 운전조건에서 여러 개의 정상상태해를 가질 수 있다. 점동특성시스템의 다중해 및 비선형시스템의 일반적인 특성과 관련된 이론적 연구를 통하여, 점동특성시스템이 주어진 외부 입력 반응도에 대해 다중의 정상상태해를 갖기 위한 필요충분조건을 얻었다. 즉 정상상태에서의 궤환반응도가 제환변수의 어떤 값에 대해서 'Strictly Monotoruc'이 아니면, 점동특성시스템은 그 값에 대응되는 운전영역에서 다중의 정상상태해를 갖는다. 반면 정상상태에서의 궤환반응도가 궤환변수의 모든 값에 대해서 'Strictly Monotonic' 이면, 점동특성시스템은 항상 하나의 정상상태해를 갖는다.

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Controlling Mammalian Cell Metabolism in Bioreactors

  • Hu, Wei-Shou;Weichang, Zhou;Lilith F. Europa
    • Journal of Microbiology and Biotechnology
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    • 제8권1호
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    • pp.8-13
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    • 1998
  • Animal cells in culture typically convert most of the glucose they consume into lactate. The accumulation of lactate, however, is commonly cited as one of the factors that inhibit cell growth and limit the maximum cell concentration that can be achieved in culture. The specific production of lactate and the amount of glucose converted to lactate can be reduced when cells are grown in a fed-batch culture in which the residual glucose concentration is maintained at low levels. Such a fed-batch culture was used to grow and adapt hybridoma cells into a low-lactate-producing state before changing into continuous culture. The cells reached and maintained a high viable cell concentration at steady state. In a similar manner, cells that were initially grown in batch culture and a glucose-rich environment reached a steady state with a cell concentration that is much lower. The feed composition and dilution rates for both cultures were similar, suggesting steady state multiplicity. From a processing perspective the desired steady state among those is the one with the least metabolite production. At such seady state nutrient concentration in the feed can be further increased to increase cell and product concentrations without causing the metabolite inhibitory effect typically seen in a cell culture. Controlling cell metabolism in a continuous culture to reduce or eliminate waste metabolite production may significantly improve the productivity of mammalian cell culture processes.

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Nonlinear Dynamics of Homogeneous Azeotropic Distillations

  • Lee, Moonyong;Cornelius Dorn;Manfred Morari
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 1998년도 제13차 학술회의논문집
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    • pp.461-467
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    • 1998
  • In spite of significant nonlinearities even in the simplest model, some types of steady-state and dynamic behavior common for nonlinear systems have never been associated with distillation columns. In recent years, multiplicity of steady states has been a subject of much research and is now widely accepted. Subsequently, stability of steady states has been explored. Another phenomenon that. although widely observed in chemical reactors, has not been associated with models of distillation columns is the existence of periodic oscillations. In this article we study the steady-state and dynamic behavior of the azeotropic distillation of the ternary homogeneous system methanol-methyl butyrate-toluene. Our simulations reveal nonlinear behavior not reported in earlier studies. Under certain conditions, the open-loop distillation system shows a sustained oscillation associated with branching to periodic solutions. The limit cycles are accompanied by traveling waves inside the column. Significant underdamped oscillations are also observed over a wide range of product rates.

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Effect of Boundary Condition History on the Symmetry Breaking Bifurcation of Wall-Driven Cavity Flows

  • Cho, Ji-Ryong
    • Journal of Mechanical Science and Technology
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    • 제19권11호
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    • pp.2077-2081
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    • 2005
  • A symmetry breaking nonlinear fluid flow in a two-dimensional wall-driven square cavity taking symmetric boundary condition after some transients has been investigated numerically. It has been shown that the symmetry breaking critical Reynolds number is dependent on the time history of the boundary condition. The cavity has at least three stable steady state solutions for Re=300-375, and two stable solutions if Re>400. Also, it has also been showed that a particular solution among several possible solutions can be obtained by a controlled boundary condition.

A Study on Natural Convection from Two Cylinders in a Cavity

  • Mochimaru Yoshihiro;Bae Myung-Whan
    • Journal of Mechanical Science and Technology
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    • 제20권10호
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    • pp.1773-1778
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    • 2006
  • Steady-state natural convection heat transfer characteristics from cylinders in a multiply-connected bounded region are clarified. A spectral finite difference scheme (spectral decomposition of the system of partial differential equations, semi-implicit time integration) is applied in numerical analysis, with a boundary-fitted conformal coordinate system through a Jacobian elliptic function with a successive transformation to formulate a system of governing equations in terms of a stream function, vorticity and temperature. Multiplicity of the domain is expressed explicitly.

Steady states and dynamic behavior of an LDPE autoclave reactor

  • Lee, Jin-Suk;Chang, Kil-Sang;Kim, Jae-Yeon;Rhee, Hyun-Ku
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
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    • pp.813-818
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    • 1989
  • A two compartmented autoclave reactor for the polymerization of low density polyethylene is analyzed with respect to the effects of heat transfer and operation variables. Each compartment being considered as a completely mixed cell, two CSTRs model is proposed. The system shows various multiplicity features of steady state and periodic oscillatory motions. Heat removal efficiency and initiator supplement appear to have significant effect on the conversion of monomer with the temperature properly maintained, which should be taken into account in the reactor design.

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Van de Vusse 반응기 동특성을 구현하는 액위시스템 및 제어 실험 (Liquid Level System Realizing Van de Vusse Reactor Dynamics and its Control Experiments)

  • 이지태
    • Korean Chemical Engineering Research
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    • 제58권2호
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    • pp.184-189
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    • 2020
  • Van de Vusse 반응기는 정상상태 입출력 관계에서 최대값을 그리고 이 최대값을 기준으로 동특성의 형태가 크게 바뀌는 특성을 보인다. 운전영역에 따라 정상상태 이득의 부호가 바뀌고, non-minimum phase 동특성 등의 제어를 매우 어렵게 하는 특성들이 나타난다. 매우 많은 비선형제어 방법들과 새로이 고안되고 있는 방법들이 이 Van de Vusse 반응기 공정에 적용되어 그 성능 검증이 이루어지고 있다. 이 반응기의 실제 예가 보고되어 있으나, 화학반응 특성상 제어기 실험에 일상적으로 사용되기에는 어려움이 많아 대부분 모사연구에 그치고 있다. 여기서는 이 Van de Vusse 반응기의 특성을 모두 구현하는 액위시스템을 제작하고, 새로이 고안되는 비선형 제어기의 성능을 밝히는 기준이 될 수 있는 간단한 두 제어 방법의 실험 결과를 제안하고자 한다. 액위시스템 실험장치와 제안된 제어 방법들은 매우 간단하며, 비선형 제어기의 성능과 현장 적용 가능성을 검증하는데 유용하게 사용될 수 있을 것이다.

Modeling and analysis of an LDPE autoclave reactor with axial dispersion

  • Park, Seung-Koo;Wi, Jeong-Ho;Rhee, Hyun-Ku
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 22-24 Oct. 1991
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    • pp.1693-1698
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    • 1991
  • An axial dispersion model is developed for the slim reactor employed in the LDPE autoclave process so that imperfect mixing caused by large L/D ratio (10-20) may be quantified by Peclet number. The model is then used to investigate the effect of mixing on the reactor performance represented by the monomer conversion, the reactor temperature, the molecular weight, and the polydispersity. In addition, the existence of steady state multiplicity is identified with the initiator feed concentration or the feed temperature as the bifurcation parameter. The effects of the initiator feed concentration and the feed temperature are also examined.

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Modeling and adaptive pole-placement control of LDPE autoclave reactor

  • Ham, Jae-Yong;Rhee, Hyun-Ku
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 1992년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 19-21 Oct. 1992
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    • pp.146-151
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    • 1992
  • A two-compartment four-cell model is developed for the adiabatic autoclave slim type reactor for free radical polymerization of low density polyethylene(LDPE). The mass and energy balances give rise to a set of ordinary differential equations, and by analyzing the system it is possible to predict properly not only the reactor performance but also the properties of polymer product. The steady state multiplicity is found to exist and examined by constructing the bifurcation diagram. The effects of various operation parameters on the reactor performance and polymer properties are investigated systematically to show that the temperature distribution plays the central role for the properties of polymer product. Therefore, it is essential to establish a good control strategy for the temperature in each compartment. In this study it is shown that the reactor system can be adoptively controlled by pole-placement algorithm with conventional PID controller. To accomplish a satisfactory control, the estimator and controller are initialized during the period of start-up.

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