An assessment of dynamic operability measures

By using the local condition numbers, which are also measures of the conditioning of a nonlinear mapping of both transfer function and state space matrices, we investigate the way in which the system controllability varies across the anticipated range of operating conditions for two common process systems with nonlinearities. Linear techniques can lead to erroneous conclusions, shown here for a CSTR. It is also shown that the condition of the scaled state space matrix is not a reliable indication of the controllability of the system. The dynamic characteristics of a CSTR and a heat exchanger are investigated by obtaining the sensitivity indices from the model linearized at several steady states over a range of frequencies.     

Thermal regimes of exothermic processes in continuous stirred tank reactors

Thermal regimes of a CSTR are analysed from the standpoint of the thermal explosion theory. Critical phenomena and time characteristics of the process are considered. It is shown that for appropriately chosen dimensionless parameters the critical conditions of the thermal explosion and induction period in a CSTR slightly differ from those for non-flow (batch) systems. These corrections may be performed by using an additional parameter which is characteristic for flow systems. In the region of multiplicity of steady states, the critical condition of thermal explosion is characterized by a jump of self-heating, while in the non-flow systems such phenomenon occurs only for a zero order reaction. For a unique steady state the transition through the critical condition is continuous.     

Absorption with exothermic reaction in a falling film column

A gaseous reactant is absorbed in a liquid with a positive heat of absorption. It reacts with the liquid by an exothermic, irreversible first order reaction. Analysis of a CSTR for this process has shown that up to 5 steady state solutions may exist even though the system appears to be quite simple with only one reaction. The existence of an extraordinary large number of steady state solutions is explained by the coupling between absorption and reaction: A low temperature gives no reaction, a high temperature prevents absorption of the gas and hence leads to mass transfer control of the reaction, while an intermediate temperature may permit operation at a third (stable) steady state. In between the stable steady states one finds (as us two unstable steady states.We extend the analysis of the CSTR to the distributed system of a falling film reactor, and we treat both the transient situation in the entrance partAn eigenanalysis of the steady states shows that temperature rise across the gas film may lead to 3 stable steady states even if an isothermal model is     

DYNAMIC ANALYSIS OF GAS STRIPPING DURING ETHANOL FERMENTATION IN CSTR

1 INTRODUCTIONInhibition phenomena have frequently been observed in microbial reactions.When thesubstrate concentration in the broth is high enough,the contour curve of the specificgrowth rate of cells is no longer monotonically increasing in a substrate-product phaseplane.The system exhibits a substrate inhibition.Some supersession products can affectthe growth and the yield of the cells as well as the viability of the microorganisms.Forexample,in the case of using Saccharomyces,the ethanol product inhibits the growth     

Rate and oxygen activity oscillations during hydrogen oxidation on nickel films in a CSTR

The catalytic oxidation of hydrogen on polycrystalline nickel films was studied in a CSTR at 510-681°K and atmospheric pressure. The technique of Solid Electrolyte Potentiometry (SEP) was used to monitor the thermodynamic activity of oxygen adsorbed on the catalyst surface. To this end the reaction was studied in an yttria-stabilized zirconia solid electrolyte cell. Both steady state kinetics and potentiometric results indicate formation and reduction of a surface nickel oxide. In a certain range of temperature and gas composition sustained oscillatory phenomena were observed on both the reaction rate and the surface oxygen activity. A dynamic model of six differential equations that takes into account transient changes of the gas phase concentration of H₂, O₂ and H₂O as well as of the surface coverage of adsorbed hydrogen, oxygen and nickel oxide has been developed. The model explains quantitatively the stable steady state kinetic and SEP results. The same model predicts oscillatory behavior and explains qualitatively the observed unsteady state phenomena.     

Analysis of the CSTR with two-phase flow under phase equilibrium conditions

A mathematical model of the flow gas-liquid continuous stirred tank reactor (CSTR) is presented under the assumption of thermodynamic equilibrium of the two-phase flow. Phase equilibrium was calculated using the Redlich-Kwong-Soave (RKS) equation of state. An efficient algorithm based on homotopy method was used to obtain a numerical solution of the system of nonlinear algebraic equations of the model. By an example of the liquid-phase hydrogenation of benzene, steady states were analyzed in isothermal and adiabatic regimes and at partial removal of heat released as a result of exothermic reaction. It was shown that under certain conditions, a multiplicity of stationary solutions is possible due to nonlinearity of the kinetic reaction, on the one hand, and deviation of the reaction mixture properties from the ideal state, on the other hand.     

Dynamics analysis of an age distribution model of oscillating yeast cultures

The ability of an age-population balance model to capture experimentally observed oscillatory dynamics of continuous cultures of budding yeast was investigated through numerical simulations. Experiments with continuous yeast cultures have shown that several oscillatory modes can occur at the same operating condition, and that the mode attained depends on the start-up conditions. Numerical simulations of the model did reveal the existence of several stable periodic solutions. However, each occurred over a different range of dilution rates. Experiments also have shown that the steady state in continuous yeast cultures is stable, even under conditions that allow oscillatory dynamics. The stability of the steady state of the age population balance model under conditions that allow oscillatory dynamics was not resolved. The Jacobian matrix at the steady state is highly ill conditioned, with some eigenvalues very close to the imaginary axis. Using different integration routines to solve the model gave different results with regard to the stability of the steady state, one solver finding the steady state to be stable, another finding the steady state to be unstable.     

The dynamic behavior of continuous polymerization reactors—I: Isothermal solution polymerization in a CSTR

A mathematical model having no adjustable parameters is developed and compared with both dynamic and steady-states” in the neighborhood of unstable middle steady states is thought to be due to a combination of methacrylate with ethyl acetate solvent, in a CSTR, was shown to have ignition and hysteresis behavior characteristic of multiple steady states for sufficiently low solvent concentrations. The observation of “pseudosteady-states” in the neighborhood of unstable middle steady states is thought to be due to a combination of kinetic and hydrodynamic mechanisms.     

Versal matrix families,normal forms and higher order bifurcations in dynamic chemical systems

Characterization of the possible dynamic phenomena which arise when a steady state loses stability due to parametric variations is important in process and control system design and is useful for dynamic model identification and evaluation. The linearized system Jacobian Jordan block structure at bifurcation implies corresponding possibilities for nonlinear dynamic phenomena near bifurcation. The linearized system characteristic equation and the theory of versal representation of matrix families are applied to identify the number of system parameters which must be varied simultaneously to achieve different eigenvalue configurations. The theory of normal forms is used to illustrate the topological equivalence, near bifurcation, of the original system and the normal form representation which contains a relatively small number of nonlinear differential equations. This theory is used to organize and interpret studies of dynamics in two chemical reaction systems: (i) consecutive-competitive reactions in an isothermal CSTR with multivariable proportional feedback control; and (ii) coupled oscillations in two interacting CSTR's with autocatalytic reactions.     

发酵过程中气提的动力学行为探讨

依据歧点和稳定性理论探讨了在全混釜发酵过程中气提移醇的动力学行为，研究了该系统的多重定态现象、以及气提对多重稳态解的影响。通过模拟计算，确立了该系统最优稳态操作区范围，分析了菌体初始浓度和产物初始浓度之间的相互限制作用，以及对最优稳态吸引区的影响。分析结果表明：气提应用于发酵过程，能缓和产物醇对微生物的毒性，扩展系统的操作范围，控制系统移向最优稳态操作。     

Bulk copolymerization of styrene-acrylic esters: Some analysis and design considerations

A common framework for the analysis of styrene-acrylic ester systems has been developed by analyzing the pertinent kinetic information. This is shown to lead to a well defined strategy for the design of copolymerization reactors especially in the industrially relevant high conversion region. The existence of stable steady states and its influence on the system parameters has been illustrated for the case of a continuous stirred tank reactor (CSTR). A novel strategy of a CSTR operated with a recycle is proposed. This is shown to lead to an operation in the unique steady state with the added advantage of a high conversion and uniform copolymer composition. This would seem to be the first such analysis in the high conversion region.     

连续反应釜温度控制系统的设计与仿真

针对连续反应釜中进行的化学反应特性,按照过程的动力学方程和能量平衡等关系,设计了一套基于西门子PCS7的连续化学反应釜(CSTR)温度控制系统。由于连续反应釜内温度的非线性、时变等特性,采用变结构模糊控制结合前馈、串级、分程等先进的控制方式,克服了传统PID算法参数调整复杂、超调量大的缺点。仿真结果表明:对温度采用变结构模糊控制能获得较好的稳态精度和动态特性,满足了反应釜内温度控制的要求。     

FUZZY GAIN SCHEDULED CSTR WITH GA-BASED PID

In this article, a new control scheme, the gain scheduled genetic algorithm (GA)-based PID is proposed for a continuous stirred tank reactor (CSTR). A CSTR is a highly nonlinear process that exhibits stability in certain regions and instability in other regions. The proposed control scheme implements the characteristics of the genetic algorithm's (GA) global optimization to optimize the PID's three control parameters, k_p, k_i, k_d, to obtain the best control effect by minimizing the integral square error online. The PID controller parameters tuned by the GA for each region are gain scheduled by a fuzzy logic scheduler. Fuzzy gain scheduling is a special form of fuzzy control that uses linguistic rules and fuzzy reasoning to determine the controller parameter transition policy for the dynamic plant subject to large changes in its operating state. Simulation results show the feasibility of using the proposed controller for the control of the dynamical nonlinear CSTR.     

Design of Fuzzy Control for Maintaining a CSTR in the Steep Section of Its Nonlinear Characteristic

The operation of a continuous stirred tank reactor (CSTR) in the steep domain of its nonlinear process characteristic is studied, using catalyzed hydrogen peroxide decomposition as a model process because of its transparent nonlinear dynamics. Unstable equilibrium states and corresponding limit cycles exist in the steep domain, the latter representing dynamically stable modes of operation where safer control is expected due to the lower educt concentration in the reactor. For CSTR control in the steep domain, a fuzzy approach is applied based on simulations and experimental understanding of the stable and unstable states of the reactor. Simulations are carried out for the set‐point control of an unstable equilibrium state, and the tracking control of the corresponding stable limit cycle. The simulation results show that operation in the limit cycle requires much less control energy than that of the corresponding unstable equilibrium state in the case of disturbances, e. g., due to unavoidable modelling errors.     

Continuous screening of base-catalysed biodiesel production using New designs of mesoscale oscillatory baffled reactors

Base-catalysed biodiesel production was continuously screened using new designs of mesoscale oscillatory baffled reactors. Experiments were carried out at very low flow rates, less than 2 ml/min, which would be in the laminar flow regime in non oscillatory, steady state. Initially central disc baffles and helically wound wires were used, but provided insufficient mixing at this scale as demonstrated by glycerol settling. A new design of sharp-edged, helically baffled reactor was developed specifically for this application, which exhibited homogeneous mixing in the two-phase liquid reaction even at these low flow rates and low oscillatory Reynolds numbers. Methyl ester (biodiesel) was produced at a consistent quality and there were clear responses to variations in input conditions. A clear step-change between various steady state molar ratios of methanol to oil and dynamic screening was observed in these mesoscale oscillatory baffled reactors. Rapid screening technique such as this has the potential to significantly reduce process development, operating costs and environmental impact.     

Cascade closed-loop optimization and control of batch reactors

In this paper, a cascade closed-loop optimization and control strategy for batch reactors is proposed. Based on the reduction of a physical conservation model a cascade system is developed, which can effectively combine optimization and control to achieve good on-line optimization and tracking performance under the common condition where incomplete knowledge of the reaction system exists. A two-tier estimation scheme using a nonlinear observer for heat production rate and reaction rates is also developed. In the reaction rate estimation, calorimetric information is used. The on-line closed-loop optimization strategy uses a descending horizon dynamic optimization algorithm based on nonlinear programming and an additive unknown disturbance for feedback. A simple adaptive nonlinear tracking system is designed based on the generic model control concept. The efficiency of this strategy is demonstrated through simulations on a batch reactor under various operation conditions, such as noisy measurements, varying initial states and model mismatch.     

Steady state multiplicity behavior of an isothermal axial dispersion fixed-bed reactor with nonuniformly active catalyst

An isothermal, heterogeneous fixed-bed reactor packed with nonuniformly active catalyst pellets where a biomolecular Langmuir-Hinshelwood reaction occurs, is studied using an axial dispersion model. A catalyst activity distribution given by a Dirac delta function, where the active catalyst is deposited at a specific location within the pellet, is considered. This includes the common case of externally coated pellets with external mass transfer resistance. The steady state multiplicity behavior of this reactor, and its limiting cases: CSTR, PFR and pseudohomogeneous axial dispersion, are examined in detail. The nonlinearity of the reaction kinetics provides two sources of multiplicity, through the heterogeneous nature of the reactor and the presence of axial dispersion in the fluid phase. Their roles in determining reactor multiplicity behavior are fully explored. It is shown that this system can admit at most nine steady state solutions. The limiting behavior of the heterogeneous axial dispersion model as Pe → 0 or ∞ is not represented fully by the CSTR or PFR models because of ignition phenomenon. Finally, the effects of mixing on reactor conversion are discussed.     

Traveling-wave Phenomena in a Model of Autocrine Signaling Coupled with Dynamics of the MAPK Cascade

Recently we have revealed a minimal reaction subnetwork in the MAPK (mitogen-activated protein kinase) cascade that is responsible for the emergence of bistable and oscillatory behavior. Here we examine a possible mechanism that provides for the propagation of increased MAPK activity in cell populations by interconnecting the intracellular MAPK subnetwork with the ligand-receptor signaling machinery. Such approach allows for significant reduction of the dimensionality of the parameter space on one hand and the conservation of dynamical complexity of the system on the other hand. The coupled model predicts coexistence of one, two or three different stable steady states, or the coexistence of a stable steady state and periodic solution. We found two robust and physiologically relevant characteristics of the proposed model: (i) There is a very large region of coexistence of at least one stable steady state with non-zero MAPK activity and one steady state with zero MAPK activity in the parameter space. (ii) Spontaneous traveling front waves always switching originally inactive cells into ligand releasing cells emerge in adjacent cell populations, e. g. in healthy and injured tissues. Moreover, the formation of composite traveling front waves and spatial oscillatory patterns of MAPK activity are predicted and discussed.     

一种用于动态化工过程建模的反馈神经网络新结构

提出了一种新的用于非线性动态化工过程的状态集成反馈神经网络结构 (SIRNN) ,并将静态BP网络的训练算法引入到该网络的训练中 .状态反馈、时间序列延迟与集成节点的概念结合在SIRNN结构中 ,使得在用SIRNN建模过程中既可以考虑系统过去更多时刻的状态信息又可以相对降低网络的复杂程度 ,使得网络结构更趋于合理 .将SIRNN对一单输入单输出二阶非线性动态系统建模 ,并与其他反馈神经网络建模效果进行了比较 ,同时对该网络结构进行了抗干扰性检验 ,并对其在多输入单输出系统的应用中进行了尝试 ,结果表明SIRNN结构对非线性动态系统建模具有快速、高效和抗干扰的良好性能     

STABILITY OF THE CSTR BY CORRELATION OF LIAPUNOV FUNCTIONS

A general Liapunov function for a homogeneous CSTR is formally developed from available Liapunov functions which guarantee the global asymptotic stability of steady states associated with the separate mechanisms (flow mixing and chemical reaction) which compete in a CSTR. The Liapunov functions for the asymptotic systems (mixing tank and batch reactor) are combined via a one parameter correlation form to provide a one parameter family of Liapunov functions for the general CSTR. The single parameter allows for convenient optimization of regions of asymptotic stability surrounding CSTR steady states.