Double-command feedforward-feedback control of a nonlinear plant

A design approach is proposed for feedforward-feedback control systems. The basis of the proposed approach is a steady state control law which maintains the desired control output of the system and is employed as the feedforward controller. With this feedforward controller, for a wide class of systems, the stability of the control system is proved if the feedback controller is a gain with an arbitrarily high value; that is, the only limit for the feedback (transient) control command is the actuator’s practical limit. Moreover, in continuous domain, there will be no overshoot. In this article, the proposed method has been applied to a catalytic stirred tank reactor (CSTR) to control the output concentration through adjusting the flow of two valves simultaneously and resulted in an excellent control response.     

Fuzzy-based nonlinear PID controller and its application to CSTR

This study presents a new design method for a nonlinear variable-gain PID controller, the gains of which are described by a set of fuzzy rules. User-defined parameters are tuned using a genetic algorithm by minimizing the integral of absolute error and the weighted control input deviation index. It was observed in the experimental results on a continuous stirred tank reactor (CSTR) that the proposed controller provided performances: overshoot M _p ≤1.25%, 2% settling time t _s ≤1.71 s and IAE≤1.26 for set-point tracking, perturbance peak M _peak ≤0.05%, 2% recovery time t _rcy ≤3.97 s and IAE≤0.10 for disturbance rejection, and M _peak ≤0.04%, t _rcy ≤2.74 s and IAE≤0.04 for parameter changes. Comparison with those of two other methods revealed that the proposed controller not only led to less overshoot and shorter settling time for set-point tracking and less perturbance peak and shorter recovery time for disturbance rejection, but also showed less sensitivity to parameter changes.     

CSTR工艺与控制系统的集成优化设计方法

与传统的序贯设计方法相比,过程工艺与控制系统的集成优化设计可较大地提高过程的可操作性和经济性能,但基于常规动态优化的集成设计问题求解困难。采用最优控制和分层优化策略的思想,将线性二次调节器(LQR)嵌入到过程工艺与控制系统集成设计框架中,以降低集成优化设计问题的求解难度。将该方法应用于连续搅拌釜式反应器(CSTR)的设计中,通过与传统的序贯设计方法相比较,表明了该方法的有效性。     

Time-optimal control of mmama copolymerization in a CSTR for grade change

The time-optimal control of MMA-MA copolymerization in a CSTR is treated for a grade-change operation. The control objective is to bring system specifications, such as polymer production rate and polymer composition, to desired values in minimum time. The initiator concentration is chosen as a manipulated variable. Two cases are considered: One is to get the time optimal control for both a desired polymer production rate and a desired weight composition of MA in dead copolymer; the other is only for a desired polymer production rate. In numerical calculation, the final t(ⁱ)_f is chosen at each iteration as the time at which the system reached steady-state. This allows us to use a more easily manipulatable form of the performance index and at the same time not directly use the free final time boundary condition.     

连续搅拌釜的非线性模型稳定性判据及算法

针对具有强非线性、时变、有纯滞后等复杂特性的连续搅拌釜(CSTR)反应过程,提出了一种非线性鲁棒模型预测控制方法。先根据搅拌釜中物料反应和温度波动机理,强鲁棒性的系统参数假设在凸多面体中,然后,在温度工作稳定平衡点离散线性化具有高度非线性特点的系统方程。合理建立系统预报方程,提出可保成本性能指标函数并计算李雅普诺夫函数的差分。采用双线性和线性矩阵不等式(BMI和LMI)技术处理鲁棒模型预测控制系统,给出了保持较优性能条件下的闭环系统稳定性判定标准。其次,考虑稳定标准的条件中存在双线性矩阵不等式,设计相应的凸优化算法,便于利用matlab中LMI TOOLBOX求解。最后,通过系统仿真实验,与已有数值结果对比,说明了所提理论的正确性和算法的有效性、优越性。     

Periodic operation of CSTR - II practical control

The periodic operation of CSTR with a coil or a jacket for controlling the temperature is investigated with aid of the necessary conditions for the optimality of the totally singular control. Three reaction systems are examined, the parallel reaction, the consecutive reaction and the reversible reactionA sufficient condition for the superiority of the periodic control to the steady control is obtained. It is also observed by numerical calculations for a set of parameter values that the periodic control is superior to the steady control only when this sufficient condition is satisfied.     

Parametric sensitivity of a CSTR

It is shown that the generalized sensitivity criterion recently developed in the context of thermal explosions and tubular reactors can be easily applied in the case of a CSTR as well. An illustrative example concerning sensitivity analysis of a single nth order irreversible exothermic reaction in a nonadiabatic CSTR is presented. A generalized region of parametric sensitivity is identified where the reactor temperature is parametrically sensitive simultaneously to all the input parameters. Asymptotic analysis for large heats of reaction is performed to investigate limiting behaviour, which leads to the classical Semenov limit in the case of large activation energies. It is shown that parametric sensitivity can occur even when unique steady states exist for all Damköhler number (Da) values. Furthermore, if operating conditions are chosen so as to avoid completely the possibility of parametric sensitivity for all Da, then the possibility of steady-state multiplicity is automatically avoided.     

Guaranteed cost distributed fuzzy observer‐based control for a class of nonlinear spatially distributed processes

The guaranteed cost distributed fuzzy (GCDF) observer‐based control design is proposed for a class of nonlinear spatially distributed processes described by first‐order hyperbolic partial differential equations (PDEs). Initially, a T–S fuzzy hyperbolic PDE model is proposed to accurately represent the nonlinear PDE system. Then, based on the fuzzy PDE model, the GCDF observer‐based control design is developed in terms of a set of space‐dependent linear matrix inequalities. In the proposed control scheme, a distributed fuzzy observer is used to estimate the state of the PDE system. The designed fuzzy controller can not only ensure the exponential stability of the closed‐loop PDE system but also provide an upper bound of quadratic cost function. Moreover, a suboptimal fuzzy control design is addressed in the sense of minimizing an upper bound of the cost function. The finite difference method in space and the existing linear matrix inequality optimization techniques are used to approximately solve the suboptimal control design problem. Finally, the proposed design method is applied to the control of a nonisothermal plug‐flow reactor. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2366–2378, 2013     

Sampled-data control of a nonlinear system

Sampled-data proportional control of an exothermic CSTR has been studied using the classical linear analysis and by the application of the averaging te     

Nonlinear feedback control for operating a nonisothermal CSTR near an unstable steady state

Application of relay feedback controllers to maintain process states near unstable steady states is extended to a second order system, the CSTR with an irreversible, exothermic reaction. The control scheme is successful provided the bandwith (the reactor temperature deviation which causes relay switching) is not chosen too large relative to the drive levels (the deviation in coolant temperature caused by relay switching). In this context Tsypkin's analytical methods for approximate solution of this and higher order problems are elaborated and tested. Tsypkin's technique proves superior to Describing Function analysis in accuracy and in bounds on the maximum permissible bandwidth.     

Refolding of proteins in a CSTR

A model to predict refolding of proteins in a continuous stirred tank reactor (CSTR) was developed and compared to a batch refolding process with simple dilution of the protein in a stirred tank reactor. For experimental verification of the model a continuous refolding of a model protein (α-lactalbumin) was performed in a CSTR. The refolding process of denatured and fully reduced α-lactalbumin could be accurately predicted by a set of differential equations assuming a first order reaction rate for folding and a second order reaction rate for aggregation. The system composed of a CSTR with an additional diafiltration circuit for removal of denaturing agents from the feed solution and to maintain constant refolding conditions. Based on the folding kinetic the dynamic behavior of such a continuous refolding reactor was simulated under different operating conditions. It was shown that the refolding efficiency was higher compared to batch dilution under certain conditions, namely high residence times. The yield of refolded protein could further increased by recycling the outlet stream containing unfolded protein to the reactor entrance.     

A study of gain scheduling control applied to an exothermic CSTR

This paper describes how gain scheduling control is applied to a continuous stirred tank reactor model. The CSTR process, equipped with a cooling system, is modelled. Based on the resulting nonlinear model, a gain scheduling controller is designed. The gain scheduling follows a scheme denoted bias compensation. Compared to earlier reported gain scheduling schemes, the proposed scheme results in a controller that is less complex, which is advantageous in the controller implementation stage. Numerous simulations are performed, using the gain scheduling controller and two choices of control input to the reactor model. The simulation results indicate that a gain scheduling controller performs better than a linear controller. Simulations using different choices of control input to the reactor model indicate that proper process design is crucial for the controlled process performance.     

Adaptive type-2 fuzzy logic control of a bioreactor

Two adaptive type-2 fuzzy logic controllers with minimum number of rules are developed and compared by simulation for control of a bioreactor in which aerobic alcoholic fermentation for the growth of Saccharomyces cerevisiae takes place. The bioreactor model is characterized by nonlinearity and parameter uncertainty. The first adaptive fuzzy controller is a type-2 fuzzy-neuro-predictive controller (T2FNPC) that combines the capability of type-2 fuzzy logic to handle uncertainties, with the ability of predictive control to predict future plant performance making use of a neural network model of the nonlinear system. The second adaptive fuzzy controller is instead a self-tuning type-2 PI controller, where the output scaling factor is adjusted online by fuzzy rules according to the current trend of the controlled process. The performance of a type-2 fuzzy logic controller with 49 rules is used as reference.     

Control of a nonlinear continuous bioreactor with bifurcation by a type-2 fuzzy logic controller

The object of this paper is the application of a type-2 fuzzy logic controller to a nonlinear system that presents bifurcations. A bifurcation can cause instability in the system or can create new working conditions which, although stable, are unacceptable. The only practical solution for an efficient control is the use of high performance controllers that take into account the uncertainties of the process. A type-2 fuzzy logic controller is tested by simulation on a nonlinear bioreactor system that is characterized by a transcritical bifurcation. Simulation results show the validity of the proposed controllers in preventing the system from reaching bifurcation and instable or undesirable stable conditions.     

Micromixing effects on complex reactions in a CSTR

Several errors and mistakes are pointed out in a paper published by Rao and Rao under the above title, concerning the influence of micromixing on conversion and yield for consecutive-competing second order reactions. The influence of the stoichiometric ratio and the existence of limiting conversion and yield for instantaneous reactions with unmixed feed are especially overlooked in their simulations. Several of their plots are erroneous. A correct treatment of these different points is given, using in particular a deterministic micromixing model (IEM) which is found to show definite advantages over random coalescence simulation models.     

Optimization and nonlinear control of a batch crystallization process

Crystallization process has been widely used for separation in many chemical industries due to its capability to provide high purity product. To obtain the desired quality of crystal product, an optimal cooling control strategy is studied in the present work. Within the proposed control strategy, a dynamic optimization is first preformed with the objective to obtain the optimal cooling temperature policy of a batch crystallizer, maximizing the total volume of seeded crystals. Two different optimization problems are formulated and solved by using a sequential optimization approach. Owing to the complex and nonlinear behavior of the batch crystallizer, the nonlinear control strategy which is based on a generic model control (GMC) algorithm is implemented to track the resulting optimal temperature profile. The optimization integrated with nonlinear control strategy is demonstrated on a seeded batch crystallizer for the production of potassium sulfate.     

Micromixing effects on complex reactions in a CSTR

Micromixing effects on consecutive-competing second order reactions in an ideally macromixed CSTR are investigated by the use of the Two Environment Model of Ng and Rippin for mixed feed, and the model of Spielman and Levenspiel for unmixed feed.General plots are obtained for various values of reaction and mixing parameters. Yield of the desired product is found to show a maximum at intermediate states of micromixing for unmixed feed conditions. For mixed feed condition, micromixing effects are found to be very small.     

Experimental evaluation of a model-based degree of segregation in a CSTR

Conversions measured at the outlet of a CSTR, in which sodium bromoacetate reacted isothermally with sodium thiosulfate, were found to lie between the macro and microfluid conversion limits.On the basis of a reactor model, these data led to evaluations of a degree of segregation within the reacting mixture. This degree of segregation decreases linearly with increasing propeller speed. This rate of decrease is greater the larger the propeller diameter and the higher the propeller height above the reactor bottom. Feed jet velocity had no significant effect on this rate.This degree of segregation is inversely proportional to Reynolds' number to the $\text{1}\text{6}$th power.     

Dynamic simulation and control of auto-refrigerated CSTR and tubular reactor for bulk styrene polymerization

Dynamic simulation and control of a two-stage continuous bulk styrene polymerization process is developed to predict the performance of auto-refrigerated CSTR and tubular reactors. The tubular reactor is subdivided into three temperature-control jacket zones. In this paper temperature control of auto-refrigerated continuous stirred tank reactor and tubular reactor are carried out, simultaneously. Two strategies are proposed for the control of tubular reactor. At the first strategy the controlled variable is jacket temperature and in the second strategy the controlled variable is the reactor temperature at the exit of each section. The set points for polymer grade transition are obtained using optimization of reactors temperatures via genetic algorithm (GA). Simulation results show that both of the control strategies are successful but second strategy has better performance in the control of polymer properties in the presence of disturbance and model mismatch.