Dynamic On‐Line Reoptimization Control of a Batch MMA Polymerization Reactor Using Hybrid Neural Network Models

A hybrid neural network model based on‐line reoptimization control strategy is developed for a batch polymerization reactor. To address the difficulties in batch polymerization reactor modeling, the hybrid neural network model contains a simplified mechanistic model covering material balance assuming perfect temperature control, and recurrent neural networks modeling the residuals of the simplified mechanistic model due to imperfect temperature control. This hybrid neural network model is used to calculate the optimal control policy. A difficulty in the optimal control of batch polymerization reactors is that the optimization effort can be seriously hampered by unknown disturbances such as reactive impurities and reactor fouling. With the presence of an unknown amount of reactive impurities, the off‐line calculated optimal control profile will be no longer optimal. To address this issue, a strategy combining on‐line reactive impurity estimation and on‐line reoptimization is proposed in this paper. The amount of reactive impurities is estimated on‐line during the early stage of a batch by using a neural network based inverse model. Based on the estimated amount of reactive impurities, on‐line reoptimization is then applied to calculate the optimal reactor temperature profile for the remaining time period of the batch reactor operation. This approach is illustrated on the optimization control of a simulated batch methyl methacrylate polymerization process.     

Experimental validation of the optimal trajectory of initiator concentration in a batch MMA polymerization reactor

This article presents a method to determine the trajectory of initiator concentration that will produce polymer with desired number‐ and weight‐average molecular weights at a prespecified level of monomer conversion. The optimal control theory is applied to the mathematical model for a batch methymethacrylate (MMA) solution polymerization reactor system. By imposing the constraint that initiator concentration should decrease within the range of self‐consumption by the initiation reaction, one can obtain the initiator concentration trajectory that can be tracked by feeding the initiator alone. A control scheme is constructed with a cascade proportional‐integral‐derivative (PID) control algorithm for temperature control and a micropump is installed to manipulate the initiator feed rate. The experimental results show satisfactory tracking control performance despite the nonlinear features of the polymerization reactor system. Also, the monomer conversion and the average molecular weights measured are found to be in fairly good agreement with those of model prediction, respectively. In conclusion, the polymer having desired molecular weight distribution can be produced by operating the batch reactor with the initiator supplement policy calculated from the model. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 1256–1266, 2000     

Optimal policies for BMA polymerization in nonisothermal batch reactor

In this paper, the optimal policies for bulk polymerization of n‐butyl methacrylate (BMA) are determined in a nonisothermal batch reactor. Four objectives are realized for BMA polymerization based on a detailed process model. The objectives are: (i) maximization of monomer conversion in a specified operation time, (ii) minimization of operation time for a specified, final monomer conversion, (iii) maximization of monomer conversion for a specified, final number average polymer molecular weight, and (iv) maximization of monomer conversion for a specified, final weight average polymer molecular weight. For each objective, the optimal temperature policy of heat‐exchange fluid inside reactor jacket is determined. The temperature of the heat‐exchange fluid is considered as a function of a specified variable. Necessary equations are provided to suitably transform the process model in terms of a specified variable other than time, and to evaluate the elements of Jacobian to help in the accurate solution of the process model. A genetic algorithm‐based optimal control method is applied to realize the objectives. The resulting optimal policies of this application reveal considerable improvements in the batch production of poly(BMA). © 2006 Wiley Periodicals, Inc. J Appl PolymSci 102: 2799–2809, 2006     

Nonlinear control of polymerization reactor

In this work, nonlinear model based control was applied to the free radical solution polymerization of styrene in a jacketted batch reactor and its performance was examined to reach the required monomer conversion and molecular weight. Optimal temperature profiles for the properties of polymer quality were evaluated using the Hamiltonian optimization method. Total simulation program having mass and energy balances of the jacketed polymerization reactor was used to calculate the optimal trajectories. For control purposes, several experimental and theoretical dynamic studies have been made to observe the validity of simulation program. Experimental and theoretical nonlinear model based control have been investigated to track the temperature at the optimal trajectory Two types of parametric and nonparametric models were evaluated to achieve the temperature control. For this purpose, reaction curve was obtained to calculate the system dynamic matrix as a nonparametric model. In all control work, heat input to the reactor was chosen as a manipulated variable. Nonlinear auto regressive moving average exogenous (NARMAX) giving a relation between heat input and reactor temperature was chosen to represent the system dynamic and this model was used to describe the related control system as a parametric model. NARMAX model parameters were determined by using Levenberg Marquard algorithm. A pseudo random binary sequence (P.R.B.S.) signal was employed to disturb the system. Total simulation program was used to calculate the system and control parameters. Several types and orders were used to construct the NARMAX models. The efficiency and the performance of the nonlinear model based control with the NARMAX model and dynamic matrix were tested to calculate the best model. Nonlinear model based control system was used to control the reactor temperature at desired temperature trajectory experimentally and theoretically. Theoretical simulation results were compared with experimental control data. It was concluded that the control simulation program represents the behavior of the controlled reactor temperature well. In addition, nonlinear model based control keeps the reactor temperature of optimal trajectory satisfactorily.     

Application of optimal temperature trajectory to batch PMMA polymerization reactor

A mathematical model is developed for the polymerization of methyl methacrylate (MMA) in a batch reactor. The model includes chain transfers to the monomer and solvent and termination by both combination and disproportionation and also takes into account the density change of the reactor contents and the gel effect. The usual pseudo-steady-state assumption is relaxed here. The validity of the proposed model is tested by an isothermal experiment of batch PMMA polymerization. Indeed, the experimental results show that the proposed model can describe the real polymerization system very well in view of both monomer conversion and average molecular weights. The optimal control theory is applied together with Pontryagin's minimum principle to calculate the optimal temperature trajectory for a batch polymerization reactor system which would lead to a polymer product having the desired properties set a priori. The performance index of the control system is composed of three factors—the desired monomer conversion and number- and weight-average molecular weights. The desired values of number- and weight-average molecular weights are obtained at a specified monomer conversion within acceptable error ranges. Control experiments are conducted to track the optimal temperature trajectory obtained from the model and the results are found to be in good agreement with the desired values. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 59–68, 1998     

The optimal control of polymerisation reactors

Two separate but related problems are treated in this paper: (i) the optimal control policy for continuous stirred tank polymerization reactors; (ii) the optimal control program for batch polymerization reactors. The first problem concerns determining the temperature and initiator control policy which brings the reactor to the desired steady state while minimizing some objective functional (e.g. start-up time, cost of control action, etc.). The second problem is concerned with finding the best temperature and initiator program so that the product from the batch reactor has the best possible molecular weight distribution. Both free radical polymerization and linear condensation polymerization examples are considered with molecular weight distribution moments being used to characterize the polymer. Kinetic parameters typical of styrene are used for the free radical case, and realistic parameters are chosen for the condensation examples. The techniques used can be immediately carried over to other polymerization systems, and hopefully generalizations about the character of the optimal policies for such new systems can be made by considering the policies found for the systems studied. The results of the study demonstrate some of the potential gains possible through supervisory computer control of polymerization reactors.     

基于动态优化和反馈控制的聚合反应过程牌号切换策略

针对单反应器多牌号聚合物生产过程, 提出一种结合动态优化和反馈控制的牌号切换策略。以实验室规模的连续搅拌釜式反应器中苯乙烯聚合牌号切换为对象, 以原料消耗最少为优化目标, 利用迭代动态规划求得切换过程中反应条件和产品性能指标的优化轨迹。引入针对反应温度的路径约束, 使优化后的切换轨迹更易跟踪实现, 防止过渡过程中变量的剧烈波动。仿真结果表明, 这一切换策略可以显著减少牌号切换过渡时间及过渡过程中原料的消耗量, 并能够有效克服进料温度变化的干扰。     

Generalization of Takagi-Sugeno Fuzzy Controller and its Application to Control of MMA Batch Polymerization Reactor

In this research a generalization of Takagi-Sugeno fuzzy controllers is presented. In this generalization all or some of the inputs of the fuzzy controllers are fuzzy numbers. Also, it is proved that this generalization is well defined, which means that if the inputs of a generalized Takagi-Sugeno fuzzy controller are singleton fuzzy sets, then the generalized Takagi-Sugeno fuzzy controller will be reduced to a Takagi-Sugeno fuzzy controller. This controller was applied to temperature control of a methyl methacrylate (MMA) batch polymerization reactor, which uses jacket temperature error in addition to reactor temperature error. But the desired jacket temperature is affected by noise and disturbance. Therefore, there is uncertainty in the desired value of this variable. Fuzzy numbers are applied to model this uncertainty and a fuzzy trajectory was achieved for jacket desired temperature. After that an adaptation mechanism was designed. Experimental results present the fine performance of this controller in temperature control of solution polymerization of methyl methacrylate.     

Application of experimental non-linear control based on generic algorithm to a polymerization reactor

The dynamics of free radical polymerization of styrene and on-line control of temperature in a cooling jacketed batch polymerization reactor is investigated. The benzoyl peroxide initiator is introduced into the reactor once at the beginning of the reaction to obtain the desired monomer conversion and the desired average chain length in a minimum reaction time. The optimal constant set temperature, which is generally realized in industrial applications, and the set profile are used as two different optimal operating conditions. The temperature control of the polymerization reactor is achieved experimentally and theoretically. The control of nonlinear systems has progressed considerably, and various nonlinear process model based control techniques have appeared in the literature. The problem is how to tune the controller in order to obtain comparable closed loop responses. Generic model control (GMC) is applied and the performance of the control results are compared with the previously published control results.     

Optimal reaction conditions for the minimization of energy consumption and by‐product formation in a poly(ethylene terephthalate) process

We determined the optimal reaction conditions to minimize the energy cost and the quantities of by‐products for a poly(ethylene terephthalate) process by using the iterative dynamic programming (IDP) algorithm. Here, we employed a sequence of three reactor models: the semibatch transesterification reactor model, the semibatch prepolymerization reactor model, and the rotating‐disc‐type polycondensation reactor model. We selectively chose or developed the reactor models by incorporating experimentally verified kinetic models reported in the literature. We established the model for the entire reactor system by connecting the three reactor models in series and by resolving some joint problems arising when different types of reactor models were interconnected. On the basis of the simulation results of the reactor system, we scrutinized the cause and effect between the reaction conditions and the final quality of the polymer product. Here, we set up the optimization strategy by using IDP on the basis of the integrated reactor model, and the process variables with significant influence on the properties of polymer were selected as control variables with the help of a simulation study. With this method, we could refine the reaction conditions at the end of each iteration step by contracting the spectra of control regions, and the iteration process finally stopped when the profile of the optimal trajectory converged. We also took the constraints on the control variables into account to guarantee polymer quality and to suppress side reactions. Constituting six different strategies by setting weighting vectors differently, we examined the differences in optimal trajectories, the trend of optimality, and the quality of the final polymer product. For each of the strategies, we conducted the optimization to examine whether the number‐average degree of polymerization approached the desired value. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 993–1008, 2002     

Multiobjective dynamic optimization of batch free radical polymerization process catalyzed by mixed initiator systems

The optimal control policies for batch free radical polymerization of styrene catalyzed by a binary mixture of monofunctional initiators have been determined using a multiobjective dynamic optimization technique. The process objectives considered in the optimization include monomer conversion, polymer molecular weight, initiator residue level, and total reaction time. It is illustrated through model simulations and experiments that the performance of the batch polymerization process can be improved significantly through the use of optimal initiator mixture and polymerization temperature programming. This paper also illustrates how the multiobjection optimization technique can be used effectively to solve complex polymerization reactor optimization problems with detailed reaction models.     

Dynamic optimization of a semi-batch reactor for polyurethane production

In this work, the dynamic optimization of a polyurethane copolymerization reactor is addressed. A kinetic-probabilistic model is used to describe the nonlinear step-growth polymerization of a mixture of low- and high-molecular-weight diols, and a low-molecular-weight diisocyanate. The dynamic optimization formulation gives rise to a highly complex and nonlinear differential-algebraic equation (DAE) system. The DAE optimization problem is solved using a simultaneous approach (SDO) wherein the differential and algebraic variables are fully discretized leading to a large-scale nonlinear programming (NLP) problem. The main reactor operation process control objective is the maximization of the molecular weight distribution (MWD) under a desired batch time, subject to a large set of operational constraints, while simultaneously avoiding the formation of polymer network (gel molecule). Typically, polyurethane formation is carried out using batch reactors. However, batch operation leads to attain relatively low MWD values and, if the process is not efficiently operated, there is always the possibility of obtaining a polymer network. In this work, it was found that process operation is greatly enhanced by the semi-batch addition of 1,4-butanediol and diamine, and the manipulation of the reactor temperature profile, allowing to obtain high molecular weights while avoiding the onset of the gelation point.     

Online polymer molecular weight and conversion monitoring via calorimetric measurements in RAFT emulsion polymerization

BACKGROUND: Online measurements of key emulsion polymerization attributes, such as conversion and molar mass distribution, are unavailable. Costly offline measurements at low sampling frequencies with time delays usually lead to insurmountable challenges in real‐time product quality monitoring and process/product control. RESULTS: We developed an online calorimetric method monitoring the evolution of conversion and molecular weight in complex polymerization reactors. Our experiments were carried out in a 1 L reactor to produce polystyrene homopolymer. Monomer conversion was obtained in real time from polymerization rate, which was estimated from temperature measurements using platinum thermal transducers. The calorimetric model was validated offline for batch and semi‐batch emulsion polymerization of styrene with and without transfer agents. The conversion was validated using offline gravimetry. The molecular weights measured offline via size exclusion chromatography with multiple detectors compared well with those estimated online using the calorimetric method. CONCLUSION: We found that a semi‐batch emulsion polymerization process can be controlled online to approach living polymerization involving transfer agents. Thus our model is suitable as a ‘soft‐sensor’ for real‐time control applications. Copyright © 2009 Society of Chemical Industry     

Optimization of a batch polymerization reactor at the final stage of conversion. II. Molecular weight constraint

A mathematical model for the free radical batch solution polymerization of methyl methacrylate that takes depropagation into account was developed. This model was then used to derive optimal temperature and initiator concentration policies to reduce residual monomer concentration to desired levels, producing at the same time a polymer with the desired number average molecular weight. An objective function was formulated to take account of the cost of the initiator with respect to the cost of time of reaction. It was observed that when the cost of initiator increased, optimal initiator concentration decreased whereas optimal temperature increased. Finally temperature reached a limiting value above which polymer with desired number average molecular weight could not be produced. These results give insight into the factors that determine the policies that could be employed in optimizing the operation of a reactor.     

Dynamic optimization of the methylmethacrylate cell‐cast process for plastic sheet production

Traditionally, the methylmethacrylate (MMA) polymerization reaction process for plastic sheet production has been carried out using warming baths. However, it has been observed that the manufactured polymer tends to feature poor homogeneity characteristics measured in terms of properties like molecular weight distribution. Nonhomogeneous polymer properties should be avoided because they give rise to a product with undesired wide quality characteristics. To improve homogeneity properties force‐circulated warm air reactors have been proposed, such reactors are normally operated under isothermal air temperature conditions. However, we demonstrate that dynamic optimal warming temperature profiles lead to a polymer sheet with better homogeneity characteristics, especially when compared against simple isothermal operating policies. In this work, the dynamic optimization of a heating and polymerization reaction process for plastic sheet production in a force‐circulated warm air reactor is addressed. The optimization formulation is based on the dynamic representation of the two‐directional heating and reaction process taking place within the system, and includes kinetic equations for the bulk free radical polymerization reactions of MMA. The mathematical model is cast as a time dependent partial differential equation (PDE) system, the optimal heating profile calculation turns out to be a dynamic optimization problem embedded in a distributed parameter system. A simultaneous optimization approach is selected to solve the dynamic optimization problem. Trough full discretization of all decision variables, a nonlinear programming (NLP) model is obtained and solved by using the IPOPT optimization solver. The results are presented about the dynamic optimization for two plastic sheets of different thickness and compared them against simple operating policies. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Nonlinear temperature control of a batch suspension polymerization reactor

This paper concerns nonlinear temperature control of a batch polymerization reactor where suspension polymerization of methyl methacrylate (MMA) takes place. For this purpose, four control algorithms, namely, a fix proportional‐integral (PI) controller, an adaptive proportional‐integral‐derivative (PID) controller and two globally linearizing control (GLC) schemes, one for known kinetic model (GLC‐I) and the other for unknown kinetic model (GLC‐II), are selected. The performances of these controllers are compared through simulation and real‐time studies in the presence of different levels of parameter uncertainty. The results indicate that GLCI and GLC‐II have better performances than fix PI and adaptive PID, especially in case of strong gel effect. The worst performance belongs to adaptive PID because of rapid model changes in gel effect region. GLC‐II has a simpler structure than GLC‐I and can be used without requiring the kinetic model. In implementation of GLC‐I the closed loop observer should be used because of model uncertainties.     

CONTROL OF MOLECULAR WEIGHT IN A BATCH POLYMERIZATION REACTOR USING LONG-RANGE PREDICTIVE CONTROL METHODS

Recently two powerful control algorithms, namely, dynamic matrix control (DMC) and extended self-tuning regulator (ESTR), have been advocated for the design of robust industrial controllers. The present paper demonstrates the application of DMC and ESTR algorithms to a bulk methyl methacrylate batch polymerization reactor operating under strong diffusional limitations of termination and propagation reactions. A realistic mathematical model is employed to simulate the strong nonlinear, time-varying dynamics of the polymerization process. The general control objective is to maintain the monomer conversion and number-average molecular weight along some desired state trajectories despite the presence of process disturbances in the total initiator concentration. It is shown that both controllers can satisfactorily control the monomer conversion and number-average molecular weight by manipulating the polymerization temperature. The similarities and the main operating features of the two controllers are examined and their closed-loop performance is directly compared to the performance of a conventional linear quadratic controller (LQC). Finally the effects of DMC and ESTR tuning parameters on the calculated control action are investigated.     

TRACKING PERFORMANCE OF CONTROL METHODS

In this work, the optimal temperature control of a styrene solution polymerization reactor with two different control algorithms is considered. DMC and PFD control mefhods are used to accomplish the optimal temperature control of the polystyrene reactor. Reactor optimal temperature profiles at different initiator initiation concentrations were obtained by applying maximum principle to the mathematical model of the free radical batch polymerization reactor lo produce polystyrene with desired conversion and molecular weight in a minimum lime. The results obtained from the experimental implementation of DMC and PID controller for the control of optimal temperature path of the polymerization reactor were compared.     

TRACKING PERFORMANCE OF CONTROL METHODS

In this work, the optimal temperature control of a styrene solution polymerization reactor with two different control algorithms is considered. DMC and PFD control mefhods are used to accomplish the optimal temperature control of the polystyrene reactor. Reactor optimal temperature profiles at different initiator initiation concentrations were obtained by applying maximum principle to the mathematical model of the free radical batch polymerization reactor lo produce polystyrene with desired conversion and molecular weight in a minimum lime. The results obtained from the experimental implementation of DMC and PID controller for the control of optimal temperature path of the polymerization reactor were compared.     

OPTIMAL TEMPERATURE CONTROL IN A BATCH POLYMERIZATION REACTOR USING NONLINEAR GENERALIZED PREDICTIVE CONTROL

The application of Non-Linear Generalized Predictive Control (NLGPC) to the free radical solution polymerization of styrene in a jacketed batch reactor has been realized. The dynamic behavior of polymerization reactor is modelled and simulated for control purposes. The optimal temperature policies for minimum time, desired conversion and molecular chain length were obtained at different initiator concentrations by applying the optimal control theory which is based on the Hamiltonian principle. The polynomial Nonlinear auto Regressive Integrated Moving Average with external input (NARIMAX) model is used to relate the reactor temperature with heat input for nonlinear control algorithm. The linear (ARIMAX) and nonlinear (NARIMAX) models are utilized in the GPC algorithm for comparison. A Pseudo Random Binary Sequence (PRBS) signal was employed to operate the system. The model parameters are evaluated by using Levenberg Marquart Method. The NLGPC, Linear Generalized Predictive Control (LGPC) and standard PID controllers are applied experimentally to the polymerization reactor by using on-line computer control system. The performance of NLGPC control system was compared with LGPC and standard PID controller. It is concluded that the NLGPC control gives much better performance than the other.