Generalized delta rule (GDR) algorithm with generalized predictive control (GPC) for optimum temperature tracking of batch polymerization

The generalized delta rule (GDR) algorithm with generalized predictive control (GPC) control was implemented experimentally to track the temperature on a set point in a batch, jacketed polymerization reactor. An equation for optimal temperature was obtained by using co-state Hamiltonian and model equations. To track the calculated optimal temperature profiles, controller used should act smoothly and precisely as much as possible. Experimental application was achieved to obtain the desired comparison. In the design of this control system, the reactor filled with styrene-toluene mixture is considered as a heat exchanger. When the reactor is heated by means of an immersed heater, cooling water is passed through the reactor-cooling jacket. So the cooling water absorbs the heat given out by the heater. If this is taken into consideration, this reactor can be considered to be continuous in terms of energy. When such a mixing chamber was used as a polymer reactor with defined values of heat input and cooling flow rate, system can reach the steady-state condition. The heat released during the reaction was accepted as a disturbance for the heat exchanger. Heat input from the immersed heater is chosen as a manipulated variable. The neural network model based on the relation between the reactor temperature and heat input to the reactor is used. The performance results of GDR with GPC were compared with the results obtained by using nonlinear GPC with NARMAX model.The reactor temperature closely follows the optimal trajectory. And then molecular weight, experimental conversion and chain lengths are obtained for GDR with GPC.     

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     

Temperature Control of a Bench‐Scale Batch Polymerization Reactor for Polystyrene Production

Batch polymerization reactors commonly use optimal temperature control as the strategic operation parameter. This strategy allows for better operability and a more economic process. The main objective of the batch polymerization reactor control is to obtain acceptable product quality. Direct measurement of polymer quality is rarely achievable, which makes the online control of the reactor difficult. Temperature is the most controllable operational variable in the polymer reactor, which is seen to have a direct effect on the polymer properties. Temperature is chosen as the set point by using either the isothermal temperature or optimal temperature trajectory. Online control of the optimal temperature profile of a bench‐scale batch polymerization reactor was experimentally investigated in this study. The temperature trajectory was used as the target for controllers to follow. The time‐profile temperature was obtained with the objective of obtaining the desired conversion and number‐average chain length within the minimum time. Two advanced controls of fuzzy logic control and generic model control were applied to the polymer reactor. A comparison of the controllers reveals that both performed better than conventional controllers.     

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.     

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     

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.     

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.     

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.     

Computation of the near-optimal temperature and initiator policies for a batch polymerization reactor

Optimal control theory is applied to a batch polymerization reactor for PMMA to calculate the near-optimal temperature and initiator policies that are required to produce a polymer with a desired final conversion, and desired number average and weight average molecular weights. The two-point boundary value problem that results from the application of the Pontryagin minimum principle to the mathematical model of the reactor is solved by the discretization control method. According to this, the total reaction time is divided into N equal subintervals. It is assumed that the control variables remain constant in each interval and the Hamiltonian is minimized by a first-order gradient technique. It is shown that the introduction of the “target set” concept, which is well suited to industrial practice, simplifies the numerical solution of the TPBV problem. Results of the simulations demonstrate the potential gains possible from the application of the optimal control theory to the batch polymerization of PMMA.     

Emulsion copolymerization: Kinetics model and reactor performance

The Dow process for producing perfluorinated ionomeric membranes includes several emulsion copolymerizations involving gaseous tetrafluoroethylene and a second liquid phase monomer. The choice of the organic phase monomer depends on the desired product. The emulsion copolymerization reactor model was developed by extending the Smith-Ewart-Gardon theory for emulsion polymerization processes. Population balance techniques and Flory-Huggins solution theory were applied. The resulting coupled partial differential equations were solved using the method of characteristics. The reactor model, with minimal adjustable parameters, predicts most polymerization results, including molecular weight, reaction rates in the three process stages, latex particle size, polymer composition, and the composition drift as a function of reaction time. The analysis and reactor model is used in the manufacturing process to set process conditions to obtain the desired properties in the polymer product.     

Modelling and control of different types of polymerization processes using neural networks technique: A review

Polymerization process can be classified as a nonlinear type process since it exhibits a dynamic behaviour throughout the process. Therefore, it is highly complicated to obtain an accurate mechanistic model from the nonlinear process. This predicament always been a “wall” to researchers to be able to devise an optimal process model and control scheme for such a system. Neural networks have succeeded the other modelling and control methods especially in coping with nonlinear process due to their very conciliate characteristics. These characteristics are further explained in this work. The predicament that is encountered by researchers nowadays is lack of data which consequently lead to an imprecise mechanistic model that scarcely conforms to the desired process. The implementations of the neural network model not only restrict to polymerization reactor but to other difficult‐to‐measure parameters such as polymer quality, polymer melts index and mixture of initiators. This work is aimed to manifest ascendancy of neural networks in modelling and control of polymerization process.     

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.     

Hierarchical control of a train of continuous polymerization reactors

A multilayer control scheme is synthesized for a series of polymerization stirred tank reactors to control the monomer conversion over the reactor line. In this work two layers of control are implemented. In the' first level digital PI or self-tuning regulators (STR) are used to control the reaction temperature of each reactor in the series by manipulating the flowrates of the coolant streams. In the second layer, a locally linear state space model, that can predict the monomer concentration in each reactor, is derived based on steady-state energy balances. A quadratic performance index is then minimized to obtain the optimal reaction profile that will bring the monomer distribution over the reactor line to its desired target value.     

Polymer property control in a continuous styrene polymerization reactor using model-on-demand predictive controller

The model-on-demand (MoD) framework was extended to the model predictive control (MPC) to design a multiple variable model-on-demand predictive controller (MoD-PC). This control algorithm was applied to the property control of polymer product in a continuous styrene polymerization reactor. For this purpose, a local auto-regressive exogenous input (ARX) model was constructed with a small portion of data located in the region of interest at every sample time. With this model an output prediction equation was formulated to calculate the optimal control input sequence. Jacket inlet temperature and conversion were chosen as the elements of regressor state vector in data searching step. Simulation studies were conducted by applying the MoD-PC to MIMO control problems associated with the continuous styrene polymerization reactor. The control performance of the MoD-PC was then compared with that of a nonlinear MPC based on the polynomial auto-regressive moving average (ARMA) model for disturbance rejection as well as for setpoint-tracking. As a result, the MoD-PC was found to be an effective strategy for the production of polymers with desired properties.     

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.     

Optimal flowsheet configuration of a polymerization process with embedded molecular weight distributions

We consider the optimal reactor network synthesis of a polymerization process with detailed molecular weight distributions (MWDs). Based on an industrial high‐density polyethylene (HDPE) slurry process model including an embedded MWD, a fully connected process superstructure of continuous stirred tank reactors (CSTRs) is established through the introduction of splitters. Using this generalized superstructure as a basis, two nonlinear programming (NLP) problem formulations, which simultaneously maximize the monomer conversion and minimize the deviation between the calculated and target MWDs, are developed by applying multiobjective optimization (MO) methods. Different optimal flowsheet configurations are generated by systematically manipulating a set of continuous decision variables. Several case studies that consider different specifications on MWD are conducted to illustrate the effectiveness and efficiency of the proposed synthesis approach. Numerical results show that the optimal flowsheet configurations overcome the limitations of conventional reactor network structures and help to increase reactor productivity at the desired product quality. © 2015 American Institute of Chemical Engineers AIChE J, 62: 131–145, 2016     

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。     

APPLICATION OF ADAPTIVE PID CONTROL WITH GENETIC ALGORITHM TO A POLYMERIZATION REACTOR

This article describes the application of adaptive PID control with genetic algorithm (GA) to a jacketed batch polymerization reactor. This method was used to keep the polymerization reactor temperature at the desired optimal path, which was determined by the Hamiltonian maximum principle method. The reactor was simulated and the model equations of this jacketed polymerization reactor were solved by means of Runge-Kutta-Felthberg methods. A genetic algorithm can be a good solution for finding the optimum PID parameters because unlike other techniques it does not impose many limitations and it is simple. In this research, suitability of these parameters was checked by the integral absolute error (IAE) criterion. The control parameters in the PID algorithm were changed with time during the control of a polymerization reactor. It was seen that the genetic algorithm was able to tune the PID controller used in this system in terms of higher robustness and reliability by changing the parameters continuously.     

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     

Computation of near-optimal control policies for free-radical polymerization reactors

A polymer is characterized by the average degree of polymerization and the molecular weight distribution. Approximate optimization of temperature control, or catalyst feed rate control, or both are performed to attain not only the desired average degree of polymerization but also the desired molecular weight distribution. This near-optimal policy, which is a function of time only for a batch polymerization reactor, is first expressed by a polynomial, and the coefficients of the polynomial are estimated by a pattern search technique. This coefficient's estimation method coupled with a nonlinear search technique was found to be suitable for solving this type of our optimization problem involving complex chemical kinetics.