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Generalized predictive control of optimal temperature profiles in a polystyrene polymerization reactor

The performance of generalized predictive control (GPC) was examined when it was applied to the temperature of a free radical solution polymerization of styrene in a jacketed batch reactor. The optimal temperature policies were obtained at different initiator concentrations by applying the optimal control theory to the relevant polymerization reactor. The use of polynomial ARIMAX model related with reactor temperature and heat input was emphasised. Model parameters were determined by using Kalman, Bierman and Levenberg Marquardt algorithms. A pseudo random binary sequence (PRBS) signal was employed to operate the system. The GPC control method was based on ARIMAX model. The performance of the GPC method was compared with that of the PID controller.

Nonlinear control of polymerization reactor

Abstract 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.

IDENTIFICATION AND NON LINEAR POLE PLACEMENT SELF TUNING PID CONTROL OF A JACKETED WELL MIXED REACTOR

Abstract This paper describes the application of Non Linear Self Tuning PID (NLSTPID) system with the intention of controlling the temperature of a cooling jacketed polymer reactor containing toluene and styrene mixture. The use of polynomial Nonlinear AutoRegressive Moving Average with eXternal input (NARMAX) model related with tank temperature and heat input for nonlinear control was emphasised. The first part of the paper presents an identification algorithm for the construction of polynomial NARMAX and AutoRegressive Moving Average with external input (ARMAX) models. A Pseudo Random Binary Sequence (P.R.B.S) signal was utilised as a forcing function in order to determine the parameters of the models. Levenberg Marquardt algorithm was used to estimate the relevant parameters of NARMAX model. Similar work was carried out for ARMAX model using Bierman, Kalman and Least Square Estimation algorithms. The time response of the tank temperature obtained from computer simulation, identified models and experime...

Control of dissolved oxygen concentration using neural network in a batch bioreactor

Artificial neural networks (ANN) have been utilized for many chemical applications because of their ability to learn system features. This paper presents the use of feedforward neural networks for dynamic modelling and dissolved oxygen (DO) control of a batch yeast fermentation. The ARMAX model of this nonlinear process is also presented. Model verification is tested by using experimental data. Different ANNs are trained using the backpropagation learning algorithm. The resulting ANNs are introduced in a Model Predictive Control (MPC) scheme to test the control performance of the structure. At system, output variable that is DO concentration and adjusting variable that is air flow rate are chosen. The robustness of this control structure is studied in the case of setpoint changes. Results obtained with NN‐MPC is also presented and compared with those obtained with Nonlinear Auto Regressive Moving Average (NARMA‐L2) control strategy.

The prediction of SO 2 removal using statistical methods and artificial neural network

Artificial neural network and a statistical model have been applied in a laboratory scale trickle bed reactor (TBR) to investigate the SO2 removal efficiency of activated carbon. The performance of artificial neural network (ANN) model has been compared with the statistical model based on central composite experimental design. Two independent variables, which affect the amount of SO2 removal by the liquid phase in the TBR, were selected; namely liquid flow rate and gas flow rate. Amount of SO2 removal was chosen as the dependent variable (target data). A second order statistical model has been considered to show the dependence of the amount of SO2 removal on the operating parameters. A back-propagation ANN has been used to develop a model relating to the amount of SO2 removal. A series of experiments have been conducted on the basis of the statistics-based design of experimental method. It is observed that a neural network architecture having one input layer with two neurons, one hidden layer with three neurons, one output layer with one neuron and an epoch size of 20 gives better prediction. The predictions are more accurate than those obtained from regression models.

The Effects of Operating Conditions on the Product Quality of Partially Oriented Yarn

Abstract Fiber spinning is a complex manufacturing process in which the final properties of the spun fiber depend upon the polymer and the process conditions. Due to the great economical and technical importance of the Poly(ethylene terephthalate) (PET) fiber in terms of end use in variety of textile and technical applications, special attention is shown to the relevant processing conditions of the fiber manufacturing. In this study, the effects of polymer residence time, viscosity values, moisture, spinneret throughput, spinneret hole diameter, quench air velocity, friction, and winding speed upon the product quality were examined in a commercial partially oriented yarn (POY) Spinning Plant with a capacity of 70 ton/day.

EXPERIMENTAL APPLICATION OF GENERALIZED PREDICTIVE CONTROL OF THE TEMPERATURE IN A POLYSTRENE POLYMERIZATION REACTOR

The performance of generalized predictive control (GPC) was examined and compared with conventional control applied to the temperature of as free radical solution polymerization of styrene in a jacketed batch reactor. Optimal conditions were obtained at different initiator concentrations by applying Lagranges multiplier to the relevant polymerization reactor. The use of the polynomial ARIMAX model related with reactor temperature and heat input was emphasized. Model parameters were determined using the Kalman algorithm. A pseudo random binary sequence (PRBS) signal was employed in order to operate the system. The GPC control method was based on the ARIMAX model. The performance criteria of GPC in evaluating the temperature control results were the required monomer conversion and molecular weight.

Nonlinear model based control of optimal temperature profiles in polystyrene 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. NARMAX (Nonlinear Auto Regressive Moving Average eXogenous) giving a relation between heat input and reactor temperature was chosen to represent the system dynamic and this model was used to desing 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 dynamix matrix were tested to calculate the best model. Nonlinear model based control system was used to control the reactor temperature at the 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.

Amonyak boran varlığında gözenekli stiren divinil benzen kopolimer küreciklerin optimum sentez koşullarının belirlenmesi

DOI: Bu çalışmada, önemli endüstriyel polimerlerden stiren divinil benzen (SDVB) kopolimer küreciklerinin gözenekliliğini artırmak amacıyla amonyak boran varlığında sentezi ile optimum sentez koşulları araştırılmıştır. Bu amaç doğrultusunda başlatıcı olarak benzol peroksit, stabilizatör olarak polivinil alkol (PVA) ile sodyum hidroksit (NaOH), organik çözücü olarak ikili toluen-hekzan karışımı kullanılmış ve sentezler süspansiyon polimerizasyonu yöntemiyle yapılmıştır. Amonyak boran (AB) başlatıcı içine farklı miktarlarda karıştırılarak kullanılmıştır. Polimerizasyon tepkimesi azot atmosferinde, 80C sıcaklıkta ve atmosferik basınçta gerçekleştirilmiştir. Parametrik çalışmalar sonucu elde edilen kopolimer küreciklerinin yüzey alanı, gözenekliliği (BET analizleriyle), yapı tayini (Fourier transform infrared spektrometrisi, FTIR ile) ve ıslak faz şişmesi gibi bazı karakteristik özellikleri belirlenmiştir. Sentezlenen kopolimerlerde AB’nin gözenek oluşumuna ve partikül boyut dağılımına katkı sağladığı, DVB yüzdesinin artmasıyla polimerizasyon verimi artarken küreciklerin şişme yüzdesinin azaldığı görülmüştür. Design Expert 8.0.7.1 (deneme sürümü) paket programı altındaki cevap yüzey yöntemi (CYY) kullanılarak merkezi kompozit tasarım yöntemine göre optimum sentez koşullarının %90 DVB; 0,05 g amonyak boran; %200 çözücü miktarında olduğu hesaplanmış ve bu koşullarda sentezlenen kopolimerlerin BET yüzey alanını 156 m/g olarak ölçülmüştür. Asetonla yüzey modifikasyonu sonucu yüzey alanı 274 m/g değerine arttırılmıştır. 10.17341/gazimmfd.300589