Performance analysis of three advanced controllers for polymerization batch reactor: An experimental investigation
Introduction
Polymerization reactions are complex and exothermic in nature, which leads to the nonlinear behavior of polymerization reactors (Hvala et al., 2011). Control of polymerization reactors to obtain high quality polymer products is still a challenging task for researchers due to the reactor's nonlinear character (Özkan et al., 2009).
The main problem in controlling the polymerization reaction variables are whether these variables can be measured, estimated, or can be measured with some time delay (Ghasem et al., 2007). One of the major difficulties encountered in polymerization reactor control is the lack of reliable online real time analytical data. Reactor temperature as an intermediate variable is relatively easier to measure than the polymer structure properties (Zeybek et al., 2006). Therefore, an optimal control policy is essential to infer the optimal profile of intermediate variables (reactor temperature) to produce the desirable polymer structural properties such as the mechanical stress (molecular average molecular weight, number average molecular weight, and number average chain length), melt viscosity, hardness and elastic modulus. (Kiparissides, 2006).
In recent years, nonlinear model-based controllers (Dougherty and Cooper, 2003) have become popular to control the polymerization reactor (Van Brempt et al., 2001). This popularity is due to their ability to capture the nonlinear dynamics of the process (Zhang, 2008, Shafiee et al., 2008, Yüce et al., 1999). Various nonlinear model-based control techniques such as MPC, NN-based controller and GMC have appeared in the literature (Özkan et al., 2009, Alipoor et al., 2009, Ekpo and Mujtaba, 2008, Seki et al., 2001, Ali et al., 2010, Hur et al., 2003). Among all model-based nonlinear controllers, MPC is particularly popular for the dynamic optimization and control of chemical reactors (Shafiee et al., 2008, Sui et al., 2008). A number of applications of MPC in the control of batch polymerization reactor temperature control are listed in Table 1. Neural networks (NNs) offer the ability to produce nonlinear models of industrial systems owing to their ability to approximate nonlinear functions and learn through experimental data (Qin and Badgwell, 2003, Mujtaba et al., 2006, Günay and Yildirim, 2013, Grondin et al., 2013). Most of the nonlinear predictive control algorithms based on NNs imply the minimization of a cost function by using computational methods for obtaining the optimal command to be applied to the process. In a recent study, Salau et al. (2009) used MPC and a conventional PID to control the temperature of gas-phase polyethylene reactor.
Özkan et al. (2009) investigated the online temperature control of a cooling jacketed batch polystyrene (PS) polymerization reactor using GMC. They achieved the temperature control of the polymerization reactor experimentally and theoretically, and the control results are compared with the previously published literature work. Shafiee et al. (2008) applied nonlinear model predictive control (NMPC) based on a piecewise linear Wiener model to a polymerization reactor to control the reactor temperature. In another study, Karer et al. (2008) studied a self-adaptive predictive functional control algorithm as an approach to the control of the temperature in an exothermic batch reactor. Nagy et al. (2007) and Khaniki et al. (2007) also used nonlinear model predictive control (NMPC) for the set point tracking control of an industrial batch polymerization reactor.
Besides MPC, artificial intelligence (AI)-based modeling and control techniques offer flexible and powerful solutions to the dynamic optimization and control of polymerization reactors (Stephanopoulos and Han, 1996). A number of applications of AI in the control of batch polymerization reactor temperature are listed in Table 1. The literature is rich in the application of different AI-based techniques to control polymerization reactors. It includes fuzzy logic controllers (Alipoor et al., 2009, Fileti et al., 2007, Çetinkaya et al., 2006, AltInten et al., 2006, Ghasem, 2006), neural network-based controllers (Zhang, 2008, Ekpo and Mujtaba, 2007, Ekpo and Mujtaba, 2008) and genetic algorithm-based controllers (AltInten et al., 2006, AltInten et al., 2008).
In this work, two artificial intelligence-based controllers (NN-MPC and FLC) and one nonlinear model-based controller (GMC) are developed and used to track the optimum set point of batch polymerization reactors. PS polymerization in a batch reactor is adopted for this study to check the efficiency of different advanced controllers.
Section snippets
Modeling of batch polystyrene reactor
Polystyrene product is produced by following a complex reaction mechanism in a batch reactor. The free radical polymerization process is commonly used to produce PS (Özkan et al., 2000). It is necessary to thoroughly understand the reaction mechanism and effective operating variables in order to develop a detailed model for the PS polymerization reactor. Researchers are still facing challenges to develop an effective model that leads to optimize the performance of a PS reactor (Herrera and
Minimum time optimal temperature profile
Recently, researchers have successfully developed and used the optimal temperature profile to control the polymerization reactor to get the desired polymer product quality and quantity (Zeybek et al., 2004, Zeybek et al., 2006, AltInten et al., 2008, Özkan et al., 2001). In this work, the optimization problem involving minimum time optimal temperature policy has been formulated and solved for the PS batch reactor based on previous work (Zeybek et al., 2006, Sata, 2007). This optimal temperature
Batch polystyrene reactor system
The experimental system of the batch PS reactor used in this study is shown in Fig. 3. The apparatus consists of a 2.0 l jacketed glass reactor with a mechanical agitator and other utility items. The top of the reactor has four inlets for the agitator, heater, thermocouple and reflux condenser. The turbine agitator is used to stir the reactor mixture. The operating range of the agitator motor is 50 to 2000 rpm. An electric heater of 500 W is used to heat up the reactor mixture. A device called the
Design of proposed controllers
In this work, two artificial intelligence-based controllers (NN-MPC and FLC) and one nonlinear model-based controller (GMC) are used to control the PS polymerization reactor. The previously developed hybrid model is used to determine the control parameters in a simulation study. Minimal time optimal temperature profiles are used as the setpoint reference trajectory. The controller's performance criterion, integral absolute error (IAE) along with other performance metrics are used to check the
Results and discussion
In this study, three controllers are applied to investigate the accuracy and performance in controlling the batch reactor for PS production. The aim of the study is to implement these controllers in the regulation of the optimal temperature profile to produce the desirable (predetermined) polymer target, namely Xn, and end-of-reaction monomer conversion (X). Before the initiator is introduced into the reactor to initiate the polymerization, the reaction mixture consisting of monomer (styrene)
Conclusion
In this work, a simulation and an experimental investigation are performed for the temperature control in the batch solution polymerization of styrene. The polymerization reactor control is a challenging task as the polymerization reaction is complex and nonlinear in nature. Three advanced nonlinear controllers are designed and implemented in a real PS plant. The controllers used are NN-MPC, FLC and GMC. Due to the lack of available online sensors to measure the polymer properties, temperature
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