Chemical Papers 66 (7) 654–663 (2012) DOI: 10.2478/s11696-012-0165-z
ORIGINAL PAPER
Neural network model predictive control of a styrene polymerization plant: online testing using an electronic worksheet Brunno F. Santos, Manuela S. Leite, Flávio V. Silva, Ana M. F. Fileti* School of Chemical Engineering, University of Campinas, Av. Albert Einstein 500, 13083-852 Campinas, SP, Brazil Received 14 October 2011; Revised 25 January 2012; Accepted 29 January 2012
The batch styrene polymerization process presents transient and nonlinear temperature behavior. In this work, manual control and open loop experiments were carried out in order to build a process knowledge database. Initially, a cascade feedback control loop was implemented by manipulating the thyristor unit of the electrical heater in the thermal fluid tank. Aiming at the MPC development, algebraic equations of a neural network and its adjusted parameters were implemented in an electronic worksheet. Every five seconds, the worksheet was updated with measurements (reactor temperature, thermal fluid temperature and thyristor position) by means of the OLE for the Process Control protocol (OPC). The one-step-ahead temperature prediction was then employed in the objective function of the worksheet solver which used Visual Basic Applications programming. The manipulated variable action was then calculated and sent to the process. A hybrid controller (cascade feedback and MPC) outperformed the pure strategies since the time-integral performance indexes, IAE and ITAE, were reduced by around 22 % and 32 %, respectively. Methodology for the Model Predictive Control presented in this study was considered feasible because the solver of Microsoft Office Excel (2007) is very friendly, easy to understand and ready to implement using VBA. c 2012 Institute of Chemistry, Slovak Academy of Sciences Keywords: predictive control, artificial neural networks, styrene polymerization, electronic worksheet
Introduction Polymerization processes are important due to the variability of products that can be obtained. One of the most produced polymers is polystyrene. From the technical and scientific points of view, polymerization process of polystyrene is quite challenging because it involves complex temperature-dependent chain reactions and heat transfers depending on diffusion effects described by sets of highly nonlinear algebraic and differential equations (Lepore et al., 2007). Temperature variation in polymerization reactor systems significantly affects the kinetics of the polymerization process and consequently changes the physical properties and quality characteristics of the ¨ produced polymers (Ghasem et al., 2007; Ozkan et al., 2001). In order to ensure the final product quality it is
crucial to maintain suitable operating conditions during the polymerization reaction process. Conventional feedback controllers may not work properly because their design is based on linear process assumptions. Studies using model based predictive controllers (MPC) to improve the control performance can be found in literature. Aumi and Mhaskar (2011) found a control for batch processes subject to the input constraints and model uncertainly to ensure the desired product quality. For this purpose, a scheme of MPC based on robust Reverse-Time Reachability Region (RTRR) has been developed. The use of MPC was possible because a multilevel optimization for specified characteristics of the process was done previously. In the controller design, the problem of process uncertainty, to finite duration faults in control actuators, had to be considered. Results showed that it was pos-
*Corresponding author, e-mail:
[email protected]
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Table 1. Experimental (nominal operating) conditions in the styrene solution polymerization reactor Parameter
Value
Reactants volume, VR /mL Reactor stirring speed, MR /min−1 Nominal oil tank volume, VT /L Tank stirring speed, MT /min−1 Jacket flow rate, FJ /(L h−1 ) Maximum heating power, WT /W Initiator, I Initiator concentration, [I] /(mol L−1 ) Temperature setpoint, Tsp / ◦C
1100 200 7 200 300 1500 BPO 0.0185 90
sible to develop a robust safe-steering to operate the input during faults repair periods, keeping the correct direction of control. Aumi et al. (2011) addressed the problem of modeling and control of the complex nonlinear behavior of the nylon 6,6 batch polymerization process assessing the use of MPC. The proposed model, in which local linear models were identified from previous batch data, was used to formulate a trajectory tracking predictive control of temperature and pressure. According to the authors, when compared to the linear controller (PI), the MPC offered advantages like minimizing the integral of errors (ITAE) of temperature and pressure variables. In digitally controlled systems, the use of nonlinear model predictive control (MPC) based on artificial neural network modeling allows simulation and quick online prediction of the process variables behavior based on the input-output data rendering thus a good solution of this problem. This controller calculates the manipulated variable by minimizing the deviation between the predicted and measured controlled variables. Using an electronic worksheet, Fujiki et al. (2009) implemented a neural model based MPC for the online control of the bromelain recovery process. Process identification for tobacco solid waste composting in an aerobic adiabatic batch reactor was carried out by Bolf et al. (2007) using neural network based models. Two soft sensors were developed for the conversion estimation. The developed models showed that the neural networks can be applied as intelligent software sensors providing the possibility of continuous process monitoring. The authors concluded that the models have a potential to be used for inferential control of composting processes in batch reactors. Mahmood and Mhaskar (2008) enhanced stability regions for the Model Predictive Control (MPC) of nonlinear systems based on the Lyapunov theory. The authors applied this method to a simulated batch styrene polymerization reactor in order to compensate for the disturbances and deviations occurring in a con¨ ventional feedback control loop. Ozkan et al. (1998) developed a generalized predictive control of optimal
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temperature profiles in a polystyrene polymerization reactor. The first principles modeling was employed. An explicit moving horizon control and an estimation algorithm were applied to a batch polymerization case study by Sui et al. (2008). The least squared procedure was used coupled with the state estimation algorithm. From the simulated run, the high performance of the proposed control scheme was observed. In literature, there are no experimental investigations of MPC based on a neural model for the control of styrene polymerization. Usually, neural modeling is applied to the conversion and average molecular mass predictions (Zhang, 2004). In the present work, an alternative controller using artificial neural networks and a solver of an electronic worksheet was developed in order to control the experimental styrene polymerization batch reactor.
Materials and methods Experimental system A pilot plant was built specifically to observe the solution polymerization reaction behavior. This plant was used to generate the input–output experimental data and to evaluate the performance of different control strategies. It consists essentially of a 1.2liter-stainless-steel-stirred batch reactor (R-1), 7-literoil-storage tank (TK-1), positive displacement pump (P-1) and temperature sensors (TT). Thermal oil was used as the heat transfer medium in the reactor jacket. An electrical heater, connected to a thyristor, provides heating to the thermal fluid inside the storage tank. Pump P-2 drives the density measurement circuit in order to infer the reaction conversion. Dissolved oxygen was purged by bubbling pure nitrogen gas through the reaction mixture. The monomer was obtained in 99 % purity from Sigma– Aldrich (Steinheim, Germany). Toluene was used as the solvent and it was purchased from Ecibra (S˜ ao Paulo, Brazil), with the purity of 99 %. No further purification was needed. Benzoyl peroxide (BPO) from Sigma–Aldrich, of 70 % purity, was used as the initiator agent for the reaction. After loading the monomer and the solvent into the reactor, this was heated to reach the desired operating temperature of 90 ◦C (Ghasem et al., 2007). As soon as this was reached, the initiator, BPO, was added to start the polymerization reaction (Altınten, 2008). Typical experimental operating conditions are shown in Table 1. Experimental runs were conducted using the 50 % monomer to solvent volume ratio. Supervisory control system A computational monitoring system was built using the software Indusoft Web Studio v6.1 (IWS,
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Austin, USA ). The bulk temperature, Tk , was set as the controlled variable (PV) because it significantly affects the kinetics of the polymerization process and consequently changes the polymer quality. By manipulating the oil tank resistance power (MV), using a thyristor, the automatic control was implemented. The proposed feedback cascade controller was developed in the Simulink/MATLAB software R2007b (The Math Works, Inc., Natick, MA, USA), editing block diagrams, which communicates with the IWS Supervisory system by means of the OPC (OLE for Process Control) protocol. The neural model calculations and the Model Predictive Control were implemented in Microsoft Office Excel (2007) communicating with IWS via a DDE (Dynamic Data Exchange) driver. Considering time for online calculations and communications, besides the process time constant, the time interval was set to 5 s. Building the database Before designing the Model Predictive Control (MPC), a database was built to show the network how the process variable (one-step-ahead temperature) behaves as a function of the present bulk temperature, oil tank temperature and the resistance power implemented. Some experimental runs were performed under open loop conditions and also under manual and cascade feedback control. In the manual control, a human operator monitored the bulk temperature on screen display, analyzed the information and implemented the control actions via a PC keyboard. The performance of these controllers does not matter at this moment because the aim is to determine dynamic behavior of the process. The cascade feedback control consists of two parts: principal loop, where bulk temperature control provides the set point for the oil tank temperature; and the secondary loop, in which the resistance power supply (MV) is changed automatically in order to match the oil tank temperature setpoint. In the primary loop, a proportional–integral (PI) controller, using the Ziegler–Nichols tuning method, was employed. A proportional (P) controller was used in the slave loop. Data obtained by the cascade control were not only used for the network training but also for performance comparisons with the MPC. In this case, trial-anderror fine tuning was performed using the parameters found by the Ziegler–Nichols method as initial guesses. The reaction heat and the heat loss in the density measurement circuit were considered as the plant disturbances, d1 and d2 . Nonlinear model predictive control (MPC) This control system is based on artificial neural network (ANN) predictions of bulk temperature. Mea-
sured variables at current time, k, were used as the input parameters of the network; e.g. bulk temperature, Tk , oil tank temperature, Ttq , and the current resistance power, MV. By minimizing the objective function, subject to the process constraints, the solver calculates the control action to be implemented (MVk+1 ). The process was modeled using the Levenberg– Marquardt algorithm with Bayesian regularization from the Neural Network Toolbox of MATLAB 7.0 (The Math Works, Inc., USA). The database (formed by an open loop run, manual control run, and cascade control) was used to train and test the multilayered feed forward network. The neural model performance was assessed through dispersion plots of the testing runs, with the desirable result represented by a slope coefficient of the linear fitting of the dispersion plots (network output vs. target vector) close to the unity and by a linear coefficient around zero. In the hidden layer, the hyperbolic tangent activation function was applied to the same number of nodes of the input layer (three). The linear activation function was applied to the node of the output layer which predicts the one-step-ahead controlled variable (Tk+1 ). A closed loop run, under well tuned cascade feedback control, was used in the offline tests as the neural model was expected to provide accurate predictions when working together with the optimizer for the process control. Following the offline tests, closed loop online validation was also performed in order to verify the prediction ability of the implemented model. The optimized weights and biases, from MATLAB, were inserted in an electronic worksheet to reproduce the algebraic equations of the trained neural model. The calculated output generates a quadratic error (relative to the setpoint) defined as the objective function to be minimized by the solver (see Eq. (1)). The solution was found through the quasi-Newton method of generalized reduced gradient, available in the software Excel, by changing the manipulated variable value (MV) that should be implemented in the plant. Min (Tk+1 − Tksp )2 MV
(1)
Subject to the constraints shown in Eqs. (2)–(4): MV ≥ MVmin MV ≤ MVmax |M V − M Vk−1 | ≤ maximum step allowed
(2) (3) (4)
where MV is the manipulating variable, Tk+1 the onestep-ahead temperature, and Tksp the setpoint temperature, and MVmin = 0 % and MVmax = 100 % (related to the nominal heating power value, 1500 W). Flow chart for the design of the model predictive control scheme is shown in Fig. 1.
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Fig. 2. Reactor temperature deviation from the reference temperature (90 ◦C).
Fig. 1. Flow chart for the design of the MPC control system (Fujiki et al., 2009).
reach the desired operating temperature of 90 ◦C. As soon as this temperature was reached, the initiator, BPO, was added to start the solution polymerization reaction (time = 0 s). The resistance power supply was maintained at 45 % (0.67 kW). The bulk temperature deviation is shown in Fig. 2. Because the reaction is exothermic and the batch process is transient, a variation in the heat exchange was detected as previously cited by Hungenberg et al. (2005) and Yoo et al. (1999). In consequence, an overshoot of 4 ◦C occurred at the reaction beginning. During the process, the temperature decreased since the power supply to the thermal fluid heating was fixed. At the end of the reaction, the thermocouple (TT2) indicated 3 ◦C bellow the desired operating point (90 ◦C). Manual control run
The last blocks of the flow chart were realized using VBA programming (Visual Basic for Applications). Every sample interval, the solver runs the optimization procedure because the worksheet is updated by the supervisory system. This formulation of MPC, using just one-step ahead prediction, is especially useful for sluggish processes and very short sampling intervals.
Results To better understand the polymerization plant behavior, some experimental runs were performed under open loop conditions and also under manual and cascade feedback control to enable the development of a neural MPC. Open loop run In this experiment, after loading the monomer and the solvent into the reactor, the mixture was heated to
Observing the open loop temperature behavior, a run in which a human operator implemented the control actions (MV) was carried out. As soon as BPO was added to the mixture, the manipulation started. Fig. 3 shows the temperature deviation and the heating power manipulation as well. Initial value of the manipulated variable (MV) was set to 45 % of the nominal heating power. It was observed that the bulk temperature was kept closer to its setpoint presenting an overshoot of 1 ◦C and rise time of 263 s. At the beginning, heat generated by the reaction is high and, consequently, severe changes were required in the manipulated variable to maintain the desired temperature. Cascade control Using the curve response procedure at pseudostationary operating conditions, an approximation to the First Order Plus Time Delay (FOPTD) was found and the Ziegler–Nichols tuning equations could be em-
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Fig. 3. Process behavior under manual control: PV (a) and MV (b).
Fig. 4. Process behavior under cascade control (without fine tuning): bulk temperature (a); manipulated variable (b); oil tank temperature (line 1) and its setpoint from the primary loop (line 2) (c).
ployed. After disturbing the heating power supply, and monitoring the process temperatures, the following controller parameters were found: Kc = 12 ◦C %−1 and τ i = 1600 s (primary loop), and Kc = 17 ◦C %−1 (secondary loop). The closed loop experiment results are shown in Fig. 4. An overshoot of 2.5 ◦C and rise time of 457 s were found. The controller performance was not considered
suitable since the manipulated variable changed as if driven by on–off controllers consequently causing oscillations in both temperatures. This fact suggests that the control gain, Kc , is very high. These results were added to the database but they were not used for the assessment of the controller performance. Using the trial-and-error fine tuning, the controller parameters were adjusted. It was found that Kc =
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Fig. 5. Process behavior under well-tuned cascade control: bulk temperature (a); manipulated variable (b); oil tank temperature (line 1) and its setpoint from the primary loop (line 2) (c).
5.4 ◦C %−1 and τ i = 699 s (primary loop), and Kc = 7.5 ◦C %−1 (secondary loop); the results are shown in Fig. 5. This run resulted in an overshoot of 2.5 ◦C and rise time of 702 s. Although at the beginning, the welltuned controller did not work better than the previous one, after 1000 s, the control actions were smoother eliminating thus the oscillations in both temperatures. Less effort was required in the thyristor. The following performance criteria were obtained: integral of absolute error (IAE) of 1407.7 and integral of the timeweighted absolute error (ITAE) of 3809542. As expected, in the secondary loop, the proportional controller induced an offset in the tank oil temperature (Fig. 5c). The process data shown in Figs. 2–4, corresponding to 8233 input–output pairs, were used to train the neural network. Looking for the prediction capacity assessment in closed loop situations, the well-tuned cascade control (Fig. 5), which presented 3110 input– output pairs, was employed in the offline neural model testing. Neural model Using the database, a neural model was developed to predict the bulk temperature behavior. Table 2
◦
Fig. 6. Offline testing: actual (—), line 1, and predicted ( ) temperature behavior.
shows the training results obtained from the Neural Network Toolbox of MATLAB. The Levenberg– Marquardt method coupled with the Bayesian regularization was employed. From Table 2, the best topology was observed when the neural model had three hidden layers of neurons, the effective number of parameters (13.5) was very close to the initial number of parameters (16), indicating that the network is well dimensioned in terms of hidden layers of neurons. By consider-
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ing that 8233 input–output pairs were used in the training set, it was verified that the medium squared error was very small (2.03 × 10−6 ◦C2 = SSE per pair); with the temperature error in the third decimal number. The last three columns (Table 2) refer to the linear fitting from the dispersion plot (actual vs. predicted temperature) of the validation set. The linear coefficient column shows the negligible average error obtained in the validation tests. The offline test presented in Fig. 6 supports the topology choice. It can be concluded that the neural model meets the prediction requirements of MPC. In order to validate the neural model for online predictions, an experimental run under well-tuned cascade control was carried out. The optimized weights and biases, from MATLAB, were inserted in an electronic worksheet to reproduce algebraic calculations of the trained neural model. Specific cells were designated to acquire the three input parameters (Tk , MV, and Ttq ) every sample time. The predicted temperature (Tk+1 ) was then compared to the next acquired value of temperature resulting in the graph in Fig. 7. The online test enabled the developed neural model to be used in the MPC loop. Model predictive control Using the Excel worksheet that runs the neural network and according to Eqs. (1)–(4), the solver was
Fig. 7. Online validation of the neural model (— experimental and – ANN model).
activated and implemented using the VBA programming. The process behavior the under MPC control is shown in Fig. 8. At the beginning of the run, the MPC presented the best control performance: overshoot of 1.7 ◦C and rise time of 252 s. On the other hand, during the rest of the time, abrupt changes in the manipulated variable caused oscillations in the bulk temperature. This controller presented the following performance criteria indexes: IAE = 864.6 and ITAE = 3167639. In
Fig. 8. Model predictive control results: Tk (a) and MV (b). Table 2. Model topology choice Effective number of parameters
Hidden layer neurons
SSE
R
Linear coefficient
Angular coefficient
13.55 14.86 17.98 30.36 36.30
3 4 10 12 18
0.016619 0.020837 0.019480 0.016970 0.016960
0.99997 0.99997 0.99997 0.99998 0.99998
–0.0081 –0.0056 –0.0045 –0.0058 0.0014
1 1 1 1 1
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Fig. 9. Hybrid control results: Tk (a) and MV (b). The arrow in both diagrams indicates controller transition. Table 3. Performance indexes
Open loop Manual control Cascade control MPC Hybrid control
Overshoot/ ◦C
Rise time/s
IAE
ITAE
4.0 1.0 2.5 1.7 1.7
1500 263 702 252 190
3727.7 778.5 1407.4 864.6 676.2
17648140 2711278 3809542 3167639 2165876
comparison with the cascade control, the indexes were reduced by around 38 % and 17 %, respectively. Hybrid control From Figs. 5 and 8, results that MPC best performed at the beginning of the experiment and the cascade feedback control after reaching the setpoint for the first time. Teixeira (2001) successfully developed a hybrid neural network and feedback PID approach to control the movements of a robot with six joints. Based on his concept, a hybrid MPC and cascade controller for the polymerization process was developed in the present work. The MPC initiates the plant control and, after reaching the setpoint for the first time, the cascade structure starts to drive the process; Fig. 9. The turning point is shown by arrows. An overshoot of 1.7 ◦C was obtained (equal to MPC results) and the rise time was reduced to 190 s. As expected, the hybrid control overcame the individual failures of the cascade and MPC: Tk was kept very close to its setpoint and the control moves smoother. Table 3 summarizes the performance indexes obtained. Table 3 shows that the overshoot was reduced by applying MPC. The rise time was better when MPC worked together with the cascade controller. Using a hybrid controller, the time-integral criteria, IAE and ITAE, were reduced by around 22 % and 32 %, respectively.
Fig. 10. Conversion rates from gravimetric analysis: predicted data (1), cascade control (2), MPC (3), and hybrid control (4).
After the implementation of the hybrid controller, the temperature remained closer to the setpoint as in the system under manual control. Although the molecular mass had similar values for all batches, the benefit of using hybrid controllers is in the small temperature changes around the reference value. Samples were taken during the reactions in order to determine conversion rates and the number average molecular mass (Mn ) and mass average molecular mass (Mw ) of the product. Gravimetric analysis and gel permeation chromatography (GPC) were employed, respectively, and the results are shown in Figs. 10 and 11. Conversion rates were found to be very similar in
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Fig. 11. GPC analysis: number averaged molecular mass (Mn ) (a) and mass averaged molecular mass (Mw ) (b). Predicted data (1), cascade control (2), MPC (3), and hybrid control (4).
all experiments (about 55 % at the end), which is compatible with the styrene solution polymerization using a 50 % monomer to solvent volume ratio. Using the Coriollis sensor, the bulk density value was obtained following the conversion curve behavior. After 3 h of the reaction, the density variation reached 30 kg m−3 . According to the first principles modeling, the number average molecular mass (Mn ) and mass average molecular mass (Mw ) decrease during a batch process (predicted curves in Fig. 11). For the solution polymerization reactions, Sim˜ oes (2001) argues that the presence of solvent lowers the bulk viscosity and induces chain transference to the monomers thus reducing the polymer molecular mass. From the present work follows that most experimental runs showed this tendency as well. Under cascade control, the large temperature overshoot inhibits the molecular mass increase even at the beginning of the reaction. Since the obtained polymer is very resistant and has low molecular mass, it can be concluded that it is a crystal polymer. Because of its various properties, this kind of polymer is used to produce mechanical parts, food containers, and in other applications requiring chemical inertness and high strength. It was noticed that the number of chains formed in all batches was higher than that predicted from the first principles model because the average molecular mass of the polymer product – the ratio of the total mass of the polymer and the number of chains – was lower. This can be explained by the fact that the model considered perfect control of temperature at 90 ◦C and, in the real world, the temperature oscillated around the setpoint. In spite of the same magnitude, molecular mass of the polymer obtained by the hybrid control was higher because with undesired temperature increase, more free radicals and chains are formed and consequently the molecular mass decreases. In summary, hybrid control reduced the process variables’ integral of error (IAE and ITAE), which
helps the producer to match the product target, i.e. the type of polymer for a specific application.
Conclusions In the present work, the development and online tests of a polystyrene plant control was addressed. First of all, to establish communication between software environments was required. The simulink/MATLAB software communicated with the Indusoft Web Studio Supervisory system by means of the OPC protocol. The Microsoft Office Excel communicated with IWS via the Dynamic Data Exchange driver. After the communication, experiments were carried out under manual and cascade feedback control in order to build a knowledge database. It was noticed that cascade control presented smooth control actions after the initial moments of the batch process. At the beginning of the process, when the initiator agent was added, the exothermic effect was very high and the feedback control did not work properly. Using the database, a neural network was trained in order to predict the reactor temperature. After validating the model using an Excel worksheet to perform neural model calculations, a model predictive control was developed using VBA programming. When compared to the cascade control, the MPC strategy reduced the overshoot, the rise time and the timeintegral performance criteria (IAE and ITAE). However, the abrupt control actions were not considered suitable for this process. Monitoring the features of each controller, a hybrid control structure involving cascade and predictive controllers in series was proposed. The MPC initiates the plant control and, after reaching the setpoint for the first time, the cascade structure starts to drive the process. The experimental results showed that the hybrid controller reduced the rise time, the IAE and the
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ITAE. This structure was considered the most appropriate for the polystyrene production control. The methodology presented for the model predictive control in the present work was considered feasible because the solver of Microsoft Office Excel is very friendly, easy to understand and ready to implement using VBA. Because the obtained polymer is very resistant and has low molecular mass, it can be concluded that it is a crystal polymer. This kind of polymer is useful in the production of mechanical parts, food containers, and in other applications requiring chemical inertness and high strength. References Altınten, A., Ketevanlio˘ glu, F., Erdo˘ gan, S., Hapo˘ glu, F., & Alpbaz, M. (2008). Self-tuning PID control of a jacketed batch polystyrene reactor using genetic algorithm. Chemical Engineering Journal, 138, 490–497. DOI: 10.1016/j.cej.2007. 07.029. Aumi, S., Corbett, B., & Mhaskar, P. (2011). Data-based modeling and control of nylon-6,6 batch polymerization. American Control Conference on O’Farrell Street, June 29–July 01, 2011 (pp. 2540–2545). San Francisco, CA, USA: American Automatic Control Council. Aumi, S., & Mhaskar, P. (2011). Robust model predictive control and fault handling of batch processes. AIChE Journal, 57, 1796–1808. DOI: 101002/aic.12398. Bolf, N., Kopči´c, N., Briški, F., & Gomzi, Z. (2007). Software sensors for monitoring of a solid waste composting process. Chemical Papers, 61, 98–102. DOI: 10.2478/s11696007-0005-8. Fujiki, T. L., Schulz, C., da Silva, F. V., & Fileti, A. M. F. (2009). Artificial intelligence based controllers applied to a bromelain recovery process. In Proceedings of the 11th IASTED International Conference on Control and Applications, July 13–15, 2009 (Vol. 1. pp. 219–224). Cambridge, UK: ACTAPress. Ghasem, N. M., Sata, S. A., & Hussian, M. A. (2007). Temperature control of a bench-scale batch polymerization reactor for polystyrene production. Chemical Engineering & Technology, 30, 1193–1202. DOI: 10.1002/ceat.200700165.
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