Ian David Lockhart Bogle and Michael Fairweather (Editors), Proceedings of the 22nd European Symposium on Computer Aided Process Engineering, 17-20 June 2012, London. 2012 Elsevier B.V. All rights reserved A Comparison of Predictive Control and Fuzzy- Predictive Hybrid Control Performance Applied to a Three-Phase Catalytic Hydrogenation Reactor Mylene C. A. F. Rezende, a Nádson M. N. Lima, a Rubens Maciel Filho a a Chemical Engineering School, State University of Campinas (UNICAMP) Cidade Universitária Zeferino Vaz, CP 6066, CEP 13081-970, Campinas-SP, Brazil Abstract The present work aims to compare the performance of a Predictive Control and a Fuzzy- Predictive Hybrid Control applied to a three-phase catalytic reactor in which the reaction of the hydrogenation of o-cresol producing 2-metil-cyclohexanol occurs. The control of the reactor exit concentration of o-cresol in the liquid phase, manipulating reactor feed temperature (Tf) is the control configuration considered. In fact, the control of the concentration is important since one of the most important variables in three phase reactors is the liquid component conversion. The three-phase catalytic reactor considered in this paper is a multivariable reactor represented by a non-linear mathematical and high dimensional model, requiring advanced control techniques to deal with this process. Thus, in order to perform the control of this reactor, a Dynamic Matrix Control (DMC) Predictive Control is an efficient method, as presented by Rezende et al. (2004). The present paper compares the performance of the DMC Predictive Controller and the Fuzzy-DMC Hybrid Controller, as an alternative to control of the reactor. For this, the identification of Fuzzy models is showed. Keywords: Predictive Control, Fuzzy-Predictive Hybrid Control, Hydrogenation reactor, multivariable reactor, Model identification. 1. Introduction Three phase catalytic reactors are widely used in industrial processes like hydrogenation and oxidation with usually high throughput production. The control of these reactors is important to reach objectives such as a safe operation without causing environmental impact, a high product quality and an economically feasible. The mathematical models that describe the dynamic behaviour of the three-phase catalytic reactor employed in this work are characterized by nonlinearity and high dimensionality (Rezende et al., 2008). Multivariable, nonlinear and random process, in general, requires advanced control techniques. In this way, a DMC controller is proposed as an efficient technique, as presented on Rezende et al. (2004) work. Another technique that appears as interesting approach is the Fuzzy-Predictive Hybrid Control using the potential of predictive strategies coupled with the ability to represent systems using fuzzy logic (Lima et al., 2010). The present paper proposes the comparison the DMC controller based on the work of Rezende et al. (2004) and the Fuzzy-DMC Hybrid controller. One of the most important variables in three phase reactors is the liquid component conversion putting the exit concentration of the liquid component as an important controlled variable. In this way, the objective of the control in this work is to maintain the exit concentration of o-cresol in the liquid phase at the set point, manipulating
2 M. Rezende et al. reactor feed temperature (Tf). The decision of the manipulated variable is based on the dynamic behaviour of the reactor. 2. Mathematical Modeling Three phase catalytic reactors are systems in which both gas and liquid phases are in contact with a catalyst in the solid phase, which is wet and adequately contacted by reactants (in both liquid and gas phase) to promote the chemical reaction.. In order to represent the main phenomena and be able to describe the real behaviour, the mathematical model should take into account the different phases (heterogeneous model) (Rezende et al., 2008). The process considered in this work is the three phase catalytic slurry reactor in which the reaction of the hydrogenation of o-cresol on Ni/SO 2 catalyst producing 2-metil-cyclohexanol occurs: H ( g ) C H OHCH (l ) C H OHCH (l ) 3 2 6 4 3 6 10 3 (1) The kinetic model and the mathematical model of the reactor can be found in Rezende et al. (2008) and Vasco de Toledo et al. (2004). The reactor length used in the studied case presented in this work is 2 m. More details about reactor parameters can be found in Vasco de Toledo et al. (2004). With the aid of the mathematical model it is possible to identify the important input and output variables of the process. The input variables on the system are linear velocity of gas (ug), of liquid (ul) and of coolant (ur), feed concentration of hydrogen in both the gas phase (Agf) and in the liquid phase (Alf), feed concentration of o-cresol in the liquid phase (Blf), reactor feed temperature (Tf) and feed coolant temperature (Trf). The output variables are exit concentrations of hydrogen both in the gas phase (Ag) and in the liquid phase (Al), exit concentration of o-cresol in the liquid phase (Bl), reaction medium temperature at the exit of the reactor (T), temperature of the coolant fluid at the exit of the reactor (Tr). 3. Control configuration One of the most important output variables of the reactor is the exit concentration of o- cresol in the liquid phase (Bl) whose value is 0.0130 Kmol/m 3 in the steady state in which a 2-methyl-cyclohexanol productivity is 0.44x10-4 Kmol/m 3 s and the o-cresol conversion is 46%. According to the dynamic behaviour of the reactor evaluated by Rezende et al. (2008), the input variable that exert influence on the output variable is the reactor feed temperature (Tf). The effect of Tf on Bl is negative, i.e., an increase in Tf leads to a decrease in Bl. An increase in the feed reactor temperature favors a decrease in the exit concentration of o-cresol in the liquid phase, which means a larger consumption of o-cresol over time and, consequently, a higher conversion of o-cresol at the reactor exit. In this way, the present work shows a suitable configuration of control in which the aim is to maintain exit concentration of o-cresol in the liquid phase (Bl) at the desired set-point, manipulating the reactor feed temperature (Tf). 4. DMC Process Control One of the most used modern controllers in the process industry is Model Predictive Control (MPC) that uses a dynamic model of the process as part of the controller. The model is used to predict the future values of the output for a certain period of time.. DMC makes use of a linear model, the convolution model, which is obtained by making step disturbances in the input variables. The DMC algorithm is based on the calculation of NC (Control Horizon) future values of the manipulated variables from a minimization of NP (Prediction Horizon) future values of the square of the difference
A Comparison of Predictive Control and Fuzzy-Predictive Hybrid Control Performance Applied to a Three-Phase Catalytic Reactor 3 between set point and output predicted by a convolution model with NM (Model Horizon) output values obtained from the step response to the manipulated variable. The model horizon (NM), the prediction horizon (NP), the control horizon (NC) and the suppression factor (f) are parameters to be tuned in order to obtain a good performance of the controller (Rezende et al., 2004). 4.1. Control of the o-cresol concentration at the reactor exit The aim of the reactor control is to control the exit concentration of o-cresol in the liquid phase (Bl), manipulating the reactor feed temperature (Tf), is to maintain Bl at the set-point of 0.0130 Kmol/m 3. For this, many simulations were performed considering disturbances of 5% in the manipulated variable (Tf) and step disturbance of 5% in the feed coolant temperature (Trf). A different set of parameters was tested in order to find a set of parameters that permit a good fitness of the controller. This set of parameters is: NM=4, NP=3, NC=1 and f=0.0001. On-line concentration measurement can be obtained by near-infrared measurement with a good and robust performance in industrial environment. In this work, a sampling time of 100 s is used since that is the value normally found in industrial practice. Figure 1 and 2 shows the behaviour of the exit concentration of o-cresol in the liquid phase (Bl) and the behaviour of the manipulated variable (Tf), respectively, during action of the DMC controller when step disturbance of 5% in the feed coolant temperature (Trf) occurs. Figure 1. Open loop response and behaviour of (Bl) during action of the DMC controller when +/-5% of disturbance in Trf occurs. Figure 2. Behaviour of the manipulated variable (Tf) during action of the DMC controller when Bl is the controlled variable. The behaviour of (Bl) shows that the controlled variable reaches to the set point rapidly, with a small overshoot and few oscillations around the set point. The manipulated variable behaviour is satisfactory, since the reactor feed temperature reaches the steady state and remains on it too. Both profiles indicate the efficiency of the DMC controller. 5. Fuzzy-DMC Hybrid Control 5.1. Identification of Fuzzy Models The identification of Fuzzy models is important for step of process control. The Fuzzy model can be presented as an alternative to the convolution model of the Dynamic Matrix Control in the present work generating a Fuzzy-predictive controller. In order to compare the performance of the Fuzzy-DMC Hybrid Controller and DMC Predictive
4 M. Rezende et al. Controller the same control objective is employed in this section, to known, to maintain the exit concentration of o-cresol in the liquid phase at the set point, manipulating reactor feed temperature (Tf). The complete description of the Identification of Fuzzy Models can be found in Rezende et al. (2011). The results showed that the Fuzzy model is close to the deterministic model. The value of the output variable, concentration of o- cresol in the liquid phase (Bl) at the exit of the reactor in relation to the input variable, feed reactor temperature (Tf) obtained by Fuzzy model presented a very good approximation to the value deriving from deterministic model. This result confirms that this Fuzzy model can be used in substitution to the rigorous model of the reactor in control applications. 5.1.1. Control of the o-cresol concentration at the reactor exit In the same way the DMC controller was done, the Fuzzyi-DMC Hybrid Control is to employed in order to control the exit concentration of o-cresol in the liquid phase (Bl) control, manipulating the reactor feed temperature (Tf), maintaining Bl at the set-point of 0.0130 Kmol/m 3. For this, many simulations were performed considering disturbances of 5% in the feed coolant temperature (Trf). A different set of parameters of the controller was tested in order to find a set of parameters that permit a good fitness of the controller. This set of parameters is: NP=3, NC=1, f=0.0001 and a sampling time of 100 s. Figures 3 and 4 show the behaviour of the exit concentration of o-cresol in the liquid phase (Bl) and the behaviour of the manipulated variable (Tf), respectively, during action of the Fuzzy-DMC controller when step disturbance of 5% in the feed coolant temperature (Trf) occurs. Figure 3. Open loop response and behaviour of (Bl) during action of the Fuzzy-DMC hybrid controller when +/-5% of disturbance in Trf occurs. Figure 4. Behaviour of the manipulated variable (Tf)) during action of the Fuzzy-DMC controller when (Bl) is the controlled variable. The behaviour of (Bl) shows the efficiency of the Fuzzy-DMC controller in to reach the controlled variable to the set point rapidly. A short overshoot and few oscillations around the set point are observed. The manipulated variable reaches a new steady state and remains on it confirming the efficiency of the Fuzzy-DMC controller. The results presented on this section proving a high performance of the Fuzzy-DMC controller for the considered structure which puts this controller an important tool to the process control and can be employed as a layer at the process real time integration.
A Comparison of Predictive Control and Fuzzy-Predictive Hybrid Control Performance Applied to a Three-Phase Catalytic Reactor 5 6. Comparing DMC and Fuzzy-DMC Hybrid Controllers Performance Comparing the performance of DMC and Fuzzy-DMC Hybrid Controllers, it is possible to observe in the Figures 1-4 that the DMC outperforms Fuzzy-DMC Hybrid, since the overshoot is shorter, the oscillations are fewer and the response time is shorter. Although the DMC had presented a better result, the Fuzzy-DMC controller has some advantages. It does not need the deterministic model which in some cases it is difficult to be obtained. The input/output data is sufficient to generate a Fuzzy model. In the case presented in this paper, a better performance of the Fuzzy-DMC controller can be obtained through the generation of a different Fuzzy model as internal model of the DMC algorithm, as well as a better tuning of parameters of the Fuzzy-DMC controller. 7. Conclusions In this work, the control of the multiphase reactor of o-cresol hydrogenation was considered. A suitable configuration of control was proposed in order to compare the performance of the DMC and the Fuzzy-DMC Hybrid controllers. Although the results have showed that DMC outperforms the Fuzzy-DMC Hybrid controller, the Fuzzy- DMC controller has the advantage of not requiring a deterministic model of the reactor, since through input/output data it is possible to generate a new Fuzzy model and this new model can present a better performance of the Fuzzy-DMC Hybrid controller. In addition, a tuning of the parameters of the Fuzzy-DMC Hybrid controller can find parameters that allow a better performance of this controller. Acknowledgements The authors would like to thank FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo), for the financial support, process number 2008/01230-1. References Hichri, H.; Armand, A.; Andrieu, J., (1991), Kinetics and slurry type reactor modeling during catalytic hydrogenation of o-cresol on Ni/SiO 2, Chem. Eng. Process., v. 30, p. 133-140. Lima, N.M.N., Liñan, L.Z., Manenti, F., Maciel Filho, R., Wolf Maciel, M.R., Embiruçu, M., Medina, L.C., (2010a), Fuzzy Cognitive Approach of Molecular Distillation Process. Chemical Engineering Research and Design, doi:10.1016/j.cherd.2010.08.010. Lima, N.M.N., Liñan, L.Z., Maciel Filho, R., Wolf Maciel, M.R., Embiruçu, M., Grácio, F., (2010b), Modeling and Predictive Control Using Fuzzy Logic: Application for a Polymerization System. AIChE Journal, 56, 4. Rezende, M. C. A. F., Costa, A. C., Maciel Filho, R., (2004), Control and Optimization of a Three Phase Industrial Hydrogenation Reactor. International Journal of Chemical Reactor Engineering. v. 2, A21. Rezende, M.C.A.F., Costa, C.B.B., Costa, A.C., Wolf Maciel, M.R., Maciel Filho, R., (2008), Optimization of a Large Scale Industrial Reactor by Genetic Algorithms. Chem. Eng. Sci., v. 63, p. 330-341. Rezende, M.C.A.F., Lima, N.M.N., Maciel Filho, R. (2011), Identification of Fuzzy Models Applied to a Three-Phase Catalytic Hydrogenation Reactor. XIX Congreso sobre Métodos Numéricos y sus Aplicaciones Vol. XXX, n.27, 2145-59. Optimization and Control (C). Takagi T, Sugeno M., (1985), Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Sys Man Cybern., 15:116 132. Vasco De Toledo, E.C., Maciel Filho, R., (2004), Detailed Deterministic Dynamic Models for Computer Aided Design of Multiphase Slurry Catalytic Reactor. European Symposium on Computer-Aided Process Engineering 14., 18, 823-828.