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A feedforward control strategy for distillation columns
Artificial Intelligence in Engineering 11 (1997) 40-412 0 1997 Elsevier Science Limited. All rights reserved Printed in Great Britain PII:
ELSEVIER
0954-1810/97/317.00
SO954-1810(97)00002-2
A feedforward control strategy for distillation columns Roberto Baratti,” Stefano Corti Dipartimento
di Ingegneria Chimica e Materiali,
Universit6 di Cagliari, Piazza D’Armi, I-09123 Cagliari. Italy
Alberta Servida Dipartimento
di Chimica e Chimica Zndustriale, Universitci di Genova. via Dodecaneso 31. I-16146 Genova, Italy
(Received for publication 6 January 1997) The prime objective of this work is to demonstrate the potential of neural network modeling for advanced nonlinear control applications. In particular, for the case of a single composition distillation column, a model-based neural controller is developed to regulate the composition of the distillate stream. The neural controller relies on process inversion for the evaluation of the actuator action on the manipulated variable (reflux flowrate) to maintain the controlled variable (distillate composition) at the prescribed value. The performance of the neural controller is assessed and compared with that of a conventional temperature control loop and of a neural inferential control structure. The neural controller by far outperforms the other two in terms of the response speed by which the upsetting loads are compensated. 0 1997 Elsevier Science Limited. Key words: model-based control, inferential networks, distillation columns.
neural
Approximate process models can be classified in structured and unstructured models. While the former are based on first principles, and thus require good understanding of the process physics, the latter are based on some sort of black-box modeling and, in principle, would not require any a priori knowledge of the process. Neural network modeling represents an effective framework to develop unstructured models when relying on an incomplete knowledge of the process under examination.‘-3 Because of the simplicity of neural models, they exhibit great potentials in all those model-based control applications that require real-time solutions of dynamic process models. The better understanding acquired on neural network modeling has driven its exploitation in many chemical engineering applications: data reconciliation and rectification, process identification and optimization, software sensor development (inferential measurements), state estimation, fault analysis, multivariable control (for a list of references cf. the recent review by Stephanopoulos and Han’). The common belief that effective and efficient neural models can be developed without any a priori
INTRODUCTION Nowadays, advanced control systems are playing a major role in plant operations because they allow for effective plant management. The prime advantage of a full plant automation stands in the improvement of plant profitability and productivity that lead to short term payoffs of the investment required for the implementation of advanced automation systems. Typically, advanced control systems rely heavily on real-time process modeling, and this puts strong demands on developing effective process models that, as a prime requirement, have to exhibit real-time responses. Because in many instances detailed process modeling is not viable, efforts have been devoted towards the development of approximate dynamic models. The models suitable for real-time applications result from a trade-off between model complexity and degree of representability of the actual process dynamics. *To whom correspondence
control, process inversion,
should be addressed. 405
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Fig. 1. Schematic of a distillation column showing the controlled and manipulated variables used in a conventional temperature control loop.
understanding of the investigated process is not fully correct. This misconception may lead to neural applications exhibiting poor performance, and this may have been the reason for preventing the full exploitation of neural modeling potentials in real-world applications. Indeed, the selection of the proper inputs and outputs to be fed to the network represents a critical step when developing a neural network model, and an adequate understanding of the process under examination is demanding. Recently Baratti et af.415 have demonstrated the potentials of neural modeling to develop effective inferential control strategies of industrial multicomponent distillation columns. Figure 1 schematically shows a tray distillation column with the typical controlled (temperatures on specified trays, the so called pilot temperatures) and manipulated (reflux, Lo, and boilup, V, flowrates) variables. Figure 1 refers to a case where the pilot temperatures are the ones of the 16th and 3rd trays. The prime aim of this work is to investigate and fully exploit neural modeling in advanced model-based control applications of distillation columns. The basic idea is to construct a neural tool-box that, on the basis of detected disturbances, is capable of acting properly on the manipulated variable so as to compensate for the upsetting loads as soon as they are detected. This action relies on a process modeling that must provide the description of the effect of disturbances and manipulated variables on the process performance. The direct identification of the action on the manipulated variable so as to meet the specifications requires a process inverse model. In this work, we discuss the use of neural modeling to develop an inverse model of a multicomponent distillation column. The neural model provides the controller action law. The direct action on the
manipulated variable allows the control engineer to overcome the problems associated with the optimal tuning of the parameters of conventional feedback controllers. Furthermore, the action of the neural controller resembles that of a feedforward strategy, and thus it may be expected to exhibit a good control performance also in the case of a crude description of the process inverse model.6 For the case of a single composition control problem of a distillation column, neural network modeling is used to develop a model-based neural control strategy to compensate for upsets in the operating pressure, feed flowrate, and feed composition so as to hold constant the content of the key component in the distillate stream. The neural controller is developed for a five-component distillation column (propane, butane, n-pentane, i-pentane and hexane) that is representative of actual stabilizer units, so commonly encountered in the refinery industries. The performance of the neural controller is compared with that of a conventional temperature control loop and of a neural inferential controller.
CASE STUDY
The neural controller is developed for a multicomponent distillation column for which the set of calibration data are produced making use of a dynamic simulator. A 18-trays (ideal stages), five component (propane, hexane, butane, n- and i-pentane) distillation unit is selected as prototype of a gasoline stabilizer tower. The column is also equipped with a reboiler and a total condenser. The feed (saturated liquid) is fed at the 11th stage from the bottom and is constituted of a mixture of propane (lo%), butane (5%), n-pentane (15%), i-pentane (30%) and hexane (40%) (the composition is given on a mole basis). The control objective is to maintain as low as possible the content of i-pentane (i-C,> is the distillate and that of propane (C,) is the residue when the main upsets are due to variations or fluctuations in the feed composition, operating pressure and feed flowrate. The variation in the feed composition is the result of mixing the primary stream with a secondary one (slop) whose composition (on mole basis) is: CX, 2%; c4, 2%; c6, 45%; t&5, 20%; i-C+ 31%. Typically, the secondary stream accounts for about 515% of the total feed flowrate entering the distillation unit. The dynamics of distillation columns can be simulated by various model approaches, involving different levels of complexity.7 Here, we are mainly concerned with addressing the issue of process inversion via neural modeling, thus we have adopted a simple description of the distillation unit that relies on the following assumptions: each tray is an adiabatic ideal equilibrium stage, all the involved species have the same latent heat of vaporization, the vapor and liquid are ideal mixtures,
407
Feedforward control strategy Table 1. Relevant operating parameters wed for the simulation of the reference case
Feed flowrate: 0.229kmol/s Boilup flowrate: 0.063kmol/s Lb,: 5s
Reflux flowrate: 0.035kmol/s Pressure: 821 kPa
the vapor and liquid holdups are negligible. From these assumptions it follows that the vapor and liquid flowrates are constant along the column but different in the stripping and enriching sections. Moreover, the reboiler and the condenser dynamics have been described as first order processes. Under the prescribed assumptions, the mass and energy balance equations are decoupled, and the process model is simply constituted of the transient liquid mass balances. Within the framework of this description the tray temperatures are evaluated by computing the bubble points corresponding to the composition of the liquids on the trays. The equilibrium vapor pressures are calculated through the Antoine equation.8 The adopted dynamic model of the distillation column is rather simplified but, nevertheless, is capable of capturing the most significant dynamical features of the unit that are mainly related to the dynamics of the liquid compositions on the tray. Indeed, these are known to exhibit the largest characteristic times. The design specifications are: i-Cs content in the distillate less than 0.5% (on mole basis) and C3 content in the residue less than O-1%. The parameters corresponding to the reference case are summarized in Table 1.
MODEL-BASED
NEURAL
actual net inputs, the second layer (hidden) contains n2 nodes, and the third layer (output) contains n3 nodes that correspond to the number of the monitored state variables. The configuration of such a network is simply indicated as (nl - n2 - q). The feed and hidden layers are also augmented with a bias unit that represents the threshold value. The input value of the bias node is held constant and equal to 1. Two pilot temperatures, located at the 3rd and 16th tray from the bottom, are also used as inputs to the neural network. It is worth pointing out that we have selected as network inputs those that closely resemble the field measurements available for actual distillation units. Further details on the development of the multilayer neural network, on the selection, and on the pre-processing of the inputs are given elsewhere.415 For the dual composition problem, three control systems based on the El V strategy have been developed: a conventional temperature control loop, a neural inferential system, and a neural controller based on process inversion. The inferential control strategy relies on a neural observer that provides compositions as setpoints to a conventional PI feedback controller. The actions of the inferential and neural controllers are schematically shown in Fig. 2. In the neural controller the actuator actions (on V and E) are modeled as first order filters, with a time constant typical of the industrial control valves. The actuator model is given by the following first order filter equation:
dy
7-&+y=x
CONTROLLER
The relative gain array analysis has been used to select the most proper control strategy, and has indicated the E (reflux ratio)/V (vapor boilup) strategy as the most appropriate for the prescribed objectives. In particular, the distillate prescription should be controlled with V while E should be preferred to regulate the residue specification. The control of the residue specification exhibits rather serious problems due to the high volatility of propane that makes the residue C3 content almost insensitive to E. This results in high gains that lead to serious pitfalls when trying to implement the neural controller that is based on process inversion. Overall, the dual composition control problem exhibits rather ill-conditioned characteristics so as to prevent the neural controller from achieving a reasonable performance. Indeed, for the reference case, the condition number of the steadystate gain matrix is >>1. In this work, we use a multilayer feed-forward neural network trained through the backpropagation algorithm. The adopted network has three layers: the first layer (input) contains nl nodes corresponding to the
Manipulate Variable *
Process
Control Variable ---)
Inferred Control Variable
1
Disturbances
Manipulate Variable
Neural Controller
Fig. 2. Schematic of the actions of the inferential (a) and neural
(b) controllers.
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where r represents the time constant of the actuator device (control valve) and is given by At,,/a; At_ represents the acquisition interval; y is the filtered signal (actuation); x is the manipulated signal, that is, the reflux ratio (E) or the boil-up rate (V) as predicted by the process inverse model. The parameter Q governs the response speed of the actuator, in other words, it determines the rate at which the control action is able to compensate for the upsetting loads to the unit. The process model inversion is simply carried out by inverting the trained neural network exchanging the manipulated variables (E and V) with the controlled ones (the C3 content in the residue and the i-C5 content in the distillate). As anticipated earlier, the dual composition control problem exhibited an ill-character that has prevented us from efficiently performing the process inversion, thus, making unsuccessful any attempt to develop a model-based neural controller. The problem has been overcome by reconsidering the control objectives and discovering that the ill-condition character of the distillation unit is mainly related to the weak sensitivity of the residue composition (C, content) on the reflux ratio, E. This suggested releasing the control specification on the residue by only maintaining the one on the distillate, thus reducing the control problem from dual composition to single composition, Indeed, numerical experiments showed that, for the investigated column upsets, the specification on the residue composition was met anyway when controlling the i-C5 content in the distillate. For the single composition control problem, the analysis of the steady-state gain matrix has led to selection of the reflux flowrate as a manipulated variable to control the distillate specification. The neural network used for the single composition problem has been furtherly simplified to a (5-l-l) configuration that has proved to be very efficient for process inversion, even though it was less accurate than the (7-2-2) network in representing the distillation unit.
DISCUSSION
OF THE RESULTS
For the reference case, the relevant parameters used for simulating the distillation unit are summarized in Table 1. All the results discussed for the neural controller refer to the single composition control problem where the i-C5 content in the distillate (controlled variable) is regulated by acting on the reflux flowrate (manipulated variable). The neural networks used to develop the inferential control strategy and the neural controller were trained using sets of calibration data spanning 50 h of operation. The calibration data were generated by making use of the dynamic simulator previously described. The simulations have been designed so as to capture the principal response features of the distillation units to variations in
feed flowrate, feed composition, distillate and residue specifications, reflux and boil-up flowrates, and operating pressure. At first, the performance of the neural controller has been evaluated with respect to the value of the parameter Q, to test the response sensitivity of the neural controller to changes in the time constant of the actuator device. Increasing cr, the response speed of the neural controller increases, at least up to a critical value cr,, above which the controller response is not significantly affected anymore. In reality, for values of (Y very close to 1 the neural controller exhibits an unstable behavior. For the case of a change of setpoint in the i-C=, content in the distillate, the response of the neural controller is shown in Fig. 3 for two values of a, corresponding to valve time constants of 50s (a) and 125s (b). As expected, increasing the value of Q, the response rate of the neural controller increases, and thus it takes a shorter time to compensate for the setpoint change. Above the value of (Y= 0.1 no detectable changes in the controller response occurred. By further increasing CY,the neural controller exhibited an unstable behavior above the value of O-9. This is the reason why in all the following simulations the value of a = 0.1 has been adopted. The results of Fig. 3 also show the insensitivity of the residue composition (C, mole fraction) that does not exhibit any significant change when the operating conditions are changed to accommodate for the new setpoint in the i-C5 content in the distillate stream. This explains why the neural controller is capable of meeting both the specifications on distillate and residue, even though it directly acts only on the manipulated variable that regulates the distillate composition. A second series of tests have been carried out to compare the performance of the neural controller with that of the inferential strategy. The results, shown in Fig. 4, refer to a setpoint change in the distillate composition. The neural observer is based on a (7-2-2) neural network configuration, while the neural controller relies on a (5- I- 1) network topology. The responses of the two control systems (inferential and neural controller) are compared in terms of the capability in setpoint tracking. The neural controller exhibits a much faster response than the inferential strategy. The first is able to accommodate to the new operating conditions within about 8min, while the second requires about 20min. To verify that the control action of the neural controller is indeed achievable, the required load on the manipulated variable is shown in Fig. 5 in terms of the percentage load variation with respect to the reference case. The results show that the neural controller is able to achieve a good setpoint tracking performance by requiring at most a 3% change in the manipulated variable. Finally, the performance of the three control structures (temperature loop, inferential and neural controllers) are compared in Fig. 6 in terms of the disturbance
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in the distillate stream; (- - - -) C3 mole fraction in the residue stream; (. . .) distillate composition characteristics. The data of Fig. 6, spanning over an operating window of about 1000 h, refer to unit upsets due to fluctuations in feed flowrate (?L l-2%), feed composition (& 5- 15%) and operating pressure (k 3-4%). The results show that the control system based on the temperature loop (Fig. 6(a)) fails to meet the desired distillate specification (i-C5 composition), even though the temperature setpoint, not shown here, is met. The nonunique relationship between temperature and composition, for multicomponent systems, is the prime reason for the observed faulty performance of the temperature control strategy. On the other hand, the C3 specification on the residue stream is well satisfied, and this is due to its insensitivity to the operating conditions rather than to an actual efficacy of the temperature loop policy. The tall peaks exhibited by the i-CS response correspond to perturbations in the feed composition that represent the most critical type of upsets to be faced by the temperature loop control. The response of the inferential system is illustrated in Fig. 6(b), which clearly shows the improvement achieved over the temperature loop performance. The inferential controller also performs well in rejecting the critical disturbances in the feed composition, the response peaks are attenuated by a factor of about 4, with respect to those detected with the temperature loop strategy. The neural controller response is illustrated in Fig. 6(c). The
rejection
i-C5 mole fraction setpoint.
results show that this control strategy by far outperforms the previous two policies since it is capable of completely compensating for the upsetting loadings. In practice, with the neural controller a complete disturbance rejection is achieved. This is mainly due to the intrinsic characteristics of the neural controller that acts on the manipulated variable as soon as the upsetting conditions are detected, and this makes the correction action much faster. It is worth pointing out that the slight inaccuracy exhibited by the (5-l-l) net topology has not affected at all the rejection disturbance performance of the neural controller. This may be due to the feedforward characteristics of the neural controller structure that can also lead to good controller performance in the case of an approximate description of the process inverse model.5 The achievability of the control action has been verified by checking the required load on the manipulated varir.ble. The results are illustrated in Fig. 7 and show that the neural controller is able to achieve a good disturbance rejection performance by requiring at most a 6% change on the manipulated variable. The case of Fig. 6(c) refers to the single composition control problem, and again shows the weak sensitivity of the residue composition on the operating conditions, and this explains why the neural controller is capable of meeting both specifications.
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Response of the inferential control strategy (a) and of the neural controller (b) to changes in the distillate key component setpoint; notation as in Fig. 3.
CONCLUSIONS
(the inferential and neural controllers) perform better than the conventional temperature control loop.
For a multicomponent distillation column, representative of an actual stabilizer unit, three control policies are discussed: a conventional temperature loop, an inferential strategy and a neural controller. The results show that control strategies based on process modeling
The neural controller is based on process inversion that is performed by simply inverting the neural network model of the distillation unit. The results indicate that for ill-conditioned processes, such as the one investigated here, the implementation of nonlinear control
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strategies based on process inversion requires a careful revision of the control objectives as well as of the input set to be fed to the neural network. The neural controller by far outperforms the temperature loop and the inferential control strategies. In reality, the neural controller is the only one capable of achieving an almost complete disturbance rejection, even for the most critical upsetting loadings represented by fluctuations in the feed composition.
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All this suggests that for multicomponent distillation units the conventional temperature loop strategies should be abandoned in favor of more advanced control policies. The results clearly demonstrate the potentials of neural modeling for developing advanced nonlinear control strategies based on process inversion. It is remarkable that even for ill-conditioned processes, such as the one investigated here, neural modeling
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ACKNOWLEDGEMENT Support from the Council for National Researches (CNR) through the research contribution 96.02598.cTO3 is gratefully acknowledged. REFERENCES 1. Stephanopoulos, G. and Han, C., Intelligent systems in process engineering: a review. Comput. Chem. Engng, 1996, 20, 743-79 1. 2. Bulsari, A. B. (ed.), Neural Networks for Chemical Engineers. Elsevier Science B.V., Amsterdam, 1995.
3. Page, G. F., Gomm, J. B. and Williams, D. (ed.), Application of Neural Networks to Modelling and Control. Chapman & Hall, London, 1993. 4. Baratti, R., Vacca, G. and Servida, A., Neural network modeling of distillation columns. Hydrocarbon Processing, 1995, 74(6), 35-38. 5. Baratti, R., Vacca, G. and Servida, A., Control of distillation columns via artificial neural networks. In Engineering Applications of Arttficial Neural Networks, ed. Bulsari, A. B. and Kallio, S. Finnish Artificial Intelligence Society, Helsinki, 1995, pp. 13-16. 6. Luyben, W. L., Process Modeling, Simulation and Control for Chemical Engineers. McGraw-Hill, New York, 1990. 7. Gani, R., Ruiz, C. A. and Cameron, I. T., A generalized model for distillation columns - I. Comput. Chem. Engng, 1986, 10, 181-198. 8. Gmehling, J. and Onken, U., Vapour-Liquid Equilibrium Data Collection Chemistry Data Series, Vol. I/6. DECHEMA, Frankfurt, 1977.
ELSEVIER
0954-1810/97/317.00
SO954-1810(97)00002-2
A feedforward control strategy for distillation columns Roberto Baratti,” Stefano Corti Dipartimento
di Ingegneria Chimica e Materiali,
Universit6 di Cagliari, Piazza D’Armi, I-09123 Cagliari. Italy
Alberta Servida Dipartimento
di Chimica e Chimica Zndustriale, Universitci di Genova. via Dodecaneso 31. I-16146 Genova, Italy
(Received for publication 6 January 1997) The prime objective of this work is to demonstrate the potential of neural network modeling for advanced nonlinear control applications. In particular, for the case of a single composition distillation column, a model-based neural controller is developed to regulate the composition of the distillate stream. The neural controller relies on process inversion for the evaluation of the actuator action on the manipulated variable (reflux flowrate) to maintain the controlled variable (distillate composition) at the prescribed value. The performance of the neural controller is assessed and compared with that of a conventional temperature control loop and of a neural inferential control structure. The neural controller by far outperforms the other two in terms of the response speed by which the upsetting loads are compensated. 0 1997 Elsevier Science Limited. Key words: model-based control, inferential networks, distillation columns.
neural
Approximate process models can be classified in structured and unstructured models. While the former are based on first principles, and thus require good understanding of the process physics, the latter are based on some sort of black-box modeling and, in principle, would not require any a priori knowledge of the process. Neural network modeling represents an effective framework to develop unstructured models when relying on an incomplete knowledge of the process under examination.‘-3 Because of the simplicity of neural models, they exhibit great potentials in all those model-based control applications that require real-time solutions of dynamic process models. The better understanding acquired on neural network modeling has driven its exploitation in many chemical engineering applications: data reconciliation and rectification, process identification and optimization, software sensor development (inferential measurements), state estimation, fault analysis, multivariable control (for a list of references cf. the recent review by Stephanopoulos and Han’). The common belief that effective and efficient neural models can be developed without any a priori
INTRODUCTION Nowadays, advanced control systems are playing a major role in plant operations because they allow for effective plant management. The prime advantage of a full plant automation stands in the improvement of plant profitability and productivity that lead to short term payoffs of the investment required for the implementation of advanced automation systems. Typically, advanced control systems rely heavily on real-time process modeling, and this puts strong demands on developing effective process models that, as a prime requirement, have to exhibit real-time responses. Because in many instances detailed process modeling is not viable, efforts have been devoted towards the development of approximate dynamic models. The models suitable for real-time applications result from a trade-off between model complexity and degree of representability of the actual process dynamics. *To whom correspondence
control, process inversion,
should be addressed. 405
406
R. Baratti et al.
I
11
3
4
;
/
/
-I-
Fig. 1. Schematic of a distillation column showing the controlled and manipulated variables used in a conventional temperature control loop.
understanding of the investigated process is not fully correct. This misconception may lead to neural applications exhibiting poor performance, and this may have been the reason for preventing the full exploitation of neural modeling potentials in real-world applications. Indeed, the selection of the proper inputs and outputs to be fed to the network represents a critical step when developing a neural network model, and an adequate understanding of the process under examination is demanding. Recently Baratti et af.415 have demonstrated the potentials of neural modeling to develop effective inferential control strategies of industrial multicomponent distillation columns. Figure 1 schematically shows a tray distillation column with the typical controlled (temperatures on specified trays, the so called pilot temperatures) and manipulated (reflux, Lo, and boilup, V, flowrates) variables. Figure 1 refers to a case where the pilot temperatures are the ones of the 16th and 3rd trays. The prime aim of this work is to investigate and fully exploit neural modeling in advanced model-based control applications of distillation columns. The basic idea is to construct a neural tool-box that, on the basis of detected disturbances, is capable of acting properly on the manipulated variable so as to compensate for the upsetting loads as soon as they are detected. This action relies on a process modeling that must provide the description of the effect of disturbances and manipulated variables on the process performance. The direct identification of the action on the manipulated variable so as to meet the specifications requires a process inverse model. In this work, we discuss the use of neural modeling to develop an inverse model of a multicomponent distillation column. The neural model provides the controller action law. The direct action on the
manipulated variable allows the control engineer to overcome the problems associated with the optimal tuning of the parameters of conventional feedback controllers. Furthermore, the action of the neural controller resembles that of a feedforward strategy, and thus it may be expected to exhibit a good control performance also in the case of a crude description of the process inverse model.6 For the case of a single composition control problem of a distillation column, neural network modeling is used to develop a model-based neural control strategy to compensate for upsets in the operating pressure, feed flowrate, and feed composition so as to hold constant the content of the key component in the distillate stream. The neural controller is developed for a five-component distillation column (propane, butane, n-pentane, i-pentane and hexane) that is representative of actual stabilizer units, so commonly encountered in the refinery industries. The performance of the neural controller is compared with that of a conventional temperature control loop and of a neural inferential controller.
CASE STUDY
The neural controller is developed for a multicomponent distillation column for which the set of calibration data are produced making use of a dynamic simulator. A 18-trays (ideal stages), five component (propane, hexane, butane, n- and i-pentane) distillation unit is selected as prototype of a gasoline stabilizer tower. The column is also equipped with a reboiler and a total condenser. The feed (saturated liquid) is fed at the 11th stage from the bottom and is constituted of a mixture of propane (lo%), butane (5%), n-pentane (15%), i-pentane (30%) and hexane (40%) (the composition is given on a mole basis). The control objective is to maintain as low as possible the content of i-pentane (i-C,> is the distillate and that of propane (C,) is the residue when the main upsets are due to variations or fluctuations in the feed composition, operating pressure and feed flowrate. The variation in the feed composition is the result of mixing the primary stream with a secondary one (slop) whose composition (on mole basis) is: CX, 2%; c4, 2%; c6, 45%; t&5, 20%; i-C+ 31%. Typically, the secondary stream accounts for about 515% of the total feed flowrate entering the distillation unit. The dynamics of distillation columns can be simulated by various model approaches, involving different levels of complexity.7 Here, we are mainly concerned with addressing the issue of process inversion via neural modeling, thus we have adopted a simple description of the distillation unit that relies on the following assumptions: each tray is an adiabatic ideal equilibrium stage, all the involved species have the same latent heat of vaporization, the vapor and liquid are ideal mixtures,
407
Feedforward control strategy Table 1. Relevant operating parameters wed for the simulation of the reference case
Feed flowrate: 0.229kmol/s Boilup flowrate: 0.063kmol/s Lb,: 5s
Reflux flowrate: 0.035kmol/s Pressure: 821 kPa
the vapor and liquid holdups are negligible. From these assumptions it follows that the vapor and liquid flowrates are constant along the column but different in the stripping and enriching sections. Moreover, the reboiler and the condenser dynamics have been described as first order processes. Under the prescribed assumptions, the mass and energy balance equations are decoupled, and the process model is simply constituted of the transient liquid mass balances. Within the framework of this description the tray temperatures are evaluated by computing the bubble points corresponding to the composition of the liquids on the trays. The equilibrium vapor pressures are calculated through the Antoine equation.8 The adopted dynamic model of the distillation column is rather simplified but, nevertheless, is capable of capturing the most significant dynamical features of the unit that are mainly related to the dynamics of the liquid compositions on the tray. Indeed, these are known to exhibit the largest characteristic times. The design specifications are: i-Cs content in the distillate less than 0.5% (on mole basis) and C3 content in the residue less than O-1%. The parameters corresponding to the reference case are summarized in Table 1.
MODEL-BASED
NEURAL
actual net inputs, the second layer (hidden) contains n2 nodes, and the third layer (output) contains n3 nodes that correspond to the number of the monitored state variables. The configuration of such a network is simply indicated as (nl - n2 - q). The feed and hidden layers are also augmented with a bias unit that represents the threshold value. The input value of the bias node is held constant and equal to 1. Two pilot temperatures, located at the 3rd and 16th tray from the bottom, are also used as inputs to the neural network. It is worth pointing out that we have selected as network inputs those that closely resemble the field measurements available for actual distillation units. Further details on the development of the multilayer neural network, on the selection, and on the pre-processing of the inputs are given elsewhere.415 For the dual composition problem, three control systems based on the El V strategy have been developed: a conventional temperature control loop, a neural inferential system, and a neural controller based on process inversion. The inferential control strategy relies on a neural observer that provides compositions as setpoints to a conventional PI feedback controller. The actions of the inferential and neural controllers are schematically shown in Fig. 2. In the neural controller the actuator actions (on V and E) are modeled as first order filters, with a time constant typical of the industrial control valves. The actuator model is given by the following first order filter equation:
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The relative gain array analysis has been used to select the most proper control strategy, and has indicated the E (reflux ratio)/V (vapor boilup) strategy as the most appropriate for the prescribed objectives. In particular, the distillate prescription should be controlled with V while E should be preferred to regulate the residue specification. The control of the residue specification exhibits rather serious problems due to the high volatility of propane that makes the residue C3 content almost insensitive to E. This results in high gains that lead to serious pitfalls when trying to implement the neural controller that is based on process inversion. Overall, the dual composition control problem exhibits rather ill-conditioned characteristics so as to prevent the neural controller from achieving a reasonable performance. Indeed, for the reference case, the condition number of the steadystate gain matrix is >>1. In this work, we use a multilayer feed-forward neural network trained through the backpropagation algorithm. The adopted network has three layers: the first layer (input) contains nl nodes corresponding to the
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where r represents the time constant of the actuator device (control valve) and is given by At,,/a; At_ represents the acquisition interval; y is the filtered signal (actuation); x is the manipulated signal, that is, the reflux ratio (E) or the boil-up rate (V) as predicted by the process inverse model. The parameter Q governs the response speed of the actuator, in other words, it determines the rate at which the control action is able to compensate for the upsetting loads to the unit. The process model inversion is simply carried out by inverting the trained neural network exchanging the manipulated variables (E and V) with the controlled ones (the C3 content in the residue and the i-C5 content in the distillate). As anticipated earlier, the dual composition control problem exhibited an ill-character that has prevented us from efficiently performing the process inversion, thus, making unsuccessful any attempt to develop a model-based neural controller. The problem has been overcome by reconsidering the control objectives and discovering that the ill-condition character of the distillation unit is mainly related to the weak sensitivity of the residue composition (C, content) on the reflux ratio, E. This suggested releasing the control specification on the residue by only maintaining the one on the distillate, thus reducing the control problem from dual composition to single composition, Indeed, numerical experiments showed that, for the investigated column upsets, the specification on the residue composition was met anyway when controlling the i-C5 content in the distillate. For the single composition control problem, the analysis of the steady-state gain matrix has led to selection of the reflux flowrate as a manipulated variable to control the distillate specification. The neural network used for the single composition problem has been furtherly simplified to a (5-l-l) configuration that has proved to be very efficient for process inversion, even though it was less accurate than the (7-2-2) network in representing the distillation unit.
DISCUSSION
OF THE RESULTS
For the reference case, the relevant parameters used for simulating the distillation unit are summarized in Table 1. All the results discussed for the neural controller refer to the single composition control problem where the i-C5 content in the distillate (controlled variable) is regulated by acting on the reflux flowrate (manipulated variable). The neural networks used to develop the inferential control strategy and the neural controller were trained using sets of calibration data spanning 50 h of operation. The calibration data were generated by making use of the dynamic simulator previously described. The simulations have been designed so as to capture the principal response features of the distillation units to variations in
feed flowrate, feed composition, distillate and residue specifications, reflux and boil-up flowrates, and operating pressure. At first, the performance of the neural controller has been evaluated with respect to the value of the parameter Q, to test the response sensitivity of the neural controller to changes in the time constant of the actuator device. Increasing cr, the response speed of the neural controller increases, at least up to a critical value cr,, above which the controller response is not significantly affected anymore. In reality, for values of (Y very close to 1 the neural controller exhibits an unstable behavior. For the case of a change of setpoint in the i-C=, content in the distillate, the response of the neural controller is shown in Fig. 3 for two values of a, corresponding to valve time constants of 50s (a) and 125s (b). As expected, increasing the value of Q, the response rate of the neural controller increases, and thus it takes a shorter time to compensate for the setpoint change. Above the value of (Y= 0.1 no detectable changes in the controller response occurred. By further increasing CY,the neural controller exhibited an unstable behavior above the value of O-9. This is the reason why in all the following simulations the value of a = 0.1 has been adopted. The results of Fig. 3 also show the insensitivity of the residue composition (C, mole fraction) that does not exhibit any significant change when the operating conditions are changed to accommodate for the new setpoint in the i-C5 content in the distillate stream. This explains why the neural controller is capable of meeting both the specifications on distillate and residue, even though it directly acts only on the manipulated variable that regulates the distillate composition. A second series of tests have been carried out to compare the performance of the neural controller with that of the inferential strategy. The results, shown in Fig. 4, refer to a setpoint change in the distillate composition. The neural observer is based on a (7-2-2) neural network configuration, while the neural controller relies on a (5- I- 1) network topology. The responses of the two control systems (inferential and neural controller) are compared in terms of the capability in setpoint tracking. The neural controller exhibits a much faster response than the inferential strategy. The first is able to accommodate to the new operating conditions within about 8min, while the second requires about 20min. To verify that the control action of the neural controller is indeed achievable, the required load on the manipulated variable is shown in Fig. 5 in terms of the percentage load variation with respect to the reference case. The results show that the neural controller is able to achieve a good setpoint tracking performance by requiring at most a 3% change in the manipulated variable. Finally, the performance of the three control structures (temperature loop, inferential and neural controllers) are compared in Fig. 6 in terms of the disturbance
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in the distillate stream; (- - - -) C3 mole fraction in the residue stream; (. . .) distillate composition characteristics. The data of Fig. 6, spanning over an operating window of about 1000 h, refer to unit upsets due to fluctuations in feed flowrate (?L l-2%), feed composition (& 5- 15%) and operating pressure (k 3-4%). The results show that the control system based on the temperature loop (Fig. 6(a)) fails to meet the desired distillate specification (i-C5 composition), even though the temperature setpoint, not shown here, is met. The nonunique relationship between temperature and composition, for multicomponent systems, is the prime reason for the observed faulty performance of the temperature control strategy. On the other hand, the C3 specification on the residue stream is well satisfied, and this is due to its insensitivity to the operating conditions rather than to an actual efficacy of the temperature loop policy. The tall peaks exhibited by the i-CS response correspond to perturbations in the feed composition that represent the most critical type of upsets to be faced by the temperature loop control. The response of the inferential system is illustrated in Fig. 6(b), which clearly shows the improvement achieved over the temperature loop performance. The inferential controller also performs well in rejecting the critical disturbances in the feed composition, the response peaks are attenuated by a factor of about 4, with respect to those detected with the temperature loop strategy. The neural controller response is illustrated in Fig. 6(c). The
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results show that this control strategy by far outperforms the previous two policies since it is capable of completely compensating for the upsetting loadings. In practice, with the neural controller a complete disturbance rejection is achieved. This is mainly due to the intrinsic characteristics of the neural controller that acts on the manipulated variable as soon as the upsetting conditions are detected, and this makes the correction action much faster. It is worth pointing out that the slight inaccuracy exhibited by the (5-l-l) net topology has not affected at all the rejection disturbance performance of the neural controller. This may be due to the feedforward characteristics of the neural controller structure that can also lead to good controller performance in the case of an approximate description of the process inverse model.5 The achievability of the control action has been verified by checking the required load on the manipulated varir.ble. The results are illustrated in Fig. 7 and show that the neural controller is able to achieve a good disturbance rejection performance by requiring at most a 6% change on the manipulated variable. The case of Fig. 6(c) refers to the single composition control problem, and again shows the weak sensitivity of the residue composition on the operating conditions, and this explains why the neural controller is capable of meeting both specifications.
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CONCLUSIONS
(the inferential and neural controllers) perform better than the conventional temperature control loop.
For a multicomponent distillation column, representative of an actual stabilizer unit, three control policies are discussed: a conventional temperature loop, an inferential strategy and a neural controller. The results show that control strategies based on process modeling
The neural controller is based on process inversion that is performed by simply inverting the neural network model of the distillation unit. The results indicate that for ill-conditioned processes, such as the one investigated here, the implementation of nonlinear control
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strategies based on process inversion requires a careful revision of the control objectives as well as of the input set to be fed to the neural network. The neural controller by far outperforms the temperature loop and the inferential control strategies. In reality, the neural controller is the only one capable of achieving an almost complete disturbance rejection, even for the most critical upsetting loadings represented by fluctuations in the feed composition.
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ACKNOWLEDGEMENT Support from the Council for National Researches (CNR) through the research contribution 96.02598.cTO3 is gratefully acknowledged. REFERENCES 1. Stephanopoulos, G. and Han, C., Intelligent systems in process engineering: a review. Comput. Chem. Engng, 1996, 20, 743-79 1. 2. Bulsari, A. B. (ed.), Neural Networks for Chemical Engineers. Elsevier Science B.V., Amsterdam, 1995.
3. Page, G. F., Gomm, J. B. and Williams, D. (ed.), Application of Neural Networks to Modelling and Control. Chapman & Hall, London, 1993. 4. Baratti, R., Vacca, G. and Servida, A., Neural network modeling of distillation columns. Hydrocarbon Processing, 1995, 74(6), 35-38. 5. Baratti, R., Vacca, G. and Servida, A., Control of distillation columns via artificial neural networks. In Engineering Applications of Arttficial Neural Networks, ed. Bulsari, A. B. and Kallio, S. Finnish Artificial Intelligence Society, Helsinki, 1995, pp. 13-16. 6. Luyben, W. L., Process Modeling, Simulation and Control for Chemical Engineers. McGraw-Hill, New York, 1990. 7. Gani, R., Ruiz, C. A. and Cameron, I. T., A generalized model for distillation columns - I. Comput. Chem. Engng, 1986, 10, 181-198. 8. Gmehling, J. and Onken, U., Vapour-Liquid Equilibrium Data Collection Chemistry Data Series, Vol. I/6. DECHEMA, Frankfurt, 1977.