- Email: [email protected]
Data-based control of an industrial tubular reactor
Control Engineering Practice 8 (2000) 783}790
Data-based control of an industrial tubular reactor K. Akamatsu *, S. Lakshminarayanan , H. Manako , H. Takada , T. Satou , S. L. Shah Mitsubishi Chemical Corporation, 3-10 Ushiodori, Kurashiki, Okayama 712-8054, Japan Department of Chemical & Materials Engineering, University of Alberta, Edmonton, Canada T6G 2G6 Accepted 4 February 2000
Abstract This paper describes the empirical modelling and control of a tubular reactor producing alpha-ole"ns at the Mizushima (Japan) site of Mitsubishi Chemical Corporation (MCC). Initially, the reactor was operated manually resulting in inconsistent run-to-run performance. Using archived data from several past runs and by performing statistical and time-series analysis of the data sets, satisfactory and consistent automatic feedback and feedforward control of the reactors was achieved. An overview of the modelling e!orts involved and the performance of the automatic control strategies is provided here. 2000 Elsevier Science ¸td. All rights reserved. Keywords: Statistical analysis; Time-series analysis; Reactor modelling; Closed-loop control
1. Introduction Alpha-ole"ns are versatile chemical intermediaries that "nd a wide range of application in the plastics and detergent industries. At the Mizushima site of MCC complex, a parallel train of "ve reactors produce alphaole"ns by the oligomerization of ethylene in the presence of the triethyl-aluminum (TEA) catalyst via simultaneous chain growth and displacement reactions. In each reactor, the reactor tube is housed inside a cylindrical shell as shown in Fig. 1 giving a shell and tube heat exchanger appearance to the system. The reaction is exothermic and the shell #uid (water) is used to remove the heat generated due to the reaction. Due to the deposition of coke along the reactor walls, the heat transfer characteristics change with time resulting in the need for a stop-and-decoke operation after a run length of approximately 35 days. During the reactor run, the hot spot temperature along the tube must be regulated below a certain value in order to prevent undesirable reactions and potentially unsafe reactor conditions. The feed-water #ow rate is manipulated to maintain an appropriate level of water in the shell. The shell pressure and the #ow rate of the main reactant feed are the available manipulated variables to achieve the desired * Corresponding author. E-mail address: [email protected] (K. Akamatsu).
conversion, satisfactory reactor run length and safe reactor temperatures. Ethylene inlet temperature has proved to be the major disturbance variable. Clearly, the task of achieving these multiple and con#icting objectives using only two manipulated variables poses a challenge to the operation team. A logic-based control system has been implemented to monitor the hot spot temperature and regulate it by adjusting the shell pressure. Thus, the authors were left with one degree-of-freedom to achieve the remaining objectives * namely acceptable conversion levels and reactor run length. The reactor is well instrumented and measurement of various #ow rates (feed, sub-feed, catalyst, steam), temperatures (from 20 or more locations along the length of the reactor), exit pressure, shell pressure, etc., are logged on to the process computer every minute. In addition, conversion is measured using composition analyzers once in about every 20 min. This measurement in combination with a soft-sensor provides estimates of the conversion every minute. Such data can be easily retrieved by the data analyst using an excellent data retrieval software Dbsave4 developed in-house.
2. PCA-based modelling and control The reactor was originally operated in manual mode. The manipulated variable moves were highly dependent
0967-0661/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 7 - 0 6 6 1 ( 0 0 ) 0 0 0 3 9 - 3
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K. Akamatsu et al. / Control Engineering Practice 8 (2000) 783}790
Fig. 2. PCA-based modelling and control.
Fig. 1 . The alpha-ole"n reactor.
on the skill and judgement of the operators. Further, the control moves were unduly conservative due to a large emphasis on reactor and personnel safety. Inconsistencies in the operation of the reactors, variability in the product quality from run-to-run, etc., highlighted the need to automate the ethylene feed rate to the reactor. In the absence of a fundamental model for the process, emphasis was laid on a data-based modelling and control approach. Viewing the start}run}shut nature of the process as a batch unit operation, Shah, Miller and Takada (1998) utilized the data available from three previous good runs to construct a principal components analysis (PCA) model. Besides capturing the relationships between the di!erent process variables, this model also provided an optimal target trajectory over which future process operation must slide upon. This is essentially along the lines suggested in other studies for the monitoring of continuous (Kresta, MacGregor & Marlin, 1991) and batch processes (Nomikos & MacGregor, 1995). Invoking the concept of inverse mapping, the PCA model in conjunction with online measurements was used to compute the input moves (ethylene-feed #ow rate) and constrained the process to track the desired trajectory. The PCA modelling and control philosophy can be graphically described as shown in Fig. 2. This strategy was "rst tested on Reactor E and was subsequently implemented on the other reactors. Some of the results obtained using the PCA model-based control are illustrated in Shah et al. (1998). The PCA model was able to make control moves taking many process variables into consideration. However, since the feed rate was computed once every two hours, the dynamic response of the closed-loop to disturbances was poor. This is not due to the drawback of the technique * rather, it is due to the fact that the PCA model was built using pseudo steady-state data. Also, the PCA model had many parameters (scaling parameters, loadings matrix) making the controller implementation and maintenance somewhat laborious. The physical meaning of the target trajectory is also di$cult to comprehend. However, the PCA-based control strategy pro-
vided a more consistent and uniform operation of the reactors and relieved the operators for other important operational tasks. In order to improve the dynamic characteristics of the control system, a plan to build a dynamic model based on data collected on a minute-by-minute basis was envisaged. The model was built with the canonical variate analysis (CVA) technique and a conventional PI controller was designed. This activity is described next.
3. CVA model and PI control Subspace-based state-space system identi"cation (4SID) methods have recently attracted much attention owing to their computational simplicity and e!ectiveness in identifying dynamic linear multivariable systems. The 4SID methods estimate a fairly general linear model and can automatically identify the `optimala model order using information theoretic criteria or by analyzing the singular values of a certain `extended observabilitya matrix. Of the most popular 4SID methods (canonical variate analysis (CVA), numerical algorithms for subspace state-space system identi"cation (N4SID) and multivariable output error state-space identi"cation (MOESP)), the relative superiority of CVA over N4SID and MOESP (see Deistler, Peternell & Scherrer, 1995; Favoreel, 1998) has been demonstrated. Consequently, the CVA algorithm was used in this investigation. The CVA technique was originally developed by Larimore (1990) and employs singular value decomposition as the core computational machinery. This makes it computationally stable and accurate. The CVA procedure is scale independent and has been shown to provide optimal parameter estimates even with small sample sizes, small signal to noise ratios and in the presence of unknown feedback mechanisms. In CVA, a multivariate technique named canonical correlations analysis (CCA) is used to generate the states of the following state-space model: X "'X #G; #= R> R R R > "HX #A; #B= #< . R R R R R
(1) (2)
K. Akamatsu et al. / Control Engineering Practice 8 (2000) 783}790
The model matrices [', G, H, A, B] and the noise covariance matrices [Q, R] are then obtained via ordinary least squares. In this representation, X refers to the `statesa, > refers to the outputs, ; refers to the manipulated inputs, = refers to the state or process noise and B=#< represents the measurement noise. Though = and < are independent zero-mean white-noise sequences, the above model allows for the existence of correlation between the state and measurement noise channels through the use of a non-zero B matrix. It must be pointed out that the states generated by this identi"cation approach are not the true (physically meaningful) states. Rather, they are optimal linear combinations of the past inputs and outputs of the plant. Without resorting to any iterative and nonlinear optimization procedures, CVA has been shown to provide a near maximum likelihood-estimate of the system parameters. Consequently, it has become one of the most popular tools for multivariable linear system identi"cation. For the application of the CVA technique the authors regard the alpha-ole"n manufacturing process as being of the continuous type. This is easy to justify since reactants are added to and the products are removed from the reactor during the entire duration of its operation. Furthermore, the process will be considered linear as well as time-invariant. These assumptions can be checked by validating the identi"ed model using data taken during the early, middle and late stages of other reactor runs. Since conversion is measured at relatively slow sampling rates, an indirect strategy for its control is "rst employed. The steam generation rate can be regarded as a measure of the reaction's activity and conversion. Therefore, steam generation will be employed as the control variable (later, the steam generation controller will be cascaded to a conversion controller). The input/ output variables for the CVA model are shown in Fig. 3. A third-order state-space model was determined using the CVA procedure. The "t and validation for this model are shown in Fig. 4, where the noisy line represents the plant data and the relatively smooth line represents the model output. For cross validation, data taken at di!erent stages of the other runs was examined. From Fig. 4, it is clear that the model predictions are in good agreement with the actual data. This also means that the assumptions of a linear, time-invariant model are not seriously violated for the current choices of input and output variables * the CVA model can be considered adequate for purposes of designing the PI feedback controller and the lead-lag feedforward controller. The relationship between the ethylene feed-rate and steam generation was approximated by a "rst-order plus dead-time (FOPDT) model while the relationship between the ethylene-feed temperature (disturbance) and the steam generation was found to follow roughly "rstorder plus time-delay dynamics. The feedback PI controller was designed using the Direct Synthesis approach.
785
Fig. 3. The CVA model.
Fig. 4. Fit (panel A) and validation (panels B}D) of the steam generation model.
An approximate lead-lag type feedforward controller was designed to handle the disturbance originating from the ethylene-feed temperature. The controller parameters were tuned online with a view to obtain satisfactory performance.
4. Results 4.1. Ewect on shell pressure and run length Shown in Figs. 5 and 6 are trajectories of key process variables under manual and automatic control, respectively. These data sets belong to the same run where the reactor was operated under manual control for a period of time before regulation was turned over to the PI controller. The manual operation represents an operation period of little more than 2 days just after the reactor startup. The automatic operation is shown for about 3.5 days of operation roughly 10 days after startup. In the manual mode of operation, the ethylene feedrate was kept constant (this depends on the judgement of the operator) even in the face of disturbances in ethylene
786
K. Akamatsu et al. / Control Engineering Practice 8 (2000) 783}790
Fig. 5. Performance of the alpha-ole"n reactor under manual control.
Fig. 6. Performance of the alpha-ole"n reactor under automatic control.
feed temperature. This resulted in an upward drift in ethylene conversion, which is desirable if unaccompanied by other e!ects. However, the shell pressure had to be reduced by 0.06 units within a time span of roughly 7 h.
Such a decrease in shell pressure is unwarranted during the early stages of the reactor run. Under automatic control, it can be clearly seen that the changes in feed temperature are negotiated very well by
K. Akamatsu et al. / Control Engineering Practice 8 (2000) 783}790
787
Fig. 7. Response of manual, PCA and PI control strategies to a disturbance in ethylene feed temperature.
manipulating the ethylene feed-rate. No sustained shift is seen in the ethylene conversion trajectory. Steam generation regulation remains satisfactory throughout. Note that the shell pressure has decreased by 0.2 units over a period of 2 days. This works out to be an average of about 0.03 units for a 7 h period. Considering the fact that this smaller decrease rate comes after 10 days of operation, one can surmise that automatic operation with the PI controller facilitates a more stable operation of the reactor. This also means that with the PI controllers in place, it should be possibe to extend the reactor run lengths over an extra 5}7 days of operation. With the current control system, economic bene"ts of several hundred thousand dollars every year compared to the past operation are expected. 4.2. Response to disturbances in ethylene feed temperature In Fig. 7, the performance of the manual, PCA and PI control strategies are compared when the ethylene-feed temperature undergoes a step-like change (this is a common type of disturbance owing to the startup or shutdown of other four alpha-ole"n reactors). In all cases, the ethylene #ow-rate is increased to compensate for this disturbance. However, only in case of the PI controller, does the steam generation rate stay more or less at the desired set point value and not increase. In the case of manual control, there is a perceivable upward drift. The
PCA controller is not successful in eliminating this disturbance * a step-type change is noticed in the steam generation trajectory. Any upward drift in the steam generation can be considered to arise out of increased temperatures inside the reactor tubes. Such increases in temperatures lead to enhanced coking, prompting the process operators to lower the shell pressure and ultimately resulting in shorter reactor run lengths. 4.3. Comparison of overall performance Finally, the overall changes that were noticed in the reactor operation under manual control, PCA model-based control and with PI control will be demonstrated. Actual operating data covering a period of 700 h is shown in Figs. 8}11. These "gures are all drawn to the same scale so that a direct comparison is possible. Fig. 8 shows the operation under manual control, Fig. 9 relates to PCA-based control, Fig. 10 illustrates the situation under PI control of the steam generation and Fig. 11 depicts the nature of the operation after the conversion controller (a PI controller) is used to provide the setpoint to the steam generation controller (i.e., a cascade con"guration). The conversion controller was determined after an identi"cation exercise that is not reported here. From Figs. 8}11, it is clear that the trajectory for conversion has become very steady after the implementation
788
K. Akamatsu et al. / Control Engineering Practice 8 (2000) 783}790
Fig. 8. Trajectories of the process variables under manual control.
Fig. 9. Trajectories of the process variables under PCA model-based control.
of the conversion controller. To quantify the bene"ts and the improvement with the current control strategy, we indicate in Table 1, the average ethylene conversion (using manual control as the base case equal to 100)
and the standard deviation of the ethylene conversion trajectory (using manual control as the benchmark equal to 1) covering a period of 25 days (100}700 h after startup).
K. Akamatsu et al. / Control Engineering Practice 8 (2000) 783}790
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Fig. 10. Trajectories of the process variables under PI control of the steam generation.
Fig. 11. Trajectories of the process variables under PI control of the ethylene conversion.
A 8.7% improvement in average ethylene conversion and a substantially tighter regulation of the ethylene conversion was obtained. It is also clear that the PI control strategy has resulted in an improvement that is twice the magnitude of the PCA-based control. Furthermore, most of the bene"ts were obtained once the steam generation rate was controlled.
5. Conclusions and future work In this paper, the modelling and control of an industrial tubular reactor has been described. Using multivariate statistical analysis and time-series analysis, the authors have been able to switch from manual operation to automatic control. A statistical model based on
790
K. Akamatsu et al. / Control Engineering Practice 8 (2000) 783}790
Table 1 Comparison of plant performance under various control schemes
Manual run PCA-based control Steam generation control Ethylene conversion control
Average ethylene conversion
Standard deviation of ethylene conversion
100 104.3 108.6 108.7
1 0.39 0.34 0.22
pseudo-steady-state data was built using principal components analysis technique and was inverted to provide an automated feed policy for the reactor. Later, the authors opted for a more traditional time-series-based modelling and PI control. The main emphasis of this paper has been the development of a state-space model using canonical variate analysis on dynamic plant data. This model was then employed in the design of a PI controller for feedback action and for the design of a feedforward controller to reject disturbances in the ethylene feed temperature. It was shown that this control strategy has resulted in a stable and consistent operation of the reactor.
The "nal phase of this project will focus on the modeling and monitoring of coking in the reactor tube. With this model, the authors intend to develop an operating policy that will enable the production rate to be maximized while keeping the reactor run length at 35 days or to increase the run length to 40 days.
References Deistler, M., Peternell, K., & Scherrer, W. (1995). Consistency and relative e$ciency of subspace methods. Automatica, 31(12), 1865}1875. Favoreel, W. (1998). Benchmark for subspace system identixcation algorithms. Technical Report ESAT-SISTA/TR 1998, Department Elektrotechniek, Katholieke Universiteit Leuven, Belgium. Kresta, J. V., MacGregor, J. F., & Marlin, T. E. (1991). Multivariate statistical monitoring of process operating performance. Canadian Journal of Chemical Engineering, 69(1), 35}47. Larimore, W. E. (1990). Canonical variate analysis in identi"cation, "ltering and adaptive control. Proceedings of the 29th IEEE conference on decision and control, Honolulu, Hawaii (pp. 635}639). Nomikos, P., & MacGregor, J. F. (1995). Multivariate SPC charts for monitoring batch processes. Technometrics, 37(1), 41}59. Shah, S. L., Miller, R., Takada, H., Morinaga, K., & Satou, T. (1998). Modelling and control of a tubular reactor: A PCA-based approach. Preprints of the xfth IFAC symposium on dynamics and control of process systems, Corfu, Greece (pp. 17}22).
Data-based control of an industrial tubular reactor K. Akamatsu *, S. Lakshminarayanan , H. Manako , H. Takada , T. Satou , S. L. Shah Mitsubishi Chemical Corporation, 3-10 Ushiodori, Kurashiki, Okayama 712-8054, Japan Department of Chemical & Materials Engineering, University of Alberta, Edmonton, Canada T6G 2G6 Accepted 4 February 2000
Abstract This paper describes the empirical modelling and control of a tubular reactor producing alpha-ole"ns at the Mizushima (Japan) site of Mitsubishi Chemical Corporation (MCC). Initially, the reactor was operated manually resulting in inconsistent run-to-run performance. Using archived data from several past runs and by performing statistical and time-series analysis of the data sets, satisfactory and consistent automatic feedback and feedforward control of the reactors was achieved. An overview of the modelling e!orts involved and the performance of the automatic control strategies is provided here. 2000 Elsevier Science ¸td. All rights reserved. Keywords: Statistical analysis; Time-series analysis; Reactor modelling; Closed-loop control
1. Introduction Alpha-ole"ns are versatile chemical intermediaries that "nd a wide range of application in the plastics and detergent industries. At the Mizushima site of MCC complex, a parallel train of "ve reactors produce alphaole"ns by the oligomerization of ethylene in the presence of the triethyl-aluminum (TEA) catalyst via simultaneous chain growth and displacement reactions. In each reactor, the reactor tube is housed inside a cylindrical shell as shown in Fig. 1 giving a shell and tube heat exchanger appearance to the system. The reaction is exothermic and the shell #uid (water) is used to remove the heat generated due to the reaction. Due to the deposition of coke along the reactor walls, the heat transfer characteristics change with time resulting in the need for a stop-and-decoke operation after a run length of approximately 35 days. During the reactor run, the hot spot temperature along the tube must be regulated below a certain value in order to prevent undesirable reactions and potentially unsafe reactor conditions. The feed-water #ow rate is manipulated to maintain an appropriate level of water in the shell. The shell pressure and the #ow rate of the main reactant feed are the available manipulated variables to achieve the desired * Corresponding author. E-mail address: [email protected] (K. Akamatsu).
conversion, satisfactory reactor run length and safe reactor temperatures. Ethylene inlet temperature has proved to be the major disturbance variable. Clearly, the task of achieving these multiple and con#icting objectives using only two manipulated variables poses a challenge to the operation team. A logic-based control system has been implemented to monitor the hot spot temperature and regulate it by adjusting the shell pressure. Thus, the authors were left with one degree-of-freedom to achieve the remaining objectives * namely acceptable conversion levels and reactor run length. The reactor is well instrumented and measurement of various #ow rates (feed, sub-feed, catalyst, steam), temperatures (from 20 or more locations along the length of the reactor), exit pressure, shell pressure, etc., are logged on to the process computer every minute. In addition, conversion is measured using composition analyzers once in about every 20 min. This measurement in combination with a soft-sensor provides estimates of the conversion every minute. Such data can be easily retrieved by the data analyst using an excellent data retrieval software Dbsave4 developed in-house.
2. PCA-based modelling and control The reactor was originally operated in manual mode. The manipulated variable moves were highly dependent
0967-0661/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 7 - 0 6 6 1 ( 0 0 ) 0 0 0 3 9 - 3
784
K. Akamatsu et al. / Control Engineering Practice 8 (2000) 783}790
Fig. 2. PCA-based modelling and control.
Fig. 1 . The alpha-ole"n reactor.
on the skill and judgement of the operators. Further, the control moves were unduly conservative due to a large emphasis on reactor and personnel safety. Inconsistencies in the operation of the reactors, variability in the product quality from run-to-run, etc., highlighted the need to automate the ethylene feed rate to the reactor. In the absence of a fundamental model for the process, emphasis was laid on a data-based modelling and control approach. Viewing the start}run}shut nature of the process as a batch unit operation, Shah, Miller and Takada (1998) utilized the data available from three previous good runs to construct a principal components analysis (PCA) model. Besides capturing the relationships between the di!erent process variables, this model also provided an optimal target trajectory over which future process operation must slide upon. This is essentially along the lines suggested in other studies for the monitoring of continuous (Kresta, MacGregor & Marlin, 1991) and batch processes (Nomikos & MacGregor, 1995). Invoking the concept of inverse mapping, the PCA model in conjunction with online measurements was used to compute the input moves (ethylene-feed #ow rate) and constrained the process to track the desired trajectory. The PCA modelling and control philosophy can be graphically described as shown in Fig. 2. This strategy was "rst tested on Reactor E and was subsequently implemented on the other reactors. Some of the results obtained using the PCA model-based control are illustrated in Shah et al. (1998). The PCA model was able to make control moves taking many process variables into consideration. However, since the feed rate was computed once every two hours, the dynamic response of the closed-loop to disturbances was poor. This is not due to the drawback of the technique * rather, it is due to the fact that the PCA model was built using pseudo steady-state data. Also, the PCA model had many parameters (scaling parameters, loadings matrix) making the controller implementation and maintenance somewhat laborious. The physical meaning of the target trajectory is also di$cult to comprehend. However, the PCA-based control strategy pro-
vided a more consistent and uniform operation of the reactors and relieved the operators for other important operational tasks. In order to improve the dynamic characteristics of the control system, a plan to build a dynamic model based on data collected on a minute-by-minute basis was envisaged. The model was built with the canonical variate analysis (CVA) technique and a conventional PI controller was designed. This activity is described next.
3. CVA model and PI control Subspace-based state-space system identi"cation (4SID) methods have recently attracted much attention owing to their computational simplicity and e!ectiveness in identifying dynamic linear multivariable systems. The 4SID methods estimate a fairly general linear model and can automatically identify the `optimala model order using information theoretic criteria or by analyzing the singular values of a certain `extended observabilitya matrix. Of the most popular 4SID methods (canonical variate analysis (CVA), numerical algorithms for subspace state-space system identi"cation (N4SID) and multivariable output error state-space identi"cation (MOESP)), the relative superiority of CVA over N4SID and MOESP (see Deistler, Peternell & Scherrer, 1995; Favoreel, 1998) has been demonstrated. Consequently, the CVA algorithm was used in this investigation. The CVA technique was originally developed by Larimore (1990) and employs singular value decomposition as the core computational machinery. This makes it computationally stable and accurate. The CVA procedure is scale independent and has been shown to provide optimal parameter estimates even with small sample sizes, small signal to noise ratios and in the presence of unknown feedback mechanisms. In CVA, a multivariate technique named canonical correlations analysis (CCA) is used to generate the states of the following state-space model: X "'X #G; #= R> R R R > "HX #A; #B= #< . R R R R R
(1) (2)
K. Akamatsu et al. / Control Engineering Practice 8 (2000) 783}790
The model matrices [', G, H, A, B] and the noise covariance matrices [Q, R] are then obtained via ordinary least squares. In this representation, X refers to the `statesa, > refers to the outputs, ; refers to the manipulated inputs, = refers to the state or process noise and B=#< represents the measurement noise. Though = and < are independent zero-mean white-noise sequences, the above model allows for the existence of correlation between the state and measurement noise channels through the use of a non-zero B matrix. It must be pointed out that the states generated by this identi"cation approach are not the true (physically meaningful) states. Rather, they are optimal linear combinations of the past inputs and outputs of the plant. Without resorting to any iterative and nonlinear optimization procedures, CVA has been shown to provide a near maximum likelihood-estimate of the system parameters. Consequently, it has become one of the most popular tools for multivariable linear system identi"cation. For the application of the CVA technique the authors regard the alpha-ole"n manufacturing process as being of the continuous type. This is easy to justify since reactants are added to and the products are removed from the reactor during the entire duration of its operation. Furthermore, the process will be considered linear as well as time-invariant. These assumptions can be checked by validating the identi"ed model using data taken during the early, middle and late stages of other reactor runs. Since conversion is measured at relatively slow sampling rates, an indirect strategy for its control is "rst employed. The steam generation rate can be regarded as a measure of the reaction's activity and conversion. Therefore, steam generation will be employed as the control variable (later, the steam generation controller will be cascaded to a conversion controller). The input/ output variables for the CVA model are shown in Fig. 3. A third-order state-space model was determined using the CVA procedure. The "t and validation for this model are shown in Fig. 4, where the noisy line represents the plant data and the relatively smooth line represents the model output. For cross validation, data taken at di!erent stages of the other runs was examined. From Fig. 4, it is clear that the model predictions are in good agreement with the actual data. This also means that the assumptions of a linear, time-invariant model are not seriously violated for the current choices of input and output variables * the CVA model can be considered adequate for purposes of designing the PI feedback controller and the lead-lag feedforward controller. The relationship between the ethylene feed-rate and steam generation was approximated by a "rst-order plus dead-time (FOPDT) model while the relationship between the ethylene-feed temperature (disturbance) and the steam generation was found to follow roughly "rstorder plus time-delay dynamics. The feedback PI controller was designed using the Direct Synthesis approach.
785
Fig. 3. The CVA model.
Fig. 4. Fit (panel A) and validation (panels B}D) of the steam generation model.
An approximate lead-lag type feedforward controller was designed to handle the disturbance originating from the ethylene-feed temperature. The controller parameters were tuned online with a view to obtain satisfactory performance.
4. Results 4.1. Ewect on shell pressure and run length Shown in Figs. 5 and 6 are trajectories of key process variables under manual and automatic control, respectively. These data sets belong to the same run where the reactor was operated under manual control for a period of time before regulation was turned over to the PI controller. The manual operation represents an operation period of little more than 2 days just after the reactor startup. The automatic operation is shown for about 3.5 days of operation roughly 10 days after startup. In the manual mode of operation, the ethylene feedrate was kept constant (this depends on the judgement of the operator) even in the face of disturbances in ethylene
786
K. Akamatsu et al. / Control Engineering Practice 8 (2000) 783}790
Fig. 5. Performance of the alpha-ole"n reactor under manual control.
Fig. 6. Performance of the alpha-ole"n reactor under automatic control.
feed temperature. This resulted in an upward drift in ethylene conversion, which is desirable if unaccompanied by other e!ects. However, the shell pressure had to be reduced by 0.06 units within a time span of roughly 7 h.
Such a decrease in shell pressure is unwarranted during the early stages of the reactor run. Under automatic control, it can be clearly seen that the changes in feed temperature are negotiated very well by
K. Akamatsu et al. / Control Engineering Practice 8 (2000) 783}790
787
Fig. 7. Response of manual, PCA and PI control strategies to a disturbance in ethylene feed temperature.
manipulating the ethylene feed-rate. No sustained shift is seen in the ethylene conversion trajectory. Steam generation regulation remains satisfactory throughout. Note that the shell pressure has decreased by 0.2 units over a period of 2 days. This works out to be an average of about 0.03 units for a 7 h period. Considering the fact that this smaller decrease rate comes after 10 days of operation, one can surmise that automatic operation with the PI controller facilitates a more stable operation of the reactor. This also means that with the PI controllers in place, it should be possibe to extend the reactor run lengths over an extra 5}7 days of operation. With the current control system, economic bene"ts of several hundred thousand dollars every year compared to the past operation are expected. 4.2. Response to disturbances in ethylene feed temperature In Fig. 7, the performance of the manual, PCA and PI control strategies are compared when the ethylene-feed temperature undergoes a step-like change (this is a common type of disturbance owing to the startup or shutdown of other four alpha-ole"n reactors). In all cases, the ethylene #ow-rate is increased to compensate for this disturbance. However, only in case of the PI controller, does the steam generation rate stay more or less at the desired set point value and not increase. In the case of manual control, there is a perceivable upward drift. The
PCA controller is not successful in eliminating this disturbance * a step-type change is noticed in the steam generation trajectory. Any upward drift in the steam generation can be considered to arise out of increased temperatures inside the reactor tubes. Such increases in temperatures lead to enhanced coking, prompting the process operators to lower the shell pressure and ultimately resulting in shorter reactor run lengths. 4.3. Comparison of overall performance Finally, the overall changes that were noticed in the reactor operation under manual control, PCA model-based control and with PI control will be demonstrated. Actual operating data covering a period of 700 h is shown in Figs. 8}11. These "gures are all drawn to the same scale so that a direct comparison is possible. Fig. 8 shows the operation under manual control, Fig. 9 relates to PCA-based control, Fig. 10 illustrates the situation under PI control of the steam generation and Fig. 11 depicts the nature of the operation after the conversion controller (a PI controller) is used to provide the setpoint to the steam generation controller (i.e., a cascade con"guration). The conversion controller was determined after an identi"cation exercise that is not reported here. From Figs. 8}11, it is clear that the trajectory for conversion has become very steady after the implementation
788
K. Akamatsu et al. / Control Engineering Practice 8 (2000) 783}790
Fig. 8. Trajectories of the process variables under manual control.
Fig. 9. Trajectories of the process variables under PCA model-based control.
of the conversion controller. To quantify the bene"ts and the improvement with the current control strategy, we indicate in Table 1, the average ethylene conversion (using manual control as the base case equal to 100)
and the standard deviation of the ethylene conversion trajectory (using manual control as the benchmark equal to 1) covering a period of 25 days (100}700 h after startup).
K. Akamatsu et al. / Control Engineering Practice 8 (2000) 783}790
789
Fig. 10. Trajectories of the process variables under PI control of the steam generation.
Fig. 11. Trajectories of the process variables under PI control of the ethylene conversion.
A 8.7% improvement in average ethylene conversion and a substantially tighter regulation of the ethylene conversion was obtained. It is also clear that the PI control strategy has resulted in an improvement that is twice the magnitude of the PCA-based control. Furthermore, most of the bene"ts were obtained once the steam generation rate was controlled.
5. Conclusions and future work In this paper, the modelling and control of an industrial tubular reactor has been described. Using multivariate statistical analysis and time-series analysis, the authors have been able to switch from manual operation to automatic control. A statistical model based on
790
K. Akamatsu et al. / Control Engineering Practice 8 (2000) 783}790
Table 1 Comparison of plant performance under various control schemes
Manual run PCA-based control Steam generation control Ethylene conversion control
Average ethylene conversion
Standard deviation of ethylene conversion
100 104.3 108.6 108.7
1 0.39 0.34 0.22
pseudo-steady-state data was built using principal components analysis technique and was inverted to provide an automated feed policy for the reactor. Later, the authors opted for a more traditional time-series-based modelling and PI control. The main emphasis of this paper has been the development of a state-space model using canonical variate analysis on dynamic plant data. This model was then employed in the design of a PI controller for feedback action and for the design of a feedforward controller to reject disturbances in the ethylene feed temperature. It was shown that this control strategy has resulted in a stable and consistent operation of the reactor.
The "nal phase of this project will focus on the modeling and monitoring of coking in the reactor tube. With this model, the authors intend to develop an operating policy that will enable the production rate to be maximized while keeping the reactor run length at 35 days or to increase the run length to 40 days.
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