4048
Ind. Eng. Chem. Res. 2002, 41, 4048-4053
PROCESS DESIGN AND CONTROL Including Levels in MPC to Improve Distillation Control Haitao Huang† and James B. Riggs* Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409-3121
This work examines the effects of including levels into MPC for distillation control via rigorous simulation of two different columns: a depropanizer and a propane/propylene splitter (C3 splitter). Three different MPC implementations for distillation control were compared: regular implementation in which the levels are controlled by PI regulatory controllers, direct implementation in which the levels are controlled by MPC directly by manipulating flow rates, and cascade implementation in which MPC moves the set points to the regulatory level controllers. The results show that directly including levels in MPC improves composition control performance significantly for fast-responding distillation columns. The cascade implementation is recommended for columns that exhibit ill-conditioning for the [L, V] control configuration or for columns that require a long time to obtain steady state. Introduction Model predictive control (MPC) has been applied widely in process industries, with over 1000 distillation applications worldwide. MPC uses linear, empirical time-series models of the process to predict the response of the process and compute appropriate corrective action to drive the controlled variables to the desired target values. MPC handles constraints, coupling, dead time, and complex dynamics, as well as multiple and often contradictory control objectives, for MIMO systems explicitly in the time-series-modeling framework. A two-product column is a four-input/four-output (4 × 4) system, as shown in Figure 1, if pressure control is considered separately, as it is in many cases. The control problem is to adjust the four independent variables, reflux (L), top product flow (D), boilup flow (V), and bottom product flow (B), to keep the top product impurity (1 - y) and bottom product impurity (x) onspecification in the face of various disturbances and constraints. Variations in accumulator and reboiler levels should also be kept within certain limits so that operations run smoothly and safely. In most MPC applications to distillation control, as shown in Figure 2a, a decision is made first on configuration, i.e., choice of manipulated variables for levels and compositions. For example, the reflux (L) can be chosen for composition control and the distillate flow (D) for accumulator level control, or vice versa. If a product flow (D or B) is used for composition control, it is referred to as material balance control. If the reflux or boilup flow is used for composition control, it is called energy balance control. Shown in Figure 2a is the [L, B] configuration, in which L and B are used to control the two compositions in the MPC controllers, or energy balance is used at the top and material balance is used at the bottom. After a configuration is selected, the level * Corresponding author. Fax: (806)742-1765. E-mail: cpjbr@ ttacs.ttu.edu. † Current address: Motorola, Inc., Tempe, AZ 85282.
Figure 1. Two-product column.
control loops are closed at the regulatory control level, and step tests are conducted to identify the time-series process model for the column as a 2 × 2 composition control system. For the [L, B] configuration, the MPC controller uses the reflux and the bottom product flow as the two manipulated variables to control the top and bottom product compositions. Although this approach reduces the model dimensions to a 2 × 2 system and facilitates the step tests, it also introduces some problems in certain cases. First, it does not fully exploit the decoupling power of the MPC, and it might exhibit inferior performance for composition control in some cases. Consider a scenario for a two-product column using the material balance control at the top, in which the distillate flow (D) is used by an MPC controller to control the overhead product and a PI controller uses the reflux (L) to control the accumulator level. When the feed becomes heavier, less light component goes up to the top of the tower. Consequently, the accumulator level decreases, and the top impurity increases. The PI level controller decreases the reflux to maintain the level, while the MPC controller decreases the product flow to reduce the impurity. However, the decrease in the reflux called for by the
10.1021/ie0005396 CCC: $22.00 © 2002 American Chemical Society Published on Web 07/04/2002
Ind. Eng. Chem. Res., Vol. 41, No. 16, 2002 4049
Figure 2. MPC implementations for distillation control: (a) regular MPC implementation for [L, B] configuration, (b) MPC with direct level control, (c) MPC with cascade level control for [L, B] configuration.
level controller would further increase the overhead impurity. Therefore, the level controller actually amplifies the composition variation caused by the disturbance. Second, for the MPC controller implemented with closed level control loops, the composition control performance of MPC is directly related to the choice of the manipulated/controlled variable pairings. In the extreme case, a poor configuration choice can amplify the effect of a disturbance on the product compositions. In some applications, step tests are performed with level loops opened, and the levels are included in the MPC as integral process variables, as shown in Figure 2b. In this implementation, the MPC has full control of the 4 × 4 distillation process. It should be emphasized at this point that this approach assumes that there is adequate inventory in the reboiler and accumulator. Consider the scenario discussed above. This time, the MPC controller will increase the reflux to reduce the impurity and simultaneously decrease the product flow to maintain the level. However, this implementation introduces difficulties for step testing. The size, order,
and switching time for step changes of manipulated variables should be planned carefully to ensure that the level only varies within limits and around its nominal values during step tests. It is more challenging to perform these step tests while maintaining the levels and producing uncorrelated process results. If test data for an MPC controller contain correlated results, the MPC models will likely lack the fidelity necessary for a successful application. Additional MPC tuning effort is also required for the model dimensions because the control problem increases from a 2 × 2 system to a 4 × 4 system. Another implementation option is shown in Figure 2c for the [L, B] configuration, in which the set points to the regulatory level controllers are used as manipulated variables in the MPC controller. The levels are included in MPC as self-regulated variables. Step tests can be performed in the same way as for MPC without levels included. For the column discussed above that uses the distillate product flow for composition control at the top, the problem of moving reflux in the wrong direction by the level controller still exists. However, this implementation allows the MPC to coordinate the moves made by the level controllers and moves for other manipulated variables and to make a compromise between level control and composition control. It should be noted that the process models developed for the regular application (Figure 2a) are exactly the same as the models for the cascade approach (Figure 2c), except that two additional manipulated variables (i.e., the set points for the accumulator and the reboiler) are required for the cascade approach. The process models for the direct application (Figure 2b) would be different from those for the other two applications. This means that a regular application can be more easily converted to the cascade form, whereas the direct application would require the development of a completely new set of process models. Lundtrom and Skogestad1 applied MPC to 5 × 5 distillation control, i.e., control of levels, pressure, and compositions, implemented in a manner similar to Figure 2b. However, they only compared the MPC with a decentralized control system with the [L, V] configuration. Effects of using different implementation schemes of MPC shown in Figure 2 were not studied by Lundtrom and Skogestad, whereas this is one of the main purposes of this work. In summary, allowing MPC to control distillation column levels is advantageous (1) when there is plenty of surge capacity available, (2) for true multivariable control that can exploit the flexibility of surge capacity for economic advantage or for improved composition control, (3) for improved and simplified MPC model identification, and (4) for better averaging level control for downstream units. In this study, DMCPlus of AspenTech is used to examine the effects of including levels into MPC for distillation control by comparing different implementations. To differentiate the three implementations, the implementation in Figure 2a is referred as DMC with regular implementation, that in 2b as DMC with direct implementation, and that in 2c as DMC with cascade implementation. DMCPlus controllers with all three implementations are applied to two simulated distillation columns: a depropanizer and a C3 splitter. Their performances for composition control are compared.
4050
Ind. Eng. Chem. Res., Vol. 41, No. 16, 2002
Table 1. DMCPlus Controllers for the Depropanizer DMC number of model coefficients model horizon (min)
regular
direct
cascade
360
210
360
360
210
360
move suppressions 0.02 N/A 0.02 N/A
0.05 0.05 0.05 0.05
0.02 0.02 0.02 0.02
equal concern errors 0.1 0.1 N/A N/A
0.1 0.1 60 20
0.1 0.1 60 20
MD MB
ramp rates N/A N/A
0.8 0.8
N/A N/A
MD MB
rotation factors N/A N/A
0.2 0.2
N/A N/A
L D or MD set point B V or MB set point yD (mol %) xB (mol %) MD (mol) MB (mol)
Case Studies Both the depropanizer simulator and the C3 splitter (superfractionator) simulator use rigorous tray-to-tray models, and the dynamic responses of both columns have been benchmarked with their industrial counterparts.2-5 Simulation details can be found in previous studies for the configuration selection problem.4,5 It was found that the [L/D, V/B] configuration has the best performance for the depropanizer, whereas the [L, B] configuration is the best for the C3 splitter. Hence, in this study, various implementations for DMCPlus were applied to the [L/D, V/B] configuration for the depropanizer and to [L, B] for the C3 splitter. DMCPlus software was designed to run in real time with a minimum allowed control interval of 1 s. An interface was developed to synchronize the DMCPlus and simulators. Depropanizer. The depropanizer is a fast column relative to the C3 splitter. Its time to steady state is about 5 h. A move size of 1% for all four manipulated variables [L/D, D + L, V/B, V + L] was used when step tests were performed with the regulatory level loops opened (for DMC with direct level control). This was the same move size as used for step tests with the level loops closed (for DMC without level control and DMC with cascade level control). However, the order and timing of the moves have to be scheduled carefully to maintain the levels. For example, a -1% change in D + L for 2 h should be followed by a +1% change in D + L for 2 h to bring the levels back to the nominal value. The simulation for the depropanizer runs at a speed 20 times faster than real time. The DMCPlus control interval is set to 3 s, i.e., 1 min in simulated time, and the model horizon is 360 min in simulated time for the regular and cascade implementations and 210 min for the direct implementation. Table 1 contains model and tuning information for the three DMCPlus implementations for the depropanizer. DMCPlus controllers were tuned using four set-point changes: changes in the overhead impurity set point from 0.5 to 0.375 to 0.625 mol %, followed by changes in the bottom impurity set point from 0.5 to 0.375 to 0.625 mol %. The tuning parameters such as move suppression, ramp rate, and rotation factor were selected to minimize the total
integral of absolute error (IAE) for both the overhead and the bottom product. C3 Splitter. The C3 splitter is a relatively slow column, and it has a time to steady state of more than 50 h. For such a slow process, it is very difficult to perform step tests with the level loops opened. For example, when a change is made for the reflux, one has to wait for more than 50 h for the composition to settle out. If no change is made for the top product flow during this period, or if the change of the reflux is not small enough, the accumulator becomes empty for an increase in reflux or overfull for a decrease in reflux. The same problem occurs at the bottom when a step change is made for the boilup flow. The levels not only should be prevented from becoming empty or full but also should be kept within a relatively narrow range about the nominal operating point during the whole period of the step test. Without level controllers in function, this is a very complex scheduling problem and requires a great amount of process knowledge or expensive trial-anderror experimentation. In addition, when the levels are open, the composition controls for this column are equivalent to the [L, V] configuration, which is wellknown to be ill-conditioned for high-purity columns. Because of the ill-conditioning, any test data will be highly correlated, resulting in a low-fidelity MPC model. Therefore, DMC with direct level control is not recommended for superfractionators in practice. However, to make the comparison complete in this study, DMC with direct level control was also implemented on the C3 splitter. Several trial-and-error simulation runs were performed to determine the appropriate move sizes for step tests. It was found that the move sizes for both the reflux and the boilup flow had to be reduced to 0.01% to maintain the level variations within limits. Note that such small move sizes typically can not be realized in industry. In contrast, 1% changes were used in step tests with the level loops closed (for the regular and cascade implementations). The C3 splitter simulator ran 100 times faster than real time, and the control interval was still 3 s in real time but 5 min in simulated time. The top product impurity was log-transformed to linearize the overall process behavior3,4
y′ ) log10(1 - y)
(1)
Table 2 contains the model and tuning information for the three DMCPlus implementations for the C3 splitter. Because the overhead product is used as a feedstock to a polymer reactor and the bottoms is fuelgrade propane, the impurity of the overhead product was weighted as 15 times more important than that of the bottom product. The tuning parameters such as move suppression, ramp rate, and rotation factor were obtained using overhead impurity set-point changes from 0.3 to 0.15 to 0.45% so that the IAE for the top product was minimized. Results Depropanizer. Each implementation for the depropanizer was tested using a feed composition step change: propane in the feed was reduced from 31.54 to 26.54 mol % while isobutane was increased from 8.44 to 13.44 mol %. Figure 3a and b shows the composition responses of all three implementations on the depropanizer for the feed composition step change. DMC with
Ind. Eng. Chem. Res., Vol. 41, No. 16, 2002 4051
Figure 3. Comparison of different DMCPlus implementations on the depropanizer: (a) overhead product impurity response, (b) bottom product impurity response, (c) accumulator level response, (d) reboiler level response. Table 2. DMCPlus Controllers for the C3 Splitter
Table 3. IAE Comparisons for Different Implementations
DMC number of model coefficients model horizon (min) L D or MD set point B V or MB set point yD (log[mol %]) xB (mol %) MD (mol) MB (mol) MD MB MD MB
top
regular
direct
cascade
600
600
600
3000
3000
3000
move suppressions 0.0101 0.0101 N/A 0.0101 0.0101 0.0101 N/A 0.0101 equal concern errors 0.1 0.1 1.5 1.5 N/A 1000 N/A 1000 ramp rates N/A N/A
0.0101 2 0.0101 2 0.1 1.5 1000 1000
0.8 0.8
N/A N/A
rotation factors N/A 0.2 N/A 0.2
N/A N/A
direct level control has the best performance. As shown in Table 3, the direct implementation reduces the IAE by 69% for the overhead product and by 48% for the bottom product compared to the regular implementation. The cascade implementation is less effective than the direct implementation, but it still reduces the IAE by 40% for the overhead product compared to the regular implementation. Figure 3c and d shows the responses of the top and bottom levels to the same feed composition change for all three implementations. Comparing the accumulator level responses of the three implementations, it is clear that the PI level controller used in the regular implementation drove the level in the wrong direction and caused poor composition control performance. The DMCPlus controller with direct implementation was able to move the accumulator level in the direction opposite to that of the PI controller with regular implementation and achieved better composition control and level control at the same time. The DMCPlus with cascade
DMC regular DMC direct DMC cascade
depropanizer 1.047 0.361 0.630
DMC regular DMC direct DMC cascade
C3 splitter 0.02 0.03 0.01
bottom 0.33 0.170 0.310 8.27 10.2 6.24
implementation was also able to adjust the level set points to correct the moves made by the PI level controllers, thereby still providing better composition control than the DMCPlus controller with regular implementation. C3 Splitter. Each implementation for the C3 splitter was tested for a step change in feed composition from 70 to 65 mol % in propylene. Figure 4 shows the composition and level responses of all implementations to the same feed composition change. The performance of the cascade implementation is significantly better than that of the regular implementation for both the overhead product and the bottom product composition control. The IAEs for each implementation and for both products are also listed in Table 3. Compared to the regular implementation, the DMC with cascade level control reduces the IAE by 50% for the overhead product and by 25% for the bottom product. The DMCPlus controller with cascade implementation recognized the impact of the bottom level control on the composition control and moved the bottom level in the direction opposite to that used by the PI controller in the regular implementation. The direct implementation for the C3 splitter reduced the maximum deviation of the overhead product impurity from the setpoint but resulted in an extremely long closed-loop response time and had the biggest IAEs among the three implementations. Because the product flows (D and B) have little impact on compositions, the direct implementation could use only the reflux and the boilup flow to control the product compositions. Thus,
4052
Ind. Eng. Chem. Res., Vol. 41, No. 16, 2002
Figure 4. Comparison of different DMCPlus implementations on the C3 splitter: (a) overhead product impurity response, (b) bottom product impurity response, (c) accumulator level response, (d) reboiler level response.
this implementation is similar to the regular implementation with the [L, V] configuration, which is an extremely ill-conditioned configuration for a high-purity column. Therefore, poor performance resulted, as shown in Figure 4. Discussion Both the direct and cascade implementations allow the MPC controller to coordinate moves for all four manipulators in the distillation control and to make a compromise between level control and composition control. The cascade implementation improved composition control in both case studies, whereas the direct implementation performed better only in the depropanizer case. The direct implementation did not improve composition control for the C3 splitter because it is similar to the regular implementation with the ill-conditioned [L, V] configuration. In fact, the direct implementation is equivalent to the [L, V] configuration for composition control. Therefore, for columns for which the [L, V] configuration is not preferred, a cascade implementation with a material balance configuration such as [L, B], [D, V], or [D, B] should be considered, or ratio schemes should be used. The direct implementation has a high reliability because of its independence from the regulatory level controllers, and it offers potentially better performance than the cascade implementation, as shown in the case study for the depropanizer. However, the direct implementation introduces difficulties for applying step tests and produces low-fidelity models as a result of illconditioning in certain cases. In contrast, the cascade implementation does not require step tests with level loops opened, but it still provides a significant improvement in composition control. Furthermore, if the regular implementation is already in place, the cascade implementation does not require that the whole step test be redone. Instead, one need only do tests on the level setpoint changes and simply include the step responses to the level set points into the model.
Loosely tuned level controllers are used for all of the results presented above, because in most industrial settings, tight level control can produce excessive disturbances for downstream units or cause instability in the plant when the flow used by the level controller is heat integrated with another stream in the plant.6 The level tuning for the cases considered was determined with a criterion given by industry, i.e, the settling time of the level is about one-third of the composition settling time.4 Variations in the aggressiveness of the tuning of the level controller for the cascade implementation were studied. It was found that increasing or decreasing the aggressiveness of the level controllers resulted in a deterioration of composition control performance. Conclusion Including levels into MPC for a distillation column improves composition control significantly in most of the cases considered here. Two types of implementations for including levels into MPC, i.e., the direct implementation and the cascade implementation, are introduced and demonstrated for the depropanizer and C3 splitter case studies. For columns that are fast enough for step tests to be performed easily with the level loops opened, direct implementation is preferred. For relatively slow columns or high-purity columns (e.g., superfractionators), cacade implementation is recommended because it can be more easily added to an existing MPC application; because the models are more easily identified; and because it avoids the ill-conditioning problem by maintaining the existing control configuration, thus avoiding the [L, V] configuration. Acknowledgment This work was supported by the member companies of the Texas Tech Process Control and Optimization Consortium. The authors thank Scott Boyden, AspenTech, for providing guidance on the DMCPlus software interface and controller tuning.
Ind. Eng. Chem. Res., Vol. 41, No. 16, 2002 4053
Literature Cited (1) Lundstrom, P.; Skogestad, S. J. Process Control 1995, 5, 249-261. (2) Riggs, J. B. Improve Distillation Control. Chem. Eng. Prog. 1998, 94, 31-47. (3) Gokhale, V.; Hurowitz, S.; Riggs, J. B. A Comparison of Advanced Distillation Control Techniques for a Propylene/Propane Splitter. Ind. Eng. Chem. Res. 1995, 34, 4413-4419. (4) Hurowitz, S. E. Superfractionator Process Control. Ph.D. Dissertation, Texas Tech University, Lubbock, TX, 1998. (5) Duvall, M. P. On Control of High Relative Volatility
Distillation Columns. Ph.D. Dissertation, Texas Tech University, Lubbock, TX, 1999. (6) Boyden, S. AspenTech, Cambridge, MA. Personal communication, 1999. (7) Riggs, J. B. Chemical Process Control, 2nd ed.; Ferret Publishing: Lubbock, TX, 2001.
Received for review June 1, 2000 Revised manuscript received December 7, 2001 Accepted May 31, 2002 IE0005396
