Ind. Eng. Chem. Res. 1996,34, 4413-4419
4413
A Comparison of Advanced Distillation Control Techniques for a PropylenePropane Splitter Vikram Gokhale, Scott Hurowitz, and James B. Riggs*p+ Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409
A detailed dynamic simulator of a propylene/propane ((23) splitter, which was bench-marked against industrial data, has been used to compare dual composition control performance for a diagonal PI controller and several advanced controllers. The advanced controllers considered are DMC,nonlinear process model based control, and artificial neural networks. Each controller was tuned based upon setpoint changes in the overhead product composition using 50% changes in the impurity levels. Overall, there was not a great deal of difference in controller performance based upon the setpoint and disturbance tests. Periodic step changes in feed composition were also used to compare controller performance. In this case, oscillatory variations of the product composition were observed and the variabilities of the DMC and nonlinear process model based controllers were substantially smaller than that of the PI controller. The sensitivity of each controller to the frequency of the periodic step changes in feed composition was also investigated.
Introduction It has been estimated that there are about 40 000 distillation columns in the U.S. chemical processing industries (CPI) alone (Humphrey et al., 1991). These columns are estimated to consume 3%of the total U.S. energy usage. Moreover, distillation columns almost always determine the quality of products produced by these industries and many times limit process production rates. Improved distillation control can result in very significant economic advantages for the CPI. Listed below are the major benefits of improved distillation control: (1)Reduced utility usage. Industry many times tends to overflux their columns, producing overpurified products, in an effort to maintain product specifications in the face of significant process upsets (e.g., feed composition and flow rate changes). Therefore, reduced product variability would allow them to produce products that have impurity levels closer to their true specification, resulting in significant energy savings (20-30% energy reduction) in many cases. This can be particularly important in the refining and high-volume chemical industries. (2) Reduced product variability. Reduced product variability means producing products that contain less variability in the impurities in the products. There is a rapidly growing trend in the chemical industry toward producing low variability products (Downs and DOSS, 1991). For example, many polymer manufacturers have realized that they produce a better polymer product when they use more uniform quality feedstocks. As a result, the polymer companies are requiring their feedstock producers t o provide them with a more uniform feedstock. As the producers of chemical intermediates learn the benefits to their business of more uniform feedstocks, they are placing more and more restrictive limits on the variability of their feedstocks. Quality has become a watchword of the 199Os, and quality for the chemical industry means low product variability. (3) Increased processing rates. When a distillation column represents a bottleneck to a process, improved control on that column can result in increased through-
* To whom correspondence should be addressed. t
Fax: (806) 742-3552. Email: cpjbr@ ttacs.ttu.edu.
0888-5885/95/2634-4413$09.00/0
put for the whole process. Obviously, for such cases, improved control provides a major economic improvement. Improved column control for such a situation allows the column to be operated closer to its product specifications without violating them, which in turn allows greater processing rates. Distillation control is a challenging field because of the following characteristics of industrial columns: (1)The inherent nonlinearity of columns particularly for producing high-purity products. (2) The severe coupling present for dual composition control. (3) The variation in process gains due t o process and operating changes. (4) Large upsets in feed flow rate and feed composition. These problems are particularly important for dual composition control. When single-ended control is used, coupling is eliminated and the resulting control problem is greatly simplified. Unfortunately, single-ended control results in suboptimal operation in many cases due to the issues of energy usage and product recovery. Due to the development and implementation of a number of advanced control techniques over the last 10 years, industry is faced with the decision of whether or not to use advanced control and if so which one should they select for their application. This decision has largely been based upon a “leap of faith”. We have begun a program aimed at developing comparisons between conventional PI controls and several of the major advanced control options which can help industry make economic-based advanced control decisions. The control techniques considered in this study are conventional PI controls, linear model predictive control (DMC; Cutler and Ramaker, 19791, nonlinear process model based control (nonlinear PMBC; Lee and Sullivan, 1988), and artificial neural networks (ANN; Bhat and McAvoy, 1990). This paper presents the results of these controllers applied to a detailed dynamic simulation of a propylene/propane (C3) splitter.
Case Study and Simulator A simulation of an industrial C3 splitter has been used as a test case t o compare a conventional PI controller and the advanced controllers for dual composition 0 1995 American Chemical Society
4414 Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995 Table 1. Design Specifications for PropylenePropane Sditter 232 no. of trays feed tray location (from bottom) 64 13.44kgls (106400 lb./HR) feed flow rate feed comp. (mol %) light key C3- - 70 C3 - 30 heavy key 1.3 factor times minimum reflux for design 3.96 m (13ft) column diameter 14.4atm (211psia) overhead pressure C3 - 0.3 mol % overhead product impurity C3- - 2.0mol % bottoms product impurity 9.21 kg/s (73 100 lb./HR) overhead flow rate 34.7 "C (94.4"F) overhead temperature 4.21 kg/s (33 400 lb./HR) bottom flow rate 42.3 "C (108.1O F ) bottom temperature 131.24 kg/s (1 041 165 lb./HR) reboiler vapor flow rate 12.6 reflux ratio saturated feed quality ~~
~~~
Table 2. Modeling Assumptions for PropylenelPropane Splitter liquid dynamics neglible vapor holdup value dynamics on all flows accumulation and reboiler level control analyzer delays on product composition eqimolal overflow residence time in reboiler residence time in accumulator heat transfer dynamics modeled saturated liquid feed subcooled reflux pressure dynamics modeled perfect mixing of liquid on trays ideal VLE
hydraulic time constant Yes no
PI 5 min Yes 5 min 5 min no Yes no no Yes no
control. Table 1 contains the design conditions for the C3 splitter. The overhead composition is 99.7 mol % propylene, the bottoms composition is 2 mol % propylene, and the feed composition is 70 mol % propylene. There are 232 trays with a Murphree tray efficiency of 85% and an operating pressure of 14.4 atm. The modeling assumptions used in developing the dynamic model of the C3 splitter are listed in Table 2. The dynamic column model is based upon dynamic mole balances on propylene for each tray. A hydraulic time constant is used to model the liquid dynamics for the trays with one value of the hydraulic time constant for the entire column. The equimolal overflow assumption is used t o calculate the flow rate of vapor leaving each stage. The vaporfliquid equilibrium was described using a relative volatility which was modeled as an explicit function of pressure and composition (Hill, 1959). As a result, each tray had its own relative volatility. Product composition analyzers and feed composition analyzers (when used) were assumed t o have 5 min cycle times. The test column simulator has the (L,B)configuration implemented on it. Gokhale (1994) evaluated nine possible control configurationsfor this column and found that the (L,B) configuration yielded the best performance for diagonal PI dual composition control. When the simulation was equipped with perfect level control, the control performance of the (D,B)structure was found to be equivalent to the performance of the (L,B) configuration. The dynamic model equations were integrated using a Euler integrator (Riggs, 1994) with a maximum
reliably stable step size of 0.3 s. A 50:l ratio of simulated time t o CPU time was obtained for a 66 MHz 486 PC using Microsoft FORTRAN 5.1. The dynamic model was bench-marked against dynamic step test data from an industrial C3 splitter. The industrial data were based upon the (L,B) configuration. The (L,B) configuration is also used industrially (O'Conner, 1993). First, the simulator was found to provide the same general behavior as the industrial plant data (O'Conner, 1993) for open-loop step changes in the manipulated variables and the feed rate. Then, based upon response times, the hydraulic time constant of each tray was adjusted to match the industrially observed reponse times as closely as possible. For example, the overhead composition was observed to have an open-loop response time of approximately 7 h for a 0.5%change in the reflux rate. In addition, for a 1%change in the bottom flow rate, the response time for the bottom composition was approximately 25 h (O'Conner, 1993). A hydraulic time constant of 3 s was found to provide the best overall dynamic match. The following test scenarios were used to test the composition controllers. 1. Setpoint change to 99.85% propylene in the overhead product at t = 100 min followed by a setpoint changed to 99.55% at t = 1000 min. 2. A ramp change in pressure from 211 to 226 psia from t = 100 min t o t = 160 min followed by a step change in feed composition t o 65% at t = 1000 min. 3. Negative and positive 5% step changes in feed composition with changes applied every 250 min. At time ( t )equal to 250 min, the feed composition ( z ) was decreased to 65% propylene. At t = 500 min, z was set to 70%. At t = 750 min, z was set t o 75%, at t = 1000 min, z was changed t o 70%. At t = 1250 min, z was set to 65%, etc. Each controller was tuned for scenario 1 and tested on scenarios 2 and 3. Controller performance was evaluated by consideringthe variability in the propylene product while keeping the bottom product in the vicinity of 2% propylene.
Implementation Approach for Each Controller Conventional PI controls, DMC, nonlinear PMBC, and C3 splitter for dual composition control. The PI and nonlinear PMBC controllers were applied using the (L/F,B/F) configuration and DMC was applied using the (L,B) configuration, but each controller was tuned for test scenario 1based upon the overhead composition control performance. Setpoint changes using 50% changes in impurity were chosen for controller tuning in order to provide a consistent tuning procedure that is likely to be robust for a wide range of upsets. All controllers used a 5 min control interval since new analyzer readings were available every 5 min. All controllers were treated as unconstrained, although the column model did not allow for negative flow rates. The diagonal PI composition controllers were tuned using Auto Tune Variation tests ( A m , Astrom and Hagglund, 1988) with on-line determination of the overall detuning factor. ATV tests were used to identify the ultimate gain and ultimate period for the overhead and bottoms. The Ziegler-Nichols (Ziegler and Nichols, 1942)PI settings were then calculated. Both controllers were detuned t o provide minimum IAE for setpoint changes in the overhead product using 50% impurity changes (test scenario 1). Detuning was accomplished
ANN were applied t o the simulator of the
Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995 4416 by dividing both controller gains and multiplying both reset times by the same detuning factor. The diagonal PI controllers were also tuned using pulse tests for the identification of transfer function models followed by the application of the BLT tuning procedure (Luyben, 1986) as a comparison t o the ATV tuning procedure. The control performances of the controllers tuned by each procedure were found to be essentially equivalent. Since the ATV test with on-line detuning was easier to implement and is more realistically applied in an industrial setting, it was chosen as our PI tuning procedure. A lead-lag feedforward element for the PI controllers was developed for feed composition changes for the composition control loop on the bottom of the column and for the top. The feed rate used in the L/F and B/F manipulated variable configurations was dynamically compensated using a dead time plus a lag. The tuning settings for the PI controllers and the feedfonvard controllers are listed in Table 3. The DMC controller was provided to us by the Dynamic Matrix Control Corp. The step response models for the DMC controllers were developed for each input (z, F, L,B)/output (x,y ) pair. The output for the overhead product was log transformed in an effort to linearize the overall process behavior: y' = log(1 - y )
(1)
At least 12 independent step tests were conducted for each input variable. Identification software (DMI provided by DMC Corp.) was applied to all the step test data in order to develop the step response models for each input/output pair used by the DMC controller. The step response models were supplied to the DMC controller, and the final controller tuning was performed for test scenario 1. Since the impurity level in the overhead is 6.67 times lower than the bottoms and since it is more important to minimize the variability of the overhead product, the deviations in the overhead product were weighted to be 15 times more important than the bottoms product. A move suppression factor of 1.0 for the reflux and 0.1 for the bottoms flow were selected for the DMC controller. Standard tuning of the DMC controller was used, i.e., a control horizon of 30 control intervals and a model prediction horizon of 120 control intervals (the maximum available). The nonlinear PMBC controller using the tray-to-tray binary model was applied using the approach presented by Riggs et al., 1990. The control law calculates target setpoints (XSS, yss) based upon proportional and integral feedback.
Y s s = Y + K12bSP - Y)+ K 2 2 j b S P - Y) dt
(3)
Then, the values of xss and yss are used by the trayto-tray binary model to calculate the reflux rate. Since eqs 2 and 3 can result in values of xss that are negative and values of yss that are greater than 1.0, limits are used to restrict the maximum and minimum values of xss and YSS. An overall material balance was used to calculate the value of the bottoms flow rate. Since the column responds much faster to energy changes (e.g., reflux flow) than t o material balance changes (e.g., bottoms flow), the target product compositions (xss and yss) are
Table 3. Controller Settings for PI Controllers overhead control loop bottom control loop
~-
Feedback Only Controller KC 232.15 lb. mol/mol %.s 1.7 lb. moVmol %.s 400 rnin TI 75 min Feedback with Feedforward KC 309 lb. moVmol 4.53 lb. mol/mol %*s 5r 36.3 min 1.50 min Feedforward Controller for Feed Composition Changes -0.71 lb. moVmol %.s gain 5.08 lb. moVmol %-a deadtime 20 min 10 min lead 120 min 600 min 1% 240 min 450 rnin Dynamic Compensation for Feed Rate deadtime 5 min 20 min 100 min 150 min 1% %as
amplified by K&B according to the following equations in an effort t o improve the response of the bottom product composition. XMB
= XSP + &MB(XSS - XSP)
(4)
YMB
= YSP + K ~ M B ~ YSP) SS
(5)
Then,
B - YMB-Z F - Y M B - xMB
(6)
The feed rate and the feed composition used by the model were each dynamically compensated using a firstorder lag and a deadtime. When a feed compensation analyzer is not available, the product purities and product flow rate are used to calculate an estimate of the feed composition. This backcalculated feed composition is filtered, and the filtered value is used as the feed composition by the tray-to-tray steady-state model. When eqs 2 and 3 are used for setpoint changes, the resulting changes in the manipulated variables are much too sharp; therefore, a filter on the setpoint changes was used to stabilize the controller for setpoint changes. The nonlinear PMBC controller was tuned for test scenario 1based upon minimizing the IAE for the overhead product. Table 4 contains the tuning settings for the nonlinear PMBC controller. The tray-to-tray steady-state controller model used by the nonlinear PMBC controller used the relative volatility modeled as a function of liquid composition and pressure but used a stagewise tray efficiency while the dynamic simulator used a Murphree tray efficiency. At the base case the controller model required a stagewise efficiency of 92% to match the simulator a t steadystate conditions with a 85% Murphree efficiency. An ANN steady-state model was used to replace the tray-to-tray steady-state binary model used by the nonlinear PMBC controller. The feedfonvard ANN model consisted of three input nodes, three hidden nodes (one hidden layer), and two output nodes. The transfer functions used were sigmoidal, and the learning algorithm applied was the Levenberg-Marquardt method (Marquardt, 1963). The ANN model considers XSS, yss, and z as input and calculates the reflux rate and bottom flow rate as its output. Since the ANN model did not always match the simulator a t steady state, a filtered bias was used to keep the ANN model in agreement with the process (dynamic column simulator). For example, for the reflux, the difference between the measured reflux flow and the value calculated by the ANN model was filtered on-line. When control calculations were
4416 Ind. Eng. Chem. Res., Vol. 34,No. 12, 1995 Table 4. Controller Settings for Nonlinear PMBC Controller
r
overhead bottoms control loop control loop Feedback Controller Ki 3.0 Kz 0.0 material balance gain 10.0 ( K yand ~ ~ &MB) Feedforward Controller filter factor on feed rate deadtime on feed rate filter factor on z deadtime on z
3.0 1 -
0.0 6.0
1
4
P-
.
-E
8
0.014 10 min 0.10 5 min
0.2
-PMBC
-DMC
0.1
Filters for model efficiency parametrization for back calculated feed composition for setpoint changes for overhead for setpoint changes for bottom
IV
0
.@ 0.3
0.025 0.025 0.085
0
200
400 800
800
1oM)12001400180018002oO0 Time ( min )
Figure 1. Comparison of overhead composition control for test scenario 1.
0.10
Table 5. k2ontroller Settings for ANN Controller overhead bottoms control loop control loop Feedback Controller K1 3.0 Kz 0.0 material balance gain 10.0 W y and ~ &MB) ~ Feedforward Controller filter factor on feed rate deadtime on feed rate filter factor on z deadtime on z
4.0 0.0 6.0
0.04 10 min 0.10 5 min
I 0
0
Filters for model efficiency parametrization for back calculated feed composition for setpoint changes for overhead for setpoint changes for bottom
0.02 0.001 0.085
200
400
800
I
800 1 o o o 1 2 0 0 1 4 0 0 180018002GfJo Time ( min )
Figure 2. Comparison of bottoms composition control for test scenario 1.
0.10
required, the values of XSS, yss, and z were fed to the ANN model and the resulting reflux flow rate and bottoms flow rate were added to the current value of their respective filtered bias. A similar procedure was used for calculating an on-line bias for the bottom flow rate. The ANN model was trained over the expected range of inputs using 700 steady-state data sets from a tray-to-tray steady-state simulator. The ANN model based controller was tuned for test scenario 1, and the resulting controller settings are listed in Table 5 .
-PMBC
-DMC
--
8.8
-8
PI
8.86.4-
1
*- 8.2-
Results 5.44
Figures 1 and 2 show the control results for the PI, nonlinear PMBC, and DMC controllers for setpoint changes in the overhead product (test scenario 1). Each controller was tuned for this test based upon optimizing the performance of the overhead composition, and the resulting tuning parameter remained unchanged throughout the remainder of the tests. From Figure 1, the nonlinear PMBC and DMC had essentially equivalent performance, while the PI controller performed well but was somewhat slower settling than the multivariable controllers. There is a slight glitch in the DMC performance a t about 700 and 1600 min. This resulted because the model horizon in the DMC controller (600 min) was significantly smaller than the actual process setting time of about 1800 min. We used version 4.0 of DMC which limits the number of model coefficients to 120, while the more recent release (version 5.0) has up to 600 coefficients which would have easily elimi-
0
200
400 800
800 1OOO12001400180018002OOO Time ( min )
Figure 3. Reflux flow rate for various controllers for test scenario 1.
nated the glitch. Figure 2 shows the performance of each controller for the control of the bottom product composition during the setpoint changes on the overhead. Note that the nonlinear PMBC controller had the shortest settling times. Overall considering Figures 1 and 2, there is not a great deal of difference between the controllers, although the multivariable controllers did outperform the PI controller. Figures 3 and 4 show the reflux and bottoms flow rates for each controller for test scenario 1. The nonlinear PMBC controller clearly shows the smoothest use of the manipulated variables. The nonlinear PMBC controller that used the ANN steady-state model is compared with the nonlinear
Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995 4417 0.35
A
0.3
PI -PMBC
-DMC
............... PI
-PMBC DMC
0.2
A" PMBC
0.1-I 0
200
-PMBC DMC
400 600 800 loo0 1200 1400 1800 1800 Moo
0
Time ( min )
Figure 5. Comparison of overhead composition control for nonlinear PMBC and ANN controllers for test scenario 1.
0
200
400
800
800 lo001200 1400 1800 l8002OOO Time ( min )
Figure 8. Comparison of bottoms composition control for test scenario 2 without a feed composition analyzer. 0.35
44
..
..............
3 -Q
0.34 0.33
a9
E
-E 8 +
04 0
200
400
600
800
I
0.32
0.31 0.3 020 0 28
1000 1200 1400 1800 1800 Moo
Time ( min )
Figure 6. Comparison of bottoms composition control for nonlinear PMBC and ANN controllers for test scenario 1.
PMBC controller that used the tray-to-tray steady-state model in Figures 5 and 6 for test scenario 1. The A" controller actually performed slightly better for the overhead composition control, but it was quite sluggish with greater deviations from setpoint for the bottom composition control. Figures 7 and 8 show the control results for the PI, nonlinear PMBC, and DMC controllers for test scenario 2 with no feed composition analyzer readings available. Note that each controller seemed to handle the column pressure changes more or less with the same proficiency for the overhead composition, while the multivarible controllers showed smaller maximum deviation from setpoint for the step change in feed composition. For the bottoms composition, the nonlinear PMBC control-
0 27
0
500
lo00
1500
Moo
2500
3OOo
3500
4000
Time ( min )
Figure 9. Comparison of overhead composition control for test scenario 3 without a feed composition analyzer.
lers demonstrated tighter control than the DMC and PI controllers. Figures 9 and 10 show the control results for the PI, nonlinear PMBC, and DMC controllers for test scenario 3 with no feed composition analysis available. For the overhead product the multivariable controllers had variabilities that were about 2.5 times lower than the PI controller. The DMC controller had a variability that was slightly larger than the nonlinear PMBC controller. For the bottom composition,the PI and DMC controllers had very nearly equivalent performance while the nonlinear PMBC controller performed considerably better.
4418 Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995
"
I
PI PMBC
" " I .
~
0.06
0 05 0.04
0.03 0 02
00\50
-
I
0
5b
1000
1500 2000 25bO Time ( min )
3doo 35bo ab0
Figure 10. Comparison of bottoms composition control for test scenario 3 without a feed composition analyzer.
NO
250
I+
PI
300 350 400 450 Hold Time (minutes)
PMBC * DMC
+
500
550
600
1
Figure 13. Variation in overhead product composition as a function of hold time for test scenario 3 without a feed composition analyzer. . o
6-
-g s
5I
1
45 4
> 3.5
.€ 2 E
'
3 1
+
200
250
If
+
+
+
.+
L
3bo 350 460 450 Hold Time (minutes)
PI
+
PMBC *
DMC
c -
560
550
610
'
,Figure 14. Variation in bottoms product composition as a function of hold time for test scenario 3 without a feed composition analyzer.
PI
-PMBC 5-
DMC
Figure 13 shows the average total variation in the overhead product for each controller as a function of hold time for the periodic feed composition changes (test scenario 3). The DMC controllers showed significant variability reduction over the PI controller for the full range of hold times with variability reductions ranging between 4/1 to 211. The nonlinear PMBC controller shows results equivalent to the DMC controller up to a hold time of 300 min, but above 300 min the results of the nonlinear PMBC controller approach those of the PI controller. The deteriorating performance of the nonlinear PMBC controller at larger hold times is probably due to the lack of flexibility of this controller and the dynamic difference between the overhead and bottom of the C3 splitter. Figure 14 shows the average total variation in the bottoms product for each controller as a function of hold time for test scenario 3. The PI and DMC controllers exhibit essentially equivalent performance, while the results from the nonlinear PMBC controller are consistently better. A PI controller with a log transformed overhead composition (i.e.,y' = log(1- y ) ) was also tested'. It was tuned for test scenario 1 using the same procedure as was used for the conventional PI controller. It was tested for scenario 2 and scenario 3 over the full range of hold times and found t o yield results equivalent to those obtained for the conventional PI controllers.
' r
00
500
lo00
1500
2Ooo
2500
3ooo
3500
4OOo
Time ( min)
Figure 12. Comparison of bottoms composition control for test scenario 3 with a feed composition analyzer.
Figures 11and 12 show the control results for the PI, nonlinear PMBC, and DMC controllers for test scenario 3 using a feed composition analyzer. The results improved for the PI and DMC controllers but worsened for the nonlinear PMBC controller. This results because the feedforward controllers for PI and DMC were adjusted for the overhead and bottoms products separately, but the nonlinear PMBC controller has only one feed composition which is filtered. Moreover, the top and bottom behave quite differently dynamically which significantly penalizes the nonlinear PMBC controller. The bottoms composition control for the DMC and PI controllers seemed to benefit the most from the addition of feedforward from the feed composition analyzer.
Conclusion Although the difference in performance for the PI and the multivariable controllers for setpoint changes and step changes in disturbances is not large, significant improvement in performance was observed for the
Ind. Eng. Chem. Res., Vol. 34,No. 12, 1995 4419 multivariable controllers over the PI controller for a periodic variation in feed composition. In fact, the variability reduction observed in the simulation study for nonlinear PMBC over PI controls is similar to those observed industrially (Riggs et al., 1993). The periodic variation in disturbances results in a product variability with characteritics similar to the product variabilities observed industrially (Riggs et al., 1993). Usually industrial feed composition upsets involve some variation in feed composition with respect t o time but are not well-represented as step changes. Industrial disturbances are likely to have an amplitude/ frequency distribution that would combine with the frequency sensitivity of the controller to produce the resulting overall product variability performance. Periodic variation of disturbances (preferably sine wave disturbances) are proposed here as a more critical analysis of controller performance than classical step tests particularly if the frequency of the disturbance is changed.
Acknowledgment The authors thank Professor Bill Luyben for guiding and reviewing the PI results. DMC Corp. is gratefully acknowledged for providing DMC software as well as a DMC training course. Dan O'Conner and Dave Hoffman of DMC Corp. provided guidance during the implementation phase. Financial support for this work was provided by the member companies of the Texas Tech University Process Control and Optimization Consortium and the U.S. Department of Energy (Contract No. DR-PC04-94 Al 98747).
Nomenclature B = bottom product flow rate F = column feed rate Kl = the proportional gain in the GMC control law (eqs 2 and 3) Kz = the integral gain in the GMC control law (eqs 2 and
MB = material balances SP = setpoint SS = steady-state target
Literature Cited Astrom, K. J.; Hagglund, T. Automatic Tuning of PZD Controllers; ISA Research Triangle Park, NC, 1988. Bhat, N.; McAvoy, T. J. Use ofNeural Nets for Dynamic Modeling and Control of Chemical Process Systems. Comput. Chem. Eng. 1990,4,517-532. Cohen, G. H.; Coon, G. A. Theoretical Considerations of Retarded Control Trans ASME 1953, 75, 827. Cutler, C. R.; Ramaker, B. L. Dynamic Matrix Control: A Computer Control Algorithm. Presented a t the AIChE 86th National Meeting, San Francisco, CA, 1979; also in Joint Autom. Control Conf. Proc. 1979. Downs, J. J.; Doss, J. E. Present Status and Future Needs-A View from North America Industry. Proceedings of CPC N; Elsiever Publishing: New York, 1991. Gokhale, V. B. Control of a PropylenePropane Splitter. M.S. Thesis, Texas Tech University, Lubbock, TX, 1994. Hill, G . E. Propylene-Propane Vapor-Liquid Equilibria. Presented at the AIChE National Meeting, Atlantic City, NJ, 1959. Humphrey, J . L.; Seibet, A. F.; Koort, R. A. Separation Technologies-Advances and Priorities. DOE Contract AC07901D12920, Feb 1991. Lee, P. L.; Sullivan, G . R. Generic Model Control. Comput. Chem. Eng. 1988,12, 573-83. Luyben, W. L. A Simple Method for Tuning SISO Controllers in Multivariable Systems. Znd. Eng. Chem. Process Des. Dev. 1986, 25, 654. Marquardt, D. W. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. Z Soc. Znd. Appl. Math. 1963, 11 (2), 431-441. OConner, D., DMC Corp., Houston, TX, personnel communication, 1993. Riggs, J. B. An Introduction to Numerical Methods for Chemical Engineers, 2nd ed.; Texas Tech University Press: Lubbock, TX, 1994. Riggs, J. B.; Beauford, M.; Watts, J. Using Tray-to-Tray Models for Distillation Control. In Advances in Industrial Control; P. L., Lee, Ed.; Springer-Verlag: New York, 1993. Ziegler, J. G.; Nichols, N. B. Optimum Settings for Automatic Controllers. Trans. ASME 1942, 54, 759.
3)
Received for review January 17, 1995 Accepted September 6, 1995@
L = reflux flow rate x = the mole fraction of propylene in the bottoms product y = the mole fraction of propylene in the overhead product y' = the log transformed value of y z = the mole fraction of propylene in the feed Subscripts
IE9500511
@
Abstract published in Advance ACS Abstracts, November
15, 1995.
