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PROCESS DESIGN AND CONTROL Nonlinear Inferential Parallel Cascade Control Thomas J. Mc Avoy,*,† Nan Ye, and Chen Gang Institute for Systems Research, Department of Chemical Engineering, University of Maryland, College Park, Maryland 20742
This paper discusses the use of nonlinear inferential parallel cascade control (NIPCC) to improve control system performance. The goal of NIPCC is to detect and compensate for the effects of unmeasured disturbances faster than the feedback control being employed. NIPCC behaves in a manner that is similar to normal cascade control, but NIPCC has a parallel feedback architecture. NIPCC can be thought of as a limiting case of developing a soft sensor, and thus, NIPCC draws from both parallel cascade control and inferential sensing. The effectiveness of NIPCC is demonstrated on the Tennessee Eastman test process. NIPCC holds promise as an effective means of improving plant-wide control. Introduction Parallel cascade control differs from normal cascade control in that the inner cascade loop is in parallel with the primary loop rather than in series. A classical example of parallel cascade control involves distillation tray temperature control cascaded to a composition loop. Recently, several papers on parallel cascade control have been published. Luyben (1973) appears to have been the first researcher to coin the phrase parallel cascade control. Yu (1988) discussed the design of parallel cascade control for disturbance rejection. Brambilla and Semino (1992) have discussed the use of a nonlinear filter between the outer and cascade loops to improve control system performance. Brambilla et al. (1994) recently discussed an approach to the design of parallel cascade controllers for multicomponent distillation columns where top and bottom compositions are controlled. Shen and Yu (1992) have published an indirect feedforward control approach, which is actually feedback in nature, that is based on the parallel cascade structure. The objective of their approach is good disturbance rejection, which is the same as that in this paper. Finally, Pottmann et al. (1994) discussed a parallel control strategy based on reverse engineering the baroreceptor reflux which is used in animals for short-term regulation of arterial blood pressure. Inferential sensing, also called soft sensing, involves the use of readily available process measurements to infer variables that are difficult to measure online, e.g., composition. Inferential sensing has received a great deal of attention recently, and numerous papers on the subject have appeared. Willis et al. (1990) and Tham et al. (1991) have discussed the use of oxygen uptake rate and carbon dioxide evolution to estimate biomass in an industrial fermenter. The use of distillation tray temperatures to estimate and control product compositions has been discussed by several authors (Mejdell and Skogestad (1991a,b); Kresta et al. (1991)). Potential difficulties in closing feedback loops around soft sensors have been pointed out by Macgregor et al. (1991). In such applications the closure of a loop can result in a change in the correlation structure of the input infer†
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ential variables, with the result that the soft sensor can be inaccurate. In this paper a somewhat different approach to parallel cascade control is taken. The approach is nonlinear and inferential in nature, and it is based on steady-state modeling. This approach may be generally applicable to a broad range of process regulation problems where disturbance rejection is the goal. As discussed in the literature, parallel cascade control involves two feedback controllers, each of which needs to be tuned. The approach presented in this paper involves determining an accurate steady-state model which can be used to compensate for the effects of unmeasured disturbances. If necessary, linear dynamic compensation can be added to the inferential controller. The steady-state model can be multivariable and nonlinear, and in the present application it is implemented using neural networks (Qin and Mc Avoy (1992)). A first principle model could also be used if the necessary computations could be carried out effectively online. After giving a general discussion of NIPCC, it is applied to the Tennessee Eastman process (Downs and Vogel (1993)) to illustrate its effectiveness. In addition to applying NIPCC on top of a published base control system (Mc Avoy and Ye (1994)), results are given as well for a modified base control system (Ye et al. (1995)). It is shown that NIPCC is capable of achieving a significant reduction in the variance of the product composition fluctuations for the test process. It is concluded that NIPCC holds promise as an approach for improving the performance of plant-wide control systems. Nonlinear Inferential Parallel Cascade Control (NIPCC) In order to discuss NIPCC, a distillation column, shown in Figure 1, is used for illustration. The manipulated variable is the reflux flow to the tower. The control problem is to keep the overhead composition as close to set point as possible in spite of fluctuations in the feed flow and composition. Figure 1 illustrates a standard parallel cascade control system to achieve this objective. A tray temperature controller is cascaded to a composition controller, and a number of authors have © 1996 American Chemical Society
Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996 131
Figure 1. Distillation parallel cascade control system.
Figure 4. Soft sensor control system.
Figure 2. Block diagram for the parallel cascade controller.
Figure 5. NIPCC control system.
Figure 3. Block diagram for the normal cascade controller.
discussed how the control tray should be chosen. The rationale behind the parallel cascade approach is that the feed upsets will affect the tray temperature faster than the product composition, and thus compensation for the upset can begin sooner than if composition control alone is used. Figure 2 gives the block diagram for the control system shown in Figure 1. As can be seen, the manipulated reflux flow affects the tray temperature through block G1, which is different from its effect on product composition, G2. These two transfer functions are in parallel, and this is where the control approach gets its name. By contrast, the block diagram for a normal cascade control system is shown in Figure 3. In this case G1 and G2 are in series with one another. If there were a reflux flow controller that got its set point from the tray temperature controller, then the flow and temperature controllers would form a normal, or series, cascade control system. Now consider the case where more than one tray temperature is used as part of an inferential scheme to estimate the distillate composition. Such a scheme is illustrated in Figure 4. As can be seen, the estimated composition is fed to a composition controller which manipulates the reflux valve. When actual composition measurements become available from the laboratory they can be added into the feedback system as discussed by Piovoso and Kosanovich (1994). The control scheme in Figure 4 ty-
pically is able to respond to upsets much faster than if the laboratory values are used for control. As Macgregor et al. (1991) have pointed out, one potential problem with the scheme shown in Figure 4 is that the closure of the control loop around the inferential sensor may result in an inaccurate model due to a change in the correlation structure of the inferential variables used. The NIPCC control system considered in this paper uses the same inputs as the soft sensor system shown in Figure 4. However, rather than estimating the controlled variable, the NIPCC scheme estimates the manipulated variable. The estimation is steady state, and it is carried out subject to the controlled variable(s) being exactly at its setpoint. The NIPCC scheme is illustrated in Figure 5. As with the scheme in Figure 4, when a laboratory measurement of composition becomes available, it can be used to bias the output of the NIPCC. The composition controller shown in Figure 5 would be a slow controller that would act to eliminate the effects of plant/model mismatch at steady state. If necessary, a dynamic element can be added between the soft sensor and the reflux valve to match the disturbance and manipulated variable dynamics. The block diagram for the NIPCC system is shown in Figure 6. As can be seen, Figure 6 is similar to Figure 2 in that there are different blocks that affect distillate composition and tray temperatures. In developing data for the NIPCC model, one can either use a process model or take data on the process while it is operating at its setpoint. In developing the data base, it is importantthat all significant disturbances be included. Ultimately, the feedback system in place deals with both
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Figure 6. Block diagram for the NIPCC controller.
the modeled and unmodeled disturbances. If an important disturbance is left out, then there could be a problem with the NIPCC approach if its actions make the job of the feedback system more difficult. The steady-state model between inferential and manipulated variables can be nonlinear, nonsquare, and multivariable. To develop the model in this case, a nonlinear partial least squares approach (Qin and Mc Avoy (1992)) can be used, with the inputs being the inferential variables and the outputs being the manipulated variables. The NIPCC approach avoids the correlation problem, discussed above, since it is developed under precisely the closed loop conditions where the model will be used. Illustration of NIPCC (1) Tennessee Eastman Process. To illustrate the inferential parallel cascade approach, the Tennessee Eastman process (Downs and Vogel (1993)), shown in Figure 7, will be used. The Tennessee Eastman process involves a real plant that has been disguised for proprietary reasons. The process produces two products from four reactants. Also present are an inert product and a byproduct, making a total of eight components: A, B, C, D, E, F, G, and H. The reactions are
A(g) + C(g) + D(g) f G(liq)
product 1
A(g) + C(g) + E(g) f H(liq)
product 2
A(g) + E(g) f F(liq) 3D(g) f 2 F(liq)
byproduct byproduct
The process has five major unit operations: the reactor, the product condenser, a vapor/liquid separator, a recycle compressor, and a product stripper. The gaseous reactants are fed to the reactor where they react to form liquid products. The gas-phase reactions are catalyzed by a nonvolatile catalyst dissolved in the liquid phase. The reactor has an internal cooling bundle for removing the heat of reaction. The products leave the reactor as vapors along with the unreacted feeds. The catalyst remains in the reactor. There are three modes of process operation corresponding to three G/H product ratios. The product mix is normally dictated by product demands. The plant production rate is set by market demand or capacity limitations. The process has 41 measurements and 12 manipulated variables. A prerequisite for most studies on this problem is a process control strategy for operating the plant. The control objectives for this process are typical of those for a chemical process: 1. Maintain process variables at desired values. 2. Keep process operating conditions within equipment constraints.
3. Minimize variability of product rate and product quality during disturbances (stream 11). 4. Minimize movement of valves which affect other processes (in this case the gas feeds and product). 5. Recover quickly and smoothly from disturbances, production rate changes, or product mix changes. The authors of the Tennessee Eastman problem point out that it is an appropriate testbed for a number of topics. These include plant-wide control strategy design, multivariable control, optimization, predictive control, estimation/adaptive control, nonlinear control, process diagnostics, and education. (2) NIPCC Applied to Base Control System. Earlier a base control system for the Tennessee Eastman process was published (Mc Avoy and Ye (1994)). To smooth out product flow variations, optimal averaging level control of the separator level and the stripper reboiler level was added to the base control system (Ye et al. (1995)). However, although averaging level control smoothes out product flow variations, it increases fluctuations in the product compositions. In this paper averaging level control is not employed. Figures 8 and 9 show the performance of the base control system, given in Figure 7, for random composition upsets in feed stream C (disturbance IDV(8)). The controller tuning parameters are given by Mc Avoy and Ye (1994). The G composition is plotted, even though the G/H ratio is actually controlled. Operation at three different product ratios, 10/90, 50/50, and 90/10, is shown. The base case 50/50 operating point was given by Downs and Vogel (1993). The setpoints for the 10/90 and 90/10 operations have been calculated by Ye (1994), by minimizing the process’ operating cost, subject to all the control valves being used. If one does not use the constraint that all valves are used, then the condenser and steam valves saturate at the 10/90 and 90/10 optima. Additional details on the optimization are given by Ye (1994). Table 1 gives the measurements and the manipulated variables at the three operating points. The inferential parallel cascade control system is illustrated in Figure 10. As can be seen, this scheme consists of a steady-state model followed by first-order filters. In order to build the model, one solves the steady-state process equations for random changes in dusturbance IDV(8), subject to achieving perfect product composition and flow control. A total of 720 data sets were generated for the three operating modes, with 240 points generated for each mode. A nonlinear partial least-squares approach, based on neural networks (Qin and Mc Avoy (1992)), was used to model the resulting data. The inputs to the steady-state model consist of variables not used in the base control system, as well as setpoints of inner cascade loops, and valve positions. Two separate models were used for predicting the D and C feed setpoints. For the D feed, a total of 15 variables, shown in Table 2, were used as inputs. The output was the setpoint for the D feed flow controller. The reason for inputting both the A and E feed flows and the deviations from their values with IDV(8) ) 0 can be explained by referring to Figure 11. In this figure plots of the required values of D at the three operating points (10/90, 50/50, and 90/10) for various values of IDV(8) are shown. As can be seen, it is necessary to model very small changes in D at each operating point. However, the three operating points require significantly different values of D. If one does not input the deviations as indicated in Table 2, then it was found that the resulting neural network model was not accurate enough to model
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Figure 7. Schematic of the Tennessee Eastman process and base control scheme.
Figure 8. Control results for the base system and base system plus NIPCC with averaging level control.
Figure 9. Control results for the base system and base system plus NIPCC with averaging level control.
the small deviations around the large changes that result from the three different operations. The net result was that the inferential control using only the total flow variables as inputs did not offer any significant improvement over the base control. For the C feed setpoint, the inputs were the A feed setpoint, its difference from its value for IDV(8) ) 0,
and the G/H ratio setpoint, since it was found that these three inputs dominated the correlation of the C feed setpoint. One of the operating constraints that must be met for the Tennessee Eastman plant involves the fact that some streams are constrained with regard to how fast they can be changed. Both the C and D feeds are so constrained. In order to meet these constraints,
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Table 1. Measurements and Manipulated Variables for 10/90, 50/50, and 90/10 Operation manipulated variables (%) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
measurement
units
50/50
10/90
90/10
A feed D feed E feed A + C feed recycle flow reactor feed reactor pressure reactor level reactor temp purge rate separator temp separator level separator pressure separator underflow stripper level stripper pressure stripper flow stripper temp steam flow comp. power reactor coolant T condenser coolant T reactor feed A reactor feed B reactor feed C reactor feed D reactor feed E reactor feed F purge A purge B purge C purge D purge E purge F purge G purge H product D product E product F product G product H
kscmh kg/h kg/h kscmh kscmh kscmh kPa % C kscmh C % kPa m3/h % kPa m3/h C kg/h kW c C mol % mol % mol % mol % mol % mol % mol % mol % mol % mol % mol % mol % mol % mol % mol % mol % mol % mol % mol %
0.251 3664 4509. 9.348 26.90 42.34 2705 75.00 120.4 0.337 80.11 50.00 2634 25.16 50.00 3102 22.95 65.73 230.3 341.4 95.60 77.30 32.19 8.893 26.38 6.882 18.78 1.657 32.96 13.82 23.98 1.257 18.58 2.263 4.844 2.299 0.018 0.836 0.099 53.72 43.83
0.255 688.9 7517. 8.129 28.81 42.28 2800 65.00 122.3 0.430 84.48 50.00 2726 23.72 50.00 3213 21.40 69.01 175.0 347.1 107.2 86.60 34.47 6.49 26.32 1.231 23.74 3.109 36.09 9.380 24.38 0.129 19.82 4.081 1.155 4.968 0.002 0.781 0.156 11.68 85.86
0.183 5185 697.8 7.850 28.07 40.66 2800 65.00 122.1 0.091 96.57 50.00 2728 18.69 50.00 3202 18.42 78.01 155.0 325.7 101.7 92.67 22.99 29.95 19.25 10.70 4.472 1.703 19.15 43.24 13.76 2.517 4.827 2.260 13.51 0.729 0.020 0.109 0.050 90.16 8.173
1 2 3 4 5 6 7 8 9 10 11 12
D feed E feed A feed A + C feed recycle valve purge valve separator valve stripper valve steam valve reactor coolant condenser coolant agitator speed
50/50
10/90
90/10
63.05 53.98 24.64 61.30 22.21 40.06 38.10 46.53 47.45 41.11 18.11 50.0
11.86 89.99 25.12 53.31 20.15 50.00 32.93 40.07 39.87 24.82 13.01 100.0
89.23 8.354 18.01 51.48 19.95 11.68 30.12 39.40 49.75 36.30 8.576 100.0
Table 2. Input Varibles for NIPCC Model Development Output Variable D feed flow setpoint Input Variables A feed flow setpoint A feed flow setpoint - A feed setpoint for IDV(8) ) 0 E feed flow setpoint E feed flow setpoint - E feed setpoint for IDV(8) ) 0 purge rate setpoint separator underflow setpoint stripper flow setpoint reactor cooling temperature setpoint condenser cooling temperature setpoint compressor recycle valve position total feed to reactor separator temperature separator pressure stripper pressure G/H ratio setpoint Figure 10. Nonlinear inferential parallel cascade control system applied to the Tennessee Eastman process.
first-order filters were added to the NIPCC scheme as shown in Figure 10. The filter for the D feed was 1/(0.56 (h) s + 1) and for the C feed 1/(0.36 (h) s + 1). It was determined that these filters keep the changes in the C and D feeds within their specifications. Figures 8 and 9 show the improvement that can be achieved using the inferential approach. As can be seen, the variance in both the product flow and G composition
is reduced. Table 3 gives the percent reductions in variance that are achieved between the base control system and the NIPCC system. The NIPCC scheme is able to achieve both good flow filtering and good composition filtering. For this particular application, inferential parallel cascade control is very effective. It should be possible to apply the approach used in this problem to a broad range of processes. (3) NIPCC Applied to an Alternative Base Control System. One of the problems with the base control
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Figure 11. D feed flows to achieve perfect composition control in the product.
Figure 12. Reactor pressure control results for IDV(8).
Table 3. Percent Reduction in Variance of the NIPCC Scheme over the Base Scheme G/H ) 90/10 % reduction
G/H ) 50/50
G/H ) 10/90
flow
G
flow
G
flow
G
50.9
21.8
38.6
37.7
30.2
11.1
system, discussed above, is that the reactor pressure loop shows wide variations under normal process upsets, IDV(8). A typical response is shown in Figure 12, where it can be seen that the reactor pressure undergoes very wide fluctuations. Other than pressure not violating a high limit, no specification was placed on pressure in the problem statement (Downs and Vogel (1993)). However, in a series of papers, Ricker (1994) and Ricker and Lee (1994a,b) have demonstrated the importance of good pressure control on the process economics. Ricker (1994) showed that steady-state optimization favors operating the reactor at as high a pressure as possible. A 100 kPa increase in reactor pressure cuts operating costs by roughly 10% (Ricker (1994)). If the pressure exceeds 3000 kPa, then the plant shuts down. The original problem statement suggests a maximum operating pressure of 2895 kPa. Given the very wide pressure fluctuations shown in Figure 12, one would have to use a pressure setpoint around 2795 kPa or less in order to avoid having pressure exceed 2895 kPa. Ricker and Lee (1994b) question the utility of using the A feed to control reactor pressure, as was done in the base control system (Mc Avoy and Ye (1994)). Better pressure control allows for higher operating pressures, which lead to more optimal plant operation. Ricker and Lee (1994b) discuss nonlinear model predictive control of the Tennessee Eastman process. Their approach achieves significantly better pressure regulation than that shown in Figure 12 for the base control system. In their approach, reactor temperature was used as a manipulated variable. Thus, they did not attempt to control both pressure and temperature, as was done in the base control system.
Figure 13. Reactor controllers in an alternative base scheme.
To improve reactor pressure control, an alternative base control system has been developed (Ye and Mc Avoy (1995)). For the methodology used to develop the original base control scheme, shown in Figure 7, one has to specify what variables need to be controlled in the reactor (Mc Avoy and Ye (1994)). For Figure 7 these variables were reactor level, pressure, and temperature. By specifying that one less variable has to be controlled, namely, reactor temperature, it is possible to achieve much better control of the reactor pressure than was achieved in the original base system. The two reactor controllers that are changed, namely, the pressure control and the loop involving the A feed, are shown in Figure 13. In this control system, the reactor temperature does not float, but rather it is used in a cascade arrangement to control the reactor pressure. In addition, the recycle flow and compressor power controllers are not closed in the alternative scheme due to interaction. Table 4 gives the controller tuning parameters that are used in the alternative base scheme. Figure 12 shows a comparison between the results achieved with the original and the alternative base control systems for handling the random IDV(8) fluctuations. As can be seen, the pressure is much more
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Table 4. Controller Settings for the Alternative Base Schemea manipulated
reactor pressure reactor temp A/C in feed stripper temp
temp setpt cooling setpt A feed flow A feed flow steam flow E feed flow separator outlet product flow purge flow
-0.1 °C/kPa 1.0 1.0 kscmh 10.0 kg/(h °C)
10.0 50.0 100.0 10.0
500.0 kg/(h %) -2.5 m3/(h %) -0.5 m3/(h %) -0.03 kscmh/%
200.0 300.0 300.0 100.0
C feed flow D/E ratio
0.08 kscmh/(m3/h) 0.05
reactor level separator level stripper level B composition in purge product flow product G/H ratio
KC
TR (min)
controlled
45.0 40.0
a Cascade settings are the same as those in Mc Avoy and Ye (1994).
Figure 15. Control results for the alternative base system and alternative base system plus NIPCC with averaging level control. Table 5. Percent Reduction in Variance of the NIPCC Scheme over the Alternative Base Scheme
% reduction
G/H ) 90/10
G/H ) 50/50
G/H ) 10/90
flow
G
flow
G
flow
G
56.2
20.8
73.1
38.5
73.9
62.6
Conclusions
Figure 14. Control results for the alternative base system and alternative base system plus NIPCC with averaging level control.
tightly regulated. The product G composition and flow still fluctuate for IDV(8), and, thus, there is an opportunity to apply NIPCC to this alternative base control system to decrease these variations. The same input variables that were used for the base system to build the inferential model and the same modeling approach, discussed earlier, are used for the alternative base system. For the D feed no first-order filter is used, while for the C feed a filter with a time constant of 5 h is used. Figures 14 and 15 show the results of using the NIPCC controller on top of the alternative base control system. As can be seen, it reduces significantly the G product composition and the product flow variations. Table 5 gives the percent reductions in variance that are achieved between the alternative base control system and the NIPCC system. The final control results achieved with the alternate base control together with the inferential cascade controller are excellent. As Table 5 shows, very significant reductions in the variance of both the product flow and composition are achieved.
This paper has discussed the use of nonlinear inferential parallel cascade control (NIPCC) to improve control system performance. NIPCC is a feedback approach that detects unmeasured disturbances through inferential measurements. It then compensates for these disturbances in a manner that is similar to feedforward control. NIPCC can be thought of as a limiting case of developing a soft sensor. The effectiveness of NIPCC has been demonstrated on the Tennessee Eastman test process, under two different base control systems. It has been shown that for random feed composition fluctuations the variance in product flow and composition can be reduced significantly by using NIPCC, for all of the process operating modes. The NIPCC control approach is a promising method for improving the performance of existing plant-wide control systems, particularly when a steady-state model is available. Further work is required to assess stability aspects of the proposed approach, and how dynamic elements in the approach should be tuned, and how they affect overall performance. Literature Cited Brambilla, A.; Semino, D. Nonlinear Filter in Cascade Control Schemes. Ind. Eng. Chem. Res. 1992, 31, 2694-2699. Brambilla, A.; Semino, D.; Scali, C. Design and Control Selection of Cascade Loops in Distillation. Preprints of the IFAC Workshop on Integration of Process Design & Control, Baltimore, MD, June 27-28, 1994, p 171. Downs, J.; Vogel, E. A Plant-Wide Industrial Process Control Problem. Comput. Chem. Eng. 1993, 17, 245-255.
Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996 137 Kresta, J.; Macgregor, J.; Marlin, T. Multivariate Statistical Monitoring of Process Operating Performance. Can. J. Chem. Eng. 1991, 69, 35-47. Luyben, W. Parallel Cascade Control. Ind. Eng. Chem. Fundam. 1973, 12, 463-467. Macgregor, J.; Marlin, T.; Kresta, J.; Skagerberg, B. Multivariate Statistical Methods in Process Analysis and Control. Proceedings of the Fourth International Conference on Chemical Process Control, South Padre Island, TX, 1991, 665-672. Mc Avoy, T.; Ye, N. Base Control for the Tennessee Eastman Problem. Comput. Chem. Eng. 1994, 18, 383-413. Mejdell, T.; Skogestad, S. Estimation of Distillation Compositions from Multiple Temperature Measurements Using Partial Least Squares. Ind. Eng. Chem. Res. 1991a, 30, 2543-2555. Mejdell, T.; Skogestad, S. Composition Estimator in a Pilot-Plant Distillation Column Using Multiple Temperatures. Ind. Eng. Chem. Res. 1991b, 30, 2555-2564. Piovoso, M.; Kosanovich, K. Applications of Multivariate Statistical Methods to Process Monitoring and Controller Design. Int. J. Control 1994, 59, 743-765. Pottmann, M.; Henson, M.; Ogunnaike, B.; Schwaber, J. A Parallel Control Strategy Abstracted From The Baroreceptor Reflex. Proceedings of the American Control Conference, Baltimore, MD, 1994, pp 97-101. Quin, J.; Mc Avoy, T. Nonlinear PLS Modeling Using Neural Networks. Comput. Chem. Eng. 1992, 16, 379-391. Ricker, N. L. Optimal Steady State Operation of the Tennessee Eastman Challenge Process. Comput. Chem. Eng. 1995, 19, 949-959. Ricker, N. L.; Lee, J. Nonlinear Modeling and State Estimation for the Tennessee Eastman Challenge Process. Comput. Chem. Eng. 1994a, 19, 983-1005. Ricker, N. L.; Lee, J. Nonlinear Model Predictive Control of the Tennesseee Eastman Challenge Process. Comput. Chem. Eng. 1994b, 19, 961-981.
Shen, S.; Yu, C. Indirect Feedforward Control: Multivariable Systems. Chem. Eng. Sci. 1992, 47, 3085-3097. Tham, M.; Morris, A.; Montague, G.; Lant, P. Soft Sensors For Process Estimation and Inferential Control. J. Process Control 1991, 1, 3-14. Willis, M.; DiMassimo, C.; Montague, G.; Tham, M.; Morris, A. Inferential Measurements via Artificial Neural Networks. Proceedings of the Symposium on Intelligent Tuning and Adaptive Control, Singapore, 1991. Ye, N. Control of Complex Chemical Processes With Conventional Methods and Neural Networks. Ph.D. Dissertation, University of Maryland, College Park, MD, 1994. Ye, N.; Mc Avoy, T. An Improved Base Control for the Tennessee Eastman Problem. Proceedings of the American Control Conference, Seattle, WA, 1995, pp 240-244. Ye, N.; Mc Avoy, T.; Kosanovich, K.; Piovoso, M. Optimal Averaging Level Control for the Tennessee Eastman Problem. Can. J. Chem. Eng. 1995, 73, 234-240. Yu, C. Design of Parallel Cascade Control for Disturbance Rejection. AIChE J. 1988, 34, 1833-1838.
Received for review May 18, 1995 Revised manuscript received August 25, 1995 Accepted September 19, 1995X IE950298F
X Abstract published in Advance ACS Abstracts, November 15, 1995.
