010835 Use Model-Predictive

010835 Use Model-Predictive - Process Control Use...

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Unformatted text preview: Process Control Use Model-Predictive Control to Improve Distillation Operations Umesh Mathur, P.E. Advanced Control Engineering Services Robert D. Rounding BP Oil and Gas Daniel R. Webb Ineos Olefins and Polymers USA Robert J. Conroy Consultant Use this approach based on steady-state and dynamic simulation to develop the necessary models — and avoid disruptive and costly step testing to the extent feasible. magine an equipment investment with a payback time of only 10 days. A major petroleum refiner experienced just that when it implemented linear multivariable model-predictive control (MPC) on its cat-cracker. Using a linear programming optimizer, the MPC determined the unit’s optimal constraints, and then moved the unit close to those limits over a few days. Although this is an extreme example, it is generally accepted that MPC can add significant value when coupled with an optimizer that drives the plant to maximum profitability, with typical paybacks of two years or less. Model-predictive control has been practiced commercially for well over 25 years, and many papers have been published on the theory and practice of MPC (e.g., 1, 2). This article summarizes what has been learned in the art of implementing MPC on large-scale fractionation plants, using first-principles steady-state and dynamic simulation methods to enhance the quality of the MPC models, and it recommends a procedure that avoids the need for step testing, which is often difficult and expensive. Traditionally, implementing model-predictive controllers in the process industries has required the creation of a fixed, linear, dynamic model that relates changes in each input to each output. The vast majority of projects described in the literature have been executed using extensive step tests to develop such linearized control models, using processmodel identification techniques (3). Because such deliberate step tests can be quite costly, disruptive, invasive and lengthy in duration (often lasting many weeks or months in a large unit), a significant incentive exists to minimize step tests, if not eliminate them entirely. I However, the importance of a reliable and predictable base-level regulatory-control scheme cannot be overemphasized. In numerous instances, a poor regulatory control configuration in a distillation column has jeopardized the viability of any MPC control scheme. Improving MPC projects using chemical engineering models Several approaches to improving MPC projects are worth considering. • If the MPC controller requires specifying the full dynamic model for each MV/CV and DV/CV pair (i.e., the manipulated (MV), controlled (CV) and disturbance (DV) variables), use a carefully calibrated dynamic simulation model of the process to develop the required MPC curves (4). • If the MPC controller requires specifying only the steady-state gains, use a carefully calibrated steady-state simulation model of the process (5). • When using a step-testing approach to build dynamic models for difficult distillation systems, it is possible to obtain good MPC models. Gains determined using a calibrated steady-state simulation model can be inserted into the dynamic models, and the shape of the dynamic portion of the curve adjusted appropriately. • One might expect the process-model identification software provided with the major MPC packages to allow users to fix the steady-state gain for one or more MV/CV or DV/CV pairs and to identify only the dynamic shape of the curve(s). We know of no available software with which this is feasible. Fixing gains that have been obtained reliably and independently as described here could dramatically shorten CEP January 2008 www.aiche.org/cep 35 Process Control the duration of the step tests required for determining the dynamic shape of the MPC models for most projects. Note that these approaches all require creating a calibrated steady-state simulation model as a pre-requisite. This can be done fairly easily for distillation columns and most other process equipment. The exception is catalytic chemical reactors with complex kinetics where the reactor effluent composition is far from thermodynamic equilibrium. In such cases, equilibrium reactor models (which can be formulated far more easily than non-equilibrium kinetic models describing catalytic phenomena) cannot be used to estimate the relevant gains. Fortunately, most major catalytic reactors have fairly quick settling times (i.e., the time for control to reach steady state) and identification of the relevant MPC models using step tests is not a major undertaking. Process nonlinearity issues in MPC projects It is imperative to consider two kinds of nonlinear control issues that are frequently encountered in chemical processes that include distillation columns with high-purity products — dynamic nonlinearity and gain nonlinearity. Use of a linear MPC controller for inherently nonlinear processes always involves correcting for a mismatch between the process and the MPC model controlling it. This mismatch must not be excessive. There have been several valiant, but utimately unsuccessful, efforts in the past to control highly nonlinear processes with linear MPC technology. For instance, many continuous polymer processes are known to be extremely nonlinear and have required deployment of nonlinear MPC control technologies. These nonlinear MPC technologies are available commercially but are not discussed here. Dynamic nonlinearity Dynamic nonlinearity is a very common problem in processes subject to strong fluctuations, for example, in the process feed rate. As the process flow increases, the process dead time and other dynamic parameters all change proportionately, so that the process comes to a steady state sooner. For example, a 50% decrease in feed flow would, typically, nearly double both the dead time and the process settling time. If a dynamic controller that uses a fixed dynamic model were deployed, such a drastic change in process dead time or settling time would create a severe mismatch between the control model predictions and the real world. Accordingly, the performance of the MPC controller would DISADVANTAGES OF STEP TESTS btaining the dynamic models that describe the effect of making changes in any independent variable, whether a manipulated variable (MV) or an external disturbance (DV), on all controlled variables has traditionally been done using a lengthy series of step tests. Each such test requires the operator to make a step move and wait for a lengthy period of time while the process responds to this move. These results for all variables are captured in a data historian, typically once per minute. Generally, 8–15 moves are made in both directions for each MV. To estimate the steady-state gain reliably, it is recommended that the plant be allowed to come to a steady state after the last move is made. Note that the number of MV moves required is quite large, as this is necessary to arrive at the proper shape of the dynamic response curves for each CV. The entire series of tests is then repeated for each of the other MVs. Control engineers (relying on considerable skill and judgment) then identify the required time-dependent input-output relationships based on the data captured from all such tests. This approach has several drawbacks (4): • The test period is often very lengthy, extending over many weeks or months. • Aggressive testing is required to obtain a meaningful signalto-noise ratio for process model identification. • Large moves risk violations of process and equipment safety limits, environmental criteria, and product quality specifications. • Qualified engineers usually must be present in the plant during the testing period to provide guidance and supervision. • Important variables that are external disturbances cannot be step-tested, so the models for these variables often lack sufficient accuracy. • The quality of the MPC models can be affected quite adversely O 36 www.aiche.org/cep January 2008 CEP by large unmeasured disturbances, such as sudden rainstorms. In such cases, the test data must be discarded and the tests repeated. If feed composition is subject to fluctuation but is not measured, the identified models for the remaining variables might be corrupted. • Especially in slow-moving distillation columns, ambient temperature variations can cause distortions in step test data that require additional step testing to be resolved. Unfortunately, this procedure cannot be simplified by reducing either the number of step test moves or the magnitude of the moves made. This is mainly because obtaining a reliable process gain for each critical MV/CV or DV/CV pair requires aggressive moves that provide an adequate signal-to-noise ratio to ensure reliable determination of the model shape. Furthermore, such moves must be maintained until steady state is reached simply to ensure that the process gain is estimated reliably. Most practitioners feel that this is the single most important parameter in the entire model-identification process. A poor gain for even one critical MV/CV pair can often destroy the effectiveness of an otherwise well-defined MPC controller. Lengthy step tests can be very costly in terms of lost production, high costs for engineering supervision throughout the test period, and compromised product quality, especially in situations where the duration of such step testing is so long that product quality fluctuations cannot be “blended out” using tankage. The following table summarizes the high costs of step testing on an MPC project (14). Reduced throughput, 5–10% for 6–9 weeks $50,000 One off-spec excursion, 100% production loss $60,000 Engineering (testing), 6–8 wk, 24 h/d $140,000 Engineering (commissioning), 2 wk, 24 h/d $20,000 Total $270,000 in the most challenging regions of interest where system nonlinearities are most vexatious. The use of linearizing transforms can be beneficial in solving distillation control problems, even in high-purity columns. Such decisions require considerable judgment and caution. The ultimate test of a model’s validity is obtained when the MPC model is placed online in an open-loop, predictive mode prior to commissioning (4). The dynamic model predictions for all CVs should be checked against real-time data for a period of time, to ensure that the MPC controller will perform satisfactorily. Cases of severe mismatch between the model and any CV should be investigated to ensure that they are not a result of large unmeasured disturbances, such as rainstorms. If no such explanation is found, the models for the most important MVs with that CV must be re-examined to determine the proper corrective actions. The corrected models must then again be checked in openloop, predictive mode. Gain nonlinearity Nonlinearity in process gains is far more commonly understood as a control problem than nonlinear dynamics. Figure 1 shows examples of nonlinearities in gains and dynamics for a typical distillation column (10). When using linear control models (i.e., a controller with fixed gains), an attempt is usually made to find some nonlinear transformation that will linearize the gain. For highpurity distillation columns, the logarithm of the concentration of the impurity, rather than the concentration itself, is often used because it is almost linearly related to the reflux flow or the reboiler duty. In previous projects, other nonlinear transforms have also been used, for example, for valve positions. However, nonlinear transforms do not solve Change in Controlled Variable Y, % be impacted severely, owing to excessive reliance on feedback corrections to handle the prediction error. In other instances, changing the size, or even the direction, of an MV move can alter the dynamic shape of the CV responses dramatically (6). This phenomenon has been confirmed in several high-purity distillation columns, where the dynamic shape of the product-purity response curve was altered when reflux flow or reboiler duty were either increased or decreased (4, 5). Large increases in reflux flow resulted in a considerably shorter settling time for overhead purity than small moves. In all high-purity columns, increasing reflux flow had a much smaller effect on overhead impurity levels than decreasing the reflux flow. Also, the settling times for the composition changed noticeably. In one case, the product-composition response curve for a change in column pressure went from a normal shape to a bilinear response (6) as the size of the move was changed drastically. In other cases, columns operating close to flooding limits had highly nonlinear dynamic responses to increased reboiler loads as a result of near-exponential increases in liquid entrainment (7, 8). Detecting and analyzing such phenomena using dynamic simulation represents a technological challenge, as the quality of the mathematical models used must account realistically for numerous complex tray hydraulic phenomena in distillation columns. More recently, even the theoretical validity of the equilibrium-stage/efficiency approach has been challenged, and an approach based on mass-transfer rates was suggested as an alternative (9). These phenomena show conclusively that the dynamics of distillation columns can be highly nonlinear. Practitioners should conduct careful analyses to avoid the many potential pitfalls that could result from inadequate step-testing regimens. When the causes of the observed deterioration in performance of a previously successful MPC controller were analyzed, it was often found that the current behavior of the column had drifted far away from the original MPC curves to such an extent that normal MPC controller feedback corrections were ineffective. In normal (i.e., linear, nonadaptive) MPC practice, it is necessary to use an “averaged” curve for each MV/CV or DV/CV response curve. Therefore, the methods and procedures by which the perturbations of the dynamic model (or the real plant when conducting step tests) are carried out have a major effect on the final MPC model shapes. We recommend that these moves be made with the unit (or its base dynamic model) set close to the operating conditions where such nonlinearities are most likely to be dominant. Also, the magnitude, direction and number of the MV and DV moves must be planned in a way that will improve MPC controller performance when it is up against the most difficult constraint limits. This will ensure good controller performance 0.5 0.4 0.3 ∆u = +5% 0.2 0.1 0 ∆u = +1% –0.1 –0.2 ∆u = –1% –0.3 ∆u = –5% –0.4 –0.5 0 50 100 150 Time, min 200 250 I Figure 1. Change in controlled variable Y in response to step changes in independent variable u. CEP January 2008 www.aiche.org/cep 37 Process Control the issue of dynamic nonlinearity as previously discussed. Past efforts to deploy linear MPC controllers for nonlinear polymer processes, however, have not succeeded, despite the use of quite complex linearizing transforms. This is partially explained by the fact that the principle of superposition (an essential assumption in linear MPC theory) does not apply for such nonlinear processes. In other words, for such polymer processes, the effects of moving any MV on a given CV are not independent of the effects of simultaneous movements in other MVs or DVs. Calibrating steady-state models against plant data A procedure for developing a steady-state simulation model and calibrating it against plant data, so that it can be used for real-time control projects, is outlined in the box on the next page. This approach is based on the authors’ many years of experience. When using a dynamic model created using step tests, it can be extremely valuable to develop a steady-state simulation model of the process and use it to crosscheck the steady-state gains in order to ensure that the MPC controller will perform well. Creating reliable dynamic-simulation models Some commercially available dynamic simulators have recently incorporated a capability to develop a linearized MPC model approximation using the rigorous dynamic simulator as the engine. It remains the user’s responsibility, however, to understand the assumptions and limitations implicit in the use of such software. The following procedure is recommended. 1. Develop a reliable steady-state simulation for the entire unit. This rigorous model must be complete and specified in a way that matches the unit’s current regulatory control configuration. Developing a good overall model requires choosing calibrated thermodynamic models, studying the process and equipment design basis for the entire unit, and ensuring that the simulation model mirrors the input variables (IVs) and DVs as they exist in the regulatory control system. Operating data obtained under reasonably steady conditions for each section of a unit can be used to help calibrate the main simulation parameters, such as stage efficiencies. Use of a data historian that periodically archives real-time values is valuable for this purpose. 2. Perform a series of rigorous steady-state simulations for each distillation column. Cover the full range of seasonal CALIBRATING STEADY-STATE MODELS AGAINST PLANT DATA his procedure is recommended for developing a steady-state simulation model and calibrating it against plant data. 1. Re-calibrate all major instruments in the unit in preparation for a performance test run. 2. Determine the settling time for the unit (typically 4–16 h). 3. Schedule the test run. 4. Advise the laboratory of any special sampling and analysis requirements during the test run. 5. Advise the planning, scheduling and operations groups that it is necessary to avoid changing throughputs or operating conditions at upstream units, as well as at the unit selected for the test, for a period of time equal to the process settling time prior to the test run. 6. Ensure that all major required measurements (pressures, temperatures, flows, levels, compositions) can be collected once a minute in the data historian without data compression for the duration of the test run plus two days. 7. Check the unit feed rates against independent data sources (e.g., upstream units, tank levels or custody meters). Eliminate any discrepancies by meter recalibration as necessary. 8. Check the product rates against independent data sources (e.g., downstream units, tank levels or custody meters). Eliminate any discrepancies by meter recalibration as necessary. 9. Adjust the unit operating conditions to match the desired base-case simulation model and maintain those conditions for at least 8 h prior to commencing the test run. 10. Check the overall unit material balance using 2-h average data for all flows. 11. Commence the test run. Maintain steady-state unit operation throughout the test. Ensure that the data historian is capturing data once a minute. T 38 www.aiche.org/cep January 2008 CEP 12. Draw all feed, product and intermediate samples, with careful time-stamps, mid-way through the test run. Send the labeled samples to the laboratory for analysis. 13. Draw all feed, product and intermediate samples, with careful time-stamps, at end of the test run. Send the labeled samples to the laboratory for analysis. 14. Obtain laboratory results for all samples. 15. Analyze the online data to ensure that the unit was steady prior to and during the entire test run. 16. Perform suitable data smoothing and averaging to obtain representative values for model calibration. 17. Build the steady-state simulation model for the entire unit. The plant MVs and DVs must be independent inputs to the model, and the CVs must be calculated outputs from the model. Otherwise, it will be impossible to obtain reliable calculated gains. 18. Adjust simulation model parameters to match observed online and laboratory data as closely as possible. 19. Validate model predictions against steady-state plant data captured at conditions different from those used for model calibration. Define the base case. Pay special attention to models for column pressure drop and liquid entrainment, as these tend to behave in an extremely nonlinear fashion when pushing up against flooding constraints. 20. Starting with the base case, perturb each independent variable in the model (MV or DV) several times in both directions. For each perturbation, record the change in each CV, calculate the gains, and plot the results for evidence of nonlinearity in gains for each CV. operating pressures with an ample margin of safety. Capture the temperature, pressure and phase equilibrium constants (K-values) for each tray in each case and combine all cases into a single file. 3. Regress simplified K-value and enthalpy models (if feasible). This will help to ensure accurate results in cases where model execution time would otherwise be excessive. Use the combined case files to regress simplified K-values. The functional forms chosen should be adequate to ensure that errors are always less than 2%, especially in the high-purity regions. For hydrocarbon systems, vapor and liquid enthalpies from the Lee-Kesler equation of state may also be regressed to simpler functional forms. The use of such simplified K-values and enthalpy correlations usually dramatically reduces model execution times for the dynamic simulation cases. We recommend running multiple perturbations for each independent variable (MV or DV) to obtain reliably averaged gains. 4. Estimate material holdups for all subsections as accurately as possible. Holdups in each portion of the unit have a marked effect on the overall process settling time and on the shape of the dynamic responses. For distillation columns with trays or packing, reliable holdup estimation requires incorporating geometric design details, downcomer layout data, etc. Specialized methods for performing tray-rating calculations are generally required to ensure accurate estimation of tray hydraulics and material holdups. For horizontal and vertical cylindrical vessels, normal liquid levels must be taken into account in determining holdup. 5. Develop the dynamic simulation model for the unit, ensuring that each major section that contributes a dynamic lag is included. Thus, all distillation trays and vessels with holdup must be modeled explicitly. In the overhead section, this includes the condenser and reflux accumulator. In the bottom section, the reboiler and bottom-liquid holdup sections must be included. As with the steady-state model, this model must mirror the current regulatory control configuration of the unit. Initialize the dynamic model using results from a validated steady-state simulator in which identical K-value and enthalpy models are embedded. This minimizes dynamic transients when commencing a dynamic simulation run and improves stability. All IVs must be perturbed starting from the same base condition. After the final move, the simulation should be returned to the original steady state. 6. Model pressure drop and entrainment across the column reliably. This requires sufficient accuracy in the tray hydraulics routines. If sufficiently serious, the liquid entrainment from each tray to the one above may need to be modeled explicitly. Such entrainment not only increases a tray’s hydraulic loading and pressure drop, but it can also dramatically affect the column’s separation efficiency. This effect would require increased reflux and reboiler duties for maintaining the desired product purities and further exacerbate tray loading, entrainment and approach to flooding. 7. Ensure that steady-state gains from the dynamic model match those from the rigorous steady-state simulation with acceptable accuracy. When the dynamic solution reaches steady state (i.e., after effects of the IV perturbations have died out), results should be consistent with predictions from the steady-state model. It is unreasonable to expect an exact match, however, since the model’s differential equations are solved numerically using finite time steps. In addition, modeling computations even in double precision are subject to convergence tolerances that preclude an exact match. Note that the rigorous steady-state model solutions are determined using entirely different solution techniques and are based on exact, not simplified, thermodynamics for the phase equilibria and enthalpies. Choosing the proper integration technique (explicit vs. implicit, and integration step size) is extremely important, since it affects dynamic simulation accuracy and execution time. Press et al. (11) suggested halving the step size repeatedly until the final solution deviates only marginally from that obtained using the next larger step size. Although this approach can theoretically fail for problems whose nature requires a variable step size, that has not happened in our work to date. In general, many numerical criteria need to be considered when solving large systems of nonlinear ordinary differential equations (ODEs) and nonlinear algebraic equations. These are too numerous to discuss fully here, but good references are available (e.g., 12, 13). Special attention needs to be placed on stability and accuracy issues. 8. Examine the need to retain the dynamic model for those pairs of variables that have relatively minor gains and transient responses. When based on a first-principles dynamic simulation model, such responses may be correct theoretically, but of no practical significance to an operating multivariable controller. To get a good grasp of the relative effect of the IVs for each CV, it is useful to enter the identified Laplace transforms and an appropriate realistic move size for each IV. Thus, one may plot the dynamic trajectory of the CV responses for each IV on the same plot. For each IV move, this shows graphically the direction and shape of the CV move, the rate at which the CV reaches its final value, and the magnitude of the CV move from its base value at steady state. This information is valuable in understanding the identified model and comparing it against the steady-state simulator for the all-important steady-state gains. Also, it enables judging which IV/CV pairs ought to be deleted from the final MPC model. 9. Build an offline dynamic simulator and controller using the identified linear MPC model, and perform validation runs. Select the controller execution frequency to ensure CEP January 2008 www.aiche.org/cep 39 Process Control proper handling of the expected unmeasured disturbances. Exercise the simulation model to ensure that the predicted CV responses to changes in each IV are reasonable with respect to direction and magnitude, as well as elapsed time. Similarly, exercise the controller in an offline mode to verify that the appropriate MVs will be moved to counteract errors in CVs and that the direction and magnitude of the controller MV moves are reasonable. The latter will require some trial and error in the preliminary MPC controller tuning for the MVs as well as the CVs. Such offline simulation runs are very useful, but they cannot determine the adequacy of disturbance rejection by the controller for unmeasured DVs in an online environment. If such disturbances are very large, the online controller tuning may again have to be adjusted. An example of this is a severe rainstorm that dumps a large amount of liquid to the column bottom section and may even disrupt product quality. In addition, first-principles dynamic simulation models can reveal the existence of sharp dynamic transients in the CVs when one or more of the IVs are moved. It is important to decide whether or not such transients are of practical significance and, if so, what level of signal filtering, if any, would be appropriate prior to their incorporation into the final control model. 10. Place the identified linear control model online in an open-loop prediction mode on the distributed control system (DCS). Predictions from such models take some time to settle down. In general, it takes about as long as the time needed for the slowest CV transient modeled in the system to reach steady state. Most often, these are the terminal product purities, which are also among the most important CVs. After the predictions have become established, study the shape and magnitude of the unbiased model predictions against the actual values for all dependent CVs over a period of time. Fluctuations in the IVs should be examined on the same charts for each CV. This allows one to determine which of the input variables is responsible for any potential mismatches that might be noted, which pair of gain/delay parameters needs adjustment, and the magnitude and direction of the required modifications. Thus, it becomes possible to make reliable decisions on the directional and quantitative accuracy of the identified model. However, it is worth emphasizing that an exact match between the unbiased predictions and reality is neither reasonable to expect, nor even theoretically possible. This is due to the effects of hidden or unmeasured DVs on the process, and the use of a linear MPC model for real-world processes that are known to be nonlinear. The latter issue can be especially significant in superfractionators, despite the use of linearizing transforms. Additionally, it is important to review the control moves 40 www.aiche.org/cep January 2008 CEP planned by the controller while it is in open-loop mode. The MPC controller should use the dominant MVs to control a given CV unless those MVs are at their limits. Since the MPC uses feedback to correct for model mismatch and unmeasured disturbances, it is very important to keep track of the bias updates and ensure that they are random and close to zero, rather than being disproportionately skewed to one side or the other. CV bias updates that remain skewed over a long period probably indicate model mismatch for one or more of the relevant IV/CV pairs. 11. Consider making minor adjustments to the online gain and process delay times for the critical controlled variables prior to commissioning. Excessive deviations over time or directionally incorrect predictions are likely indications of a potentially serious modeling discrepancy that requires a re-examination of the underlying dynamic modeling basis. The offline MPC controller software permits making simulations to assess the adequacy of controller performance when confronted with deliberate changes in CV targets or DV values. This capability should be used extensively — the effort is extremely worthwhile, since it helps validate the control models in a visual way that is quite meaningful to operations staff. An additional benefit is that it allows reasonable preliminary MPC controller tuning for the main variables to be achieved before online commissioning. At least initially, operations staff are better able to grasp this aspect of controller behavior than the IV/CV dynamic model matrix. 12. Place the controller in an online, closed-loop mode. Initially, it may be wise to consider limiting the aggressiveness with which MV moves are made to ensure that the MPC controller does not immediately begin to move the plant too rapidly. Also, the relative importance of the CVs may require some review at this stage, based on the nature and magnitude of the unmeasured DVs. Study the moves the controller is making, understanding system dynamics and, especially, the settling times for each CV. Relax the MV move limits gradually to achieve stable and predictable performance. Continue to examine the unbiased model predictions. Also, study the biased predictions (i.e., future CV trajectories taking feedback corrections into account) to ensure that the controller tuning is adequate. Some trial and error may be necessary to arrive at the best compromises. In such efforts, the identified MPC models should be evaluated both in offline and online openloop modes. This helps ensure that the predicted responses to changes in the MVs are of reasonable magnitude and direction, and that the online unbiased predictions for the CV trajectories match the actual values. Online adjustments to the model gain and/or time delay may still be needed for selected MV/CV model pairs. Dynamic inferential calculations Many stream properties crucial for MPC control applications are either not available online or are measured at such a low frequency that the MPC application is unable to control them reliably within their required limits. Various methods have been used over the years to estimate such properties. Distillation column overheads and bottoms. There is often a substantial temperature gradient in the column a few trays away from the overhead and/or bottom trays. This indicates that the impurities in the column are decaying rapidly from tray to tray. In such instances, it is generally feasible to infer stream composition at the ends of a column using temperatures a few trays away. However, since column pressure also affects temperature, it is necessary to perform pressure compensation calculations to adjust the measured temperature at the current tower pressure based on some reference tower pressure. This pressurecompensated temperature can then be related to the logarithm of the concentration of the impurity in the product stream. Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Richalet, J. A., et al., “Model Predictive Heuristic Control: Applications to Industrial Processes,” Automatica, 14, pp. 413–428 (1978). Cutler, C. R., and B. L. Ramaker, “Dynamic Matrix Control — A Computer Control Algorithm,” Proceedings of the Joint Automatic Control Conference, San Francisco, CA (June 1980). Hokanson, D. A., and J. G. Gerstle, “Dynamic Matrix Control, Multivariable Controllers,”Chapter 12, in “Practical Distillation Control,” W. J. Luyben, ed., Van Nostrand Reinhold, New York, NY (1992). Mathur, U., and R. J. Conroy, “Successful Multivariable Control Without Plant Tests,” Hydrocarbon Processing, pp, 55–65 (June 2003). Mathur, U., et al., “Adaptive Multivariable Fractionator Control without Step Tests Maximizes Profit,” 86th Annual Gas Processors Association Convention, San Antonio, TX (2007). Pearson, R. K, “Discrete-Time Dynamic Models,” Oxford Univ. Press, Oxford, U.K. (1999). Fair, J. R., “Tray Hydraulics: Perforated Trays,” Ch. 15 in “Design of Equilibrium Stage Processes,” Smith, B. D., McGraw-Hill, New York, NY (1963). Stichlmair, J. G., and J. R. Fair, “Distillation Principles and Practice,” Wiley, Hoboken, NJ (1998). Taylor, R., and R. Krishna, “Multicomponent Mass Transfer,” Wiley, Hoboken, NJ (1993). Henson, M. A., and D. E. Seborg, “Nonlinear Process Control,” Prentice-Hall, Upper Saddle River, NJ (1997). Press, W. H., et al., “Numerical Recipes in Fortran 77,” 2nd ed., Cambridge Univ. Press, Cambridge, U.K., p. 707 (1992). Rice, J. R., “Numerical Methods, Software and Analysis: IMSL Reference Edition,” McGraw-Hill, New York, NY (1983). Schiesser, W. E., “Computational Mathematics in Engineering and Applied Science: ODEs, DAEs and PDEs,” CRC Press, Boca Raton, FL (1994). Mathur, U., and R. J. Conroy, “Multivariable Control Without Plant Tests,” paper presented at the AIChE Annual Meeting, Indianapolis, IN (Nov. 2002). Feedback from an online analyzer or time-stamped laboratory samples can be used to correct these predictive models. Sidestreams. Inferring the online quality of sidestreams is very helpful in petroleum refining applications such as crude units, and in the main fractionators of units such as cat crackers, delayed cokers, hydrocrackers, etc. These stream-quality measurements are often defined in terms of petroleum fraction properties, such as an atmospheric or vacuum ASTM distillation temperature. Unfortunately, such stream properties are affected by many column variables, including feed rate, sidestream draw rate, pumparound cooling duties, overhead reflux flow, reboiler or feed preheater duty, stripping steam flow, and so forth. It is feasible to develop steady-state models that predict such properties. However, these predictions are valid only at the steady state, and can often be inaccurate if instantaneous values of the predictor variables are used at times when the column is going through a sharp transient. For such properties, it helpful to use dynamic simulation to develop the required predictive models. A relationship is found that enables dynamic prediction of the desired stream property using the cumulative variations in the independent variables (MVs and DVs) over time. These relationships can be identified readily and implemented online as dynamic predictions. Corrections to the predicted values are made using time-stamped laboratory samples. Others have reported using neural networks or other nonlinear functions, with time-delayed inputs, for such predictions. However, we have insufficient experience with such techniques to recommend them. CEP UMESH MATHUR, P.E., is a principal of Advanced Control Engineering Services (Houston, TX; E-mail: u.mathur@yahoo.com or mathuru@gmail.com). He is a professional engineer with over 40 years experience in the process industries, and has worked for more than 15 years in process and equipment design, modeling and simulation. During the last ten years or so, he developed the methodologies and techniques described in this article for application in multivariable control and realtime optimization. He has a bachelor's degree in chemical engineering from the Indian Institute of Technology, Delhi, a post-graduate diploma from the Indian Institute of Petroleum, Dehradun, and an MS in chemical engineering from the Univ. of Tulsa. He welcomes queries or information about similar project-implementation issues, and would be happy to share additional information about these tools and methods. ROBERT D. ROUNDING works for BP's North America Gas SPU as the technical authority for instrumentation and control systems. He supervised several of the projects that were executed using the techniques described in this article. DANIEL R. WEBB is the plant manager for the Ineos (formerly BP) Hobbs Fractionation Complex, where he managed the implementation of a plantwide model-predictive controller over three years ago. This application has run unchanged since then. ROBERT J. CONROY has over six years experience in regulatory and modelpredictive control, and helped implement several of the projects using the methodologies described in this article. He graduated summa cum laude from Rice Univ. with a BS in chemical engineering. CEP January 2008 www.aiche.org/cep 41 ...
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