Unformatted text preview: Process Control Use Model-Predictive
Control to Improve
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
• 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
• 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
One off-spec excursion, 100% production loss $60,000
Engineering (testing), 6–8 wk, 24 h/d
Engineering (commissioning), 2 wk, 24 h/d
$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
0.3 ∆u = +5% 0.2
0 ∆u = +1% –0.1
–0.2 ∆u = –1% –0.3 ∆u = –5% –0.4
0 50 100
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
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
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Mathur, U., and R. J. Conroy, “Successful Multivariable
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Schiesser, W. E., “Computational Mathematics in Engineering
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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: [email protected] or
[email protected]). 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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