Article pubs.acs.org/IECR
External Reset Feedback for Constrained Economic Process Operation Rahul Jagtap,† Nitin Kaistha,*,† and William L. Luyben‡ †
Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, United States
‡
ABSTRACT: Efficiency and sustainability considerations increasingly require control systems to drive process operation as close as possible to optimally active process constraints. Because the active constraint set is changeable, override control structures are employed to transfer the control of important control objectives from one controller to another and to manage the transition between the different constraint regions. Reset windup problems can occur when these controllers have integral action with large swings (bumps) in controller output as control is transferred from one controller to another. This work considers the Shinskey− Buckley external reset feedback control structure in override control applications for a smooth transition between active constraint regions. Three example processes with increasing levels of complexity are used to quantitatively demonstrate the significant improvement in dynamic control and consequent process economic performance (compared to internal reset). The quantitative results suggest widespread application of external reset controllers for handling process constraints to realize significant process operation efficiency and sustainability benefits.
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INTRODUCTION
a change in the process fresh feed rate), an alternative manipulated variable is needed for regulating the PV. In conventional control systems, this reconfiguration is done using overrides, where two (or more) controllers compete for adjusting a manipulated variable (MV) through a low/high select. When the competing controllers have reset action, windup problems occur with the controller whose output signal is not selected continuing to integrate the error and driving its output to a high/low limit (wind-up). When operating conditions change and this controller should start positioning the MV, the controller output must unwind from its saturated position. It may take a long time for the unwinding to occur until the controller takes up control. Also, at the point where the high/low select passes control to this controller, the controller output would have significant unwinding momentum causing large bumps in both the PV and the MV. Reset wind-up problems can be significantly mitigated by applying “external reset feedback” as suggested by Shinskey3 more than 45 years ago and extensively applied by Buckley4 to a variety of process applications, particularly distillation columns. Even though the concept has existed for almost half a century, there are (surprisingly!) very few literature reports that demonstrate and quantify its economic and sustainability benefit in chemical process systems. In addition, external reset feedback is not directly available in commercial dynamic process simulators such as Aspen dynamics/Hysys. The purposes of this article on external reset feedback are twofold: (1) to quantify its dynamic and consequent economic benefits in conventional override process control applications and (2) to illustrate its implementation in Aspen dynamics, a popular
Since its inception, the dictates of economic prudence have driven the continuous chemical process industry to routinely apply material and energy integration for designing energy efficient, zero-discharge, and green chemical processes. Operating such highly integrated processes in a safe, stable, and economic manner can pose a significant challenge with “local” disturbances propagating through the entire plant as a consequence of the several available recycle paths, possibly resulting in large plantwide transients. The design of an effective plantwide control system for “smooth” process operation in order to reap the sustainability and economic benefits of green processes thus remains a much researched area.1 Over its life span, a plant is operated over a very wide operating space, which includes a large throughput range (from below design throughput to maximum throughput), significant changes in raw material and feedstock quality, equipment degradation, etc. Optimal steady operation then naturally partitions the operating space into regions with different optimally active constraints. A robust control system that manages the transition between different active constraint regions with smooth transients is then highly desirable. Smooth transients imply that large swings in the constraint variables are avoided and the plant can be driven closer to the hard active constraint limits for potentially significant economic benefit. A constraint going active corresponds to losing a control degree of freedom. In the simplest case, if the constraint variable is directly manipulated to control a process variable (PV), regulation of the PV is lost when the constraint variable reaches its limit (i.e., becomes active). If control of the PV is critical for safety, for economic (e.g., product quality control) reasons, or for process stabilization (e.g., preventing snowballing,2 which is the very high sensitivity of recycle flow rate to © 2013 American Chemical Society
Received: Revised: Accepted: Published: 9654
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Figure 1. Modifying a P only controller to a PI controller by output feedback.
process simulator. The first point above is particularly relevant in today’s fiercely competitive environment, where the ability of a control system to drive process operation closer to the hard active constraint limits increasingly determines competitiveness.5−7 It is pertinent to note that model predictive control (MPC), with its natural ability to handle process constraints, is a possible alternative to conventional multiloop decentralized control systems with overrides. Since the original MPC formulation more than two decades ago,8 the idea of a centralized MPC calculating all the control moves on a process plant has particularly grabbed the attention of the academic community. The usual approach is to obtain the economic optimal steady state at which the process must operate and then let the nonlinear MPC (NMPC) optimize the control moves to minimize the weighted dynamic deviations of controlled variables from this steady state, as captured in a scalar objective function (see, e.g., ref 9). In possibly the only study comparing conventional multiloop decentralized control with overrides and centralized NMPC on a complete plant, namely, the Tennessee Eastman challenge process,10 Ricker11 concluded that NMPC cannot outperform decentralized control because of “too many competing goals and special cases to be dealt with in a conventional MPC formulation”. More recently, Rawlings and co-workers have proposed economic MPC12,13 that directly calculates the control moves to optimize a dynamic economic objective using a terminal constraint formulation. Because of the complexity of the approach, the current illustrations are however limited to standalone process units such as a reactor. Its applicability and benefit to plantwide control problems, which are much more complex because of the separation in time scales of individual unit operations and material/energy recycle effects, thus remain untested. To the best of our knowledge, convincing evidence of the significant superiority of MPC approaches over conventional multiloop decentralized control with overrides, particularly in the plantwide context, is not forthcoming in the literature. As such centralized MPC entails significant development and maintenance overhead, the conventional approach is likely to remain the industrial state of the art for the foreseeable future. A focused quantitative study, including implementation details of external reset feedback in conventional override control systems, thus remains relevant, particularly in terms of its simplicity, ease of implementation and maintenance, and practicality, when compared with MPC approaches.
We highlight that in the context of the recent monograph by Glattfelder and Schaufelberger14 on handling input/output constraints in control systems, external reset feedback is a standard PID technique. Advanced techniques such as generalized antireset wind-up are not studied here. In the following, we briefly discuss external reset feedback and its Aspen dynamics implementation. This is followed by its application in override control systems on three example processes along with quantitative dynamic and economic performance results. The examples are, in order, a compressor, a ternary distillation column, and, finally, a complete ethyl benzene process. The main findings from the three examples are then summarized.
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EXTERNAL RESET FEEDBACK IN OVERRIDE CONTROL SYSTEMS Consider the P controller block diagram in Figure 1a. The controller output (u) is u = K Ce + b where KC is the controller gain, e is the PV error (e = PVSP − PV), and b is the bias term. The reset feedback method evolved from how in the early days operators would adjust b in a P controller to drive e to zero for offset free control. If b is adjusted such that at the final steady state, b = u, then the final steady e must be zero. Forcing b to match u thus achieves offset free control. This may be automated by using reset (integral) feedback on b with u as its set point, as in Figure 1b. Simplification of the block diagram shows that b is obtained by simply lagging u (Figure 1c). Further simplification of the block diagram shows its equivalence to a PI controller (Figure 1d). Now consider two PI controllers competing for the manipulation of a control valve position through a low/high select as in Figure 2. Instead of the controller outputs being fed back through the lags (dashed IR lines in Figure 2) to update the respective bias terms, consider the alternative configuration of feeding back the implemented control signal (dashed ER lines in Figure 2), which is the output of the low/high select. Because resetting of the bias term uses feedback of a signal external to the controller, this alternative configuration is aptly termed external reset feedback. The usual configuration of feeding back controller output, a signal internal to the controller, is then termed internal reset. To appreciate the difference between internal and external reset feedback, consider an initial state in which the selector block passes the output of controller 1 so that the valve 9655
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Generate the Error Signal. The process variable signal PV from the transmitter of the controlled variable is subtracted from the set point signal SP to generate an error signal using the Comparator block. The Input2 signal (PV) is subtracted from the Input1 signal (set point SP). Controller Input Scaling. Controllers usually take in PV and SP signals that are between 0 and 100% and not in their original units (e.g., degrees Celsius). The Scale block provides the necessary conversion. Instead of separately scaling the PV and SP signals, we scale the error signal (PV and SP are then in original units). Multiply by Controller Gain (P action). The scaled Comparator output (percent error) is fed to the Multiply block whose other fixed input is the controller gain. The sign of the gain determines the controller action. A positive gain corresponds to a “reverse” action: when PV increases, controller output (OP) decreases. Add the Output of Lag (bias). The output of the Multiply block is added to a signal coming from a Lag block, discussed later. A MultiSum block is used, and its output is the controller output in percent. Select Lower/Higher Signal. The controller output, OP, and the signal OR from the competing override controller are the two inputs to a MultiHiLo block, which is configured to select either the higher or the lower of the two inputs. The selector output is clipped to within the 0−100% range using the Scale block. The clipped signal (VS) is lagged to provide external reset feedback. In cases where the MV is not a 0−100% signal (e.g., an energy stream), the VS signal is converted into the appropriate MV range using a Multiply block and a Multisum block (for non-zero offset). Setting up the Lag Block. A Lag block with unit gain and a time constant of τI (reset time) is used. Proper initialization of this circuit can be tricky. A procedure that works is not to close the reset feedback loop and feed a fixed signal into the lag that corresponds to the expected signal from the selector. For example, if the control valve is designed to be half-open under normal conditions, the valve signal will be 50% and the selector output is 50%. Therefore, insert a control signal, specify its value to be 50%, and make it a “fixed” variable type. Then open up the “all variables” view of the lag block, specify the output variable to be an “initial” variable type, and make an initialization run. The lag block output should be 50%. Finally, reconnect the source of the lag block input to be the selector output. The “run” button at the bottom of the screen will turn red (overspecified system). Change the lag block input signal to a “free” variable type. The red light should turn green, and the simulation should run properly.
Figure 2. External vs internal reset feedback in override controllers.
position is being adjusted to maintain PV1. Controller 2 is then unselected, and PV2 is not being controlled. Error e2 is then non-zero and unlikely to undergo a change in sign unless process conditions change significantly. Assuming that control remains with Controller 1 and the sign of e2 does not change, in the case of internal reset, the integral action will keep on adjusting b2 until u2 saturates. This is the well-known reset wind-up problem due to reset (integral) action. When operating conditions change sufficiently and control of the valve must pass to Controller 2, typically e2 would reverse sign and u2 would then unwind until the selector block passes control to Controller 2. Now because u2 must unwind from its saturated position, the unwinding gap is large, which delays the passing over of control. Also at the point where control passes, Controller 2 has significant unwinding momentum causing large swings in u2 and consequently in PV2. The switching between the two controllers is then accompanied by large transients and is not smooth. In the case of external reset, because the implemented control signal is fed back, the unselected Controller 2 output remains close to the implemented control signal, differing only by KC2e2. Error e2 would usually be small, leading to a small unwinding gap. Thus when control is to be taken up, one has to unwind only by KC2e2, instead of from 100 or 0%. External reset thus facilitates quick taking up of control by a PI controller. The small unwinding gap leads to smoother transients and relatively “bumpless” switching.
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IMPLEMENTING EXTERNAL RESET IN ASPEN DYNAMICS External reset is not directly available in Aspen and must be implemented using available Aspen dynamics library blocks. A typical implementation in Figure 3 is briefly described below.
Figure 3. External reset feedback in Aspen dynamics. 9656
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Figure 4. Gas header compressor example with control system and base design conditions.
Figure 5. Aspen dynamics external reset feedback controllers for the compressor example.
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EXAMPLE APPLICATIONS WITH QUANTITATIVE DYNAMIC AND ECONOMIC BENEFIT RESULTS We now study three process control applications for handling constraints using override controllers with external reset feedback. These are in order, a compressor, a ternary distillation column, and a complete ethyl benzene plant. The dynamic control and consequent economic benefit of using external reset is quantified and compared with that of internal reset. Gas Header Compressor System. This simple example is taken from Shinskey,3 and the flowsheet with the override
control system is shown in Figure 4. A variable-speed compressor compresses gas into a gas header supplying multiple downstream users. When the downstream demand is not very high, the compressor work (or rpm) must be adjusted to maintain the header at its maximum pressure limit (PMAX). This allows the highest maximum flow to be delivered to the individual downstream users, on request. As the downstream demand increases, the header outflow cannot be allowed to exceed a maximum limit (FMAX) to avoid damaging the compressor drive. Thus, should the downstream demand 9657
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bump at ∼0.02 h is due to the large unwinding gap that the unselected controller output (the flow controller) must overcome before taking over control, because the unselected controller output is saturated (see subplots 4 and 5). Similarly, the internal reset header pressure response shows a small bump at ∼0.4 h. The occurrence of these bumps requires back-offs in the maximum header pressure and maximum flow controller set points to avoid violation of the respective PV maximum limits. In contrast, the transient PV responses when both controllers use external reset feedback are significantly smoother (almost bumpless). The header pressure response does not show any overshoot and/or oscillations, so that the header pressure controller set point can be set at PMAX. Similarly, the flow transient response shows a very small overshoot above the maximum limit so that the maximum flow controller set point can be set only slightly below FMAX. The smoothness of the response may directly be attributed to the smaller unwinding gap that the unselected controller must overcome before taking over control (see subplots 4 and 5). The unselected controller output is not saturated and differs only marginally from the implemented signal due to external reset feedback so that the taking over or giving up of control is (almost) bumpless. For a quantitative comparison between internal and external reset feedback, Table 1 lists dynamic control and economic
exceed FMAX, the control of header pressure must be given up and compressor work must be adjusted to maintain the flow at this limit. The override control system then consists of the maximum header pressure controller and the maximum header outflow controller. The lower of the two controller outputs, obtained from a low selector, is used to set the compressor work. Both the maximum pressure and maximum flow controllers are PI with reverse action. The controller tuning parameters are shown in Figure 4. For the specific example, FMAX is taken to be 1.4312 × 104 kmol/h and PMAX is taken to be 50 bar. Both these limits are assumed to be hard so that the steady process operation must be sufficiently backed off from the limits to ensure that they are not exceeded during the (expected) worst-case transients. For the purpose of illustration, a 20% step increase (based on design throughput) in the flow demand is considered the worstcase disturbance. An Aspen dynamics simulation is built to simulate the setup described above. A labeled Aspen dynamics block diagram for implementing external reset in the header pressure and header outflow controllers is shown in Figure 5. For the sake of clarity, the blocks corresponding to the header pressure controller and flow controller are grouped separately. Notice the use of “%2W” block to convert the 0−100% clipped low selector output to compressor work between 0 and 53.2 MW. Figure 6 plots the transient response of the header outlet flow, header pressure, compressor work (low selector output),
Table 1. Dynamic Control and Economic Metrics for the Compressor Example external reset
internal reset
PV
IAE
back-off
IAE
back-off
flow pressure
236.645 2.3852
160.5 kmol/h ∼0
562.263 4.8446
1392.5 kmol/h 2.59 bar
metrics. To quantify the dynamic control benefit, the integral absolute error (IAE) of the PV that is supposed to take up compressor work manipulation upon throughput step up/step down, i.e., header outflow for step up (0−0.2 h) and header pressure for step down (0.3−0.5 h), is noted. The IAE values are significantly smaller for external reset, suggesting a marked improvement in dynamic control. To quantify the economic benefit, the back-off in the two PV set points is noted in Table 1. The large back-off from FMAX due to large PV transients in internal reset causes the maximum flow through the process to be 3.6% lower, compared to external reset. The flow transients using internal reset thus directly translate to a significant loss of maximum achievable throughput. Also, when internal reset is used, the process must be operated at a steady-state header pressure that is 2.59 bar lower than PMAX, i.e., 50 bar − 2.59 bar = 47.41 bar. With external reset, the steady header pressure is PMAX (50 bar; no back-off). For a downstream user pressure of 30 bar, using the proportionality of flow to the square root of pressure drop across a fully open valve, this directly translates to the maximum flow that can be delivered to a downstream user to be 6.7% lower for internal reset than for external reset. The loss of maximum deliverable flow to a downstream user is thus significant. Ternary Distillation Column. We now consider the simple ternary distillation column in Figure 7. The control structure on the column is also shown. An equimolar benzene−toluene− xylene feed stream is separated into nearly pure benzene distillate with toluene and xylene leaving in the bottoms. We assume that the benzene impurity in the bottoms must be
Figure 6. Transient response of the gas header compressor system to large step changes in downstream flow demand: (solid black line) external rest, (dashed gray line) internal rest, (dashed red line) hard constraint limit, and (dashed black line) downstream demand.
maximum flow controller output (low selector input), and header pressure controller output (low selector input) to a 20% step increase in flow demand to 1.4885 × 104 kmol/h from an initial steady-state flow of 1.2595 × 104 kmol/h followed by a subsequent step decrease back to the initial flow demand. Responses are shown for the cases in which both PI controllers use external reset (ER) or both use internal reset (IR). In each case, the set points of the two controllers are backed off from the respective hard maximum PV limits to ensure these limits are just touched from below and not exceeded during the transients. The transient responses in Figure 6 show a large bump in the gas flow when both the controllers use internal reset. This 9658
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Figure 7. Ternary column with base design and control structure.
override temperature controller set point, the OTC output is high, so that the desired feed flow signal, TPM, passes through the low select to the set point of the feed flow controller. When throughput increases and boil-up manipulation passes to the ΔP controller, T10 starts to decrease because more cold feed is being put in than can be boiled up. The override temperature controller output then decreases and eventually becomes smaller than the TPM signal passing feed manipulation to the OTC. The control structure thus is altered from fixed feed − varying ΔP to varying feed − fixed ΔP. The temperature override controller acts to cut the feed to the column with the column at (or close to) its flooding limit (ΔPMAX). The ΔPMAX constraint is considered hard with excursions beyond ΔPMAX implying major hydraulic problems in the column requiring significant manual operator intervention, which must be avoided. The normal and override temperature controllers as well as the ΔP controller are PI, and their output signals pass through a low select. We consider two cases corresponding to the use of internal reset or external reset to realize integral action in these PI controllers. An Aspen dynamics simulation is built using the controller parameters listed in Table 2. The external reset feedback controllers are implemented in a manner similar to the compressor example, and the detailed block diagram is not shown for the sake of brevity. A 2 min lag is applied to the tray
tightly regulated. Conventional single-end temperature inferential control is implemented on the column. The reflux drum and bottom sump levels are controlled using the distillate and bottoms, respectively, while the column pressure is controlled using the condenser duty. During normal operation, a sensitive stripping tray temperature (10th from top; T10) is controlled by manipulating reboiler duty. In the simulation, we manipulate the flow rate of the vapor boil-up. In practice, the flow rate of the heating medium (steam) would be manipulated. Holding this tray temperature maintains a low concentration of benzene impurity in the bottoms. The reflux is maintained in ratio with the feed to keep the impurity of toluene in the distillate at an acceptable level at all throughputs. Now as the throughput is increased, the boil-up increases, causing the column flooding limit to be approached. This is indicated by the pressure drop (ΔP) across the column approaching a maximum limit (ΔPMAX). A ΔP controller must then take over boil-up manipulation to maintain ΔP close to (but below) ΔPMAX. This is accomplished by comparing the ΔP and temperature controller outputs in a low selector, which allows the smaller of the two signals to pass to the boil-up controller (see Figure 7). With boil-up under ΔP control, the stripping tray temperature becomes unregulated and decreases. This is unacceptable because the level of the benzene impurity in the bottoms will increase. Because the benzene impurity in the bottoms must still be tightly regulated, an alternate manipulation handle is needed for stripping tray temperature control. This is accomplished by controlling temperature with the feed flow rate. An override temperature controller is installed with its set point slightly below the normal temperature controller set point. The output of the override temperature controller (OTC) is compared to the desired column feed flow signal (TPM) in a low selector. The lower of the two signals is passed as the set point of the column feed flow (see Figure 7). During normal operation, T10 is tightly controlled by the boil-up. Because the temperature is above the direct acting
Table 2. Ternary Column Controller Parametera controlled variable
KC
τi (min)
SP
sensor span
V1 T10 ΔP T10ord
1 2 2 0.3
2 10 2 30
from low select 114.17 °C 15.8 kPa 112.17 °C
0−354.4 kmol/h 94.17−134.17 °C 0−40 kPa 94.17−134.17 °C
a
All level loops use a KC of 2 unless specified otherwise. Pressure/flow controllers tuned for tight control. 9659
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Figure 8. Ternary column transient responses to ramped throughput changes: (solid black line) external reset, (dashed gray line) internal reset, and (dashed red line) hard constraint limit.
temperature measurement to account for sensor dynamics. Also, two 1 min lags in series are applied to the output of the boil-up flow controller to account for reboiler thermal lag. The hard ΔPMAX constraint is taken to be 19.25 kPa. The transient response for the override control system is obtained for a ramped increase in desired fresh feed set point at a rate of 6 kmol/h per hour from the design feed rate until the overrides (external or internal reset) act to cut the column feed, followed by a subsequent ramped decrease back to the design feed rate. The transient responses of the column feed flow (FCOL), ΔP, T10, boil-up (V), and the bottoms benzene mol fraction (xBZB) using internal and external reset controllers are shown in Figure 8. The transient responses of the controlled PVs (ΔP, T10, and FCol) are significantly smoother when external reset feedback is used. For internal reset feedback, the ΔP and T10 responses show large swings when boil-up manipulation is transferred from the normal temperature controller to the override ΔP controller and vice versa. Also, when throughput is increased, it takes significant time for the override temperature controller to take up column feed manipulation to cut it down after boil-up manipulation is taken over by the ΔP controller. The tray temperature then decreases significantly before returning to the override set point. Similarly, when throughput is ramped down, it takes the normal temperature controller significant time to take up boil-up manipulation after the override temperature controller gives up feed flow manipulation. The tray temperature then increases significantly before returning to the nominal set point. The giving up and taking over of control is thus much delayed for internal reset feedback, the delay being attributable to the large unwinding gap in the controller that must take over control (data not shown). Consequently, the control of column temperature is significantly poorer for
internal reset feedback, which results in significantly poorer regulation of the benzene impurity in the bottoms. Similar to large swings in tray temperature for internal reset feedback, swings are also observed in the ΔP transient response for internal reset, when boil-up manipulation is transferred between the ΔP and nominal temperature controllers. Because the ΔPMAX limit is a hard one, some back-off in the ΔP controller set point below ΔPMAX is needed to ensure the limit is not violated during the transients. On the other hand, for external reset feedback, no back-off is needed from ΔPMAX because the ΔP transient response is smooth with no oscillations. The back-off from ΔPMAX has severe economic implications because the boil-up corresponding to the backed off ΔP set point is noticeably lower. This implies the maximum steady boil-up at which the column is operated is lower. The maximum achievable steady-state feed processing rate (throughput) is then significantly lower compared to that of external reset. For a quantitative comparison, Table 3 reports the IAE of T10 and the bottoms benzene mole fraction for the transient response in Figure 8 for internal and external reset feedback. The PV deviations for IAE calculation are taken from the initial steady-state values. The significantly lower IAE for external reset quantitatively corroborates the marked improvement in Table 3. Dynamic Control and Economic Metrics for the Ternary Column Example
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parameter
external reset
internal reset
T10 IAE xBzB IAE ΔP back-off (kPa) maximum feed rate (kmol/h)
12.44 0.0045 0 117.3
44.58 0.1611 0.77 113.1
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Figure 9. Ethyl benzene process with base-case design and operating conditions.
article by Luyben15 and shown consists of a two-reactor reaction column separation section along streams. The principal reactions section are
dynamic control compared to internal reset. In Table 3, we further report the back-off from ΔPMAX and the consequent loss of maximum feed processing capacity. For the same equipment, the maximum achievable throughput is ∼3.6% lower when using internal reset feedback compared to using external reset feedback. The use of external reset thus significantly improves the dynamic control and economic performance of the ternary distillation column. We also note that the significantly poorer regulation of bottoms benzene impurity when using internal reset can result in substantial quality control issues and consequent economic loss. The higher level of benzene impurity will contaminate the downstream product and lead to off-spec product. Assuming a bottoms benzene composition of >1 mol % is off-spec, 13.4% of the total bottoms product produced over the 14 h period is offspec when using internal reset. We have no off-spec product when external reset is used. To ensure the downstream product is always within the maximum allowed benzene impurity spec for internal reset, the normal operating benzene composition would have to be significantly lowered. This would imply extra column energy consumption (higher boil-up per kilogram of product) as well as lower feed processing capacity, because the nominal boil-up is now closer to the flooding limit. The application of external reset, on the other hand, provides significantly tighter control of the benzene impurity, which translates into higher maximum achievable throughput. This example indicates that the external reset feedback configuration allows smoother transients for handling the flooding constraint with higher maximum achievable throughput and energy efficiency and lower quality give-away. Ethyl Benzene Process. Unlike the previous examples with stand-alone isolated process units, we now consider constraint handling using overrides for a complete plant manufacturing ethyl benzene (EB) via alkylation of benzene with ethylene. The basic flowsheet and process design are taken from a recent
in Figure 9. The process section followed by a twowith two material recycle occurring in the reaction
main alkylation reaction: C6H6 + C2H4 → C8H10 benzene
EB
ethylene
side alkylation reaction: C8H10 + C2H4 → C10H14 EB
ethylene
DEB
transalkylation: C10H14 + C6H6 → 2C8H10 DEB
benzene
EB
In the first cooled CSTR, the recycle and fresh benzene are fed along with the fresh ethylene. To suppress the side reaction, an excess benzene environment is maintained in the CSTR so that the total (recycle + fresh) benzene flow is significantly more than the fresh ethylene flow. Nearly complete conversion of ethylene occurs in the two reactors. The first CSTR is cooled, while the second CSTR is adiabatic. The effluent from the latter is fed to a recycle column separating it into nearly pure benzene distillate, which is recycled to the first CSTR, and benzene free bottoms, which is fed to the product column. The product column recovers nearly pure EB product as the distillate and discharges DEB with some EB as the bottoms. The DEB is recycled to the second CSTR. The DEB in the recycle loop is allowed to build to an extent that its consumption by transalkylation exactly matches the generation by the side reaction. The net DEB generation rate is then zero, implying the DEB is recycled to extinction (zero-discharge process). The reaction kinetics and other modeling details are available in Luyben15. For continuous processes, the economic optimal steady state often corresponds to the maximum achievable throughput, which is usually limited by a hard equipment capacity 9661
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Figure 10. Plantwide control structure on the ethyl benzene process.
recycle column feed valve manipulation through a low select (LS1). With the OTC taking over recycle column feed manipulation, level control on the second CSTR is maintained by taking over manipulation of its feed (FRxr2). Further upstream, level control on the first CSTR is maintained by manipulating fresh ethylene feed (FC2), which maintains the liquid level by the changes in the total benzene flow produced by the benzene:ethylene ratio (nested action). Override level controllers OLC2 and OLC1 compete for manipulation of FRxr2 and FC2, respectively, via low selects LS2 and LS3. Thus, when V1MAX becomes active, the overrides act to alter the material balance control structure to be in the opposite direction of process flow from the recycle column (constrained unit) to the fresh feeds. The control structure thus is altered from fixed FC2 − varying V1 to fixed V1 − varying FC2. For the override scheme to work properly, the set points of override level controllers must be sufficiently above the respective normal level controller set points to ensure they are not triggered during routine transients. Similarly, the override temperature controller set point should be somewhat below the normal temperature set point. The normal and override temperature controllers on the recycle column must be PI to ensure offset-free temperature control and hence tight regulation of the benzene impurity in the bottoms. For economic efficiency reasons,15 the normal and override reactor level controllers must be PI for offset free tracking with their set point close to but below the maximum reactor level constraints (U1MAX and U2MAX). In the first CSTR, this maximizes ethylene conversion so that the very low reactor ethylene composition results in a low level of DEB formation. In the second CSTR, maximizing the residence time minimizes the DEB recycle rate required for recycling DEB to extinction.8 The feed to the two columns then contains less DEB, which minimizes the total steam consumed in the reboilers per kilogram of product. External reset should be applied in all the normal and override controllers regulating the recycle column temperature and the two CSTR levels. As with the previous case studies, we consider two scenarios: using external reset feedback and using internal reset feedback.
constraint, also termed the bottleneck constraint. For illustration, we consider the recycle column approaching its flooding limit as the bottleneck that limits maximum throughput. For convenience, we consider flooding to correspond to a maximum column boil-up, V1MAX, instead of the usual ΔPMAX. The plantwide control system, including overrides for handling V1MAX, is shown in Figure 10. The conventional normal control system (V1MAX not active) consists of a flow controller on the fresh ethylene (limiting reactant) feed (FC2) as the throughput manipulator (TPM). The total (fresh + recycle) benzene flow is maintained in a ratio with the fresh ethylene flow by adjusting the fresh benzene feed flow. The ratio set point is adjusted to maintain the DEB recycle streamflow (B2) and prevent snowballing in the DEB recycle loop. The material balance control is in the direction of flow with the two CSTR levels being maintained by the respective reactor outflows and reflux drum and bottom sump levels on the two columns being maintained by manipulating the distillate and the bottoms, respectively. Column pressures are controlled by the respective condenser duty valves. The temperature of the first CSTR is maintained by manipulating the CSTR cooling duty. The reflux on the recycle column is maintained in ratio with the column feed flow. The reflux in the second column is adjusted to maintain the DEB mole fraction in the EB product (xDEBD2). Sensitive stripping tray temperatures (T14, recycle column; T21, product column) are controlled by manipulating the respective column boil-ups (V1 and V2). The recycle column temperature set point is adjusted to maintain the benzene impurity in the EB product (xBzD2). When V1MAX becomes active as the TPM set point (FC2SP) is increased, temperature control on the recycle column is lost, which implies regulation of the benzene impurity in the bottoms is lost. Because the benzene necessarily contaminates the EB product, an alternative manipulation handle for the recycle column temperature controller is needed. An override temperature controller (OTC) must take over recycle column feed flow manipulation from the second CSTR level controller (LC2). The two controllers (OTC and LC2) compete for 9662
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subsequent ramped decrease to the initial steady state. Appropriate back-off below the respective maximum limits is provided in the U1 and U2 controller set points such that the limits are just touched from below and not violated during the transients. No back-off is needed below V1MAX because the low select LS ensures V1MAX is never violated. The plantwide transient responses for external and internal reset are compared in Figure 11. For the case using external reset, mild transients are observed in the two reactor levels and the recycle column temperature as the overrides act to alter the material balance control structure. When the V1MAX constraint becomes active on TPM ramp-up, flow rates are adjusted all the way upstream to the process fresh feeds. During the TPM ramp-down, override control is given up and the structure reverts back to the original material balance control structure. On the other hand, the transients are much more severe for the case using internal reset feedback. Large swings in the reactor levels and recycle column temperature occur when the overrides take over and give up valve manipulation. This is caused by the large unwinding gap that occurs when unselected controller output is saturated. The large transients in U1 and U2 when using internal reset require that their normal steady-state set points be sufficiently backed-off to avoid U1MAX and U2MAX violation during the ensuing transients. The normal steady-state operation of the CSTRs is then significantly below the maximum reactor holdup. The corresponding back-off when using external reset is much smaller because of the smoother transients, which allows reactor operation much closer to the maximum hold-up. The total steady-state boil-up (V1 + V2) is noticeably lower when using external reset than when using internal reset because of the smaller amount of DEB fed to the recycle column. This translates to a significant energy efficiency benefit with lower
Aspen dynamic simulations are built to simulate the two scenarios described above. The parameters used for the controllers (including overrides) are listed in Table 4. The Table 4. Ethyl Benzene Process Controller Parametersa Regulatory Layer set point τi (min)
CV
KC
U1 U2 TRxr1 TSCol1 TSCol2 xBzD2 xDEBD2 B2
5 5 1.5 8 4.4 0.045 0.257 0.25
CV
KC
τi (min)
U1 U2 TSCol1
5 5 1.5
250 250 40
ER
IR
sensor span
250 47.5% 36.6% 250 47.5% 39% 30 200 °C 20 xBzD2 controller 25 395.5 K 100 0.0004 66 0.0006 400 230 kmol/h Override Controllers ER
IR
52.5% 41.6% 52.5% 44% xBzD2 controller
0−100% 0−100% 0−400 °C 350−430 K 273.15−517.9 K 0−0.0016 0−0.002 0−460 kmol/h set point offset 5% 5% 2.5 K
a All level loops use a KC of 2 unless specified otherwise. Pressure/flow controllers tuned for tight control.
external reset feedback controllers are implemented in a manner similar to the compressor example. The three constraints V1MAX, U1MAX, and U2MAX are considered hard with limiting values of 600 kmol/h, 5.0648 m, and 5.0648 m, respectively. The transient response for external and internal reset feedback is obtained for a ramped increase in the TPM from an initial steady value of 630.6 kmol/h at a ramp rate of 16.5 kmol/h per hour until V1MAX goes active and the overrides act to cut down the fresh ethylene feed. This is followed by a
Figure 11. Ethyl benzene process transient response to ramped throughput change: (solid black line) external reset, (dashed gray line) internal reset, and (dashed red line) hard constraint limit. 9663
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involves operating at constraints. External reset controllers should therefore be of considerable industrial and academic importance.
boil-up per kilogram of product for nominal unconstrained operation. For constrained operation (V1MAX active), the backed-off set point of the level controllers on the two CSTRs is lower for internal reset than for external reset because of larger transients in the controlled PVs. This results in more DEB fed to the recycle column, which requires a higher V1 for a given throughput. Therefore, the V1MAX constraint is hit at a lower throughput. This leads to a maximum achievable throughput that is noticeably lower compared to the external reset. To quantify the dynamic control benefit of external reset over internal reset, Table 5 lists the IAE of PVs U1, U2, TSCol1,
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*E-mail:
[email protected]. Phone: +91 512 2597513. Fax: +91 512 2590104. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The first two authors acknowledge financial support from the Department of Science and Technology, Government of India.
Table 5. Dynamic and Economic Metrics for the EB Process parameter
external reset
internal reset
9.9749 11.93 126.5 0.008 835.2 4.8115 4.8115 22.4
23.037 20.394 131.94 0.0112 785.6 3.707 3.947 22.92
IAE U1 U2 TSCol1 xBzD2 maximum FC2 (kmol/h) nominal U1SP (m) nominal U2SP (m) energy per kilomole FC2 (kW)
AUTHOR INFORMATION
Corresponding Author
REFERENCES
(1) Luyben, W. L.; Luyben, M. L.; Tyreus, B. D. Plantwide Process Control; McGraw-Hill: New York, 1998. (2) Luyben, W. L. Snowball effects in reactor/separator processes with recycle. Ind. Eng. Chem. Res. 1994, 33 (2), 299−305. (3) Shinskey, F. G. Process Control Systems; McGraw-Hill: New York, 1967. (4) Buckley, P. S.; Luyben, W. L.; Shunta, J. P. Design of Distillation Control Systems; Instrument Society of America, 1985. (5) Jagtap, R.; Kaistha, N. Economic plantwide control of a C4 isomerization process. Ind. Eng. Chem. Res. 2012, 51, 11731−11743. (6) Gera, V.; Panahi, M.; Skogestad, S.; Kaistha, N. Economic plantwide control of the cumene process. Ind. Eng. Chem. Res. 2013, 52, 830−846. (7) Jagtap, R.; Pathak, A. S.; Kaistha, N. Economic plantwide control of the ethyl benzene process. AIChE J. 2012, doi: 10.1002/aic.13964. (8) Cutler, C. R.; Ramaker, B. L. Dynamic matrix control: A computer control algorithm. 86th AIChE National Meeting, Houston, 1979. (9) Ricker, N. L.; Lee, J. H. Nonlinear model predictive control of the Tennessee Eastman challenge process. Comput. Chem. Eng. 1995, 19, 961−981. (10) Downs, J. J.; Vogel, E. F. A plantwide industrial process control problem. Comput. Chem. Eng. 1993, 17, 245−255. (11) Ricker, N. L. Decentralized control of the Tennessee Eastman challenge process. J. Process Control 1996, 6, 205−221. (12) Amrit, R.; Rawlings, J. B.; Angeli, D. Economic optimization using model predictive control with a terminal cost. Annual Reviews in Control 2011, 35, 178−186. (13) Angeli, D.; Amrit, R.; Rawlings, J. B. On average performance and stability of economic model predictive control. IEEE Trans. Autom. Control 2012, 57, 1615−1626. (14) Glattfelder, A. H.; Schaufelberger, W. Control Systems with Input and Output Constraints; Springer: Berlin, 2003. (15) Luyben, W. L. Design and control of the ethyl benzene process. AIChE J. 2011, 57 (3), 655−670.
and benzene impurity in the product EB (xBzD2) for the entire response in Figure 11. The IAE is calculated as deviations from the respective initial steady-state PV values. The significantly lower IAE values using external reset show the marked improvement in dynamic control. To quantify the economic benefit, the backed-off nominal and bottleneck constrained set points for U1 and U2 along with the steam consumption per kilogram of product for a steady FC2 of 630.6 kmol/h (initial steady state in Figure 11) and the maximum achievable throughput are also listed in Table 5. The use of internal reset causes the steam consumption per kilogram of product to be 2.3% higher and the maximum achievable throughput to be 5.9% lower than those of the external reset. To quantify the economic implications of benzene impurity regulation in the EB product, we also report the percentage of EB product that is above the maximum allowed 0.1 mol % benzene impurity level. While all the EB product is within spec for the entire transient period when external reset feedback is implemented, ∼3.2% of the product is off-spec when internal reset feedback is implemented. These results together suggest that the economic benefits of process operation using external reset in terms of energy efficiency, maximum achievable throughput, and product quality control are significant.
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CONCLUSIONS The examples presented in this paper have demonstrated quantitative dynamic control and economic benefits of applying external reset feedback in PI controllers used in override control systems used for handling process constraints. Results show that the overall transient response is significantly smoother, which allows process operation to be driven closer to hard process constraints. This usually leads to one or more economic benefits in terms of significantly higher maximum achievable throughput, improved energy efficiency, and tighter product quality control. Override controllers have a wide area of application because the optimal operation of most processes 9664
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