Ind. Eng. Chem. Res. 2005, 44, 2241-2249
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Limitations in the Operation and Control of Continuous Middle-Vessel Distillation Columns with a Draw Stream Rosendo Monroy-Loperena, Rocio Solar, and Jose Alvarez-Ramirez* Departamento de Ingenierı´a de Procesos e Hidra´ ulica, Universidad Auto´ noma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340 Distrito Federal, Me´ xico
This paper studies the limitations in the operation and control of a continuous middle-vessel distillation column with a draw stream in the middle vessel. This separation layout can be of interest to cases where the most and less volatile components of fractions of a mixture are desired in high concentrations, as in the processing of some oil streams. It was found that to maintain distillate and bottoms products within specifications, large recycling rates can be required to compensate for the storage effects of the middle vessel. This is because, contrary to the case where a draw stream is not present, in the studied distillation column layout the middle vessel alters material balances. In this form, the middle vessel acts as both a dynamical damper to reduce bottoms and distillate control loops and an accumulator for intermediate fractions. That includes some residuals of nonseparated most and less volatile components. The control objective is to track prescribed product compositions of the most and less volatile components by means of manipulations of the reflux and vapor boilup rates. Given that the middle vessel introduces a sluggish controlled response, the recycling stream from the middle vessel to the column is taken as an additional control input to improve the operation of the column and the control performance. In this way, a rectangular control configuration is obtained, which is regularized (i.e., squared) with a habituating control parameter. It is shown that this habituating control configuration can satisfy the control objectives more easily because it provides a balance between the separation and mixing tasks provided by the distillation column and the middle vessel, respectively. Introduction Batch distillation is usually preferred for low throughputs when fine or specialty chemicals and intermittent or seasonal chemicals are produced. In contrast, continuous distillation is favored for large-scale throughputs and continuous upstream feeds. Recently, an unconventional type of batch distillation column, named middle-vessel batch distillation, consisting of a rectifying and a stripping section with a feed tray in the middle, has been studied.1,2 The liquid feed is charged into an intermediate vessel, and a liquid stream is continuously recycled between the feed/withdrawal tray and the feed vessel, so that the compositions of the liquid streams in the feed tray and in the feed vessel are kept close (see Figure 1). This class of columns combines some interesting features of both batch and continuous distillation columns. In fact, liquid streams can be continuously withdrawn from the top and bottom of the column. Robinson and Gilliland1 proposed for the first time the use of a middle vessel in distillation processes. Subsequently, Bortolini and Guarise2 carried out an analysis of the dynamics and operability of the process. Since the work of Takamatsu et al.,3 who apparently rediscovered the process, a number of papers have been published dealing with middle-vessel batch distillation columns. Recently, Barolo and Papini4 studied the dualcomposition-control problem of continuous middle-vessel * To whom correspondence should be addressed. Tel.: +52(55)5804-4900. Fax: +52(55)5804-4650. E-mail: jjar@ xanum.uam.mx.
distillation columns (CMVDCs) with different control configurations, which are commonly used in conventional continuous distillation, showing that the middle vessel provides a way to reduce the interaction between the composition loops. As a result, the control performance of middle-vessel columns may be made remarkably superior to that of conventional columns. Phimister and Seider5 expanded Barolo and Papini’s work by showing that inoperable configurations for dual composition control in conventional continuous distillation, where the distillate and bottoms flows are manipulated, can be efficiently handled with CMVDC, obtaining a quite good performance. A CMVDC configuration is proposed to enhance the control performance for binary (or quasi-binary) mixtures.4,5 The middle-vessel task is to improve the decoupling properties between the distillate and bottoms control loops. On the other hand, it is well-known that sharp separation of a ternary mixture can be made in a two-distillation-column configuration. At this point, one can ask to what extension a ternary mixture can be separated in only one column configuration, maybe using a draw stream. Of course, it is clear that, in general, a sharp separation cannot be obtained with only one column configuration. Given this fact, one should consider weaker separation conditions where sharp separation of, at most, two components is obtained. In this work, we will consider a distillation column with a draw stream to obtain the most and less volatile components as almost pure products at distillate and bottoms flows, respectively. In this way, the draw
10.1021/ie030867g CCC: $30.25 © 2005 American Chemical Society Published on Web 03/08/2005
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Figure 1. Schematic diagram of the CMVDC.
stream carries intermediate components and some residuals of separated (light and heavy) components. These types of separation processes can be of interest for the petroleum industry, where the lighter component can represent gasolines (i.e., C5-C7 components) and the bottoms product can represent asphaltenes. The intermediate product obtained from the draw stream can be fed to a subsequent separation and/or reacting equipment to obtain secondary petrochemical products. To avoid excessive coupling between control loops when almost pure compositions are desired and motivated by the works of Barolo and Papini4 and Phimister and Seider,5 we will endow the column with a middle vessel where the draw stream is located (see Figure 1). In some sense, we can consider the studies of distillation column layout as a simplified (i.e., stylized) model of the very
complex atmospheric distillation columns. In this form, our results suggest some guidelines to address the control problem of such separation equipment used in the oil industry. This layout has an additional control degree of freedom that can be exploited to enhance the performance of dual composition control. Specifically, the recycle stream from the middle vessel to the column is proposed to be used as an additional manipulated input aimed at enhancing the operability of the column and the performance of the dual composition control. This results in a rectangular control problem with more manipulated inputs than regulated outputs. The problem of synthesizing feedback controllers for processes that employ more manipulated inputs than controlled outputs (i.e., rectangular systems) has at-
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tracted the attention of the control process community. The motivation relies on the fact that additional control inputs are commonly available in practice, which can alleviate the control effort devoted by single-input controllers. Several strategies have been proposed in the standard control literature. Henson et al.6 have provided a nice discussion on the characteristics and drawbacks of these control techniques. Briefly, such techniques include valve position control,7 coordinated control,8 parallel control,9 and H∞ control.6 As has been pointed out by Henson et al.,6 the design procedures proposed for valve position, coordinated, and parallel control techniques are largely ad hoc. On the other hand, H∞ control has a certain heuristic burden because obtaining an acceptable control technique involves significant designer effort to select (ad hoc) appropriate frequencydomain weighting functions.10 In view of these features, Henson et al.6 proposed a systematic controller synthesis methodology motivated by the habituating control system responsible for mammalian blood pressure regulation. The underlying idea is to exploit specific characteristics and operating objectives of a process with different types of manipulated variables: (i) a slow, inexpensive type and (ii) a fast, expensive type. The final result is a habituating control architecture that can be seen as a generalization of the series7 and parallel9 control architectures. In a subsequent paper, McLain et al.11 extended the habituating control methodology to the case of nonlinear processes. In the nonlinear case, the habituating input-output feedback linearizing controller was obtained by minimizing the cost of affecting control. The above results constitute an important advance in the understanding of the dynamics of rectangular systems and in the design of feedback controllers for processes with more control inputs than regulated outputs. In particular, the habituating control strategy offers a framework for a systematic design of redundant controllers.6 The purposes of this work can be described as follows: (i) to study some limitation issues on the operability of CMVDC with the proposed layout and (ii) to use a habituating control approach6,12-16 to improve the performance of CMVDC when the control objective is to track prescribed product compositions via manipulations of the reflux rate, the vapor boilup rate, and the flow rate of the recycle stream from the middle vessel to the column. Rigorous nonlinear numerical simulations are used to illustrate the performance of the proposed controller under typical operating conditions. Process Description and Analysis In general, a CMVDC is a distillation column with a large vessel placed between the rectifying and stripping sections. Referring to Figure 1, a liquid stream, S, from the rectifying section is sent to an external middle vessel. Variations to this configuration include the use of a partial-liquid side draw, a heat stream added to the middle vessel, and the transmission of a vapor stream from the stripping section of the column to the middle vessel. The middle vessel is also provided with another three streams: an input feed stream, F, and two streams to dump it (one from the middle vessel, E, and a recycle stream from the middle vessel to the column, R). One important feature of this type of
distillation process is that at steady-state conditions the distillation column has to meet the constraint R - S ) D + B > 0, which implies that one can manipulate the product flow rates by means of the recycling and side stream difference. The motivation to use a middle-vessel distillation column can be explained as follows. Consider a separation of three components, which are ordered according to their relative volatilities. Despite the fact that continuous distillation operation can be carried out at total reflux conditions, it is expected that the composition of the side stream, S, which goes to the middle vessel, has a larger amount of impurities of components 1 and 3. Besides, stream S is mixed with stream F in the middle vessel, which limits the separation of component 2 as a nearly pure product. Nevertheless, one can expect that continuous operation in a middle-vessel configuration can separate the most and least volatile components to nearly pure provided the conditions D < z1F and B < z3F are met, making this configuration attractive for the separation of two components from a multicomponent mixture to two nearly pure products using only one distillation column. In the following, we will consider the continuous operation of a middle-vessel distillation column with dual composition control where the control objective is to track prescribed product compositions via manipulations of the reflux rate and the vapor boilup rate. To achieve the control objective, an LV configuration (also called the energy-balance configuration) is considered, where the reflux rate (L1) is used to control the overhead purity (xi,1, where i refers to the component of interest and 1 to the condenser stage) and the vapor boilup rate (V) is used to control the bottoms composition (xj,N, where j refers to the component of interest and N to the reboiler stage). In practice, however, the heat supply to the reboiler is manipulated instead of the vapor boilup. Although the LV configuration may not be the best one from the point of view of coupling between control loops,17 it is a commonly used control structure for dual composition control18 because it is simple to implement, easy to understand, and widely accepted among operators. For these reasons, the LV configuration will be considered in detail in this work as a base case study. However, it should be stressed that other control configurations can be studied along the same lines. From a plantwide control point of view (see, for instance, work by Luyben19), the control degrees of freedom are the number of variables that can be manipulated. In general, this number is very easy to calculate, even for quite complex processes, because it is equal to the number of manipulated variables that are equal to the number of control valves in the process. Therefore, whenever one finds a tank that serves only as a surge with no flow splitting of its exiting stream, one cannot count the control valve on this stream in the calculation of the net control degrees of freedom. Referring to Figure 1, for the CMVDC when a draw stream in the middle vessel is present, there exists an additional control degree of freedom that can be exploited to enhance the performance of dual composition control. Specifically, the recycle stream from the middle vessel to the column is proposed as a manipulated input for feedback purposes. In this way, one has 7 control degrees of freedom, namely, the following: Valve v1 is typically used to set the production rate (that is, setting
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the fresh feed flow F), and valves v2 and v3 are used to control the liquid level of the reflux drum and the liquid level of the sump of the tower, respectively (that is, holdup controllers). For a LV dual composition configuration, valves v4 and v5 are used to control the purity of the top and bottom products by manipulating the reflux rate and the heat supply to the reboiler, respectively. Valve v6 is used to control the liquid level of the middle vessel; meanwhile, valve v7 can be used to manipulate the recycle stream from the middle vessel to the column, R. In turn, this recycle stream can be used to regulate either the distillate composition or the bottoms composition. In this way, the idea that will be exploited in the following is to use the additional control input R to distribute the control effort between the column and the middle vessel. In the next section, such a control configuration design will be made with the aid of habituating control approaches. Statement of the Control Problem by a Habituating Approach Let us propose an input/output linear process with more manipulated inputs than controlled outputs. The underlying premise is that the control objectives can be satisfied more easily by utilizing additional input variables. Following standard ideas from single-column distillation processes (see, for instance, Chien et al.20 and Skogestad et al.21): a simple one-time-constant model for the CMVDC can be used, because the middle vessel induces a sort of averaging in the time constants of the column, as will be shown hereafter by carrying out step responses. Hence, by considering a time delay θ, one has that
1 Ku exp(-θs) y) 1 + τ0s
(1)
B T T where y ) {xD 1 , x3 } and u ) {L, V, R} are specified as deviation variables. In addition, τ0 is the open-loop dominant time constant, and K ∈ R3×2 is the process steady-state gain matrix. The nonsquare 3 × 2 input/ output model can be described as follows:
y1 ) y2 )
1 [K u + K1,2u2 + K1,3u3] exp(-θs) 1 + τ0s 1,1 1
1 [K u + K2,2u2 + K2,3u3] exp(-θs) 1 + τ0s 2,1 1
(2)
System (2) is a rectangular control system with more manipulated inputs than regulated outputs. Specifically, system (2) has 1 degree of freedom that can be exploited to enhance the control performance and process operation and flexibility. Commonly, if one fixes the control input u3, the control system (2) becomes a standard LV (2 × 2 square) control system, for which well-known control techniques [e.g., internal model control (IMC)22] can be used for control design. In the nonsquare case, one has to specify a strategy for the additional control input u3. One alternative is to use a sort of regularization technique to square the rectangular control system (2). We propose to split the input/output model by
introducing a habituating parameter, β, as follows:
y1 )
1 [K u + K1,2u2 + K1,3u3] exp(-θs) 1 + τ0s 1,1 1
y2,1 )
1 [K u + K2,2u2 + βK2,3u3] exp(-θs) 1 + τ0s 2,1 1 y2,2 )
(1 - β)K2,3u3 exp(-θs) 1 + τ0s
(3)
where
y2,1 ) βy2 y2,2 ) (1 - β)y2
(4)
so that y2 ) y2,1 + y2,2. Notice that the control output signal y2, corresponding to the composition of the bottoms product, has been partitioned into two components: y2,1 and y2,2, corresponding to fractions of the regulated output y2 affected respectively by the control inputs u2 and u3. Physically, this splitting of the controlled output y2 can be seen as a distribution of the control effort between the heat supply to the reboiler and the recycle stream from the middle vessel to the column. By introduction of the variables
z1 ) y1 z2 ) y2,1 z3 ) y2,2
(5)
the resulting nonsquare 3 × 2 input/output model can be expressed as a square 3 × 3 input/output model, namely
z)
1 Bu exp(-θs) 1 + τ0s
(6)
where the square steady-state gain matrix is given by
[
K1,1
K1,2
K1,3
B ) K2,1
K2,2
βK2,3
0
(1 - β)K2,3
0
]
(7)
Note that, to obtain a regular control system, the matrix B must be invertible, which implies that the determinant ∆B ) (1 - β)K2,3[K1,1K2,2 - K1,2K2,1] * 0. Therefore, the habituating parameter β * 1, and the process gain K2,3 * 0. Besides, the process gain of the LV nonhabituating process must be invertible; that is, ∆* ) K1,1K2,2 - K1,2K2,1 * 0. For this type of process, a classical multi-input multioutput (MIMO) proportional-integral (PI) controller tuned with IMC tuning guidelines can be used. In fact, if
(
u ) Kc I +
)
1 Ie τIs
(8)
is a multivariable PI controller, then the following
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assignments can be used:22
Table 1. Case Study Configuration
Kc ) [τ0/(τc + θ)]M
(9)
τI ) ω1τ0, 0.5 e ω1 e 1
(10)
τc ) ω2τ0, 0.5 e ω2 e 0.75
(11)
where M is a control gain matrix, τc is a desired closedloop time constant, I is the identity matrix, and e ) zref - z is the regulation error, with ref zref 1 ) y1 ref zref 2 ) βy2
zref 3
) (1 -
β)yref 2
(12)
where superscript ref indicates the reference value (i.e., set points). When unnecessary computations, which are beyond the scope of this paper, are avoided, it can be seen that the stability of the controlled process is completely determined by the stability of the closed-loop matrix BM. In fact, a sufficient condition for the stability of the controlled system (8) is that BM must be an antistable matrix (BM must have all of its eigenvalues in the right-half complex plane). This condition can be interpreted as the preservation of control input directionality by the assigned control gain matrix. A straightforward selection to meet such a sufficient stability condition corresponds to the so-called inverse controller where M ) B-1, such that BM ) I. In some special cases of MIMO processes, one can exploit the structure of the matrix B to provide a diagonal M that guarantees the antistability of the matrix BM. For instance, we can consider decentralized control by choosing M ) diag(b1,1-1, b2,2-1, b3,3-1). Therefore
[
1
K1,2 1 K1,3 K2,2 1 - β K2,3
BM ) K2,1 1 K1,1 0
0
β 1-β 1
]
(13)
with determinant ∆BM ) 1 - K1,2K2,1/K1,1K2,2 * 0 and a characteristic polynomial given by
s3 - 3s2 -
(
) (
)
K1,2K2,1 K1,2K2,1 -3 s- 1)0 K1,1K2,2 K1,1K2,2
(14)
Interestingly, the characteristic polynomial (14) does not depend on the habituating parameter β. In this way, if the characteristic polynomial (14) is antistable, the controlled process given by eqs 6 and 8 is stable regardless of the habituating parameter β. This can be seen as a sort of robustness property of the control scheme with respect to the distribution of the control effort between the different control inputs. In this way, variations of the habituating parameter β only have effects on the performance but not in the stability of the habituating control strategy. Notice that the habituating parameter β is used to balance the control effort between the vapor flow rate and the middle-vessel recycle stream. In this way, for β
specifications stages, including condenser and reboiler recycle and side-stream stages feed flow rate (F) [mol/h] side-stream rate (S) [mol/h] recycle flow rate (R) nominal distillate product; component 1 (x1,1) [mole fraction] nominal distillate product; component 2 (x2,1) [mole fraction] nominal distillate product; component 3 (x3,1) [mole fraction] nominal bottoms product; component 1 (x1,N) [mole fraction] nominal bottoms product; component 2 (x2,N) [mole fraction] nominal bottoms product; component 3 (x3,N) [mole fraction] condenser holdup [mol] reboiler holdup [mol] stage holdup [mol] middle-vessel holdup [mol] nominal reflux (L1) [mol/h] nominal vapor boilup (V) [mol/h] hydraulic time constant (τh) [s]
35 17 10 22 30 0.7640 0.2360 0.0 0.0 0.2622 0.7378 10.0 10.0 1.0 100.0 26.0 30.0 4.0
) 1, one recovers the standard LV configuration. On the other hand, for β ) 0, one sees that all of the control effort to regulate the bottom product composition is devoted by the middle-vessel recycle stream. The former results in an expensive (because of vapor generation) option, while the second, although inexpensive, can lead to a sluggish closed-loop response. To balance this tradeoff situation, β should take values of around 0.5. In this form, it is expected that manipulation of the middlevessel recycle stream can help the feedback controller to reduce the vapor usage. Numerical Simulations In this section, we will consider the problem of the separation of an equimolar mixture of a ternary ideal mixture, where the components are ordered according to their relative volatilities and are referred to as component 1 for the most volatile and component 3 for the least volatile. The components have the following relative volatilities: RT ) [9, 3, 1]. According to the CMVDC column described in Table 1, several numerical simulations using a model based on the usual collection of material balances, vapor-liquid equilibrium relationships, and liquid hydraulics correlations (see, for instance, Monroy-Loperena and Alvarez-Ramirez23), where the assumptions of negligible vapor holdup, theoretical trays, perfect mixing on trays, constant operating pressure, total condensation with no subcooling, and adiabatic operation are made. Energy balance for the column is not performed. A constant molar overflow assumption is used, but the model takes into account the dynamics of the molar holdups on each tray, and the internal liquid rate on each stage is determined by means of the linearized version of the Francis weir formula:
Lk ) L ˜k +
Mk - M ˜k τh
where L ˜ k and M ˜ k are nominal liquid flow rate and holdup in the k tray, respectively, and τh > 0 is the hydraulic time constant. The input/output model parameters τ0 and K were estimated from step responses (see Figure 2), where the
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Figure 2. Step response of the CMVDC under a (2% disturbance in the control inputs.
following estimates were obtained: τ0 ) 5h and
K)
[
0.211 903 1 -0.165 246 0.034 068 -0.161 634 0.216 183 -0.119 631
]
Referring to Figure 2, notice that a variation of the flow rate of the recycle stream, R, affects the bottoms composition in the same range as those of variations of the reflux rate or the vapor boilup. This means that the distillate composition is less sensitive to the variations of the recycle stream, R. Resorting in this observation, we will take the bottoms composition to be habituated with the vapor boilup and the recycle flow rate. Consider the following conditions and parameters to be used in the proposed control scheme to regulate the distillate and bottoms compositions: (1) The regulation task will consist of keeping the composition of component 1 in the distillate as x1,1 ) 0.9 and the bottoms composition for component 3 as x3,N ) 0.9. (2) The IMC tuning parameters are taken as ω1 ) ω2 ) 0.5. Under this set of control parameters, the following numerical simulations were carried out: 1. Effect of the fresh feed flow rate over a traditional LV dual composition control configuration. Figure 3 shows the internal vapor boilup rate, V, and the reflux rate, L1, as functions of the fresh feed flow rate, F, for different values of the recycle flow rate, R, when the column is providing the regulation dual composition task, keeping the composition of component 1 in the distillate as x1,1 ) 0.9 and the bottoms composition for component 3 as x3,N ) 0.9, by manipulating the reflux rate, L1, and the vapor boilup, V, respectively. Notice the large effect of the middle vessel as a mixing tank. In fact, the main effect of the mixing tank is to average composition dynamical variations by mixing the com-
Figure 3. Internal vapor boilup rate, V, and the reflux rate, L1, as functions of the fresh feed flow rate, F, for different values of the recycle flow rate, R.
position of the feed to the column, reflected in the stream R. Note that for small feed rates the internal flows of the column are large because small amounts of the desired products (components 1 and 3) are introduced to the system. In turn, this effect is compensated for by the column by means of a large recycling (larger separation task) to preserve the distillate and bottoms
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Figure 4. Internal vapor boilup rate, V, and the reflux rate, L1, as functions of the recycle flow rate, R, for different values of the product composition, when the side-stream flow rate, S, is fixed to 20 mol/h.
flow rates (recall that R - S ) D + B) required to achieve the regulation dual composition task. As the fresh feed flow rate is increased, the separation task of the distillation column tends to decrements in favor of the mixing task of the middle vessel. This suggests that a habituating control approach can be used to balance the separation and the mixing task provided by the column and the middle vessel, respectively. Notice that, in general, the former task is more expensive than the latter. 2. Effect of the recycle stream over the internal flow rates. Figure 4 shows the reflux rate, L1, and the internal vapor boilup rate, V, as functions of the recycle flow rate, R, when the side-stream flow rate is fixed at 20 mol/h, for different specifications of the product compositions. Notice that, in general, the recycle stream, R, has a large effect over the internal flow rates. That is, for a small change of the recycle stream, a large change is reflected over the internal flow rates for a fixed composition in the distillate and bottoms products using a LV dual composition control configuration. Hence, one can expect that when this recycle stream is manipulated, one can achieve lower requirements to get the prescribed product compositions. 3. Inverse control. To show the performance of the proposed habituating approach with respect to a traditional LV dual composition control configuration, let us consider a common operating situation where, after 500 h of normal operation, the composition of the fresh feed is changed from equimolar to zT ) [0.4, 0.2, 0.4]. Referring to Figures 5 and 6, the standard LV configuration provides a smooth behavior in the manipulated variables (reflux rate, L1, and vapor boilup, V). However, an excessively long time is necessary, nearly 1000 h, to reach the steady state induced by the cushion effect of
Figure 5. Response of the regulated outputs under inverse PI control.
Figure 6. Response of the control inputs under inverse PI control.
the middle vessel. In contrast, when the proposed habituated control scheme is used and the habituating parameter is fixed to β ) 0.5 (that is, equidistribution of the control effort), a smooth behavior in the manipulated variables (reflux rate, L1, vapor boilup, V, and recycle flow rate, R) is observed. However, the time necessary to reach the steady state has been reduced
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Figure 7. Response of the regulated outputs under decentralized PI control.
drastically to near 30 h. Notice also that less variations in the manipulated variables are necessary because of the balanced task between the distillation column and the middle vessel. To illustrate the beneficial effects of habituating control in the column operation, let us consider the following situation. Assume that after 3000 h of operation it is decided to change the set points of the distillate product and bottoms product to 0.95. In this situation, the proposed habituated controller leads to a better performance over the traditional LV control configuration. In general, the habituated control scheme drives the column to have smaller internal flow rates than those of the traditional LV configuration because of the balance of the mixing task provided by the middle vessel and the separation task provided by the distillation column. In turn, this habituating control based operation of the distillation column will resound in economic savings because less refrigerant and heat agents will be used. It should be mentioned that we have presented only the behavior for a habituated parameter β ) 0.5. However, the habituated control scheme was tested for different values, yielding similar results mainly because of the large effect that the middle vessel has on decoupling of the control signals (with respect to this point, see the interesting work by Farschman and Diwekar24 for middle-vessel batch distillation columns). 4. Decentralized control. Decentralized controllers are often preferred, in practice, because they are robust and relatively simple to understand and tune. The proposed traditional LV dual composition control configuration and the habituated control configuration can be easily transformed to a decentralized form (single-loop controllers) by taking the matrix M as diagonal, avoiding the range of the matrix involved in each configuration. Figures 7 and 8 show the behavior of the CMVDC for the same changes in the operation conditions as those used in the inverse control case. Nevertheless, although
Figure 8. Response of the control inputs under decentralized PI control.
the diagonal controller gives an acceptable behavior, one can observe that a better behavior is obtained with more information for the traditional LV dual composition control configuration. However, the diagonal habituated control scheme presents a behavior very similar to that of the full habituated control scheme because it has a better advantage over the decoupling of the control signals. Conclusions Through the analysis of CMVDC when a draw stream in the middle vessel is present, one can expect that this configuration is appropriate for the separation of the most and less volatile components using only one column. A habituating control approach was used to balance the separation and mixing tasks provided by the distillation column and the middle vessel, respectively. This resounds in economic savings because the separation task provided by the column is more expensive than the mixing task provided by the middle vessel. The main idea was to manipulate simultaneously the flow rate of the recycle stream from the middle vessel to the column and the vapor boilup rate to regulate the bottoms product composition to distribute the control effort among the middle vessel and the distillation column. As a result, under expected operating conditions (that is, a change in the charge composition to the CMVDC and a change in the set point), the disturbances are reduced by means of relatively small changes in the internal flows of the column, giving as a consequence a better performance with respect to the traditional LV dual composition control configuration. Literature Cited (1) Robinson, C. S.; Gilliland, E. R. Elements of Fractional Distillation; McGraw-Hill: New York, 1950.
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Received for review December 7, 2003 Revised manuscript received November 10, 2004 Accepted January 28, 2005 IE030867G
