Startup of Distillation Columns Using Profile Position Control Based on

startup of distillation systems using nonlinear wave model based control ... variables and is based on the nonlinear wave model by Hwang (AIChE J. 199...
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Ind. Eng. Chem. Res. 1999, 38, 1565-1574

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Startup of Distillation Columns Using Profile Position Control Based on a Nonlinear Wave Model Myungwan Han and Sunwon Park* Chemical Engineering Department, Chungnam National University, Taejon 305-764, Korea, and Chemical Engineering Department, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea

Startup of distillation columns is a very challenging control problem because of its strong nonlinearity and a wide operating range during the transient period. A nonlinear wave model captures the essential dynamic behavior of the distillation process so that it is possible to deal with the difficulties encountered during startup operation. This paper is concerned with the startup of distillation systems using nonlinear wave model based control developed by Han and Park (AIChE J. 1993, 39 (5), 787). This control scheme uses profile positions as controlled variables and is based on the nonlinear wave model by Hwang (AIChE J. 1991, 37, 705) and generic model control scheme by Lee and Sullivan (Comput. Chem. Eng. 1988, 12, 573). It can be applied to a binary or a multicomponent distillation system that can be represented as a pseudobinary. The proposed control scheme is shown by simulation studies to provide a safe and economic startup operation not only for dual composition control of a simple distillation column but also for a complex distillation configuration. Introduction Startup of distillation columns is a challenging control problem because of its strongly nonlinear transition nature as well as the wide range of operating conditions. During startup there are very drastic changes in state variables so that in many cases it is difficult to apply a linear controller over the wide operating range. The dynamic behavior of distillation during startup operation can often be viewed as a very large change in setpoint or large disturbance (Ruiz et al.1 and Ganguly and Saraf2). A good model to represent the dynamic behavior may be a prerequisite for a safe and economic startup operation. The control objective for startup operation is reduction of waste products, reduction of startup time, and reduction of utility consumption. Several researchers have studied the startup policy for distillation columns. Camelon et al.3 and Ruiz et al.1 have studied distillation column startup using manual control, especially the dynamic behavior during startup operation and proposed appropriate startup policies based on the dynamics. They divided the startup period into three phases: discontinuous, semicontinuous, and continuous. Yasuoka et al.4 presented a simple characteristic function for determining the optimal switching time from total reflux to steady-state operation of a distillation column. The characteristic function is the sum of the difference between the present and steadystate liquid compositions at each tray. Barolo et al.5 have proposed an on-line control algorithm for the startup of a binary distillation column based on generic model control. They have selected the inventory of the light component from the top to any convenient intermediate plate in the enriching section of the column as a controlled variable. This idea was drawn to control the temperature profile position along the column. Barolo et al.6 modified the algorithm based on the GLC algorithm instead of the GMC algorithm. Fieg et al.7 * To whom correspondence should be addressed.

used an approach similar to that of Yasuoka to minimize the time necessary from initial startup or product switch over to steady-state operations. Ganguly and Saraf2 have applied nonlinear analytical model predictive control to distillation column startup between the time when the trays are hydraulically sealed and the time when steady-state operation is reached. These previous studies have been limited to the startup of only one section in a distillation column, e.g., the rectifying section. Most control schemes need very careful and conservative tuning for the control parameters. In this study, we provide a control policy based on the nonlinear wave propagation model for the startup of distillation columns. The distillation systems used for our study have two sections (simple distillation column) and four sections (complex distillation configuration) so that the startup operation is very difficult and the interaction becomes severe as the product purity goes high. The simulation studies show that the proposed control scheme can improve the startup operation of the distillation columns substantially. Profile Position Control Design of optimal control strategies during the transient phase of a distillation startup requires a model representing the dynamic behavior of the distillation column. Ruiz et al.1 reported that the startup operation consists of three phases according to the dynamic behavior of the column during startup. (i) The discontinuous phase: During this phase, hydraulic variables experience drastic changes and the sealing of downcomers from vapor flow and sealing of plate holes from liquid flow occur. (ii) The semicontinuous phase: Thermodynamic variables undergo sharp changes, and the hydraulic variables undergo small changes. The trays are hydraulically sealed, and the column gets shifted from total reflux conditions to the required reflux rate. The dynamic behavior during this period is equivalent to the behavior of a column subjected to large disturbances.

10.1021/ie980444s CCC: $18.00 © 1999 American Chemical Society Published on Web 03/11/1999

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moving the profile to the desired point from the ends of the column. During the startup, the profile propagates while maintaining the original shape, which can be interpreted as a “wave”. Here the wave is defined as a spatial structure moving at a constant propagation velocity with a constant shape along a spatial coordinate (Marquardt8,9). During the transition phase, the column temperature or composition profile propagates with a small change of the profile shape to a steady-state one. Therefore, to make the profile coincide with that at the desired steady state, it is very important to locate the profile position at the desired spatial point. The travel of such a constant pattern wave can be characterized by shock wave velocity developed by Hwang.10 Han and Park12-14 have developed a control scheme using the velocity equation to control the profile position at a spatial position in the column. The column operation for startup needs the control policy to move the column profile to the desired spatial point along the column. In this sense startup operation can be regarded as tracking the position of the composition or temperature profile to the desired one. The approach using the profile position as a controlled variable during the startup operation should improve the operation considerably. Startup operation experiences very large changes on a wide operating range such that the controller used in startup operation is often differentiated according to the phase of the startup operation (Ruiz et al.1 and Ganguly and Saraf2). The proposed control scheme does not require switching the controller from startup operation mode to the steady-state operation mode because the controller can deal with large setpoint changes and disturbances and is robust on the wide operating range. Figure 1. Propagation of the column composition profile during startup using total reflux: (a) composition; (b) temperature.

(iii) The continuous phase: The operation during this period is similar to maintaining the operation of a distillation column around a steady state subject to small disturbances. At the end of this stage, all variables reach their steady-state values. The time period of the first stage is very short and independent from the operational procedure employed, and the hydraulic stability conditions are satisfied during the first stage. During this period, total reflux operation is generally done and the effect of this phase on the whole startup is small. During this phase, concentration and temperature profiles develop gradually. At the second stage, the profiles have been developed already and the trays are sealed with vapor from reboiler, preventing the liquid from flowing through tray holes. Figure 1 shows propagation of column composition and temperature profile during total reflux operation for startup. The initial composition on each tray is assumed to be the same as the feed composition. This assumption is reasonable in that the thermodynamic variables start with constant values on all plates and gradually form profiles.1 Soon after the discontinuous stage, a composition or temperature profile has been developed. The profile, especially the portion with a sharp gradient, forms at the ends of the column and propagates to the center of the column, making the end compositions purer as time goes by. During this propagation, there is a little change in the shape of the profile. The process of distillation startup may be viewed as

Profile Position Controller Design for Startup Operation Recently, dynamics of the distillation column has been well explained as wave propagation theoretically as well as experimentally (Marquardt,8,9 Hwang,10 Hwang et al.,11 and Han and Park12-14). The concentration or temperature profile in the column section moves along the column after a disturbance occurs or a control action is taken with little variation of the profile shape. When we choose the profile position of a column section as the state vector in a generic model control equation (Lee and Sullivan15), the equation can be expressed as

∫0t(S* - S) dt′

dS ) K1(S* - S) + K2 dt

(1)

where S and S* are the profile position and its setpoint, respectively, and dS/dt is the propagation rate of the profile. The propagation rate of the profile can be written from the nonlinear wave model by Hwang10 as follows:

dS V ∆y/∆x - L/V ) u∆ ) dt F 1 + r(∆y/∆x)

(2)

A simple distillation column has a rectifying section and a stripping section. Combining eqs 1 and 2 gives one equation for each section

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V ∆y/∆x - L/V - K11(S/1 - S1) F 1 + r(∆y/∆x)

∫0t(S/1 - S1) dt ) 0

K12

(3)

V ∆yj/∆xj - L/V - K11(S/2 - S2) F 1 + r(∆yj/∆xj)

∫0t(S/2 - S2) dt ) 0

K22

(4)

where subscripts 1 and 2 represent rectifying and stripping sections, respectively. S* denotes the profile position for each section at which one wants to locate the profile, and it is determined by an operator or product composition controller. The profile position S and the slope of the equilibrium curve at the representative concentration (∆y/∆x) can be estimated by the profile position observer. Mass balance around the feed tray gives

L h ) L + qF;

V)V h + (1 - q)F

(5)

where q is the liquid mole fraction of the feed. Therefore, if we know the feed condition, L, V, L h , and V h can be determined from eqs 3-5. The proposed control scheme needs an observer for estimating the profile position for each section of the column. The observer incorporates the wave eq 2 into the form of a Luenberger type equation as follows:

S˙ )

dS dt

)

V ∆y/∆x - L/V F 1 + r(∆y/∆x) ∆y/∆x )

m

+

K1(T ˆ j) (T ˆ j - Tj) ∑ j)l

S˙ + L/F L/F - rS˙

(6) (7)

T ˆ j ) K2(Sj - S) + Ts

(8)

ˆ j - Ts)2] K1 ) K0 exp[-b(T

(9)

The observer computes the temperature of each measurement tray from the estimated profile position. The profile is assumed to have a linear form, as shown in eq 8, where Sj is the normalized distance at which the jth tray is located, Tj is the temperature at the jth tray, and Ts is the representative temperature. The feedback of the weighted output errors between the estimated and real temperatures provides a correction to the nonlinear wave model in eq 6. The details of the equations are given in the work by Shin et al.16 The proposed controller was tuned by using the GMC tuning procedure suggested by Lee and Sullivan.15 In summary, temperatures of several trays in the column are measured and the information is used for estimating the profile position of each section. The profile position is controlled by GMC to locate at the desired position along the column. Here, the liquid and vapor rates are manipulated for the control. The profile position controller (GMC) is used for instantaneous control to move the profile position to the desired location (S*) in the column. However, an offset from the setpoint in a product composition may occur when the profile position of the column is fixed at a specific point. Especially, during the startup, the temperature profile can experience a noticeable change in the profile shape. Besides, some model-plant mismatch in the proposed controller can bring about an offset from the setpoint in the temperature of the control tray.

Therefore, to remove the offset, a control tray temperature or product composition controller can be employed and cascaded as a primary controller to the profile position controller to remove the offset. A PI controller is used as the primary controller and provides a setpoint to the profile position controller. One should be cautious in tuning the control parameters for the primary controller because large control gain may even make the closed-loop system unstable. The primary controller was tuned by using the tuning method proposed by Lee et al.18 at the steady state with the profile position controller in the automatic mode and detuned to get stable operation. Results and Discussion Startup Procedure. Two startup procedures are commonly used in industry. The procedures are differentiated depending on whether the column base is full (“wet”) or empty (“dry”). Bertucco et al.17 and Ganguly and Saraf2 showed that startup time could be considerably shortened by filling the reflux drum as well as the column base with a feed mixture before the startup operation. The modified startup procedure is advantageous as indicated by Ganguly and Saraf2 in that the total reflux constraint does not exist so that the disturbance and delay caused by it are diminished. Furthermore, this policy allows a large reflux flow rate, which is often required at the beginning. We have chosen the modified startup procedure. The proposed controller begins its action soon after the hydraulic stability conditions are satisfied by total reflux operation. The initial tray compositions along the column are assumed to be equal and constant. Thermodynamic variables start with constant values on all trays and gradually form profiles as indicated by Ruiz et al.1 During startup, the profile moves up and down the column because of the disturbances that enter the column (feed and reflux flows and vapor flows). Startup Control. The common startup strategy in industry is to switch from manual operation during the total reflux condition to a standard PID controller to maintain the desired temperature on the control tray. We compare the performance of the proposed controller and the temperature control scheme. We use nonlinear rigorous simulations for the distillation column of Skogestad and Morari19 including linear liquid flow dynamics. The liquid flows depend on the liquid holdup on the stage above as the following:

Lj ) L0j + (Mj - M0j)/τ

(10)

where L0j and M0j are the nominal values for the liquid flow and holdup on stage j and the parameter τ is the hydraulic time constant. The condenser and reflux drum holdups are not assumed to be constant. The holdups are controlled by the P controller. The specification of the column is given in Table 1. The model used the following assumptions: binary separation, constant pressure and negligible vapor holdup, constant molar flows, linear liquid dynamics, equilibrium on all stages, total condenser. The sampling times for the profile position controller and PI controller were chosen as 1 min, and the one for the primary controller in the case of the cascade scheme was chosen as 3 min. The PI controller was tuned using the IMC tuning method in the steady-state operating point and detuned to get stable startup operation.

1568 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 Table 1. Steady-State Designs for the Simple Distillation19 relative volatility no. of theoretical trays (including reboiler and total condenser) feed tray (1 ) reboiler) feed composition feed liquid fraction operating variables

tray holdup reflux drum and reboiler holdup time constant for the liquid flow dynamics

1.5 40 21 0.5 qF ) 1 (saturated liquid) yD ) 0.99 xB ) 0.01 F )1 kmol/min D ) 0.5 kmol/min L ) 2.706 kmol/min V ) 3.306 kmol/min MOi ) 0.5 kmol MOcondenser ) 10 kmol MOreboiler ) 10 kmol τ ) 0.063 min

Figure 2. Dynamic temperature profiles of the control tray during startup.

Figure 2 shows the dynamic temperature profiles of control trays in the column during startup. The temperature on the control tray fluctuates during the transient period. It is due to the sudden introduction of feed, which takes the role of a big disturbance to the distillation system. The feed is introduced to the column after 1 min of the total reflux operation. The control trays are at 15th and 25th trays from the bottom. The feed disturbance begins to affect the system after several minutes have elapsed from the start of feeding because of tray liquid hydraulics. The proposed control scheme is shown to deal with such a big disturbance. The PI control gives a slow response to get to the setpoints. Figures 3 and 4 show the variations of temperatures on several trays of the column and profile positions during startup. The profile position control scheme moves each tray temperature fast to its steady-state value. The PI-startup procedure shows oscillatory temperature profiles, which produces a slow settlement to a desired steady state. This seems to be due to the lack of decoupling of the control actions in the control algorithm. Figure 4 shows that the two profile positions tend to move together, indicating also the lack of decoupling. Figure 5 gives the variation of the column temperature profile during startup. The proposed control scheme is shown to track the desired column temperature profile much faster than the PI temperature controller.

Figure 3. Dynamic temperature profiles during startup: (a) nonlinear wave model based control; (b) PI control

The control scheme using temperature on a given tray as a controlled variable has the following drawbacks. (1) Saturation problem: the effective range of temperature measurement point is limited because the temperature of the measurement drops to the boiling point of the low-boiling component as the profile drops below the measurement point but shows no change thereafter as the light component moves down the column. (2) High nonlinearity and interactions: distillation columns are very nonlinear and interacting so that multiloop control using temperatures on two given trays as controlled variables is not adequate for dual composition control during startup. Because of a large change in temperature on the controlled tray during startup, the control scheme often fails to achieve any meaningful control. Operation problems such as weeping, slugging, and channeling may occur during the startup, making the control action unstable or oscillatory. Therefore, the control action should have bounds to achieve smooth operation. The following characteristic functions were proposed by Yasuoka et al.:4 n

Mx )

|xij - xst ∑ ij | j)1

MT )

|Tj - Tst ∑ j | j)1

n

(11)

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Figure 4. Dynamic variation of the profile positions: (a) nonlinear wave model based control; (b) PI control.

where xij and Tj are the liquid composition and temperature of the ith component on the jth tray. This characteristic function is used for determining the optimal switching time from total reflux to steady-state operation of a distillation column. Figure 6 shows the variation of the characteristic function for each control strategy. The optimal switching operation strategy gives a comparable response to the approach of the profile position control but a little offset. However, it still needs the switching to the steady-state operation and cannot deal with disturbances during startup. The proposed approach shows no offset from the desired steady-state profile whereas the temperature PI control on some measurement tray gives a sluggish response. Disturbance Rejection. In Figure 7, feed composition changes from 0.5 to 0.7 at 20 min and returns to 0.5 at 30 min in a pulse manner. The profile position controller shows a performance superior to that of the conventional PI control. The profile position control is not greatly affected by the feed composition disturbance while the performance of the PI control deteriorates drastically and gives an offset from the setpoint. This indicates tight control of the profile positions, making the system stable in the presence of a disturbance. Robustness with the Model-Plant Mismatch and Measurement Errors. The model-plant mismatch can make the system unstable or yields the degradation of the system performance. Especially, the model-plant mismatch cannot be avoidable over the wide operating range during startup. Therefore, to

Figure 5. Propagation of the column temperature profile during startup: (a) nonlinear wave model based control; (b) PI control.

implement the control system during the startup of a distillation column, it is necessary to check the effects of the model-plant mismatch on the control performance. The nonlinear wave model has two possible model-plant mismatches: relative volatility and input uncertainty. In many cases we do not obtain the accurate values of both the relative volatility and input uncertainty mainly because of variations in pressure and some measurement errors in the liquid and vapor flow rates. In Figure 8, the profile position control scheme yields an offset from the setpoint temperature of the control tray for the error of relative volatility. The offset increases with the error of relative volatility. We use a cascade control scheme to eliminate the offset. The primary controller controls a temperature of the control tray in each section and gives a setpoint to the profile position controller. The cascade control scheme was activated at 30 min because some time was required until the system stabilizes. A sudden change of the setpoint for the profile position control during the transient period can make the system unstable. The offset is shown to be eliminated by the cascade control scheme. The input uncertainty is defined as the following:

∆L ) (1 + ∆1)∆Lc;

∆V ) (1 + ∆2)∆Vc

(12)

Here ∆L and ∆V are the actual changes in manipulated variables, and c denotes the computed value of the

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Figure 8. Startup in the presence of model-plant mismatch (relative volatility).

Figure 9. Startup in the presence of model-plant mismatch (input uncertainty). Figure 6. Characteristic function: (a) nonlinear wave model based control; (b) PI control; (c) total reflux policy; (d) switching operation.

uncertainty. For the input uncertainty, there is no offset from the setpoints but some sluggishness to get to the setpoints. The measurements of tray temperatures cannot often be accurate because of the noise in the real plant or pressure fluctuations in the column, especially during startup. The proposed control scheme uses the temperature measurements at several points of the column to estimate the profile position so that the control system is expected to be more robust than the temperature control scheme at one tray to the measurement errors. The use of several temperature measurements for the observer tends to dampen the noise in the temperature sensors. Furthermore, temperature measurements in the middle of the column, where the temperature profile is steeper, reduce the sensitivity to variations in pressure (Quintero-Marmol and Luyben21). Startup Strategy for Complex Distillation Configuration

Figure 7. Startup in the presence of feed composition disturbance.

manipulated variables by the controller. ∆ ) ∆1 ) -∆2 is selected to yield the worst combinations of the uncertainties (Skogestad and Morari20). Figure 9 shows the response of the controller for the error of the input

Complex distillation configurations have been shown to be more energy-efficient than a simple distillation structure. However, operation and startup of these configurations pose more challenging control problems than an ordinary distillation column because of the complexity of the process. Furthermore, multicomponent mixtures are usually separated in the complex configurations, and the model-based approaches have not been

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Figure 10. Schematic diagram of a complex distillation configuration. Table 2. Steady-State Designs for the Complex Distillation Configurations feed flow rate feed temperature composition feed distillate bottom side feed tray (from base) sidedraw tray total no. of trays in the main column total no. of trays in the side column column pressure

600 lb mol/h 278 °F B/T/X mol % 40/10/40 99/1/0 0/1/99 1/99/0 13 27 40 13 29.4 psia

valid because temperature is not uniquely related to composition for a multicomponent system (Ganguly and Saraf2 and Barolo et al.5). To evaluate the applicability of the proposed control scheme on this complex configuration, we have chosen the column used by Han and Park13 which is similar to that of Alatiqi and Luyben.22 Figure 10 shows a schematic diagram of the complex distillation configuration. The feed mixture is composed of benzene, toluene, and o-xylene. This configuration uses a side stream column with the liquid side draw fed into a small stripping column. The stripper has a small reboiler that removes some of the light component from the sidestream product. Vapor from the stripper is fed back into the main column. The column specifications are listed in Table 2. The composition measurements are assumed to have a time delay of 3 min. Figure 11 shows dynamic temperature profiles of the main column during the period of total reflux operation. During the total reflux operation, the temperature profile becomes constant-pattern waves after some transient period. The waves are shown to move to the center of the column, stick to each other, and then propagate together to the column end. This means that the profile goes far away from the desired steady-state one. The policy using total reflux only does not guarantee that the column temperature profile comes close to the desired one. Therefore, the total reflux policy should be limited to a relatively short period and the manipulated variables should be adjusted to move the profile to the desired point along the column. This is a different behavior from that of a simple distillation column in which the waves move to the center of the column during total reflux, as shown in Figure 1.

Figure 11. Dynamic temperature profiles during the total reflux operations.

During the total reflux operation, one can achieve a crude separation of the mixture. The low-boiling component moves upward and accumulates in the upper part of the column while the heavy component moves downward and accumulates in the lower part. That is, the column profile forms so that the intermediate component can be easily drawn to the sidestripper. This means that the composition in each section becomes pseudobinary, which makes the proposed control scheme applicable to the startup of this configuration. A complex distillation configuration has several sections, and each section has a specific task for separating the pseudobinary mixture in concert with the other sections. Therefore, it is important to ensure that the task given in each section can be done without any great interaction with the neighbor or connected sections with mass and/or energy flow. This can be achieved by controlling the profile position in each section tightly. The most important task for starting up this complex configuration may be the one given to the middle section of the main column because the section can interact with the other three sections of the configuration. The task is mainly divided into two tasks: (1) to keep the heavy component from carrying over to the sidestripper and (2) to prevent a feed disturbance from propagating to the other sections, subsequently affecting product compositions. The middle section is connected to the other three sections. The heavy component, which entered once into the sidestripper, will remain in the reboiler drum of the sidestripper, until going out of the system as an impurity in the side product. The process takes a very long time. The heavy component may often change the sign of the process gain, which makes the composition control of the side product very difficult. Tight control of the profile position in the middle section of the main column keeps the heavy component from carrying over to the sidestripper, where the heavy component cannot be eliminated effectively, so that the startup time can be greatly reduced. The obstacle to the control of the profile position in the middle section is the fact that the middle section forms a multicomponent system, which makes the application of the proposed profile position observer

1572 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 Table 3. Control Loop Configurations for Conventional Control Schemesa CV (composition control)

CV (temperature control)

MV

XD(1) XS(2) XB(3) ∆T (T(28) - T(16))

T(33) T(7) TS(7) ∆T (T(28) - T(16))

R QB QBS LS

a

Figure 12. Dynamic response of product compositions: (a) PI composition control; (b) PI temperature control; (c) proposed control.

difficult. We have chosen a temperature front as a profile position in order to solve the problem. The temperature front can be regarded as a profile position to some extent because the temperature front and profile position indicate nearly the same point where the temperature gradient is the largest in a column section. The profile position can be determined by the following method. When the tray temperature of the column section is measured, the temperature differences between neighboring measured trays can be calculated. The front can be determined by dividing the sum of the temperature differences multiplied by its position by the sum of the temperature differences: n-1

∑ Sj∆Tj

S)

j)m

n-1

(13)

∑ ∆Tj

i)m

where j is the measurement tray number, m is the first measurement tray number, and n is the last measurement tray number in a column section. ∆Tj is the temperature difference between the jth measurement tray and the (j + 1)th measurement tray, and Sj is the midpoint between jth and (j + 1)th measurement trays. To locate the profile position at the desired point in the middle section, the liquid draw rate to the sidestripper (LS) is manipulated with a simple PI controller. Figure 12 shows the dynamic variations of product compositions when using conventional PI composition controllers, PI temperature controllers, and the proposed profile position control scheme. Table 3 shows a control loop configuration for the conventional controllers. The temperature difference between trays below and above the sidedraw tray is maintained by manipulating the sidedraw rate for the conventional controllers

CV: controlled variables. MV: manipulated variables.

Figure 13. Closed-loop responses of the profile position (profile position control during the initial 3 h and composition/profile position cascade control after 3 h).

as suggested by Alatiqi and Luyben.22 The intermediate concentration of the side product goes down at first and then increases to reach the product specification. This is because some time is required until the heavy component disappears as a bottom product of the sidestripper. The conventional composition controller shows some offset from the specification in the side product composition. This is brought about by accumulation of the heavy component in the sidestripper. This means that the control of the temperature difference between trays above and below the sidedraw cannot deal with the carryover problem of the heavy component to the sidestripper so that the heavy component accumulates in the bottom of the sidestripper. The control scheme using the temperature difference may be thought to be a kind of profile position controller in some sense. However, the determination of the profile position using the temperature difference method does not appear to be efficient, in particular during startup operation. The PI temperature control scheme shows the most oscillatory behavior among the three control schemes. This seems to be due to the fact that the temperature profile swings back and forth between the two columns. In this case, temperature does not have a unique relationship with composition any more because the distillation system constitutes a multicomponent system. Therefore, the control direction when using temperature control can be different from the one when using composition control. The proposed control scheme shows a smooth startup and no offset of product compositions from the specifications. Figure 13 shows the dynamic response of profile positions tracking their setpoint given a byproduct composition controller. Figure 14 provides the movement of the profile position for the middle section and the dynamic mole fraction of the heavy component in

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Notation K: GMC tuning constant L, V: liquid and vapor flow rates (kmol/h) F: feed flow rate (kmol/h) r: molar holdup of vapor to liquid u∆: normalized shock wave velocity xs: representative liquid mole fraction corresponding to the profile position of a self-sharpening standing wave y: vapor mole fraction of the light component ∆: prefix for the difference between the two sides of a selfsharpening wave *: setpoint ∧: observer prediction •: derivative GLC: global linearizing control GMC: generic model control PI: proportional-integral Figure 14. Dynamic profile position in the middle section and concentration of the heavy component in the sidedraw.

the sidedraw. One can notice that there is a close relationship between the mole fraction of the heavy component in the sidedraw and the profile position for the middle section. Therefore, control of the profile position for the middle section can be an effective means to prevent the heavy component from carrying over to the sidestripper. These figures indicate that tight control of the profile position in each section can be a key to the smooth startup for this complex process. Conclusion Startup operation of distillation columns experiences a very large change, which is strongly nonlinear and gets disturbed very easily during the period. The proposed control scheme, based on the nonlinear wave model representing the dynamic nature of the distillation column, has been applied to the startup operations of a simple distillation column for dual composition control and a complex distillation configuration. The control scheme uses the profile position in each column section as the controlled variable. Comparison of the performance with other schemes shows that the proposed control scheme provides a very good performance and robustness against model-plant mismatch and measurement errors. It has the advantage that no further tuning is necessary when switching from startup control to normal operational control. The proposed control scheme is also proved effective in startup control of the complex distillation configuration that is a very nonlinear, interactive, and multicomponent system. However, this work is limited to multicomponent systems that are well represented as a binary. During startup operation, the profile position control only is good enough. However, in the presence of considerable model-plant mismatch, the control tray temperature or product composition cascade to profile position control is recommended. Acknowledgment This work was supported in part by the Korea Science and Engineering Foundation (KOSEF) through the Automation Research Center at POSTECH.

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Received for review July 13, 1998 Revised manuscript received January 11, 1999 Accepted January 14, 1999 IE980444S