Experimental Verification of Bilevel Optimizing Control for SMB

Aug 3, 2010 - Experiments have been carried out in a four-zone SMB system packed ... In the experiments, RMPC revealed quite satisfactory tracking and...
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Ind. Eng. Chem. Res. 2010, 49, 8593–8600

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Experimental Verification of Bilevel Optimizing Control for SMB Technology Kiwoong Kim,† Jin-Il Kim,‡ Huiyong Kim,† Jinhyo Yang,‡ Kwang Soon Lee,*,† and Yoon-Mo Koo‡ Department of Chemical and Biomolecular Engineering, Sogang UniVersity, 1 Shinsoodong, Mapogu, Seoul 121-742, Korea, and Department of Biological Engineering and Center for AdVanced Bioseparation Technology, Inha UniVersity, 253 Yonghyundong, Namgu, Incheon 402-751, Korea

An experimental study has been conducted to evaluate the bilevel optimizing control technique for simulated moving beds (SMBs) that was proposed in a previous article (Kim et al. Ind. Eng. Chem. Res. 2010, 49, 3689-3699). Off-line optimization provides optimum time-varying flow rates for feed and desorbent in the upper level, and repetitive model-based predictive control (RMPC) is performed for regulation of the extract and raffinate purities in the lower level. Experiments have been carried out in a four-zone SMB system packed with Dow 50WX4 400-mesh resin to separate L-ribose and L-arabinose at 99.7 vol% from their mixture dissolved in water. The optimizing control technique was implemented just as in the numerical study in the previous work, except for some minor customization. In the experiments, RMPC revealed quite satisfactory tracking and disturbance rejection performance. Optimization resulted in a 45% increase in productivity and a 12% decrease in desorbent consumption from an arbitrary initial point, and the cascaded RMPC law tightly maintained the product purities at their set points by effectively compensating the changes in the feed and desorbent flow rates. Introduction The simulated moving bed (SMB), first developed by UOP for splitting xylene isomers,1-3 has now become an indispensible industrial technique in the petrochemical and food industries for the separation of various hydrocarbon mixtures and for the recovery of fructose from fructose/glucose mixtures, respectively.4,5 Since the early 1990s, SMB technology has also begun to receive keen attention as a cost-effective technique in the pharmaceutical industry for chiral separation, after Novasep introduced a scaled-down unit using the high-performance liquid chromatography (HPLC) technique. The application is now being expanded to a number of pharmaceutical companies for commercial production of enantiomeric compounds.6 There has been remarkable progress in the research as well as practice of SMB technology, especially during the past 20 years. While new process concepts have been investigated such as three-zone SMB,7 Varicol,8 and multicomponent separation,9-11 new operating techniques such as ModiCon,12 PowerFeed,13 and Outlet Stream Swing,14 have also been devised and proposed during this period. SMB operation has some unique features. The most salient one to note is that the process repeats the same operation on a certain cyclic steady state (CSS), overcoming disturbances such as column switching and variations in feed composition. As the operation continues, the process undergoes gradual changes in the adsorbent characteristics and packing state. Accordingly, the optimum operating condition shifts and needs to be updated when the process change is appreciable. A more comprehensive discussion of the problems with column aging in commercial SMB units can be found in Gomes et al.15 To address the problems mentioned above in part or in full, there has been constant research on the control and optimization of the SMB process, especially since the 1990s. Kloppenburg and Gilles16 proposed a nonlinear control method based on a hypothetical true moving bed (TMB) model. Klatt et al.17 * To whom correspondence should be addressed. E-mail: kslee@ sogang.ac.kr. Tel.: +82-2-705-8477. Fax: +82-2-3272-0319. † Sogang University. ‡ Inha University.

exploited a two-layer optimizing control architecture in which a dynamic optimizer in the upper level calculates the optimal flow rates and switching period to minimize the desorbent usage at the CSS and the multiple single-input/single-output (SISO) controllers regulate the process in the lower level. Toumi and Engell18 presented a nonlinear model predictive control scheme for a reactive SMB process. In real time, their controller determines the flow rates and switching period that minimize the production cost over a prediction horizon by handling the purity requirement using inequality constraints. In the studies reviewed above, the controller and the optimizer assume that the purity measurement and control action take place only once in a switching period. There have also been studies that assume multiple control actions within a switching period to allow for extra enhancement of productivity and desorbent curtailment as in Modicon12 and PowerFeed13 operations. Under such conditions, the SMB process can be treated as a repetitive process, and nonconventional control techniques such as repetitive model-based predictive control (RMPC)19,20 can outperform the control techniques for continuous processes. Erdem et al.21 and Abel et al.22 proposed a receding-horizon optimizing control method with the same control objective as in Toumi and Engell,18 except for allowing multiple control actions within a switching period. An RMPC law was naturally derived in the course of the controller construction. The optimizing control method was successfully implemented in an experimental SMB system with continuous purity measurement23 and also discrete purity measurement averaged over a switching period.24 Just as the research in academia has been active during the past decade, there have also been constant developments in advanced control techniques in industry. For example, Novasep25 has developed a commercial technique to control the product purity in an SMB process by adjusting the position of a certain characteristic point that is identified from the history of measurement data. As a modification of the approaches mentioned above, Kim et al.26 proposed a bilevel optimizing control structure based on a fundamental SMB model reduced to a set of nonlinear discrete-time dynamic equations using the cubic spline colloca-

10.1021/ie1000218  2010 American Chemical Society Published on Web 08/03/2010

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Figure 1. Configuration of the experimental four-zone SMB system to separate L-ribose and L-arabinose from feed mixture.

tion method27-29 and exact discretization. RMPC is used to perform regulation of the product purities in the lower level, and optimization of the feed and desorbent flow rates and the duration of the switching period is conducted in the upper level. It is assumed that the flow rates can be varied within a switching period and that the product purities are available as average values over each switching period with analysis delay. For RMPC, the SMB model is linearized successively around the operating trajectories in the previous switching period. The performance and robustness of the proposed technique has been verified through a series of numerical studies under various scenarios. In this study, the optimizing control technique proposed by Kim et al.26 has been investigated experimentally in a fourcolumn SMB system separating L-ribose and L-arabinose through the extract and raffinate streams, respectively. Experiments were carried out in two separate periods. The first period continued for about 24 h, and a plant test to gather operating data for model tuning was conducted. RMPC designed with the preliminary coarse model was put into an action during this test to investigate how robustly the controller behaves. The second period lasted for about 60 h, during which the proposed optimizing control method based on the tuned model was implemented. Set-point tracking during the initial startup, regulation against a step change in feed flow rate, and optimization of operating variables were attempted and assessed sequentially. In the subsequent sections, the term “cycle” is used together with “switching period” to denote the period of operation under a port switching. Experimental SMB System Equipment. Figure 1 shows the SMB system used for the experiments. It is a typical four-zone SMB system assembled in the laboratory. Four identical jacketed glass columns of 2.5cm inner diameter and 25-cm height were purchased from BioChem Fluidics (Boonton, NJ) and used for the adsorbent beds. Through the jacket, water at 50 °C from a constant-temperature bath was circulated. Dow 50WX4 400-mesh resin purchased from Dow Chemical Company (Midland, MI) was modified from H+ to Ca2+ by CaCl2 dissolved in distilled and deionized

water (DDW), which was prepared with a Milli-Q system from Millipore (Billerica, MA) and used as the adsorbent. The resin was packed by the slurry method with a height of 19.7-cm. The average diameter of the resin particles was 38-µm, and the void fraction of the bed was measured as 0.47. Four M50 pumps from Valco Instruments Inc. (Houston, TX) were positioned in front of the four columns for flow rate adjustment in each zone. The maximum volume precision of M50 pump is 0.02% at 1.25 mL and 0.2% at 0.125 mL. Multiposition rotary valve systems from Valco Instruments Inc. were employed for altering the directions of the feed, desorbent, extract, and raffinate streams at each port switching. To take into account overall dead volumes in a first-principles model, we measured parameters of the SMB unit from a module made up of the structured system designed to reflect dead volumes occurring in lines and equipment. Related research to analyze and compensate dead volumes has been addressed by Migliorini et al.30 and Gomes et al.31 The optimizing control algorithm was written in Matlab and embedded in LabView, which provides the interface between the Matlab control program and input-output devices such as pumps, valve systems, fraction collector, and HPLC integrator. All of these programs were run on an online personal computer with a 2.4 GHz Intel dual-core CPU. Feed Preparation and Frontal Analysis..32 Crystalline L-ribose (g99.8 wt %) and L-arabinose (g99.0 wt %) were purchased from Danisco A/S (Copenhagen, Denmark) and dissolved in DDW to make 30 g/L solution for each. L-Ribose and L-arabinose solutions were filtered using a 0.22-µm filter and degassed using an ultrasonic cleaner with a vacuum pump. Afterward, equal volumes of L-ribose and L-arabinose solutions were mixed and used as the feed solution. At a concentration of 30 g/L, adsorption equilibria for both substances were found to satisfy the linear isotherm. The equilibrium constants were determined in a preparative experiment using the single-step frontal analysis method32 such that HA ) 1.286 (g of A/cm3 of solid)/(g of A/cm3 of solution) and HB ) 0.5666 (g of B/cm3 of solid)/(g of B/cm3 of solution), where A and B denote L-ribose and L-arabinose, respectively. Purity Measurement. The raffinate and extract streams were directed to a Foxy 200 fraction collector from Teledyne Isco Inc. (Lincoln, NE) and collected in the respective vials over each switching period. At the port switching, the fraction collector was also switched to new vials, and the collected products were analyzed by HPLC after being vortexed. Separate HPLC systems from Shimadzu Co. (Kyoto, Japan) with Shodex Sugar SP0810 HPLC columns from Showa Denko K.K. (Tokyo, Japan) were used for analysis of the raffinate and extract streams, respectively. Each HPLC system was equipped with an LC-6AD solvent delivery module, an SIL-10ADvp autoinjection module, an RID-10A refractive index detector, and an SCL-10Avp system control module. The temperature of the analytical columns was regulated at 85.0 °C by an RC6CS controller from Lauda Dr. R. Wobser GmbH and Co. KG (Lauda-Ko¨nigshofen, Germany) with a constant temperature water bath. DDW was used as an eluent and the flow rate was controlled at 1.5 mL/min. Completion of an assay including sample transfer and area integration takes about 25 min. All the HPLC operations up to data transmission to the online PC were fully automated except the manual pipetting for sample transfer from Foxy 200 fraction collector to SIL-10ADvp autoinjection module. The calibration curves were produced by averaging the peak areas from redundant calibration experiments repeated three

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models for four SMB columns were integrated into a single model equation by incorporating the column switching logic and mass balances at the nodal points where the columns are connected. The dead volumes of the SMB unit cannot be disregarded in commercial systems,31 but were not considered in the model equation in the expectation that the parameter estimator could absorb their effects during model tuning. The resulting ODEs are linear in the state variable, and the exact discrete-time equivalent model was derived under the zeroorder hold assumption on the flow rates. It was assumed that the average purities over each cycle were measured at the raffinate and extract streams with analysis delay. The resulting discrete-time model can be described as

Figure 2. Four-zone SMB system and associated notation.

xk(t + 1) ) A[uk(t), vk(t), xk(t)] + B[uk(t), vk(t)], xk+1(0) ) xk(N) pk(t) ) H [xk(t)], t ) 0, ..., N - 1

(1)

m pk+1 (d) ) pk(N) + n

(2)

where t, subscript k, and N denote the discrete-time index, cycle index, and total number of sample times in a cycle, respectively; x represents the state variable, composed of the concentrations of components A and B at the collocation points of four columns plus auxiliary variables generated during the representation of average purities; p(t), pm, and n represent the purities of A (in the extract) and B (in the raffinate) averaged up to t, purity measurements, and zero-mean noise, respectively; u and v are normalized flow rates defined by Figure 3. Structure of the proposed bilevel optimizing control system.

times. For calibration, the purchased crystalline L-ribose and L-arabinose were assumed to have 100% purity, although, in actuality, they did not. Revisiting the Bilevel Optimizing Control Method In this section, the bilevel optimizing control method proposed in Kim et al.26 is described, together with the customization for the experimental implementation. Overall Structure. The four-zone experimental SMB system is shown in Figure 2 with the notation for flow rates, zones, and ports to facilitate the subsequent description of the optimizing control algorithm. The overall structure of the optimizing control system can be represented as in Figure 3. The optimizer is turned on only when requested and computes optimum flow rates and the duration of the cycle (P) on the basis of a discretized nonlinear first-principles model, where only QF, QD, and P are directly implemented in the process. The product purities are regulated by RMPC whose law is based on the linear SMB model which is updated after every cycle through successive linearization of the first-principles model around the operation trajectories in the previous run. The first-principles SMB model is revised through parameter estimation. Nominal Model for the SMB System. The governing equation of an SMB column is standard and described by partial differential equations (PDEs) in time and axial distance.26 In the construction of a nominal SMB model for controller design, the column model was simplified by assuming a linear isotherm and instantaneous adsorption equilibrium (infinite mass-transfer rate). The PDE column model was reduced to a set of ordinary differential equations (ODEs) using the cubic spline collocation method combined with far-side boundary conditions.29 The ODE

u}

[

]

QIP QIIP T , εV εV

v}

[

QFP QDP εV εV

]

T

(3)

which are used as the manipulated variable (MV) for RMPC and decision variables for optimization, respectively; and P, ε, and V denote the duration of a cycle, bed porosity, and bed volume, respectively. Equation 2 results from the measurement situation that the average concentration at the terminal time of the kth cycle is available at t ) d in the next cycle due to the analysis delay. The nominal model in eq 1 is nonlinear in u, v, and x and used by the optimizer. For RMPC construction, eq 1 is linearized successively around the operating trajectories in the previous cycle. This yields a linearized time-varying model in the form ∆xk(t + 1) ) Ak-1(t) ∆xk(t) + Bk-1(t) ∆uk(t) + w(t) pk(t) ) pk-1(t) + Hk-1∆xk(t), t ) 0, ..., N - 1 m (d) ) pk(N) + n pk+1

(4) In the above equation, ∆ means the cyclewise difference defined as ∆uk } uk - uk-1; A, B, and H are linearized time-varying system matrices; and w is a zero-mean white noise. Model Parameter Estimator. The model parameter estimator updates the key process parameters so that the sum of squared errors of the purity estimate over a window of cycles DK is minimized such that min θ

∑ ||p

k+1(d)

- pˆk(N;θ)||2

(5)

k∈DK

In eq 5, p represents the purity estimate using the Kalman filter constructed on eq 1, and θ denotes the parameter vector to be estimated. In this study, θ was chosen as [HA HB]T with an expectation that the effects of model error (in terms of purity

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estimates) from other sources can also be absorbed by appropriately adjusting HA and HB. Optimizer. The optimizer determines an initial state and flow rates that minimize the net operating cost under a cyclic steady state while satisfying the purity specifications on the basis of the nonlinear model in eqs 1 and 2. In this study, P was dropped from the decision variables unlike in the previous study,26 as there was no room for P to be shortened more because of the long analysis delay. The optimization problem can be stated as N-1

min

J)

xm(0),v(τ),u(τ), τ)t1,...,tNo

∑ a Q (t) - a Q (t) 1

D

2

{∑

Operating Conditions P ) 30 min, N ) 30, d ) 25 cA,F, cB,F ) 30 g/L QI ) 3:8, QII ) 2:3, QF ) 1, QD ) 2 (initial flow rates; mL/min) RMPC Parameters mp ) 3, Nu ) 6, Q ) 40I, R ) 0.15I psp (wt %) ) [0.997 0.997]T, Qj,min ) 0, Qj,max ) 10 for all j Optimizer Parameters

(6)

where psp denotes the purity set point and a1 and a2 are weights to reflect the unit price of desorbent and the profit earned when unit amount of feed is processed, respectively. All manipulable flow rates were optimized, but only v was implemented in the process whereas u was recalculated in the controller level. The reasoning and justification behind this implementation are given in detail in Kim et al.26 The flow rates were allowed to vary No times within a cycle; that is, the PowerFeed operation13 was presumed. In practice, the optimum v was applied to the process gradually from the old v through a first-order filter to avoid a potential bump in the process. The purity requirement in eq 6 was relaxed using a slack variable in the real implementation. RMPC. RMPC was designed to compute the future movements of u for the prediction error of the average purity over the future mp cycles, minimized together with an additional penalty term on cyclewise input change, which can be written as

∆Wk

bed height ) 19.7 cm, bed diameter ) 2.5 cm, ε ) 0.47 (HA, HB) ) (1.2860, 0.5666)initial f (1.4452, 0.5334)updated DA f DB ) 1 cm2/min (not measured, arbitrarily given) A ) L-ribose, B ) L-arabinose

F

(purity specifications) p(N) g psp xm+1(0) ) xm(0) (cyclic steady state) Qj,min e Qj e Qj,max, j ) I, ..., IV, F, D

1 2

Parameters of the SMB Unit

t)0

subject to the SMB model in eq 1 and

min

Table 1. Parameters and Operating Conditions for the Experiments

mp-1

|ek+i|k(N|d)| Q2 + |B∆Wk | R2

i)0

}

(7)

subject to linearized model in eq 4 and ∆Uk ) B∆Wk Qi,min e Qi e Qi,max,

j ) I, II

(8)

where ∆Uk represents [∆uk(0)T · · · ∆uk(N - 1)T]T and B denotes a blocking matrix. The penalty term on ∆Uk affords the cyclewise integral action, which is the key to repetitive control. The computation is carried out in every cycle at t ) d when the purity measurement is available. Then, {uk(t + d), ..., uk(N - 1)} are directly implemented in the process, whereas {uk(0), ..., uk(t + d - 1)} are carried over and implemented in the next period. By the input blocking, the input movements are confined to Nu times among N sampling instants where Nu < N. Experimental Conditions The parameters used for SMB modeling, RMPC and optimizer construction, and nominal operating conditions are given in Table 1. The HA and HB values were updated by the model parameter estimator from their initial values obtained in a preparative experiment. The flow rates were fixed during the startup operation of the unit and then manipulated as the

a1 ) 1.5, a2 ) 1.5, No ) 3

controller and optimizer began to act. The purity targets were given at much higher values than normally required for L-ribose and L-arabinose to demonstrate the regulation capability of the proposed control method. Indeed, the 99.7 wt % target purity is only a calibration value and might differ from the true purity, especially because the reagent-grade L-arabinose used in the experiment had a minimum purity of 99 wt %. The experiments were conducted continuously for about 60 h. During this period, set-point tracking, regulation against the change in the feed flow rate, and optimization of the feed and desorbent flow rates were attempted sequentially, and the performance was evaluated. Results and Discussion Preliminary Plant Test. The optimizer is completely dependent on the SMB model, and the model accuracy is critical to the final attainable cost. The model accuracy is also important for RMPC because the purity measurement is infrequent; hence, the model dependency is inevitably high even though the cyclewise feedback can asymptotically eliminate the purity offset despite the model uncertainty and repeated disturbances. A preliminary plant test was conducted before the optimizing control for the model tuning through the parameter estimation. The adsorption equilibrium constants were updated from the initial values using the method described previously. The test run began in the open-loop state with the flow rates set to the initial values shown in Table 1 and was turned to the closedloop operation under RMPC as the process tended to settle on a CSS. The data designated with the triangles in Figure 4 represent the average purity measurements from the test run. The openloop purity predictions with the untuned nominal model are represented by the circles and exhibit a large discrepancy from the experimental measurements. HA and HB were estimated according to eq 5 and updated to 1.4452 and 0.5334 from 1.2860 and 0.5666, respectively. The open-loop purity predictions from the tuned model are represented with squares and reveal a similarity to the measurements, which verifies the effectiveness of the parameter estimation. Performance of RMPC. The performance of RMPC was investigated for set-point tracking during the startup period and then for regulation against a change in the feed flow rate. Figure 5 exhibits the resulting trajectories for the purities and flow rates for set-point tracking. Until RMPC was activated, QI and QII

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Figure 4. Purity measurements from the test run and open-loop predictions of the purities with initial and updated equilibrium constants for the (a) extract and (b) raffinate streams.

Figure 5. Initial transient profiles during startup followed by set-point tracking under RMPC with QD ) 2 mL/min and QF ) 1 mL/min; (a) average purities and (b) flow rates.

Figure 6. Plots of flow rate change during set-point tracking on the Mazzotti triangle diagrams for (a) complete separation and (b) complete regeneration. The number for each circle denotes the cycle index.

were fixed at 3.8 and 2.3 mL/min, respectively, which do not correspond to complete separation conditions.33 It can be observed that the purities are subject to small oscillations as well as slow drifting during this period. Once RMPC was put into operation from the 22nd cycle, both the extract and raffinate purities were gracefully steered to their respective set points in

about 12 cycles. It is interesting to compare the tracking performance in Figures 4 and 5. One can see that set-point tracking was fulfilled in both cases; however, the transient in Figure 4 is longer than that in Figure 5 because of the larger parameter error than in Figure 5.

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Figure 7. Response of average purities under RMPC against a 15% step increase in feed flow rate at the 56th cycle.

The flow rate changes under RMPC are located on the triangle diagrams33 as in Figure 6. In this figure, mj is defined as (Qavg j P - Vε)/[V(1 - ε)], where Qavg means the average flow rate over j a cycle. Because QD and QF were invariant during this experiment, (mII, mIII) and also (mIV, mI) move only along certain fixed straight lines. RMPC steers the flow rates into the complete regeneration region (Figure 6a) and also the complete separation region (Figure 6b) and finally to an operating condition roughly in the middle of the respective line segments within the regions as the cycle evolves. The complete separation and regeneration

regions were obtained assuming no axial dispersion and local equilibrium between the fluid and solid phases; nevertheless, one can see that the SMB model under such assumptions can represent the true SMB behavior quite reasonably. Figure 7 presents the regulation performance of RMPC against the feed flow variation presuming that a malfunction occurred in the feed pump. The flow rate was increased stepwise by 15%, namely, from 1.00 to 1.15 mL/min at the 56th cycle. As shown in the figure, RMPC successfully recovered the purities in about 20 cycles. The corresponding average flow rates are depicted in the triangle diagrams33 as in Figure 8. It can be observed that (mII, mIII) departs from the straight line in Figure 6 that corresponds to k ) 40-56 and moves onto a new straight line as the feed flow rate is increased to a new value. Combined Optimization and Control. After the recovery from the feed pump failure, the optimizer was turned on, and the optimum time-varying functions QF(t) and QD(t) were calculated. Both flow rates were allowed to change three times at t ) 0, N/3, and 2N/3 in the optimization. For simplicity, the optimized flow rates are denoted as {Q*F (0), Q*F (N/3), Q*F (2N/ 3)} and similarly for QD. Because direct implementation of the

Figure 8. Plots of flow rate change during disturbance rejection on the Mazzotti triangle diagrams for (a) complete separation and (b) complete regeneration. The number for each circle is the corresponding cycle index.

Figure 9. Optimum time-varying feed and desorbent flow rates and the filtered values for real implementation: (a) as functions of cycle time and (b) on the triangle diagrams.

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Figure 10. Purity response and cost function decrease during bilevel optimizing control.

new flow rates might perturb the process, low-pass filtered values in k were generated such that QF,k(m) ) λQF,k-1(m) + (1 - λ)Q*(m), F

m ) 0, N/3, 2N/3

and implemented in the process. The same procedure was applied to QD, as well. λ was chosen between 0.75 and 0.90 but differently for different cases not based on any special reasoning. Figure 9a illustrates how the optimized QF(t) and QD(t) functions were implemented in the SMB process. The dotted lines represent the optimum flow rates for three intervals in a cycle. Each of them was gradually increased (or decreased) through low-pass filtering and was applied to the process. The average flow rate is also shown in Figure 9b on the triangle diagrams. It is interesting to note that the final condition reached at k ) 113 is closer to the triangle corners, known as the most economical operating condition according to Mazzotti et al.,33 than the starting condition, although the true optimum condition is located with some bias from the corners because of the idealized assumptions in Mazzotti et al.’s theory.33 Figure 10 exhibits the purity profiles under RMPC together with the cost function decrease when the optimum flow rates were implemented. It can be observed that the purities were scarcely affected except for some minor perturbation over the initial several cycles, even though the maximum QF variation within a cycle eventually grew to more than 1.5 mL/min. Compared to the fluctuation by the 0.15 mL/min increase in QF in Figure 8, the result is remarkable. The reason for this is that QF(t) and QD(t) were handled as known disturbances in RMPC and could be actively compensated on the basis of a fairly precise model. The cost function shown in Figure 10 is defined as avg avg - a2QF,k Ck ) a1QD,k

(9)

avg denotes the average flow rate of desorbent over the where QD,k avg . As QD decreased from 2 to 1.3 kth cycle and similarly for QF,k mL/min and QF increased from 1 to 1.4 mL/min, C was reduced from 2 to 0.6.

Conclusions An experimental assessment of the bilevel optimizing control technique for SMB processes26 has been conducted in a benchscale four-zone SMB unit separating L-ribose and L-arabinose from their mixture. The mixture was dissolved in water at 30 g/L, which is low enough for the linear adsorption isotherm to be applicable. The optimizing control system was composed of an off-line optimizer in the upper level, a repetitive controller (RMPC) for purity regulation in the lower level, and a separate off-line model parameter estimator.

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In a continuous experimental run for about 2.5 days, the performance of RMPC alone and also of the combined RMPC and optimizer was evaluated for various scenarios. The foremost observation is that the proposed optimizing control technique performs very satisfactorily as predicted in the numerical study. RMPC could attain the high-purity target without difficulty and maintain the purity against the unknown disturbances such as change in the feed flow rate. In the combined optimization and control, the optimizer could readily determine the optimum feed and desorbent flow rates, whereas RMPC could precisely compensate the implementation of the optimum feed and desorbent flow rates with virtually no perturbation in the product purities. All of these observations validate the outstanding performance of the proposed optimizing control technique. Considering that the optimizer relies only on the SMB model instead of measurements, it can be stated that such performance was not possible unless the SMB model was sufficiently accurate. This again leads us to conclude that the nominal SMB model after tuning can replicate the dynamic behavior of a real SMB process with a fairly high precision. Acknowledgment This work was supported by Mid-career Researcher Program through NRF grant funded by the MEST (No. 2010-0000495) and the Human Resources Development of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea Government Ministry of Knowledge Economy (No. 20094010100160). Literature Cited (1) Broughton, D. B.; Gerhold, G. G. U.S. Patent 2,985,589, 1961. (2) Broughton, D. B.; Neuzil, R. W.; Pharis, J. M.; Brearley, C. S. The parex process for recovering paraxylene. Chem. Eng. Prog. 1970, 66, 70. (3) Minceva, M.; Rodrigues, A. E. Two-level optimization of an exisitng SMB for p-xylene separation. Comput. Chem. Eng. 2005, 29, 2215–2228. (4) Ruthven, D. M.; Ching, C. B. Counter-current and simulated countercurrent adsorption separation processes. Chem. Eng. Sci. 1989, 44, 1011– 1038. (5) Azevedo, D. C. S.; Rodrigues, A. E. Design methodology and operation of a simulated moving bed reactor for the inversion of sucrose and glucose-fructose separation. Chem. Eng. J. 2001, 82, 95–107. (6) Zabka, M.; Gomes, P. S.; Rodrigues, A. E. Performance of simulated moving bed with conventional and monolith columns. Sep. Purif. Technol. 2008, 63, 324–333. (7) Zhang, Y.; Wankat, P. C. Three-zone simulated moving bed with partial feed and selective withdrawal. Ind. Eng. Chem. Res. 2002, 41, 5283– 5289. (8) Pais, L. S.; Rodrigues, A. E. Design of simulated moving bed and varicol processes for preparative separations with a low number of columns. J. Chromatogr. A 2003, 1006, 33–44. (9) Rodrigues, A. E.; Mata, V. G. Separation of ternary mixtures by pseudo-simulated moving bed chromatography. J. Chromatogr. A 2001, 939, 23–40. (10) Hur, J. S.; Wankat, P. C. New design of simulated moving bed (SMB) for ternary separations. Ind. Eng. Chem. Res. 2005, 44, 1906–1913. (11) Migliorini, C.; Mazzotti, M.; Morbidelli, M. Design of simulated moving bed multicomponent separations: Langmuir systems. Sep. Purif. Technol. 2000, 20, 79–96. (12) Schramn, H.; Kaspereit, M.; Kienle, A.; Seidel-Morgenstern, A. Simulated moving bed process with cyclic modulation of the feed concentration. J. Chromatogr. A 2003, 1006, 77–85. (13) Zhang, Z.; Mazzotti, M.; Morbidelli, M. PowerFeed operation of SMB units: Changing the fluid flowrates during the switching interval. J. Chromatogr. A 2003, 1006, 87–99. (14) Gomes, P. S.; Rodrigues, A. E. Outlet Streams Swing (OSS) and MultiFeed Operation of Simulated Moving Beds. Sep. Sci. Technol. 2007, 42, 223–252. (15) Gomes, P. S.; Minceva, M.; Rodrigues, A. E. Operation Strategies for Simulated Moving Bed in the Presence of Adsorbent Ageing. Sep. Sci. Technol. 2007, 42, 3555–3591.

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ReceiVed for reView January 4, 2010 ReVised manuscript receiVed July 4, 2010 Accepted July 18, 2010 IE1000218