PROCESS control did not reach where it stands today

Transcription

1 th International Conference on Control Sytem and Science Control of a train of high purity ditillation column for efficient production of 13C iotope Clara Ionecu, Roxana Both, Caba Futo, Clement Fetila, Mihai Gligan and Robin De Keyer Abtract It i well-known that high-purity ditillation column are difficult to control due to their ill-conditioned and trongly nonlinear behaviour. The fact that thee procee are operated over a wide range of feed compoition and flow rate make the control deign even more challenging. Thi paper propoe the mot uitable control trategie applicable to a erie of cacaded ditillation column procee. The condition for control and input-output relation are dicued in view of the global control trategy. The increae in complexity with increaed number of erie cacaded ditillation column procee i tackled. Uncertainty in the model parameter i dicued with repect to the dynamic of the global train ditillation proce. The main outcome of thi work i inight into the poible control methodologie for thi particular cla of ditillation procee. Index Term multivariable control, uncertainty, proce indutry, ditillation column, iotope, carbon. I. INTRODUCTION PROCESS control did not reach where it tand today if it wan t for the continuou and trenuou effort of control engineer for better and more efficient method of tackling nonlinear, time-varying, multivariable and contraint problem [1]. The extenive literature urvey from [2] on ditillation dynamic and control ugget to the reader that the proce of ditillation i the mot common unit of operation in the chemical indutry and it repreent a teacher pet when it come to illutrate control problem for training control engineer. Along with the numerou poibilitie in tackling control iue, the proce of ditillation bring numerou contraint and challenge, being in itelf a complete tandalone proce within the chain of indutrial application [1]. An excellent reader diget on dynamic and control of ditillation column are [4] and [3]. Both of thee vat work are a neceary guide through the jungle of variou ditillation column configuration and pecification for control. However, a pecial cla of ditillation procee are thoe aiming at tripping variou chemical element. There i a lack of paper in the literature dicuing thi particular cla, depite renewed interet from the control community [5]. Mot of the exiting work on control of ditillation column examine the problem from an individual column tandpoint. However, multi-column ytem have been examined in cae where C.M. Ionecu, R. Both, C.Futo and C. Fetila are with the Technical Univerity of Cluj Napoca, Department of Control Engineering, 28 Memorandumului treet, Cluj-Napoca, Romania. R. De Keyer and C. M. Ionecu are with Ghent Univerity, Department of Electrical energy, Sytem and Automation, Technologiepark 913, B9052 Gent-Zwijnaarde, Belgium. Correponding author: Clara M. Ionecu; tel: ; fax: M. Gligan i with the National Intitute for Reearch and Development of Iotopic and Molecular Technologie (NIRDIMT), Cluj-Napoca, Romania. recycle tream are preent between the column creating chain interaction, with ome application in azeotropic ditillation ytem. Multiple column in a plantwide environment have been explored in a variety of cae tudie of multiunit procee with reaction and eparation ection. In thee cae, multivariable model baed (predictive) control i an excellent candidate for plantwide control with ability to tackle dead-time and contraint, either in global control, either in ditributed control tructure [6], [7]. The Carbon element ha two table iotope: bae component (12C) with the natural abundance of at% and the heavier table iotope (13C), with 1.11 at% concentration [9] [11]. Uing dedicated equipment, it i poible to detect if a ubtance contain a larger concentration of (13C), uggeting it ynthetic origin. Baed on thi feature, the (13C) iotope may be ued in different application and field like cientific reearch, bio-medicine, environmental protection, etc [8]. The carbon monoxide with high-purity in (12C) i ued in electronic technology to produce ynthetic diamond crytal with 50% better thermal conductivity than that of the uual ynthetic crytal [9]. It i alo very effective in detecting tumour in the human body [18] and broadly ued in other clinical invetigation [17]. An effective method to produce ubtance with high-concentration of thee valuable iotope i baed on the cryogenic ditillation of carbon-monoxide [9]. There are very few plant worldwide which can perform thi complex operation. Among them i the National Intitute for Reearch and Development of Iotopic and Molecular Technologie (NIRDIMT) from Cluj-Napoca, Romania [16]. The current bottleneck in thi problem i the low efficiency of the high-purity tripping ditillation, making the proce unattractive from an economical point of view. The very complex tripping proce require large cale etup, without implicit efficiency. A pragmatic approach to olve thi iue i to ue train of triping ditillation column. However, when cloed loop control i involved, erie of ditillation column with recycle tream can endanger the tability of the overall proce and care mut be taken when chooing the control configuration. The objective of thi paper i to dicu thee problem and propoe olution for afe operation and efficient (13C) iotope production. The tructure of the paper i a follow: firt, ome theoretical background on controlling ditillation columni preented, followed by a numerical example of the column for tripping the (13C) iotope /15 $ IEEE DOI /CSCS

2 in the concentration of (13C) in gaeou phae, i achieved during the tripping proce. In order to rie the (13C) iotope concentration up to a deired level, a permanent countercurrent of the liquid-gaeou phae mut be enured. Thi i provided by an electrically heated boiler in the column bae and a condener, cooled with liquid nitrogen at the column top ide. The liquid nitrogen level in the condener and the liquid carbon-monoxide in the boiler mut be maintained at a contant level for optimal operation of the column. The generic tak of the control ytem i to keep the (13C) iotope tranfer rate contant, which can be achieved by variou control configuration. Fig. 1. Schematic of one CO tripping ditillation column with poibility to erie connect to a econd column. II. THE ISOTOPE SEPARATION COLUMN There are everal available method able to increae the concentration of the (13C) iotope in ome ubtance. One of them i that of cryogenic ditillation of carbon monoxide [9]. For pure carbon-monoxide ituation, at the vaporization temperature of nitrogen ( 190 o C), the liquid and gaeou phae co-exit [16]. Becaue the maximum vapor preure by (12CO) i higher than the preure of (13CO), the (13C) accumulate in the liquid phae, where it may be collected and extracted a final product. In the tatic contact of both phae, the increae in concentration i very mall. A given by the eparation factor (α), here we have a value very cloe to unity, i.e. α [9] [11]. A continuou counter current of an acendant gaeou tream and a decendent liquid tream of carbon-monoxide increae the (13C) concentration in the liquid phae and decreae it in the ga phae, which i then evacuated a wate. One dedicated equipment can offer an enrichment in (13C) only up to 8-10 at%, due to the above decribed phyical limitation. The (13C) iotope eparation column of the National Intitute for Reearch and Development of Iotopic and Molecular Technologie (NIRDIMT) from Cluj-Napoca i a teel packed pipe a depicted in Fig. 1, fed with pure gaeou carbonmonoxide by the flow-rate and (13C) iotope concentration at 1.11%at [9]. The iotope of interet (13C), accumulated in the liquid carbon-monoxide, i withdrawn a final product at the flow rate and concentration. The gaeou carbon monoxide with lower (13C) concentration i evacuated a wate at the top ide, by flow rate and the concentration, which i in fact the econdary product of the eparation column. The efficient thermal iolation of the column i baed on the external vacuum jacket. If cryogenic ditillation temperature i ued, the vapor preure of carbon monoxide with (12C) i greater than the preure of carbon monoxide with (13C), hence the iotope (13C) accumulate in the liquid phae. Thi proce i called the rectifying proce. Simultaneouly, a decreae III. SINGLE-COLUMN CONTROL CONFIGURATIONS A. Claical Control Approach Each ditillation column i unique through it deign and tructure and a generic rigorou modelling and control approach i not a realitic objective. However, to ome extent, ditillation column for eparation procee have ome common propertie, uch a thermodynamic principle and baic dynamic, which will be employed hereafter to dicu the claical control approach. Typically, a high purity ditillation column i connected in erie to another train of ditillation column [5]. The bottom product tream of thee prior column are buffered into a level-controlled tank and fed into the high-purity column (HPC). Hence, the feedflow i varied tepwie intead of continuou. However, the variation in the compoition are mooth. In cae of a tripping proce of erie of HPC, the top product tream directly into the feedflow of the next HPC. In thi cae, mooth continuou variation in the feedflow are expected a well a feed compoition. The monitored variable are typically top preure in the column and top level control of the cooling liquid. The compoition dynamic are mot important for control ince variation in one HPC in erie will affect the input, hence the dynamic of the next HPC. The product compoition are a nonlinear function of the reflux, boilup, and feed comdition. For intance, a 5% increae of the reflux flow rate improve the top product compoition with a certain amount, but the ame percent decreae degrade it much more. There are alo very trong interaction in the HPC; e.g. a change of reflux or boilup alter both product compoition. The interaction between both product compoition and reflux and boilup ha a evere conequence for the compoition dynamic, known a ill-conditioned behaviour. The control objective of HPC can be ummarized a threefold: control of the material balance product quality control maintaining contraint The firt objective include the control of the vapor holdup (top preure), the reflux accumulator level, and the reboiler level. Practically, thee control objective are eaily achieved by imple PI controller. The econd objective i the mot important ince it i related to the optimal economic and ecologic operation of the DHC [21]. It i well known that 50

3 tight control of both product qualitie minimize the energy comumption and deliver within-pec product. However, thi i a challenging control tak due to the preence of diturbance uch a variation of the feedflow rate and feed compoition (recall that i a erie train of HPC). Tight compoition control require advanced control cheme and ha been the ubject of everal important work [2], [3], [19], [20]. Reflux, boilup and preure drop are allowed to vary within a predefined range. Any operation of a ditillation column outide thi range may caue inufficient eparation or even phyical damage of the etup. A typical control problem of HPC ha five controlled variable: top compoition, bottom compoition, reflux accumulator level, reboiler level and top preure; and ha five manipulated variable: reflux, boilup (e.g. via reboiler duty), top product flow rate, bottom product flow rate, cooling liquid flow rate. Due to the high inherent enitivity of multivariable controller to enor or actuator failure, the inventory control (product quality) and the compoition control are independently deigned, increaing robutne of the overall proce. In a firt tep, the two manipulated variable are elected for the compoition control. In the pecialized terminology, the choice of thee manipulated variable name the control configuration. An excellent overview of the variou poible configuration i given in [19], [20]. For intance, if the top compoition i controlled by reflux (L) and bottom compoition i controlled by boilup (V), the control cheme i denoted a LV. The remaining manipulated variable are thu available for level and preure control. If a model of the HPC exit, typically in the form of a linearized model around the optimal operating point, then the choice of the input-output variable can be done on method a the relative gain array, Niederlinki index or ingular value decompoition [4], [24]. In practice, the application of thee method may lead to coniderably different olution and dynamic effect due to the interaction of inventory and compoition control are neglected. The mot common control configuration in the chemical indutry i the LV configuration [20]. Thi control tructure i rather independent of the inventory control dynamic and ha been proven to have good experiemtnal reult. In general, tight inventory control can be achieved with three imple PI controller. Some ditillation column how an invere repone of the reboiler level to an increae of boilup. In thi cae, tight control with boilup a manipulated variable become challenging and the re-election of the manipulated variable may be neceary. Invere dynamic occur in the preence of a RHP tranmiion zero in the linearized model analyi; by changing the variable election, uch RHP zero may be avoided. B. Claical Modelling Approach Robut controller are baed on the exitence of a (linear) proce model [13]. The development of a good model i therefore crucial for the control ytem ynthei. Thee model hould decribe the dynamic behaviour of the proce within a wide frequency range and they can be twofold: ytem identification model linearized model from nonlinear model Obviouly, ytem identification around the optimal (calculated) operating point i the mot pragmatic approach, but it poe ome difficultie: if time contant are large (depending on the contruction deign of the HPC), then the input-output record can be quite time-conuming; ince the HPC ha a high enitivity to change in the internal flow rate, it i difficult to define mall amplitude variation in the input which will not exceed the linear region; each identification experiment will caue diturbance in the product quality uch model are valid only around the operating point where they were identified. Thee di-advantage make ytem identification not an intereting approach; intead, linearization of nonlinear model i preferred and modelling uncertainty i allowed to be tackled by the choice of the control tructure. The problem ariing from the linearization proce are related to idealizing aumption, uch a: contant preure drop contant and equal enthalpie on all tray contant total holdup on all tray (equimolar flow) which of coure, are not realitic. The firt aumption mean a neglect of the correlation between tray preure, holdup, and boilup rate. The econd aumption implie uniform vapor flow within the tripping ection and within the rectifying ection of the HPC. The aumption of a contant tray holdup neglect in part flow dynamic. Thee aumption introduce in the model high frequency error, which may be critical if a fat performance given by a large bandwidth of the cloed loop i enviaged. C. Modelling Uncertainty Model uncertainty and lack of validity in the operating range can eriouly affect the overall plant tability and robutne [14], [15]. Typical ource of model uncertainty for HPC are meaurement error, limited actuator peed, unmodelled high frequency dynamic, proce nonlinearity. In the cae of HPC, which are highly nonlinear plant, the error of a linear model rapidly increae with the ditance from the operating point where it wa identified/linearized. Additional tochatic diturbance will alo affect the proce dynamic, in which cae the error cannot be determined. Thi error between the proce model and the proce itelf can be modelled either a a ingle frequency-dependent uncertainty bound (i.e. untructured uncertainty), or a everal frequencydependent uncertainy bound (i.e. tructured uncertaintie). Several type of uncertainty bound can be implemented, tackling variou practical apect. Of thee, we mention: input uncertainty model uncertainty meaurement uncertainty and we dicu the eential olution for each of them hereafter. 51

4 Fig. 2. Multiplicative uncertainty for the HPC input. The actual value of the manipulated variable reflux and boilup will never match exactly the value requeted by the control ytem. Moreover, thi error will alo be frequency dependent, becaue: i) tatic and dynamic meaurement error of reflux and reboiler duty; ii) actuator reolution; iii) changing heat of evaporation due to preure and temperature variation; iv) reboiler and actuator lag; v) effect of ampling (i.e. digital ytem). The bound for relative error in the column input u can be modelled by a multiplicative uncertainty decription with the frequency-dependent error bound w ul for the reflux L and the error bound w uv for the boilup V. Thee bound are combined in the matrix W u a in figure 2. The input uncertainty model i given by: with and ũ(jω) = {I + u (jω)w u (jω)}u(jω) (1) W u (jω) = u (jω) 1 (2) [ ] wul (jω) 0 0 w uv (jω) It ha been hown in [22] that the performance of the cloed loop for a HPC i very enitive to error in the manipulated variable. For controller deign (and analyi) the error bound W u need to be etimated a good a poible, epecially in the low frequency range where the condition number of the column model i high. The rik i lower control performance if overetimation occur. In thi low frequency range, the error of the manipulated variable at the plant input are trongly dominated by flow meaurement error and parameter variation. For intance, if boilup i controlled indirectly by the team flow rate, a change in the heat of evaporation will caue error in vapor flow rate leaving the reboiler. Calibration of the flow meter i therefore crucial. The effect of reboiler lag, actuator lag, dynamic meaurement error and ampling period are preent in the high frequency range. Thee error increae with the frequency and can eaily exceed 100% of the nominal value for frequencie above 1 rad/min. In thi cae, the teady-tate error together with the high-frequency error can be approximated by a firt order lead/lag tranfer function: (3) G() = K 1 + /ω N 1 + /ω D (4) with ω N, ω D, the gain K repreent the teady tate error and cut-off frequencie choen for ω D > 10ω N. The model uncertainty ha twofold origin: i) column nonlinearity and ii) un-modelled dynamic. The highly nonlinear behaviour of HPC i oberved at varying operating point and at tranient during diturbance rejection. Thi depend on the varying internal flow rate (L and V) and on the compoition profile within the ditillation column, repreented by the liquid and vapor phae compoition. Any type of control ytem for HPC will exhibit large gain in the low frequency range to achieve mall control error at teady-tate. Tranient have no ignificant effect in the low frequency range and the internal vapor and liquid flow rate a well a the compoition profile within a column become a function of feed flow rate and compoition only. However, the dynamic behaviour of a HPC depend ubtantially on the true compoition profile and the true internal vapor and liquid flow rate. Conequently, the operating range of a HPC can be bounded with a maximum and a minimum feed flow rate and compoition. In thi framework, it follow that the larget internal flow rate will exit for the mallet feed compoition and larget feed flow rate. Similar reaoning indicate that the mallet internal flow rate will exit for the larget feed compoition and mallet feed flow rate. hence, the low frequency behaviour of a HPC i bounded by the model for maximum and minimum column load. The implet way to repreent the column nonlinearity due to varying operating point would be to ue a multiplicative output uncertainty. Auming the uncertainty for each model output independent of the actual value of the other model output, one ha: with and ỹ(jω) = {I + y (jω)w y (jω)}y(jω) (5) y (jω) 1 (6) y(jω) = G N (jω) [ ] d(jω) u(jω) with G N the tranfer function matrix of the plant at nominal operating point and W y a diagonal matrix imilar to (3). Care mut be taken with uch uncertainty repreentation ince the low frequency range tend to have a high multiplicative gain, which i prohibited for any control deign. However, thing become impler if the error are highly correlated, i.e. the variation of the teady-tate operating point caue a imultaneou increae/decreae of the ingular value of the tranfer function from the control ignal u to the model output y. Thi tatement can be evaluated by mean of Nyquit plot for individual channel u i y i. Notice that the effect of tranient obey the law of a rather untructured uncertainty. Due to the nonlinear vapor/liquid equilibrium, the ingular value of the tranfer function G u yj may change in different direction, which poe other control challenge. The econd origin for model uncertainty wa un-modelled dynamic. Mot of the work in literature treat the effect of flow dynamic in an input time delay τ, with 0 < τ < 1 minute [23]. (7) 52

5 Finally, meaurement uncertainty can be well exemplified by temperature meaurement. Thee can be well approximated by a firt order lag modelling the behaviour of a temperature enor. The time contant of thi model depend on the poition of the temperature enor. If the enor i placed in the liquid phae, time contant of the order of 1 minute can be expected. However, if the enor i placed in the vapor phae, it can go up to 10 minute or more. The gain of the model i related to enor calibration and heat lo to the environment. For the cae of our HPC, heat loe are cloe to zero (vacuum jacket) and calibration i aumed to be correct. The complete uncertainty model conit of input uncertainty (1), model uncertainty (5) and performance pecification. Simple dynamic model are ued whenever poible, to avoid further uncertainy block. The advantage of uch modelling approach i that the entire operating range of the HPC i covered. D. Improved Control Approach From an economic point of view, diregarding the control and meaurement problem, two-point control i obviouly the bet, i.e. both compoition loop cloed. Thi follow ince the optimal operating point correpond to ome given purity pecification. In cae of tripping HPC, thee are not independent. There i alo a cae when one-point control i optimal, i.e. when the column i operated at maximum capacity. In the LV configuration, by controlling one compoition, inherently we control the other (i.e. trongly coupled). If one can meaure the feed rate, and implement a feedforward controller by uing the ratio L/F, then we achieve elf-regulation of F. In thi way, one achieve acceptable control of both product (top and bottom) if ingle end control of bottom compoition i ued and fixed L/F ratio. Feed compoition enitivity analyi i ued to determine of a ingle-end control tructure would be effective. Thi i achieved with dedicated oftware, baed on teady-tate imulation. Typically, one check the percent variation of the required reflux flow rate and reflux ratio over the range of feed compoition. Depending on the etimated value, it may be indicated that for HPC a ingle end control tructure with a fixed reflux-to-feed ratio would outperform a fixed reflux ratio tructure [5]. The baic control tructure i depicted in figure 3 and uggeted improved tructure in figure 4 a following. In a train of erie HPC, the feed come in on flow/level control from the uptream column. Preure i controlled by manipulating condener duty. Reflux can be ratioed to feed, and reflux-drum level i controlled by manipulating the flow rate of the ditilate product. Bae level i controlled by manipulating the flow rate of the bottom. Temperature i not controlled directly, but from the preure meaurement at top and bottom HPC tray, it reference value can be etimated and controlled by reboiler duty. Competing rule for ditillation control need to be negociated. For intance, analyi ugget that the reflux-drum level i controlled by reflux becaue of very high reflux ratio. However, it alo ugget that the reflux hould be ratioed Fig. 3. Schematic of a baic control tructure of one HPC within a train of erie HPC. Fig. 4. Propoed control tructure of one HPC within a train of erie HPC. to the feed. Obviouly, thee are not independent, hence cannot be achieved imultaneouly. An ingeniou olution i given in [5], ummarized a follow and illutrated in figure 5. Thi control tructure i imilar to the previou one 53

6 IV. N UMERICAL EXAMPLE A. Single column For the column from Fig 1, the tranfer function matrix i given by: (8) where the time delay ha been ignored for implicity and with input and output verified by the relative gain array a following: i) firt manipulated input i the output wate flow from the column to control the preure in the column at the condener zone, ii) the econd manipulated input i the feed flow to the column to control the liquid carbon monoxide level in the boiler, and iii) the third manipulated input i the electrical power upplied to the boiler reitor, to control the preure in the column at the boiler zone. The dependence of the relative gain array with frequency depicted in Fig 6 ugget that for tep change in the controlled variable, the pairing i optimal. Fig. 5. Another propoed control tructure of one HPC within a train of erie HPC. propoed, except the following: reflux-drum level i controlled by manipulating reboiler duty and the ditillate impurity i controlled by manipulating the control valve in the ditillate line. The control tructure from figure 5 i unuual becaue of the ue of reboiler heat input to control the reflux-drum level. Thi i baed on the aumption that the feed compoition enitivity analyi require very mall change in the ratio, hence it can be fixed. The liquid level in the reflux drum can be controlled by ditillate - thi will fail if the flow rate i much maller than the reflux. In the latter cae, the reboiler duty can be employed efficiently to olve thi dilemma, if the change in vapor flow rate in the column are fat. The ditillate compoition i controlled by the ditillate flow rate. Uing high gain control, it i poible to achieve fater repone of vapor boilup to level change. Thee are then detected by the level controller, which change the vapor rate up the column and affect ditillate compoition. Notice that the preure controller manipulating condener duty i neted inide the compoition control loop. Fig. 6. Dependance of frequency of the relative gain array for one column. Further analyi into the magnitude of the tranfer function matrix from (8) ugget that the bandwidth of the ytem i around 0.1 rad/, a in Fig 7. Finally, the ingular value decompoition ugget that the firt pair of input-output variable may poe mot difficulty for control if the bandwidth of the ytem i increaed to obtain better perfromance in term of maller ettling time. Fig. 8 depict thee value a a function of frequency. Two-point control will not be adreed here, but we may ugget ome idea. The liquid flow dynamic decouple the two column end (top and bottom) at high frequency. If effort i put into making the quality loop fat enough, good control can be achieved for both compoition. Thi can be done uing temperature meaurement, or in our cae inference from preure meaurement, with an outer compoition cacade loop. In other word, a combination of the control cheme uggeted in figure 4 and figure 5. B. The train of ditillation column The real life etup deal with a cacade of three column [16]. The permanent counter-current of liquid and gaeou phae i enured by a common condener cooled with liquid nitrogen and by three different boiler, one for each column, heated with electrical reitor. Studying the coupling poibilitie of the three column, the concluion wa to feed 54

7 Fig. 9. Schematic of the tripping train of ditillation column. Fig. 7. Gain of the ytem for one column. Fig. 8. Singular value of the ytem for one column. the firt column with carbon monoxide, the enriched gaeou phae from the firt column being ued a feed for the econd column and the product of the econd column a feed for the third column, enuring maximum enrichment in (13C) with minimum equipment. Previou tudie revealed that the major influence on the end product in a eparation column ha the vapor uptream, which i maintained by the electrical reitor of the boiler. Thi wa the reaon why the author have choen to implement in preent work the ditributed control of the reitor power for the cacade of three column. For the econd column from Fig 9, the tranfer function matrix i given by: (9) and for the third column i given by: (10) The interaction matrice for the reflux from the econd column to the firt and from the third column to the econd are given by (11) and (12), repectively. From a practical tandpoint, all loop within a HPC can be taken a P-controlled (proportional gain only). In thi way, fat dynamic can be achieved. However, ince compoition feedback control uually ha low dynamic, a PI-control can be ued a an outer loop. Thi reult in a cacaded control cheme, which eem to be the optimal olution from the afore mentioned analyi. The controller parameter are given by: C11() = C22() = C33() = C44() = C55() = C66() = C77() = C88() = (13) (14) (15) (16) (17) (18) (19) (20) 55

8 C99() = (21) Analyi of the enitivity function reveal in Fig. 10 that the mot difficult to control i the firt column, ince all dynamic propagate from it into the output of the lat column, a per global control objective. tudy cae wa developed around the tripping proce of the (13C) iotope, a valuable product in a manifold of application. A the control methodology i further developed, inight into the problem will become available to further improve thi complex proce. ACKNOWLEDGMENT Thi work wa upported by a grant of the Romanian National Authority for Scientific Reearch, CNDI UEFISCDI, project number 155/2012 PN-II-PT-PCCA Fig. 10. Schematic of the tripping train of ditillation column. The mot economic control cheme will only ue one ditillate compoition enor at the output of the third HPC. In thi cae, there are everal poibilitie for global control. Firt poibility i to ue cacade control with compoition of the third column output a the outer loop and temperature (via preure) control in the ame column. The firt and econd HPC are not controlled for compoition output, only kept within a deired (i.e. calculated) range for level, feed flow rate and preure value. Thi i a relatively imple olution, if tight control i not neceary. Second poibility i to ue tight control in each HPC, and global control for compoition, meaured at the output of the third column. Thi implie a hyerarchical or ditributed control trategy, where each column i controlled eparately for it optimal operation, but ince they interact with each other, a global cot index (typically related to the compoition) provide the operating condition and reference value for each of them. Thi i a more complex problem in term of tability, but till numerically acceptable for real-life implementation. Third poibility i to view the enemble of the erie train of HPC a a input-output block, with intermediate variable, in a centralized control trategy. Intuitively, input will be thoe entering the firt column and output will be thoe from the third column. The drawback of thi cheme are the model complexity and the intrinic coupling effect between column due to recirculation, a depicted in figure 9. The latter can be avoided by very good condener and reboiler operation, i.e. avoiding high variation in the preure at the column end. REFERENCES [1] B. W. Bequette, Proce Control: Modeling, Deign and Simulation, Prentice Hall; 1 edition (2003) [2] S. Skogetad, Dynamic and control of ditillation column - a critical urvey, Modeling, Identification and Control, 18, pp , (1997) [3] S. Skogetad, Dynamic and control of ditillation column - A tutorial introduction, Tran IChemE, 75, Part A, pp , (1997) [4] W. L. 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