Identification Process, Design and Implementation Decoupling Controller for Binary Distillation Column Control

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1 Identfcaton Process, esgn and Implementaton ecouplng Controller for Bnary stllaton Column Control SUTANTO HAISUPAMO ), RJ.WIOO ), HARIJONO A TJOKRONEORO ), TATAN HERNAS SOERAWIJAYA 3) ) Engneerng Physcs epartment of ITB ) Electrcal Engneerng epartment of ITB 3) Chemcal Engneerng epartment of ITB Jl. anesa 0 Bandung, INONESIA-403 Abstract: Identfcaton process of the dstllaton column s the frst step for desgn and mplementaton decouplng controller for bnary dstllaton column control. For hgh purty products, the dynamcs of the column become hghly nonlnear and coupled and the response are senstve to external dsturbances. stllaton column control systems are use to purty the mxture of methanol and water whch shows strong nteracton, nonlnear dynamcs and a large number of possble control structures. In ths paper, we consder a decouplng controller to elmnate the strong nteractons. The decoupler cancels the effect of the dstllate composton to the change of the bottom composton and the effect of the bottom composton by the dstllate composton. Smulaton result good response for dstllate control and bottom product control for decouple control systems wth feed composton change from 0.6 to Keywords: dentfcaton, dstllaton control, multvarable system, nteractons, decouplng.. Introducton Identfcaton process dstllaton column s the frst step for desgn and mplementaton decouplng controller for bnary dstllaton column. Multvarable hgh purty dstllaton columns present a number of challengng problems for both system dentfcaton and control due to ther nonlnear and ll-conon nature. These two characterstcs cause these dstllaton columns to be dffcult to dentfy and control (Luyben, 987). ecouplng of nput and output varables s one of the central control desgn problems that has attracted consderable attenton snce the early 70s, n whch, the decouplng problems has solved for the case of non uncertan system by means of statc measurement matrx s usually uncertan due to the measurement devce error[]. Ths s dffcult problem and has not yet been solved. The objectve of ths paper s to dentfy the process and desgn the decouplng controller that mnmzes the control loop nteracton between nputoutput varables of column dstllaton process.. Identfcaton Process stllaton Column For MIMO dentfcaton of hgh purty dstllaton columns, t appears that closed loop experments are preferable to open loop ones due to the drectonalty aspect of multvarable dstllaton columns. For multvarable

2 open loop experments, the usual practce s to apply mutually ndependent pseudo-random bnary sgnals (PRBSs) to all the manpulated varables (MVs) of the plant. The llcononed nature or drectonalty of a hgh purty dstllaton column means that the two MVs n open loop experments are hghly correlated[8]. We defne the systems by Auto Regressve Movng Average (ARMAX) model: A(z - )y k z -d B(z - )u k C(z - )w k () Where d s delay tme, w k s whte nose and A,B,C are: A(z - ) a z a na z -na B(z - ) b z b na z -nb C(z - ) c z c na z -nc The nput sgnal s Pseudo Random Bnary Sequences (PRBS), and the polynomal form s: P(z - ) z - z - z -3 z z - n () We fnd the result of dentfcaton process gan dstllaton columns: s (s) s (3) s (s) e s 0.44 (4) s (s) e s 0.6 (5) s ( s ) e s 0.54 (6) These model processes wll be utlzed for desgn decouplng controller. 3. ecouplng Controller The decouplng structure control system developed by Boksenborm and Hood (949) s shown n Fgure. The decouplng matrx s of the form [] : (7) For the x MIMO process control can be wrtten as: u y (8) u [w-y] (9) Where j the transfer functon, u and y denote the nput and the output and w[w,w ] T s the setpont. Substtutng (9) nto (8) yelds [w-y]y (0) Rearrange ths equaton leads to the closed loop expresson: y [I ] - w () w w decouplng Fgure. ecouplng control system (Boksenborm and Hood, 949) In order to make ndvdual loops of the closed loop system are ndependent each other, t s requred that: X [I ] - dag[x,x ] () Where X must be a dagonal matrx. Snce the sum and product of two dagonal matrces are dagonal matrces, and the nverse of dagonal matrx s also dagonal matrx. u u process y y

3 The requrement can be ensured f s a dagonal matrx. From (7) and (8), we have: so q (3) 0 q 0 0 q 0 (4) q Comparng each element of the matrces (4) results n a set of four equatons: q 0 0 (5) q If the transfer functon elements of are known, and havng specfed the dagonal element of, then the approprate off-dagonal elements of to acheve decouplng control are calculated by solvng the set of equatons n (5). Smplest way s to set to a dagonal matrx, and ths gves the followng relatonshps: (6) and (7) From equatons (3), (4), (5), and (6) we fnd the elements of decoupler: 4.4s (s).67s (8).337s 0.7 (s).59s 4.9s (9) The decouplng elements and of the decouplng matrx c can then be Proportonal-Integral (PI) controller. 4. ual Composton Control x B and y The choce of the proper confguraton for dual composton control s more challengng than a sngle composton control, because there are more vable approaches and the analyss of performance s more complex. In ths case there are a many of choces for manpulated varables (L,, L/, V, B, V/B, B/L, /V) that can be pared to the four control objectves (.e. x B, y, reboler level m B, and accumulator level m ) ndcatng that there are a large number of possble confguratons. In ths paper t s assumed that the choce for control confguraton s L and V. The setpont for reflux flow controller s set by the overhead composton controller and the setpont for the flow controller on the reboler duty s set by the bottom composton controller[5]. The L and V confguraton s used snce t provdes good dynamc response, and n general, the confguraton s least senstve to feed composton dsturbances. Moreover t s easy to mplement, but t s hghly susceptble to couplng. For ths reason we desgn decouplng controller to antcpate ths couplng. In many cases, the control of one of the two products s more mportant than control of the other. For such cases, when the overhead products are the most mportant, L s usually used as a manpulated varable. When the bottoms products are most mportant, V s the proper choce as the manpulated varable. For a low reflux column for whch the bottom product s more mportant, the L and V confguraton s preferred. 5. An Example Consder process dstllaton column wth two nputs and two outputs shown 3

4 n Fg. 4. The manpulated varables are L reflux flow rate, V bol-up flow rate, and the controlled varables are y dstllate purty, and x B bottom purty. The manpulated varables are L reflux flow rate, V bol-up flow rate, and the controlled varables are y dstllate purty, and x B bottom purty. The mathematcal model s derved from the fundamental prncples as follow: Overall materal balance: Tray feed, N F dm L{} - L V {-} - V F (0) d(mx ) L{ } x{ } V{ } y{ } Lx V y FzF () Total condenser, NT, (M NT M,L NT L T ) dm V {-} - L () d(m x ) V{ } y{ } Lx V y x (3) Reboler,, (M M B, VV V B V) dm L {} - V B (4) d(m x) L x V y V y Bx { } { } (5) At steady state conon relaton between control varable and manpulated varable are: äy äy Äy ÄL ÄV KÄL KÄV äl äv V L äxb äxb ÄxB ÄL ÄV KÄL KÄV äl V äv L (6) The K s are steady state gans that can be determned from mathematcal models or from expermental test. They descrbe how, say, L affects y when x B s not controlled. A second gan may be defned that gves a measure of how, say L would affect y f x B were under closed loop control by the relatonshp: Äy K (7) ÄL and K Äx V constant(äv 0) B (8) ÄL V constant(äv 0) Feed, F,z F Fgure. stllaton Column wth ecouplng Controller L o V o LT F,z F,q F y set x Bset M B,x B y N valve valve Reflux,L,y y,m V,y B Reboler AC decoupler stllaton column confguraton L,V decoupler Pengontrol (dekopler) Fgure 3. Block dagram dstllaton column confguraton L,V wth decoupler AC LT Water cooler Top Product,,y Bottom Product B,x B Steam y B x B 4

5 yset xbset Feedback controller Feedback controller L* V* B Fgure 4. Block dagram control system wth decoupler To smulate the proposed decouplng controller for the dstllaton column, we use the dstllaton data [4]:. number of tray 4 (nclude reboler and condenser). feed locaton 0 3. relatve volatlty alpha.5 4. nomnal reboler holdup M O () 0.5 [kmol] 5. nomnal holdup condenser M O (NT) 0.5 [kmol] 6. nomnal holdup tray M O () 0.5*ones (,NT-) ; :NT- 7. nomnal feed rate F O [kmol/mn] 8. nomnal fracton lqud n feedqf O. 9. nomnal reflux flow L O.7069/ nomnal lqud flow below fed L Ob L O qf O *F O. affect flow vapor n lqud flow lambda 0. nomnal vapor flow V O 3.069/0.5; V Ot V O (-qf O )*F O Termodynamc data: a. Bolng pont lght component 7.65 o K b. Bolng pont heavy component o K c. Heat capacty lght component 96 kj/kmol o K L V B y x B d. Heat capacty heavy component kj/mol o K e. Hvap for lght component 9575 kj/kmol f. Hvap for heavy component 8350 kj/kmol g. Vapor pressure of pure lqud component.03e5 h. Vapor pressure of pure heavy lqud component.03e5. Unversal gas constant 8.34 kj/kmol o K 6. Smulaton Result and Conclusons Smulaton result show that the response of the process control wth decoupler has smaller offset than the process control wthout decoupler. And also smulaton gve the good response for dstllate control and bottom product control for decoupler control systems wth feed composton change from 0.6 to y setpont: y0.995; F.0; zf0.6; qf.0, delay3 wth decouplng wthout decouplng Fgure 5. Comparaton between control system wth decoupler and wthout decoupler for setpont y 0.995; z F 0.5; F.0; q F ; delay tme3. tme 5

6 y setpont: y0.995; F.0; zf0.6; qf.0, delay3 wth decouplng wthout decouplng Fgure 6. Comparaton between control system wth decoupler and wthout decoupler for setpont y 0.995; z F 0.6; F0.; q F ; delay3. y Set-pont : y0.995; zf0.35; F.0; qf; delay3 wth decouplng wthout decouplng tme Fgure 7. Comparaton between control system wth decoupler and wthout decoupler for setpont y 0.995; z F 0.35; F.0; q F ; delay3 xb Set-pont : xb0.005; zf0.35; F.0; qf; delay3 tme decoupler for setpont x B 0.005; z F 0.35; F.0; q F ; delay3 Reference: [] F.N.KOUMBOULIS and M.. SKARPETIS, Robust Input-Output ecouplng va Statc Measurement Output Feedback, CSCC 99 Proc.pp [] M.T.Tham, Multvarable Control, An Introducton to ecouplng Control, ept of Chem. And Process Eng. Unv. of Newcastle upon Tyne, 999 [3] Page S.Buckley, Wllam L. Luyben, Joseph P. Shunta, esgn stllaton Column Control Systems, ISA, 985 [4] Skogestad and Morar, Understandng the ynamc Behavor of stllaton Column, Ind.&Eng.Chem.Research, 7, 0, , 988 [5] Cantrell, J.., Ellott, T.R., Luyben, W.L., Effect of Feed Characterstcs on the Controllablty of Bnary stllaton Columns, Ind. Chem. Res. 995, 34, [6] Cha, T.Y., A Self Tunng ecouplng Controller for a class of Multvarable Systems and lob Convergence Analyss, IEEE Transacton on Automatc Control, Vol. 33, No. 8, 988. [7] Rggs, J.B., Comparson of Advanced Control Technques for hgh purty stllaton Columns, Submtted to AIChE Journal, September, 989. [8] Chou C. T., H. H. J. Bloemen, V. Verdult, T. T. J. van den Boom, T. Backx, M.Verhaegen, Nonlnear Identfcaton of Hgh Purty stllaton Columns, IFAC SYSI 000, Symposum on System Identfcaton,(Santa Barbara, Calforna) June wth decouplng wthout decouplng Fgure 8. Comparaton between control system wth decoupler and wthout tme 6