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1 Korean Chem. Eng. Res., Vol. 44, No. 5, October, 006, pp { oh l om oh m -74 ne e (006 9o p r, 006 9o 3p }ˆ) Advanced Control Techniques for Batch Processes Based on Iterative Learning Control Methods Kwang Soon Lee Depart. of Chem. and Biomol. Engng., Sogang Univ.,, Shinsoo-dong, Mapo-gu, Seoul -74, Korea (Received September 006; accepted 3 September 006) k o lp r lp l r p v 0l m rl tep rl(apc) p p nr l p v p l. pl l t p s rl APC p pp kv p lvv k p. p p rp rrp o p q p p re v l q po p p. p rr p p APC p drl(ilc)l l r APC l pl p. l p p k er rl rn l nrp p, ILC p p r APC l p p e. h Abstract The operability and productivity of continuous processes, especially in petrochemical industries have made remarkable improvement during the past twenty years through advanced process control (APC) typified by model-based predictive control. On the other hand, APC have not been actively practiced in industrial batch processes typified by batch polymerization reactors. Perhaps the main cause for this has been the lack of reliable batch process APC techniques that can overcome the unique problems in industrial batch processes. Recently, some noteworthy progress is being made in this area. New high-performance batch process control techniques that can accommodate and also overcome the unique problems of industrial batch processes have been proposed on the basis of iterative learning control (ILC). In this review paper, recent advancement in the batch process APC techniques are presented, with a particular focus on the variations of the so called Q-ILC method, with the hope that they are widely practiced in different industrial batch processes and enhance their operations. Key words: Batch Process, Advanced Process Control, Iterative Learning Control. m rl(mpc, model-based predictive control) tep l rp rl v 0l krp r mp, p o ro rp trl p e q qk [, ]. pl p r q p p v rp n e MPC pp. pl l rp rl k rp n l pl. l l l po p. n r To whom correspondence should be addressed. kslee@sogang.ac.kr l o p sr p p s q v p p l t pp v o l r~l v tp lr v kp, kr e p s r p vp n rl p pp p o k rp opp qn p. e rp l rp l r l n p p pl rl ql ke n pp v l r p. rp enrp r rl p o drl(ilc, iterative learning control) p p r l mp, l rl rp pn 45

2 46 p p p. l rp l rl p ILC p p rl p n pnl rp q m.. om Š rlp rl rp l r n l p. p p rl l opp p p enrp r rl p qp lr p. rp q t, r, ~, q, pk,, e k ll k ˆ pn pv, r lp rl l ~ l r p p ˆ. () l rp rl r n p o regulation r tlvv, rp rl r tracking r tlv. p rp tracking rl regulation p rp r l l servo p l. () rl p ˆ. p p rp r~l ~ r ˆl nr l ˆ p. l r rq~ rpv r r ˆ t l nr l p. rp p o p nrp v l p. p p rl e p r p l l. (3) rp rp r. rp p nr p erl vp k p. l r l r r ep p s r p rp l., sr p vrl ee l p vrp. (4) rp sq m rl p e l p. m l p p n er n sq p r k n r rl. (5) p rp v p ˆl nr l r p ee l n p op n v k. (6) rp pr ol p p rp r nrp. rl r p r pl l s erp r p n p pr v kp p. rp rl p ol p n p p plk. p p l m p r q e p p. k rl p rll p l m v m v l l er l l sp p pv v l l. 3. PIDoh i m oh q p r p l rl m p PID rl pn rl rp rl p. rp p e l v l p l rl spp o44 o k v k rr rl p lp l n. er l~ t p p n, rl r q v kk r l rl p r n. Fig. p er t p l p m rl p p l p p. rl spp r l pv k k relay rl } q p. l t n p n t (ultimate period) p p. p p p t p p p p l n p p. p v p l p t m p p PIDrl sp p e l d u, Fig. m p rl lp pl. Fig., p p l m p r p rp l l qv k n rl p r l p lp p. v kp n, rl p l l. rl rlm v p r o qp r pr p ov pv k n rp rlm lk l. Fig. 3 p r ramp n rlm p l. er t p l r p p p m d er Œp l pp eq Fig.. Variation of the period of reactor temperature oscillation in an industrial polymerization reactor. Fig.. Improvement of temperature control in Fig. by sche-duling of PID parameters.

3 drl p rp rl 47 PID rl p r pr p ov r m n p l q rlm lk t p ppp q k r p. p r e p r o l r r p k n l. p e l r qp Fig. 3. By feedback-only action, PID control necessarily results in lagged response to ramp reference trajectory. erl p m rlp. rl pn n, rlm v erl pp p rp eq l pp, p erl p rl qp p p p m dp l n n. p r kp rlm v rl rl qp p. p rl q p p llv p p k, l t plk. p o e o r r p k p n. m l p e rp rp p t ut () R I ek ( ) ut () ut ( ) + R I et ( ) k 0. p qp rlm e(t) 0p k p kpp p lk o l u(t) v p eˆ p. R I l rlm e(t) 0p u(t) l pr p, k t v ˆ. p o R I r l p r ˆ n l. pr k rp pr k nr, r k r rp p Ž p tlv, n p Ž p p p dl r rl ()e p p f q rlm lk pp p. p p ep ˆ o l p p N er p, k w l p p, r rp p p rp q. () yt () Fut ( ()) () u k [ u k ( 0) T u k ( ) T u k ( N ) T ] T m p tlv r r(t)l r(t) y(t)p pn l u(t) p p e o e n p. rp ep m p l e p o e l p dv k rrp p. 4. om ooh i ol l rrl l rl p p / o rl p rl pn e t v l m. p e t p [3-6], p [7-0], r [-4], v r [5, 6], RTPm p ~ q [7-9] k rl e l m. p r l rl p p p r l ps, e p r p l o l np v l ll p p p. rp rn p n rp, o p p r p v n p p r k n p qœp lk. 5. ohm 5-. lm n oh q p rp rrl p m sq l l rl p p p. l l p p rln seˆ p l p p l l. p p po r rl p l p. y k [ y k ( ) T y k ( ) T y k ( N) T ] T r [ r ( )T r ( ) T rn ( ) T ] T p dl r rl k u k H ( r y k ) u k u k + He k n 0, p r rlm p po p H l e k 0p v k p. p p o l H r l l r n l. Fig. 4l o r qp rl p m. r rp Ž p pr, p Ž p n p op l H rr ˆ p l Fig. 4. Batch-wise integral control can completely remove the tracking error despite nontrivial model error. (3) (4) Korean Chem. Eng. Res., Vol. 44, No. 5, October, 006

4 48 p rlm tl mr rrl p p p. p rl k- p nr pn l k l n rlp e s v, pr l p n r dp rle rp l drl(ilc; iterative learning control) n p. u k k w p o e n p. ILC r p m l lim e k 0 seˆ r k o e pr p nr pn l rl p p. 5-. ohm i ILCl p p 35 r Garden[]l p kl pp, p Millerm Mallick[], Uchiyama [3]l p pn p. 984 Arimoto [4]l p s v qq p pv v ml. Arimoto p Žp o rp r s o l o D- ILC p rk m. p ILC rl l e p e k v, r l ps v k k v k v p k ˆ p rk l. l l ps v k k v rlm 0p o rl p p pr s p se k. p tlv n p s p seˆ p p d pp k rl l p k vp p p., p ILC SISO(single-input single-output) rp p mp l MIMO(multiple-input multiple-output) q l. p p p MIMO rl p rp e k 0p seˆ p ILC p rl e k minimum r lk. ILC r r k vp l l mp, n p s prp p r k v p l mp, p p u k u k +H e k H N e k N (5) k vp rk m [5]. r r rl k vp prp tv v, r rl qpp pp, r ILC k vp p p k v m [6]. ol ILC ee rl p l l pp, k nrp v k, rp n l p v open-loop ˆl p. p rrp m o l ee rl p l p rk m. p rp ee rl p ILCl ILC p r v p m p. ILC p r kl rk p pn le kl q. pnl HDDm p pr r r, qlp q l p pnp p lv pv, v k 0,, ~, q kp s rl pnp v p. Ahn [7]l p s ILC l l o44 o k p p p p. p rl rl p ILC p rp, k ILC t p e MIMO r ILC p p en p v prototype k v p. 6. ILCi ok oh 6-. om rp e rp v tlv r r t l nr nl p e (time-varying) rp p. rp l pv ILC m np pp p p l r m r v k. pr p p N erp p p p p e ˆ ep p. xt ( + ) At ()xt + Bt ()ut () + Kt ()vt () yt () Ct ()xt () + vt ()t, 0,,, N l v(t) rl op n rqpp op r p p innovationp p, rp zeromean,, erl p e p. kl p v(t) p v r pv kp p. (3)e p r l p e rp (6)ep p e pp y k Gu k d k l G g, g, 0 g, g N, 0 g N, g NN, g n,m C(n)A(n-)...A(m+)B(m) (8) p, d k x(0), v(τ), 0 τ Np n e p. d k kl rp zero-mean e dˆ m d k p p p. d k dˆ + d k l d k p p qp np r r d k d k + n (6) (7) (9) (0) pr y k Gu k + d k, e k r y k, e k r y k rp, km k-l p (7)ep l r p p pp rpep l.

5 drl p rp rl 49 e k e k G u k + n e k + dˆ e k () l u k u k u k- p p. o l s p Lee [8]l q l p. 6-. Q-ILC ee rl l ILC r e k-, e k-,... u k r p. p p p p r l p r p. min -- { + u k R } e kk u Q k () l x Q x T Qx, k- vp nrr l l e kk lp e k p rm p p p Kalman el p p tlv. u k e kk e k k G u k e kk e kk + K( e k e kk ) (3) Fig. 5. Comparison of tracking performance of I-ILC and Q-ILC. rks p l n, ()ep p p tlv. u k He k k ( G T QG + R) G T Qe k k (4) p k vp Q-ILC(quadratic criterion-based ILC) Lee [8]l p rk p. Q-ILC sp ILCp rrp rp p p rp, enrp p prp v p. sp l l ILC u k e eˆ, p p nonsquare MIMO rl rn l p r p. r l rks p p n, (4)em p pep tlvv kv QP(quadatic programming) r l rp e p v. Q-ILC r G 00Í m v v rlm p eˆ p p p v. Fig. 5l SISO rl Q-ILCp p l l ILCm l m. l er r Q-ILC o r p G p () s ( 5s+ ) ( 3s + ) G s., () m ( s+ ) ( s + ) (5) p t p r r m. r l qpp p p r m oh m Q-ILC ee rl(rfc, real-time feedback control) p l l p. ee rl p k l p p. l r RFCm ILC p el k vp. p k vp rp u k () t u k () t + H e k ( :t) + H e k ( :N)+ (6) p s. l H e k (:t) p RFCl, v p ILCl. pm p rl ep l l q ep (6)ep u k (t) p e k (t) ˆ ep eˆ p. p p p llv k r l p RFC ILC llv. pr r (6)ep el v(t) kl v p p qpp p dl r rp r. v k () t v k () t + nt () v k () t v k () t + vˆ () t l n(t)m vˆ (7) (t) rp qpp. pm p v(t)p l (6)ep n(t)m vˆ (t)p m p p l p. x k ( t+ ) At ()x k () t + B() u t k () t + Kt ()nt () y k () t y k () t + C()x t k () t + nt () xˆ k ( t+ ) At ()xˆ k () t + Kt ()vˆ () t ŷ k () t Ct ()xˆ k () t + vˆ () t y k () t y k () t + ŷ k () t (8) (9) (0) (8)ep ˆ ep o x k () t l y k ( ) p... y k ( N) q n ˆ rp lk. p n ˆp v y k () t y k ( t t) p y k k () t ˆ ep. p p, (8)e~(0)ep l p e k (t) p ˆ ep p. Korean Chem. Eng. Res., Vol. 44, No. 5, October, 006

6 430 p x k ( t+ ) xˆ k ( t+ ) At () 0 0 A() t + Kt () 0 0 K() t x k () t xˆ k () t nt () vˆ () t + Bt () 0 pep p p p rp q. u k () t e k () t e k ( tt) [ C() t Ct ()] x k() t n() t vˆ () t xˆ k () t z k ( t+ ) Φ()z t k () t + Γt () u k () t + Kt ()wt () ζ k () t e k () t e k ( tt) ()z t k () t + mt () () () pr RFC k vp r l k llv p. r p p LQG r p p. min --E u k N t 0 e k () t Q + u k () t R ζ k () t e k ( tt) + Q (3) u k (t) rlm p r p p d p r rl, v, ILC qp o p. e p r o l ˆ ()e u k (t) p p r p. (3)e rl r t LQG rrl r u k (t)p p l l p q re l p. p rl k vp Lee [9]p re mp BLQG(batch LQG) m. r l rks p p n LQG p l ov p p p MPC r p v. min -- u k p k Subject to linear constraints on process variables + (4) (4)el m p m e k (t+k t) o m ()ep pn l. rks p p n, (4)ep QP l rp llv. ˆ ep ˆ o mv (4)el p ILC rl Lee [30]p BMPC (batch MPC) m. l QILC, BLQG, BMPC r l ILC p Q-ILC l. p nl e k () t ζ k () t + e k ( tt) min p seˆ u k (t) ()ep el l rl RFC ILC m rrlm vrlp er r nrl q 3, 4 p vp n tn r qn. t p l v m rl p Q-ILC kl re k v p n p. o44 o k u k () t R e k ( t+ k t) Q + u k ( t+ k ) R ζ k ( t+ k t) e k ( t+ k t+ k) + u k ( t+ k ) R + Q s r p vrl, nr t o p Œp n sq p, n r k k vl lk. r s r p vp v m p, p m p er vp r m l v rlp p p. p v m ep lp p m o v p rlp p r. ()el sr p vp ζ k (t)p n t rp q. p vp q erp ˆ z k (t)m er p v p u k (τ), t τ N p p p }k ()ep e p r lk. el BLQG BMPC rr k vp rn s vrl el Q-ILC. nr t r p s m p p n q pv, e e ˆ p. Chin [3]p Q-ILC ol l r p d p p v ppp mp rp p p el m. p l p p p rn ml pn p ILCm RFCp rp ()ep, kl RFC k v (6)p p rp u k u k + H e k + H e k (5) m p p. p k vp RFCm ILC el v, v p v p. ILC u k r p o r rl p eˆ l qp v, ee l m kp n p e k l op u k rp l p r. p ILC k l np p e rp k. p rrp o l Chin [3]p p u k ILC o u k m RFC o û k u k u k + û k m p l p rp, p p l u k k vp rk TBC(Two-stage Batch Control) m. pm p p p l ()ep e k e k G u k + n + dˆ e k e k Gû k (6) m p. l u k p dˆ p m p v kp re p pn l u k H e k p, û k H e k u k (7) (8) m p ee n dˆ p m p. p ee n p m p v k p f ILCp r u k

7, 8l rl me m. porp m p mp l v m r C p q r p p. p vrll Only Tracking Control p m rl p (q m sql p ) np, Only Inferential Control p v r p pn l ee rl Nominal Case inferential control s l p o rl(ilc) p.

7 l pˆ v k. p u k u k + û k lr rl r n. e p p k k vp p. e k vr r lp e k Kalman l r. 7. Q-ILC mk i 7-. m m j pžsoh Chin [3]l p p, p l p drl p rp rl 43 A+B C B+C D (9) pp v p. p nr p n Fig. 6l p. A l Œp 30 l B l rp Œp, 00 C o k(4 mol) p nrp rp. p rl Ap 0 p r p p Cp s p r n. Cp p s. rl p q m m B Œp p sq pp, p p m o rl ove ˆ el C p l p eˆ p rk. p rl v m rlm m r rl el BMPC q l l. Fig. 7, 8l rl me m. porp m p mp l v m r C p q r p p. p vrll Only Tracking Control p m rl p (q m sql p ) np, Only Inferential Control p v r p pn l ee rl Nominal Case inferential control s l p o rl(ilc) p. BMPC pn p p m rrl Žp p l e p l p v l [30]. 7-. RTPi lmœ j m oh RTP(rapid thermal processor) op p p n l ~ rp op annealing,, v k rp n q p. op l p p tungsten-halogen lamp p Fig. 6. Operation scenario of the semi-batch reactor example. Fig. 7. Batch-wise improvement of temperature profile of the semi-batch reactor example under BMPC with model uncertainty. Fig. 8. Batch-wise improvement of the production of C under BMPC with model uncertainty. Nominal case means measurement feedback at the end of each batch plus real-time inferential control. n l l, p op m p p ov rp s k. l l np Cho [33]l p p. Fig. 9 p 40 p Kw lamp v 8p op n RTP l e p mp, lamp p 0 grouping l s q n m. op l 8 p lr l p m rl m. rl ILCm RFCp p TBC n mp, TBC 8 0 rp r l p. Fig. 0l p 8r m p rrl p l l v lt p. Fig. p rp p r p m rp (y(t) T(t)) r l l TBC rn nm p o rn l r p r m p 4dp rp l(y(t)t 4 (t)) r p TBC, rn np p. p l p m p p Korean Chem. Eng. Res., Vol. 44, No. 5, October, 006

43 p Fig.. Performance comparison between T model-based TBC and T4 model-based TBC. Fig. 9.

Progressive improvement of tracking control performance of wafer temperatures under TBC. o44 o5 006 0k p p. Fig.

-D oh -D(-dimensional) rl -D p rl p. -D edšp ˆ rp p p d p pl. rp e p d p p ˆ rp p lv -D edšp m. rp e p d o l q l p -D edš s p v p. l, -D rl r rl np.

8 43 p Fig.. Performance comparison between T model-based TBC and T4 model-based TBC. Fig. 9. Thermocouple locations and the grouping of tungsten-halogen lamps for MV use. Fig. 0. Progressive improvement of tracking control performance of wafer temperatures under TBC. o44 o k p p. Fig. 0 l temperature difference, temperature gapp 8vr rm pl q m. p rl p lp q l rn l n p. 8. oh e rp r ILCm p p rl p l ˆ p. ql p p. s np Leem Lee[6, 34]p D oh -D(-dimensional) rl -D p rl p. -D edšp ˆ rp p p d p pl. rp e p d p p ˆ rp p lv -D edšp m. rp e p d o l q l p -D edš s p v p. l, -D rl r rl np. q v -D edš rl l l m p k v o mlp p p v t l l m [35-38]. 8-. Run-to-run oh Run-to-run(RTR) rl r rp ~ rl p n l m rl p. RTRp e ILCp p, rp p n ( p ) l rr rp n, rp p e p k p nl ILC p. ~ rp n ee l op p ˆ r p n l l, nrs (p )p reˆ p ˆ ( ) r l RTR nrs p p p [6, 34, 39, 40]. RTR rl e rp r EVOP[4], batch-to-batch r [4, 43] vrp p p.

9 8-3. oh rp rp k l rp r rp pr t rp p. rl(rc, repetitive control)p pr t p nr l p t p rlp p p ILCm rp o, ILCp qrp p [44]. ILCm rp rp l rp ˆ eqrl reset r, pr t p ˆ p t p ˆl m p pr p k p. rp liftingp p p. Predictive Control Technology, Control Eng. Practice,, (003). 3. Song, I. and Rhee, H., Nonlinear Control of Polymerization Reactor by Wienr Predictive Controller based on One-Step Subspace Identification, Ind. Eng. Chem. Res., 43, (004). 4. Rantow, F. S., Soroush, M. and Grady, M. C., Optimal Control of a High-Temperature Semi-Batch Solution Polymerization Reactor, Proceedings of the 005ACC, Portland, USA, 30, June(005). 5. Sheibat-Othman, N. and Othman, S., Control of Emulsion Polymerization Reactor, Ind. Eng. Chem. Res., 45, 06-(006). 6. Cetinkaya, S., Zeybek, Z., Hapoglu, H. and Alpbaz, M., Optimal Temperature Control in a Batch Polymerization Reactor Using Fuzzy-Relational Models-Dynamics Matrix Control, Comp. Chem. Eng., 30, 35-33(006). 7. Hua, X., Rohani, S. and Jutan, A., Cascae Closed-Loop Optimization and Control of Batch Reactors, Chem. Eng. Sci., 59, (004). 8. Arpornwichanop, A., Kittisupakorn, P. and Mujtaba, I. M., Online Dynamic Optimization and Control Strategy for Improving the Performance of Batch Reactors, Chem. Eng. and Processing, 4, 0-4(005). 9. Bouhenchir, H., Cabassud, M. and Le Lann, M. V., Predictive Functional Control for the Temperature Control of a Chemical Batch Reactor, Comp. Chem. Eng., 30, 4-54(006). 0. Pieri, F., Caccavale, F., Iamarino, M. and Tufano, V., A Controller-Observer Scheme for Adaptive Control of Chemical batch Reactors, Proceedings of the 006 ACC, Minneapolis, USA, 554, June(006).. Ma, D. L, Tafti, L. KU and Braatz, R. D., Optimal Control and Simulation of Multidimensional Crystallization Processes, Comp. Chem. Eng., 6, 03-6(00).. Caliane, B. B. Costa, Aline C. da Costa and Rubens Maciel Filho, Mathematical Modeling and Optimal Control Strategy Development for an Adipic Acid Crystallization Process, Chem. Eng. and Processing, 44, (005). 3. Voller, U. and Raisch, J., Control of Batch Crystallization-A System Inversion Approach, Chem. Eng. and Processing, 45, (006). 4. Costa, C. B. B., da Costa, A. C. and Filho, R. M., Evaluation of Optimisation Techniques and Control Variable Formulations for a Batch Cooling Crystallization Process, Chem. Eng. Sci., 60, 53-53(005). 5. Vu, T. T. L., Durham, R. J., Hourigan, J. A. and Sleigh, R. W., Dynamic Modelling Optimization and Control of latose Crystallizations: Comparison of Process Alternatives, Sep. and Purif. Technology, 48, 59-66(006). 6. Ronia M. Oisiovici* and Sandra L. Cruz, Inferential Control of High-Purity Multicomponent Batch Distillation Columns using an Extnded Kalman Filter, Ind. Eng., Chem. Res., 40, (00). 7. Ulas, S., Diwekar, U. M. and Stadtherr, M. A., Uncertainties in Parameter Estimation and Optimal Control in Batch Distillation, Comp. Chem. Eng., 9, (005). 8. Da, L., Kumar, V. G., Tay, A., Al Mamun, A., Weng Khuen Ho, See, A. and Chan, L., Run-to-run Process Control for Chemical Mechanical Polishing in Semiconductor Manufacturing, Proceedx k + ( 0) Ax k ( 0) + Pu k y k x k ( 0) + Gu k + d k drl p rp rl 433 (30) e l ˆ reset (x k (0)0), p p (7)e p v. RC p l (3), (4)e p r l rl. Lee [45]p MPC r l p RC rk p RMPC(Repetitive MPC) m. 9. rp rl p lp p rl p pp, o rl el rl p p. rp r r p l p dv k l, r rp o rl p rrs p seˆ l r v p. ILC p rrp rp p p, v l ~ ILC p rp rl p krp rp m. p rl p r p rrp n, l rn MPCp qrp rl pl t pn m l. l ILC p rrl p rp, enrp p v p s m. l r v r rl l p lp p p p n l kv v rr rl p re l pv kk pnp n r rp pl p ep. ILC p rl p rrlp n qp ll p. p q r l r R vop p pl. y. Morari, M. and Lee, J. H., Model Predictive Control: Past, Present, and Future, Comp. and Chem. Eng., 3(4-5), (996).. Qin, S. J. and Badgwell, T. A., A Survey of Industrial Model Korean Chem. Eng. Res., Vol. 44, No. 5, October, 006

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<30372E31362D323028BDC5C7F6C5C32DB9CCB1B970626D292E666D> k m v r1 r1 16~20 (2009) J. Korean Academy of Managed Care Pharmacy Vol. 1, No. 1 Pharmacy Benefit Management iç 1# x sƒ, 1 w w w Overview on Pharmacy Benefit Management in USA Kyung Eob ChoiGand Hyun