CASCADE OPTIMIZATION AND CONTROL OF BATCH REACTORS

Transcription

1 CASCADE OPIMIZAION AND CONROL OF BACH REACORS Xiangming Hua, Sohab Rohani and Athu Jutan* Depatment of Chemical and Biochemical Engineeing Univesity of Westen Ontaio, London, Canada N6A B9 * ajutan@uwo.ca Abstact: In this study, a cascade closed-loop optimization and contol stategy fo batch eactos is poposed. A simple physical consevation model is used to descibe the dynamics of the batch eacto. Using model eduction a cascade system is developed, which can effectively combine optimization and contol to achieve good on-line optimization and tacking pefomance, with limited infomation on the eaction system. A two -tie estimation scheme using a nonlinea obseve fo the heat poduction ate and the eaction ates is developed. A closed-loop optimization stategy is poposed, which uses a descending hoizon dynamic optimization algoithm based on nonlinea pogamming (NLP), and an additive distubance is used fo feedback. An adaptive nonlinea tacking system is designed based on the geneic model contol (GMC) algoithm. he efficiency of this stategy is demonstated though simulations on a batch eacto unde vaious opeations conditions. Keywods: Batch eactos; Closed-loop dynamic optimization; adaptive nonlinea contol; caloimetic state estimation; nonlinea obseve. 1. INRODUCION Batch eactos povide flexible means of poducing high value-added poducts in specialty chemical, biotechnical, and phamaceutical industies. o ealize the poduction objectives, the batch eactos have to be opeated optimally in a pecise fashion; the optimization and contol of batch eactos pesent some of the most inteesting and challenging poblems fo both academia and industy in pocess contol (Bebe, 199). A taditional appoach to the batch eacto optimization and contol poblem has been off-line optimization and open-loop contol. Since thee was no feedback fom the pocess output, this scheme is vey sensitive to uncetainties in initial conditions, pocess dynamics and distubances occuing duing the batch opeation. We popose an optimization scheme which avoids the taditional singulaities and high computational buden, and is combined with a contol stategy which is able to accommodate the non lineaities of the system. Futhemoe, we take into account the pactical poblem of limited eaction kinetics infomation, by using a nonlinea obseve. In this wok, a simple physical consevation model with limited eaction kinetic infomation is used. he model is then decomposed into two pats: a educed mass balances model (RMBM) and educed enegy balances model (REBM). he RMBM is used to design the on-line optimize, and the REBM to design the contolle. As is usual in pactice, the eacto tempeatue is used as the decision vaiable fo the optimization poblem. his allows a cascade implementation, which can effectively combine optimization and contol. Using this appoach, the singulaity poblem in dynamic optimization is avoided (Palanki, et.al.,1998) and the computational buden is deceased. he system can then be decoupled, which allows independent design of the optimize and the contolle. In pevious studies some techniques have been successfully developed fo estimating the heat poduction ate (Jutan and Uppal, 1984; Faza, et al., 1999). hese so-called caloimetic state estimation techniques ae used fo on-line estimation of the heat poduction ate. Hee, a descending hoizon dynamic optimization algoithm based on nonlinea pogamming (NLP) is

2 poposed which implements an on-line open-loop optimization stategy, using caloimetic measuement infomation. he effect of modeling eo and unmeasued distubances ae teated as additive unknown distubances. his is simila to the Model Pedictive Contol stategy and allows feedback to be intoduced into the open-loop optimization algoithm. o ensue good tacking pefomance, it is necessay to apply a nonlinea contolle due to the complex chaacteistics of the batch eacto. he Geneic Model Contolle (GMC) (Lee and Sullivan, 1988) has some attactive advantages (Cott and Macchietto, 1989; Hua and Jutan, 2), and is used hee. In addition, an on -line, two-tie, estimation scheme is developed fo the heat poduction ate and the eaction ates, using a specialized nonlinea obseve developed by Faza, et al. (1999) which is both easy to tune and implement. 2. REACOR MODEL AND CASCADE IMPLEMENAION A typical batch chemical eacto is consideed hee, and it is assumed that thee ae m eactions taking place with n diffeent components (eactants and poducts) paticipating in the eacto (usually m < n ). Fo heating and cooling the eacto contents, a heat exchange can be used befoe the jacket inlet steam, in addition to a single-pass jacket system aound the eacto vessel. Without loss of geneality, it is also assumed that the jacket tempeatue is pefectly egulated by PID tempeatue contolle(s). hus, the dynamics of the heat exchange with the contol system will not be modeled. 2.1 Batch eacto model he following n + 1 diffeential equations can be deived fo the eacto. Mass balances ( n equations): M = Sc R (1) Enegy balances (one equation): 1 UA h = Q + ( j ) (2) WCp WCp whee, M = [ M1 M2 M ] n is a n 1 vecto of the mass o the numbe of mole of n components, S c is a n m stoichiometic coefficient matix, R = [ R1 R2 R ] m is a m 1 vecto of m eaction ates, which ae nonlinea functions with espect to the component mass and the eaction tempeatue, and j ae the tempeatues inside the eacto and the jacket, espectively. Q is the heat p oduction ate: Q = H R (3) whee H = [( ± H1) ( ± H2) ( ± Hm )] is a 1 m vecto of the heat of eaction,w and C p ae total mass of the eacto contents and heat capacity, espectively. U is the heat-tansfe coefficient, and A h is the heat-tansfe aea. It is assumed that all physical paametes in the model ae constant. In this wok, no knowledge of the eaction kinetics is equied fo the estimation of the heat poduction ate and the eaction ate, as well as fo the design of the tacking system. In designing the optimize, howeve, we need to pefom end point calculations, and thus need to, initially, make use of some appoximate eaction ate expessions obtained fom pio knowledge and expeimental studies. All tempeatue and flowate measuements ae available. 2.2 Model eduction and cascade system Instead of using the full model (Eq s 1-3) ( which implies full kinetic infomation) diectly, the dynamic model (Eqs. 1-2) is decoupled into an RMBM that consists of the n equations (Eq. 1), and an REBM that consists of the Eq. 2. he RMBM is used to design the optimize, and the REMB to design the contolle. he contolle design is based only on the REBM and equies just tempeatue measuements. Since the eacto tempeatue is the input of the RMBM, it is selected as the decision vaiable fo the optimization subsystem. Howeve, the eacto tempeatue is the contolled vaiable in the tacking subsystem. A cascade optimization and tacking system is then used (Figue 1) 2.3 Fomulation of closed-loop optimization poblem he on-line closed-loop optimization of the batch eacto is fomulated as: min J = φ ( M ( tf )) (4) () t subject to satisfying: M () t = ScR, R = RM (, ) () tk t tf, k =,1,, N 1 (6) M( t k) = M k (7) min () t max (8)

3 M k is the initial state vecto of the component mass at the time t k. he effect of modelling eo and unknown distubances is teated as an additive, unmeasued distubances d 1 and d 2. his appoach allows the intoduction of feedback into the algoithm. 3. ADAPIVE NONLINEAR RACKING An adaptive nonlinea contolle is developed using the REBM. he manipulated input of this tacking system is the jacket tempeatue jd and the tacked vaiable is the eacto tempeatue. he REBM can be ewitten as: ˆ = aq+ b ( jd ) (9) whee ˆQ is the estimate of heat poduction ate. he GMC contol algoithm (Lee and Sullivan, 1988) can then be epesented as jd a = + + t Qˆ 1 K1 (, sp ) K 2 (, sp ) dt b b (1) 4. ON -LINE ESIMAION An on -line two-tie estimation appoach is developed: fistly to estimate the heat poduction ate based on the REBM and tempeatue measuements, using caloimetic state estimation, and then to estimate m eaction ates based on the measued (infeed) heat poduction ate and a subset of component mass o concentation measuements. Following Faza, et al. (1999), we obtain the following heat poduction ate estimato: ˆ = aq+ b ( j ) 2 θq( ˆ ) 2 Q = θ a 1 ( ˆ ) Q (11) (12) whee, θ Q is a tuning paamete, and a and b ae constants defined by Equation 9. We can also obtain the following eaction ate estimato: ˆ ˆ M = SR c 2 θr( M M) (13) 2 1 ˆ R = θ R Sc ( M M) (14) whee, θ R is a tuning paamete.. CASE SUDY In ode to demonstate the efficiency of the poposed optimization and contol stategy, the batch chemical eacto, used by Cott and Macchietto (1989), is consideed. his is a well-mixed, liquid -phase eaction system, with two eactions taking place: Reaction 1: A+ B C (1) Reaction 2: A+ C D (16) whee, component A and B ae eactants. Component C is the desied poduct while D is an unwanted bypoduct..1 Simulation studies he batch eacto was simulated using a detailed physical model. Gaussian noise was added to the measuements. he sampling ate topt fo the online optimization and t ctl fo the contol wee selected as 4~6 min and 12 sec, espectively. Unde the constaint of the jacket inlet tempeatue jin, sp 128 o C, it was found that easonable choices of the GMC contolle paametes wee K 1 =.417 sec -1 8 and K 2 = sec -2. he esulting closed-loop contol system, with estimated heat poduction ate achieved excellent set-point tacking. Figues 2-3 show on-line estimation and cascade closedloop optimization and contol pefomance of the batch eacto opeating unde a nominal opeating condition, espectively. Figue 2 illustates the tansient behavio of the eal and estimated heat poduction ates, and two eaction ates, espectively. Fom this figue, we see that all estimatos have good dynamic tacking pefomance. he closed-loop optimal tempeatue pofile opt is shown in Figue 3. he eacto tempeatue is shown to satisfactoily tack the opt tajectoy. he change in the set-point of the jacket inlet tempeatue is also shown in this figue. he optimal objective value unde this nominal opeating condition is MC( t f ) = kmol. he mola pofiles of all the components unde closed loop contol ae shown in Figue 4. o veify the optimization pefomance of the cascade closed-loop optimization and contol system, the standad end-point dynamic optimization of this batch eacto (Palanki, et.al.,1998) was caied out off-line unde the nominal opeating conditions. he open-loop optimal tempeatue pofile is shown in Figue and is seen too be vey simila to the closed loop pofile. he pedicted

4 optimal objective value is MC( t f ) = kmol. Hence the optimal objective value of the esultant cascade closed-loop optimization with contol system, and that of the end-point dynamic optimization ae vey close. Seveal othe simulations wee conducted to demonstate the obustness of the method to measuement noise, see Figues 6 and 7. Palanki, S. and M. Kothapally, On -line Optimization of Batch Pocesses, ends in Chem. Eng.,, 4 (1998). 6. CONCLUSIONS A cascade closed loop optimisation and contol stategy fo batch eactos has been pesented. his algoithm addesses the commonly encounteed difficulty of obtaining eliable kinetic infomation and online concentation measuements. Reaction and concentation infomation is infeed fom moe eadily available tempeatue measuements using a nonlinea obseve which apidly tacks the dynamics of the system. he stategy is accomplished by educing the model into two subsystems, which allowed independent design of the optimize and the contolle. Optimisation is accomplished with a constained SQP algoithm, which is applied in a decending hoizon fashion at each time step. Feedback in intoduced indiectly by using model eo associated with the unknown kinetic infomation. A GMC contolle is effectively used to foce the nonlinea system to tack the optimal pofile. Simulations unde many diffeent opeating conditions have confimed the pefomance of the stategy and showed that it compaes favoably with the coesponding offline optimization esults obtained via standad methods. he educed computational buden and feedback stuctue make this appoach suitable fo online implementation. REFERENCES Bebe, R., Contol of Batch Reactos: A Review, Methods of Model Based Pocess Contol, NAO ASI Seies, Kluwe Academic Publis hes, he Nethelands, 293, 49 (199). Cott, B. J. and S. Macchietto, empeatue Contol of Exothemic Batch Reactos Using Geneic Model Contol, Ind. Eng. Chem. Res., 28, 1177(1989). Faza, M., H. Hammoui, C. Jallut and J. Lieto, State Obsevation of a Nonlinea System: Application to (Bio) chemical Pocesses, AIChE J., 4, 93 (1999). Hua, X. and A. Jutan, Nonlinea Infeential Cascade Contol of Exothemic Fixed-bed Reactos, AIChE J., 46, 98 (2). Jutan, A. and A. Uppal, Combined Feedfowad- Feedback Sevo Contol Scheme fo an Exothemic Batch Reacto, Ind. Eng. Chem. Pocess Des. Dev. 23, 97 (1984). Lee, P. L., and G. R. Sullivan, "Geneic Model Contol (GMC), Comptu. Chem. Eng., 12, 73 (1988). Fig. 1: Cascade optimization and tacking system Q (kj/s) ( kmol/s) R R tue estimate Fig 2: On-line estimation pefomance unde the nominal condition.

5 tue estimate 8 Q (kj/s) 1 (C) opt jin,sp Fig. 3: Closed-loop optimisation and contol pefomance unde the nominal condition. 1 M A R R M B M (kmol) M C M D Fig. 6: On -line estimation pefomance with the same condition as in Figues 2-3, but with noisy measuements Fig. 4: Mole pofiles of all components with closed-loop optimisation and contol. (C) 6 opt jin,sp opt (C) Fig. 7: Closed-loop optimization and contol pefomance with the same condition as in Figs. 2-3, but with noisy measuements Fig. : Open loop optimal tempeatue pofile calculated off-line using end-point optimisation algoithm unde the nominal condition.