Integrated Data Reconciliation with Generic Model Control for the Steel Pickling Process

Transcription

1 Korean J. Chem. Eng., (6), (3) Integrate Data Reconciliation with Generic Moel Control for the Steel Picling Process Paisan Kittisupaorn an Pornsiri Kaewprait Department of Chemical Engineering, Chulalongorn University, Bango 33, Thailan (Receive December accepte July 3) Abstract To implement an avance control algorithm, measurements of process outputs are usually use to etermine control action to a process. Nevertheless, measurements of process outputs are often subjecte to measuring an signal errors as well as noise. Therefore, in this wor, Generic Moel Control (GMC), an avance control techniue, with ata reconciliation techniue has been applie to control the ph of the picling process consisting of three picling an three rinsing baths. Here, the ata reconciliation problem involves six noes an fourteen streams. The presence of errors in the ata set is etermine an ientifie via measurement test. In aition, the measurement error covariance is initially assume to be a nown variance matrix an is upate every iteration. Simulation results have shown that the reconcile process ata give a better view of the true states of the process than raw measuring ata. With these reconcile process ata, the GMC controller can control the process at a esire set point with great success. Key wors: Data Reconciliation, Generic Moel Control, Steel Picling Process INTRODUCTION The accuracy an consistency of process ata are the ey to efficient operation of chemical plants. The measurements from a physical system are generally noisy an o not verify balance euations. These raw ata with unetecte biase errors result in false control of the process so that they nee to be reconcile to eliminate nown errors an measurement noise. The problem of ata reconciliation consists of obtaining an estimating the true states that verify balance euations. Mah et al. [976] stuie the problem of the ientification of the source of gross errors an evelope a series of rules (base on graphtheoretical results) that enhance the effectiveness of the algorithm search. Data reconciliation problems involving linear moels were well stuie. Crowe et al. [983] use a matrix projection metho to ecompose the problem so that the measure an unmeasure variables can be evaluate seuentially. Later, Crowe [986] extene this metho for problems with bilinear constraints. Various statistical tests have been propose to etect gross errors [Mah, 99; Romagnoli, 983; Romagnoli an Stephanopoulos, 98]. General reconciliation methos are base on the hypothesis that measurement errors are ranom Gaussian variables with a nown covariance matrix an zero mean. In most practical situations, this matrix is unnown or nown approximately [Keller et al., 99; Valo an Vaja, 987; Romagnoli, 983]. Recently, ata reconciliation algorithms have been evelope for input-output moels in linear ynamic systems in which the measurement errors in the input variables are optimally hanle in this approach [Kim et al., 996]. It is well nown that most chemical inustrial plants cause environmental problems ue to usage of chemicals in prouction lines. Therefore, a moel-base control scheme was evelope to control ynamic behavior of the process. The control strategy has been To whom corresponence shoul be aresse. paisan.@chula.ac.th 985 applie to chemical process system for control purposes for the past ten years. A new metho to hanle the constraints on manipulate variables for multivariable unstable processes was propose by Lee an Par [99]. Kittisupaorn an Hussain [], an Arpornwichanop et al. [] presente a moel-base control strategy together with extene Kalman Filter (EKF) for reactant concentration control of chemical reactors an for temperature control of batch reactors with exothermic reactions, respectively. Furthermore, nonlinear control algorithms using feebac input-output linearization applie to a lab-scale batch eater-interchange reaction system were iscusse by Par an Par [999]. Generic Moel Control (GMC), one of the most popular moel-base controllers, is a control algorithm capable of using a non-linear process moel irectly. In 989, Lee et al. extene the application of the moel base GMC controller to a force circulation single-stage evaporator. Later, they examine the use of GMC for controlling the level in a surge tan [99]. Cott an Macchietto [989], an Kershenbaum an Kittisupaorn [994] stuie the temperature control of an exothermic batch reactor via using a GMC controller. Farrell an Tsai [995] implemente the GMC algorithm for the batch crystallization process. The steel picling process has use concentrate chemicals in prouction lines, an wastewater release from the process contains hazarous materials an usually causes major environmental problems. Therefore, prouction scheuling an control of the picling process are inevitably neee to minimize the amount of hazarous material containe in the release wastewater as well as wastewater itself. A conventional PID controller has normally been use to control the process. However, it is nown wiely that a PID controller cannot hanle non-linearity of the ph control problem an avance control techniues are reuire [Cho et al., 999]. In aition, in reality, the process flow rates of the system are subjecte to measurement noise leaing to poor control performance of any controller. This wor then introuces the application of Generic Moel Control (GMC) couple with steay state ata reconciliation to

2 986 P. Kittisupaorn an P. Kaewprait Fig.. Picling process. control level an ph of the picling process with respect to measurement noise. PROCESS AND MATHEMATICAL MODELING In this research, the picling process (Fig. ) consists of two major steps: picling an rinsing steps. The picling step is to remove surface oxies (scales) an other contaminants such as irt out of metals by an immersion of the metals into an aueous aci solution. Metals are immerse in picling baths--5%, % an 5% by weight hyrochloric aci (HCl), respectively--to remove scales from metal. The irection of metals is countercurrent to aci stream irection as shown by otte lines in Fig.. The reaction in the baths is FeO + HCl FeCl + H O Then, metals without scales out of picling baths are immerse in rinsing baths, which consist of three pure water baths, to rinse aci covering the metals. Similarly, the irection of the metals is opposite to the rinse water flow. Here, the amount of rag-out solution of each bath is assume to be eual to the amount of rag-in solution. The objective of this wor is to control height an ph (or H+ concentration) of each bath to a esire set point as illustrate in Fig. (a) an (b). Aci concentrations of the first, secon an the last baths are set at.37 3,.74 3 an 4. 3 mole per liter, respectively, by ajusting the aci stream as shown in Fig. (a). The ph value of each rinsing bath is controlle at 5.5 (The stanar of Department of Inustrial Wor) as shown in Fig. (b). To evelop a mathematical moel of the picling process, it is assume that whole baths are perfectly mixe an isothermal. Other assumptions mae in formulating process moels are that the reaction involve is first orer, all ph values are measurable an the fee concentration is nown. Uner these assumptions, the material balances of picling baths can be written as follows: Total mass balances (Density is assume to be constant), A h = F F 5, t A h t 5 F F, () () A h 5 + F 35 F 5 F 5, t Total component balances, C 5 5 t ( C C 5 ) 5 C 5 C - 5 ( C 5 C ) + ( C 5 C ) C t (3) (4) (5) C = F ( C C 5 ) + F 35 ( C 35 C 5 )+ ( C C 5 ) 5 C 5 (6) t Similarly, with the assumptions above, the material balances of the rinsing baths are as follows: Total mass balances (Density is assume to be constant), Fig.. (a) Flow iagram of picling bath controls. (b) Flow iagram of rinsing bath controls. November, 3 A h = F F F, t A h = F t 3 F F, A h = F t w F 3 F 3, Total component balances, (7) (8) (9)

3 Integrate Data Reconciliation with Generic Moel Control for the Steel Picling Process 987 C ( C C ) + ( C 5 C ) t C t 3 ( C 3 C ) + ( C C ) C 3 3 t w ( C w C 3 ) + ( C C 3 ) () () () Here, it was assume that all process variables are measurable without noise except process flow rates with measurement noise of ±% of true values. Therefore, steay state ata reconciliation is implemente to reconcile these flow rates, an these reconcile flow rates are then use in the GMC controller to etermine control action. GENERIC MODEL CONTROL (GMC) Generic Moel Control (GMC), an avance non-linear control techniue, uses mathematical moels of a plant to etermine control action. The process moel use can be either linear or non-linear. Here, states nee to be controlle as escribe above. Therefore, manipulate variables are etermine base on the GMC control algorithm as shown below: F 5, = F F, = F 5 F AK 5, ( h 5, sp h 5 ) + K 5, h 5 ) th 5 sp F 5, = F + F 35 F 5 AK 5, ( h 5, sp h 5 )+ K 5, t( h 5, sp h 5 ) = (5) F 5 Manipulate variables in rinsing baths are shown as follows: = AK, ( h, sp h ) + K, t( h, sp h ) = K ( C 5, sp C 5 )+ K ( C 5 ) = C F 5 = C 5 = C 5 ) + C 5 tc 5 sp ( C ) K ( C 5, sp C ) + K 5 = ( C 5 C ) + C F 35 = 5 C 35 F, ( C 5 ) K ( C 35 5, sp C 5 ) + K 35 = F 5 C ) tc sp C 5 ) tc 5 sp ( C C 5 ) ( C C 5 ) + C 5 5 = F F AK, ( h, sp h ) + K, = h ) th sp (3) (4) (6) (7) (8) (9) F 3 = K 3 ( C, sp C ) + K 3 tc sp C ) ( C 3 C ) = C ( C ) 3 F w = K w ( C 3, sp C 3 ) K w tc ( wsp, C w ) ( C 3 C w ) = C ( C 3 ) 3 DATA RECONCILIATION (3) (4) Since the measurements are subject to errors, material balances are not generally obeye by the measure values. These values have to be ajuste or reconcile to obtain more accurate estimates of flow rates, which are, at the same time, consistent with the material balances. To formulate this problem, a mathematical moel of a process, relevant constraints an an appropriate objective function are neee. The following measurement moel is postulate in the absence of gross errors: x = x + ε (5) where x is the vector of measure variables; ε is a vector of ranom measurement errors. It is usually assume that (a) the expecte value of ε, E(ε)=; (b) the successive vectors of measurements are T inepenent, i.e., E( ε i ε j ) =, for i i j; an the covariance matrix is T nown an positive efinitive, i.e., cov(ε)= E( ε i ε j ) =Q. The reconcile or ajuste value x' is relate to the measure value x by the ajustment, a: x' = x + a (6) The ata reconciliation problem may be formulate as the following constraine weighte least suares estimation problem: Min lim[ ( x x) T Q ( x x) = a T Q a] xv, (7) subject to the constraint: Bx=c (8) The minimization is carrie out by using Lagrange Multipliers. The solution is given by x' = x Q ( B) T [ BQ ( B) T ] [ Bx c] The covariance of measurement errors is upate each iteration. Q = [ I H + ( H ) T H ]Q H = Q ( B) T [ BQ ( B) T ] B (9) (3) (3) F, F 3, = F 3 F AK, ( h, sp h ) + K, = = F w F 3 AK 3, ( h 3, sp h 3 ) + K 3, = h ) th sp h 3 ) th 3 sp F = K ( C, sp C ) + K tc sp C ) ( C C ) = C ( 5 C ) () () () where x = [ F 5, ; F ; F, ; F 5 ; F 5, ; F ; F, ; F ; F, ; F 3 ; F 3, ; F 35 ; F w ] B = c =. Korean J. Chem. Eng.(Vol., No. 6)

4 988 P. Kittisupaorn an P. Kaewprait In this case, it is assume that the initial covariance of measurement errors (Q) is a unit iagonal matrix with imension 3 3. Here, process ata are ajuste to satisfy conservation laws base on information of measure variables. Then this reconcile ata set is incorporate into moel-base controller to control state variables to the esire set point. Fig. 3 shows the flowchart of GMC with ata reconciliation. The measure process flow rates with measurement error ±% of true values are ajuste via steay state ata reconciliation; after that, these reconcile ata are incorporate into the Generic Moel Control (GMC) algorithm to calculate control actions for control purposes. SIMULATION RESULTS The GMC with ata reconciliation is applie to control height, aci concentration an ph in the steel picling process. Each 5%, % an 5% by weight HCl bath is controlle to maintain the concentrations at.37 3,.74 3 an 4. 3 mole per liter, respectively. Simultaneously, the ph values of three rinsing baths are controlle within 5.5. The height of each bath is controlle not over.74 meters. The performance of a GMC with ata reconcil- Fig. 3. Flowchart of GMC with ata reconciliation. Table. Tuning parameters of GMC Bath 5% HCl % HCl 5% HCl Rinsing Rinsing Rinsing 3 Height tuning parameters K 5, K 5, Concentration tuning parameters K K K, K, K 5 K K 5, K 5, K 35 K K, K, K K K, K, K 3 K K 3, K 3, K w K w Fig. 5. The control response of GMC without (left) an with (right) ata reconciliation in % by weight HCl bath. Fig. 4. The control response of GMC without (left) an with (right) ata reconciliation in 5% by weight HCl baths. Fig. 6. The control response of GMC without (left) an with (right) ata reconciliation in 5% by weight HCl bath. November, 3

5 Integrate Data Reconciliation with Generic Moel Control for the Steel Picling Process 989 Fig. 7. The control response of GMC without (left) an with (right) ata reconciliation in the first rinsing tan. Fig. 8. The control response of GMC without (left) an with (right) ata reconciliation in the secon rinsing tan. iation is then compare to that of a GMC controller. The values of GMC tuning parameters are given in Table. Figs. 4-6 show the control response of GMC without an with ata reconciliation in the picling step an Figs. 7-9 show the control response in the rinsing step. It can be seen from Figs. 4-6 that both conventional GMC without an with ata reconciliation can control aci concentrations at the set points with small overshoot. However, the GMC with ata reconciliation provies better control performance than that of GMC controller without ata reconciliation. Figs. 7-9 show that the GMC with ata reconciliation can control the ph of each bath to the esire set point, whereas the GMC without ata reconciliation cannot. Therefore, the inclusion of ata reconciliation techniue can enhance the control performance of the GMC controller. Fig. 9. The control response of GMC without (left) an with (right) ata reconciliation in the thir rinsing tan. CONCLUSION Generic Moel Control (GMC), a non-linear moel-base controller, reuires process moels of a plant as well as measurements of process outputs to etermine the control action neee to control the plant. Therefore, the performance of the GMC controller relies on the accuracy of not only the mathematical moels but also the measurements of process ata. In reality, the measurements of process outputs often contain measuring error, signal error an noise. These errors usually lea to poor performance of the GMC controller. In this wor, the steay state ata reconciliation algorithm is inclue in the formulation of the GMC control algorithm to reconcile measure process flow rates. For simplification, it is assume that the available level an concentration are certain. Simulation results have emonstrate that the GMC controller with ata reconciliation can provie better control performance than that of the GMC without ata reconciliation techniue. Therefore, in this case the inclusion of the steay state ata reconciliation techniue in the GMC control algorithm can eal with errors of flow measurements as well as noise; the GMC controller with ata reconciliation techniue is applicable to processes with measurement an signal errors. APPENDIX A. Tuning Parameters of GMC Controller Lee an Sullivan [988] outline a system for tuning the GMC controller base on choosing a target profile of the controlle variable, y sp (t). This profile is characterize by two values, ξ an τ. Lee an Sullivan present a figure that outlines the relative control performances of ifferent combinations of ξ an τ as shown in Fig. A.. Similar plots to the classical secon-orer response showing the normalize response of the system y/y sp vs. normalize time t/τ with ξ as a parameter can be prouce. The general form of GMC control algorithm can be written as ỹ = K ( y sp y) + K ( y sp y)t (A.) The value of two tuning constants, K an K are obtaine by us- Korean J. Chem. Eng.(Vol., No. 6)

6 99 P. Kittisupaorn an P. Kaewprait In tuning the GMC controller, because overshoot is unesirable, ξ is set to the expecte value. After that the value of τ is obtaine by examining the tuning charts given by Lee an Sullivan. In this wor, twelve controllers are consiere here to control the level an concentration of steel picling process; then each tuning parameter is outline as follows. From E. (A.), the first expression is to bring the process bac to steay state ue to change in y/t. The last expression is introuce in orer to mae the process have a zero offset. In this wor, the appropriate values of the tuning parameters of each GMC controller to control the concentrations to the esire targets are presente above. With these parameters the control strategy is able to hol the process without offset. NOMENCLATURE Fig. A.. Generalize GMC profile specification. ing the following relationships: ξ K = K τ = --- τ. 5% aci tan Level ξ =, t=τ Let t=. min, then τ=. K =(.)=.667 an K = (. )=.694 ph ξ=, t=.5τ Let t=5.6 min, then τ=.45 K =(.45)=.89 an K =( (.45 )) 5=.38. % aci tan Level ξ=, t=τ Let t=. min, then τ=. K =(.) =.667an K = (. ) =.694 ph ξ=.5, t=.9τ Let t= min, then τ=.775 K =(.5.775).98=.55 an K = (.775 )= % aci tan Level ξ=, t=τ Let t=. min, then τ=. K =(.) =.667 an K = (. )=.694 ph ξ=, t=τ Let t=.75 min, then τ=.75 K =(.75) =.3333 an K =( (.75 )) = The 3 r rinsing tan Level ξ=3, t=.8τ Let t=.3 min, then τ=.375 K = 3.375=6 an K = (.375 )=7. ph ξ=, t=.5τ Let t=5 min, then τ= K = = an K = ( )=.5 5. The n rinsing tan Level ξ=3, t=.8τ Let t=.3 min, then τ=.375 K = 3.375=6 an K = (.375 )=7. ph ξ=, t=.5τ Let t=5 min, then τ= K = = an K = ( )=.5 6. The st rinsing tan Level ξ=3, t=.8τ Let t=.3 min, then τ=.375 K = 3.375=6 an K = (.375 )=7. ph ξ=, t=.5τ Let t=5 min, then τ= K = = an K = ( )=.5 a :ajustment A : area of operating tan, meter B : incience matrix c : constant matrix C : HCl concentration, mole per liter F : volumetric rate, liter per min h : height of operating tan, meter : reaction rate constant,.367 (min) (mole per liter) K, K : tuning parameters of GMC controller : amount of aci solution that stuc with samples,. liter per min Q : the covariance matrix of measurement errors t : sampling time [min] x : state variables Gree Letters ε : a vector of ranom measurement errors ~ : measure value ' : estimate value Subscripts : from the first rinsing tan : from the secon rinsing tan 3 : from the thir rinsing tan 5 : from 5% by weight HCl tan : from % by weight HCl tan 5 : from 5% by weight HCl tan 35 : from 35% by weight HCl tan :rain w :water sp : setpoint Superscripts :at time ( ): at time ( ) REFERENCES Arpornwichanop, A., Kittisupaorn, P. an Hussain, M. A., Moel- Base Control Strategies for a Chemical Batch Reactor with Exothermic Reactions, Korean J. Chem. Eng., 9, (). Cho, K. H., Yeo, Y. K., Kim, J. S. an Koh, S. T., Fuzzy Moel Preictive Control of Nonlinear ph Process, Korean J. Chem. Eng., 6, 8 (999). Cott, B. an Macchietto, S., Temperature Control of Exothermic Batch Reactors using Generic Moel Control, In. Eng. Chem. Res., 8, November, 3

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