De Keyser, Robain

MELO, R

SCHAAF, M

English

Ghent University Academic Bibliography

8th   International   IFAC   Symposium   onDynamics and Control of Process Systems REDUCTION OF MATERIAL LOSS DURINGGRADE CHANGE PREDICTIVE CONTROL INA PAPER MACHINE.M. SCHAAF ∗ R. C. MELO ∗∗ R. DE KEYSER ∗∗∗A. CIPRIANO ∗∗Department of Electrical Engineering, PontificiaUniversidad Cato´lica, Chile∗∗Department of Control and Automation Enginnering,Universidad Federal de Santa Catarina, Brazil∗∗∗Department of Electrical energy, Systems andAutomation, Ghent University, BelgiumAbstract: In this contribution, the dynamical behavior of a paper-making systemis presented and an advanced controller is developed to minimize the amount ofrecycled paper used in the paper making process. The advanced controller is amodel based control strategy, and therefore, a model is developed in order toevaluate the loss of paper during the transition between two points of operation.The wastage model is adapted to be used in the cost function of an in-housedeveloped predictive control algorithm. Performance evaluation is described andthe corresponding results are presented. Copyright c©2007 IFACKeywords: Paper industry, Predictive control,nonlinear model, constraints,optimal, robust, wastage paper1. STATE OF THE ARTGrade change on a paper machine is atransition from one set of operating con-ditions to another. During the transition,without proper coordination and control, theentire process could have radical fluctua-tions and produce significant amounts of off-specification paper or even cause sheet break.The production loss and the efforts to recy-cle off-spec waste are very costly (MurphyT. F., 1999). For machines which need to makefrequent grade changes in order to producea wide variety of paper grades, they oftenspend a significant portion of their produc-tion time making off-specification productsPreprints Vol.3, June 6-8, 2007, Cancún, Mexico85through grade change transitions. Definitely,there is a strong need to improve the operationof grade change transitions. The research ofimproving control of grade change transitionshas been mostly focused on process model-ing, as in (Chen, 1992) and (Menani, 1998).Although some work on grade change con-trol has been done, as in (McQuillin, 1994)and (Ihalainen, 1996). The basic process ofmaking paper is preparing the stock, formingthe paper web, drying the sheet, and applyingcoatings and additives.This paper is organized as follows. In thesection 2 the objectives are presented and es-plained. Section 3 presents the model and thevariables involved. In section 4 the model ofwaste is explained and the cost function of thepredictive controller is designed. The resultsobtained with the proposed controller are pre-sented in the section 5, also the controlleris tested under unmeasured disturbance. Fi-nally, in section 6 the conclusions are pre-sented.2. CONTROL TASKThe main objective of this investigation is todesign a predictive controller that minimizesthe amount of paper wasted in the paper-making process. This paper will be referredto as wastage paper. The paper produced dur-ing the transition from one kind of paper toanother (depending on customer’s specifica-tions) is considered lost, since in this case thepaper does not fulfill the technical specifica-tions required by the client. Therefore, it canonly be sold at lower price or not sold at all- producing wastage. However, there is a pos-sibility to recycle this paper, but this processuses extra energy in order to transform thepaper into pulp.3. MODEL OF THE PLANTMaking paper requires a complex procedure,with different input variables. In the modelonly some of the most important inputs havebeen considered as manipulated variables.Fig. 1. Atro response in open loop, whenapplied a unit step in the Stock Flowinput variable, for different speed.These variables are stock flow, speed and pres-sure (www.paperonweb.com, 2006). The otherinputs are considered constant parameters,such as: consistency of the pulp, the temper-ature and width of the paper. The model hastwo output variables, the Atro and Moisture:Moisture (or water content in % )content iscomplementary to the Consistency indicator.Moisture =M waterM matter dry +M water· 100Atro (or grammage or dry weight)representsthe mass of dry matter reported to the surface.Atro =M matter drysurface[ gm2]More details of the process and the modelof the plant was presented in (Melo, 2006).One of the most challenging characteristicsof the process is the variable time-delay inthe output variables. The variable time-delaydepends on the speed of the machine. Figure 1shows the output variable Atro response whena unit step is applied in the Stock Flow fordifferent speeds of the machine. The faster themachine works, the smaller the time-delay inthe output variable response.4. CONTROLLER DESIGNThis section describes a mathematical modelfor evaluating the amount of lost paper duringgrade transitions. The model was adapted for86discrete time and was used in defining the costfunction of an in-house predictive controller(De Keyser, 2003).4.1 A Model for the Wasted PaperThe first step in the design of the controller isto model the amount of wastage paper. Thelength of the transition is the time needed tochange the production between two produc-tion/operation points. A point of operationmust be defined for setting the quality stan-dards of the paper (customer-based tailoring).The length of a grade transition is defined bytwo time instants (t1 and t2). The speed ofthe machine determines the amount of paperproduced per unit of time. In order to obtainthe amount of lost paper (mass) per unit oftime, is necessary to multiply the width ofthe paper by the speed and the Atro output.This product has unit of grams per second [ gs ].Calculating the integral of this product in theinterval time from t1 to t2, gives the amountof waste during the transition. Equation (1)shows the model for lost paper (LP ).LP =Wt2∫t1A(t) v(t) dt (1)where:LP : Paper Loss [g].W : Width of paper [m].A(t) : Gramage [ gm2].v(t) : Speed [ms].t : Time [s].t1 : Start time of transitiont2 : End time of transitionIt is possible to convert the continuous modelof wastage in a discrete model by approxi-mating the integral of the equation (1) in asum; notice that the term of the time nowbecomes the sample time. The discrete modelfor wastage paper becomes:LP ≈W ∆tk2∑k=k1A(k) v(k) (2)where:A(k) : Gramage [ gm2].v(k) : Speed [ms].∆t : Sample time [s]k1 =t1∆t: Start time of transitionk2 =t2∆t: End time of transitionThis discrete model allows us to write a newcost function that includes the LP in theoptimization procedure of the predictive con-troller.4.2 The Cost FunctionOne of the most common cost functions isdefined as the square error between the out-put of the system and the desired referencetrajectory. In this investigation, a term whichdescribes the amount of LP in a finite horizonof prediction is included. The cost functionused is defined by (3). The function δ (t+ k|t)predicts if the paper is into the allowed re-gion of tolerance. This function has only twovalues: 0 when the paper produced is intothe region of tolerance; and 1 when the pa-per produced is out of the tolerance’s region(=wastage paper). The principal role of thefunction δ (t+ k|t) is to predict the limits ofthe transition (k1, k2) for (2) at each sampletime, because the values of the N1L and N2Lare fixed in the cost function (3).4.3 ConstraintsThe calculation of the input variables consid-ers the physical/technical constraints of thepaper machine. The nominal range consideredwas: for the stock flow from 200 to 700 [ ls ]; forthe speed from 2 to 10 [ms ] and for the pressurefrom 2 to 8 [Bar]. In the calculation of thecontrol inputs, the restrictions in the outputswere not considered (un-constrained).4.4 The OptimizerThe cost function (3) is non-linear and for thisreason the optimization algorithm iterates inorder to obtain the optimal control value. Thepaper machine model is also non-linear, and87therefore, the prediction of the system out-put used the step response calculated at eachsample time. The reduction of the LP presentsa difficulty, because when the algorithm mini-mizes the speed, it produces an increase in thevariable time-delay, as depicted in the Atroresponse in figure 1. The increase in time-delay is predicted by the function δ (t+ k|t).In other words, when the speed of the ma-chine is decreased, the length of the transitionincreases. Therefore, there is a compromisebetween the prediction of the speed and thedelta function in the cost function (3).5. SIMULATION RESULTSThe performance of the controller was testedwith different kinds of paper (grade-changes).The first aim was to prove the controllabilityof the system in closed-loop. The second aimwas to compare the response of the controllerfor different values of the tuning parametersand evaluate the amount of wastage paper ineach case. In order to make a comparison, thetolerance used in the test was the same for allkinds of paper: for the Atro the tolerance wasTA1 = TA2 = ± 2 [ gm2 ] and for the moisture itwas TM1 = TM2 = ± 1 [%].5.1 First TestThe first test used an Atro reference whichchanged from 80 to 150 [ gm2 ] while the mois-ture reference was maintained constant in 4.5%. In this test, three different values of tuningparameters λ2 have been used to compare theeffect of the third term in the cost function (3).Figure 2 shows the result of this simulation.The amount of lost paper was evaluated withthe expression (2) for different values of thetuning parameter λ2 and the result is shownin table 1.The controller with λ2 = 0.4 has produced lessamount of lost paper. It is possible to obtaina reduction of the wastage paper equal to 28% with respect to the case with λ2 = 0, dueFig. 2. Behavior of the controller for threedifferent values of λ2 tuning parameter.Table 1. Result of the test 1λ2 range of time [s] LP [kg] reduction [%]0 [448 609] 527 00.2 [447 592] 464 11.950.4 [447 573] 376 28.65to the advantage of using a model for the lostpaper.5.2 Second TestAn analysis of controller’s behavior has beenperformed when a disturbance was introducedin the consistency of the pulp, while it was un-known in the prediction model. The controllercompares the output variables of the processand the model.In this test we have employed a step changein the consistency of the pulp from 1.4 to1.3 [%] as disturbance at time 400 [s]. Thefilter of the estimator for perturbation usedn(t+ k|t) = n(t), {k = 1, .., N2}.88J(t) =N2A∑k=N1A[A (t+ k|t)−RA (t+ k|t)]2 + λ1N2M∑k=N1M[M (t+ k|t)−RM (t+ k|t)]2+λ2N2L∑k=N1LA (t+ k|t) v (t+ k|t) δ (t+ k|t)(3)δ (t+ k|t) =0 if [abs (A (t+ k|t)−RA1) < TA1] and [abs (M (t+ k|t)−RM1) < TM1]or[abs (A (t+ k|t)−RA2) < TA2] and [abs (M (t+ k|t)−RM2) < TM2]1 in other case(4)Where:A(t+ k|t): Prediction of Atro [g/m2]RA(t+ k|t): Atro reference [g/m2]M(t+ k|t): Prediction of Moisture [%]RM (t+ k|t): Moisture reference [%]λ1, λ2: Tuning parameterv(t+ k|t): Prediction of speed [m/s]δ(t+ k|t): Prediction function (binary)N2A, N1A: Horizon range for AtroN2M , N1M : Horizon range for MoistureN2L, N1L: Horizon range paper lossRA1, RA2: Atro ref. for paper 1 and 2 resp.RM1, RM2: Moisture ref. for paper 1 and 2TA1, TA2: Atro tolerance for paper 1 and 2TM1, TM2: Moisture tolerance for paper 1 and 2Figure 3 shows the output of the process andTable 2 shows the result of the second test,when a disturbance was introduced in theconsistency.Table 2. Result of the test 2λ2 range of time [s] LP [kg] reduction [%]0 [450 548] 393 00.2 [451 552] 405 -3.080.4 [451 545] 373 5.14All controllers maintain stability when a dis-turbance unregistered in the prediction modelis applied to the process. However, the re-duction of LP was not guaranteed. This kindof behavior is due to the difference betweenthe model and the process produced for thedisturbance.Fig. 3. Behavior of the controller when anunmeasured perturbation was applied inthe consistency of the pulp from 1.4 %to 1.3% for three different values of λ2tuning parameter.896. CONCLUSIONSA model was developed for evaluating theamount of lost paper during the transition be-tween two kind of paper qualities, dependingupon the process variables.The continuous model of the wastage paperwas used to design a term of the cost functionin the predictive controller. The cost functionused the square error between output of theprocess and the reference, as the classic modelpredictive control. However, the waste papermodel was also included as a new term in thecost function.The relationship between the operation pointin the production process and the length ofthe transition was included in the wastagepaper model of the cost function. The resultsof the predictive control with the lost papermodel were successful when compared with apredictive controller with classic cost function.The use of the lost paper model in the costfunction reduces the waste during the transi-tion between two operating points. The con-troller presents good results for disturbancerejection in the process, but the performanceof the controller depends highly on the tun-ing parameters. At this moment there is notan automatic system for tuning parameter.Although there is an interesting subject forfuture studies.Concluding, the use of the wastage model ina predictive controller reduces the amount ofpaper that is recycled in the paper industry,leading to a decrease in the energy employedin the transformation process from paper topulp and then to paper again.ACKNOWLEDGEMENTSThis work was supported by the ALFAProject for Latin America II-0385-FA ProcessSystem Engineering and the authors wouldlike to thank Siemens Company (Belgium)and Clara Ionescu for their collaboration.REFERENCESChen, S. C. (1992). Modeling of paper ma-chines for control: Theory and prac-tice. Proceedings from Control Systemspp. 115–121.De Keyser, R. (2003). Model based predictivecontrol. p. 30. ISBN 0 9542 989 18-26-34.Invited Chapter in UNESCO Encyclopae-dia of Life Support Systems (EoLSS).Ihalainen, H., Ritala R. (1996). Optimal gradechanges. Proceedings from Control Sys-tems pp. 213–216.McQuillin, D., Huizinga P.W. (1994). Reduc-ing grade change time through the useof predictive multi-variable control. Pro-ceedings from Control Systems pp. 275–281.Melo, R. C., Normey-Rico J. E. De Keyser R.(2006). Grade change predictive controlfor paper industry. In: ECC.Menani, S., Koivo H.N.-Huhtelin T. Kuu-sisto R. (1998). Dynamic modeling of pa-permachine from grade change data. Pro-ceedings from Control Systems pp. 79–86.Murphy T. F., Chen, S. (1999). Transitioncontrol of paper-making processes: Papergrade change. IEEE- International Con-ference on Control Applications pp. 22–27.www.paperonweb.com (2006).90

Reduction of material loss during grade change predictive control in a paper machine

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Reduction of material loss during grade chnage predictive contorl in a paper machine

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