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Partial least squares (PLS) based monitoring and control of batch digesters
Journal of Process Control 10 (2000) 229±236
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Partial least squares (PLS) based monitoring and control of batch digesters Parthasarathy Kesavan1, Jay H. Lee*, Victor Saucedo, Gopal A. Krishnagopalan Department of Chemical Engineering, Auburn University, Auburn, AL 36849-5127, USA
Abstract In this paper, a data-based control method for reducing product quality variations in batch pulp digesters is presented. Compared to the existing techniques, the new technique uses more liquor measurements in predicting the ®nal pulp quality. The liquor measurements obtained at dierent time instances during a cook are related to the ®nal pulp quality through a partial least squares (PLS) regression model. In using the PLS regression model for control, two approaches are proposed. In the ®rst approach, optimal control moves are computed directly using the PLS model, while the second approach employs a nonlinear H-factor model of which parameters are adapted using the prediction from the PLS model. The eectiveness of the prediction and control algorithms is examined through simulation studies. Experimental study is then performed on a lab-scale batch digester, to test the eectiveness of the prediction performance of the PLS model. The control algorithms will be tested on the experimental set-up in the future. # 2000 IFAC. Published by Elsevier Science Ltd. All rights reserved. Keywords: Partial least squares; Pulp digester; Quality prediction and control
1. Introduction Over the last few decades, increased global competition has stepped up the need to produce paper of uniform quality at competitive prices. This demands a reduction in the variability seen in both paper machines and pulping processes. Pulp can be produced by using either batch or continuous digesters. In this paper, we will address the issue of controlling pulp quality variations in batch digesters. Variations in the pulp quality can be attributed largely to the variations in the characteristics of wood chips used for pulping. Moisture contents of chips, chip size and chip composition can all vary signi®cantly. The most important variable in determining the pulp quality is the Kappa number, which is a measure of the residual lignin content in the pulp. The main diculty in maintaining consistent Kappa number stems from the fact that on-line Kappa number measurements are unavailable. This is because on-line sampling of pulp is infeasible. The problem is further complicated by the absence of feed-stock quality measurements. * Corresponding author, currently at School of Chemical Engineering, Purdue University, West Lafayette, IN 47907, USA. Tel.: +1765-494-4088; fax: +1-765-494-0805. E-mail address: [email protected] (J.H. Lee). 1 Currently with ABB Industrial Systems, Houston, TX 77077, USA.
The current practice consists of statistical quality control (SQC) and model based control (MBC) approaches. In the SQC approach, historical data are used to form a statistical base for the ®nal Kappa number. If the Kappa number deviations of recent cooks fall outside the statistical bounds, the cooking conditions are altered by the operator to oset the deviation. This is essentially an o-line method that cannot deal with uncorrelated, i.e. batch-to-batch, changes. Because of this, what is considered to be ``normal variation'' by SQC can be quite signi®cant. In the MBC approach, a model for the feed-stock disturbances, measured outputs, manipulated inputs and ®nal Kappa number is ®rst developed. The model is then used to predict on-line the ®nal Kappa number based on the measured outputs and to modify the cooking conditions appropriately to achieve the target Kappa number. The model can be either fundamental [15,3] or empirical [5,1]. Due to the complexity of fundamental models, current industrial practices rely almost exclusively on simple empirical or semi-empirical models. Some of these models [1,14] utilize on-line eective alkali (EA) measurements available at a particular time instant of cook (for example, at the beginning of the bulk phase), to compensate for the uncertainty in the initial conditions. However, single EA measurement alone cannot account for all the uncertainties in the feed-stock condition, and use of more on-line measurements is highly
0959-1524/00/$ - see front matter # 2000 IFAC. Published by Elsevier Science Ltd. All rights reserved. PII: S0959-1524(99)00028-1
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desired. Recently, methods for measuring concentrations of various components of the cooking liquor in real time have been developed [13]. Bene®ts of these additional measurements in fundamental model based estimation and control has already been demonstrated by Datta and Lee [3]. The main contribution of this paper is in how the online liquor measurements are utilized for better Kappa number control. We propose ways to use these measurements for control without resorting to complex fundamental models. We discuss the issues that arise in developing a regression model between the liquor measurements and the ®nal Kappa number. We also present two dierent ways to use the regression model for control purposes. In the ®rst approach, the manipulated variables (the cooking temperature and batch length) are included as inputs to the regression model and control algorithm is drawn directly from this model. In the second approach, the regression model is used to adapt parameters of an empirical model (for example, Chari's model [1]) to compensate for feed disturbances. The empirical model is then used to adjust the manipulated variables. This paper is organized as follows: in Section 2, the batch digester control problem is formulated. Section 3 deals with the development of regression model between on-line measurements, manipulated variables and ®nal quality variables. Two dierent approaches are proposed in Section 4 for using the regression model for control. The eectiveness of so developed prediction models and control algorithms are examined through simulation and experimental studies in Sections 5 and 6, respectively. Finally, some concluding remarks are made in Section 7.
feedback control is not possible. Kappa number can be measured after completion of batch, which can be used to improve only future batches. As a result, batch-to-batch variations are mostly left untouched. Recently, techniques have been developed [13] for in-situ measurements of cooking liquor, such as the concentrations of eective alkali (EA), lignin (Li), solids (So) and sul®de (Su) Ð details on the on-line liquor measurement techniques can be found in [13]. Hidden in these liquor measurements are information about the feed-stock disturbances that ultimately aect the ®nal Kappa number. The objective of this paper is to develop algorithms for converting these on-line measurements into prediction of ®nal Kappa number so that it can be controlled before the completion of batch. The manipulated variables that are considered in this work for control purposes are the cooking temperature and batch end time. 3. Prediction model In this section, we will develop a model relating the ®nal Kappa number to the measurements available during a batch and the manipulated variables. This model will then be used to predict the ®nal quality variable and to manipulate the inputs to achieve target quality.
2. Problem description Fig. 1 displays the batch digester set-up at Auburn University, which resembles typical industrial batch digester but with some additional provision to take on-line liquor measurements. Wood chips and white liquor, consisting mainly of sodium hydroxide and sodium sul®de, are fed to the digester. The temperature of the digester is raised to 170 C and maintained at that value by recirculating the liquor through a heater controlled by a temperature controller. The chemicals react with the wood to remove lignin, the binding material present in the wood, to generate pulp containing cellulose ®bers. The amount of residual lignin present in the pulp is a measure of pulp quality and is denoted by Kappa number. The control objective is to minimize the deviation of ®nal Kappa number from some target value. The main disturbances are feed-stock disturbances such as changes in the wood composition, chip size and initial moisture content. Since on-line pulp sampling is infeasible, direct
Fig. 1. Schematic diagram of the batch digester set-up and its instrumentation.
P. Kesavan et al. / Journal of Process Control 10 (2000) 229±236
q^ 0jk AY 0k BU 0kÿ1 CU0k
3.1. Model structure Let us assume the following underlying model for quality variables: q f1 ; U Tÿ1
1
231
7
where q0 q ÿ qr ; qr being the target quality. We represent the above with the notation q^ 0jk Mxk
8
In the above, q is a vector containing the quality variables at the end of a batch, contains unknown parameters that change from one batch to another (including feed-stock conditions, T process parameters, etc.), and U Tÿ1 uT0 uTTÿ1 . Here, u represents known process input variables whose paths can potentially be manipulated (most often through tracking control systems). The subscript i denotes the ith sample time. T is the total number of samples within a single batch and fi is an unknown, possibly nonlinear function representing the eect of feed-stock disturbance and manipulated variables on the ®nal quality variables. We assume that we have additional process measurements that are determined through the following relation:
0T 0T T . For conwhere M A; B; C and xk Y 0T k ; U k ; Uk venience, we will drop the superscript (0 ) from here on.
yk f2 ; U kÿ1 k
In the above, the index (j) is used to denote the data vector corresponding to the jth batch. The least squares F is the solution that minimizes kQ ÿ MXkF , where kk Frobenious norm, is given by
2
where y represents the measurements of process variables at any given sample time k, U kÿ1 T T u0 uTkÿ1 , and is the measurement error. Let
T T
Y k yT1 yk
3
Since Y k contains information about , it can be used to estimate . Let us denote an optimal estimate Ð in some sense Ð of based on Y k as ^jk f3 Y k ; U kÿ1
4
Then, substituting (4) in (1), we get the following expression for the corresponding estimate of q: q^ jk f1 f3 Y k ; U kÿ1 ; U Tÿ1
5
The ``hat'' notation (^) is used to denote an estimate. The notation jk represents the fact that all the information available at time k is utilized. We simply rewrite the above to obtain q^ jk f Y k ; U kÿ1 ; Uk
6
T where Uk uTk uTTÿ1 . Note that at time k, Uk is the set of manipulated variable moves to be implemented in the future. For pure monitoring, we assume Uk to be at the reference values; for control, Uk is to be determined by the controller. We can linearize Eq. (6) with respect to the nominal trajectory yr1 ; ; yrk and corresponding ur0 ; ; urTÿ1 to arrive at
3.2. Regression problem The problem is to identify matrix M appearing in the predictor of Eq. (8), given historical data for xk and q. Let us form the following matrices with data available from N batches: X xk 1 . . . xk j . . . xk N
9
Q q 1 . . . q j . . . q N
ÿ ÿ1 MLS QXT XXT
10
In practice, since X contains measurements and manipulated input moves made at various sample time instants during a batch, regressor vector xk is of very high dimension and its elements exhibit strong correlation. Hence, matrix (XXT ) tends to be highly illconditioned and the least squares estimator is generally a poor choice (in terms of variance, robustness, etc.). Multivariate statistical modeling techniques such as the partial least squares (PLS) and principal component regression (PCR) should alleviate this problem [4]. The multivariable statistical modeling methods utilize correlation among dierent measurements and manipulated variables, as exhibited by model-building data, in reducing the number of regression variables. The reduction in dimensionality is achieved by projecting the original variables onto a lower dimensional subspace called the principal component space. The projection of original data to the principal component space can be represented as S PX
11
where P is a projection matrix (which is a ``fat'' matrix) and S is a matrix containing the transformed variables for each batch called the principal components (PC). Now the regression problem is solved in the principal component space, i.e. using data matrix S. The predictor takes the form of
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ÿ ÿ1 q^ 0jk QST SST Pxk |{z}
12
M
Note that the number of rows in S, i.e. the number of principal components, would be, in general, signi®cantly smaller than that in X and SST will be well-conditioned due to the nature of the projection. Ideally, the number of principal components would be equal to the number of modes of variations present in the process. However, in practice, due to the inherent nonlinearity of the process and measurement noise, a few more PCs may be needed to retain the relevant information present in the data matrix. The PCs can be chosen to maximize the variance of the X data explained, as in PCR, or to maximize the covariance between X and Q, as in PLS. Since our ultimate interest here lies in the output quality prediction, it should be to one's advantage to consider the correlation with the output quality, as is done in the PLS method [4]. Several dierent techniques are available in the literature on how to decide on the number of PCs to be retained in building a regression model (see for example [8]). PCs themselves can be used for monitoring batch processes, as suggested by MacGregor and co-workers in several related papers ([9,10] and the references therein). Monitoring the PCs is useful for detecting the occurrence of disturbances. In this paper, however, we are concerned with how the disturbances aect the ®nal quality. Hence, instead of monitoring the PCs, we monitor the ®nal quality predictions derived from the regression model. If the quality prediction is signi®cantly dierent from the desired quality, the control algorithms discussed in the next section can be utilized to minimize the ®nal quality deviations. The regression model for ®nal quality prediction could be built at several instances during the batch, as more and more measurements are taken. Depending on the quality of the measurements, the ®nal quality predictions could improve as more measurements are taken. Instead of building more than one regression model to utilize the successive measurements, one could also build a single model that utilizes the measurements in a recursive manner as discussed in the paper by Russell et al. [12].
PLS models. More recently, Russell et al. [12] presented a more general approach to batch reactor control, equipped with a recursive method for quality prediction based on Kalman ®ltering. In this section we discuss two ways to use the PLSbased prediction model for control. In the ®rst approach, we use the prediction directly in calculating the manipulated input adjustments. This approach is similar to those proposed in [16] and [12]. In the second approach, we use the prediction indirectly, as a basis for adapting some key parameters of a nonlinear model. 4.1. Direct method For control, we want to manipulate the input trajectory u to control the quality. For this, let us divide [0,T) into m intervals: 0; ; k1 ; ; kmÿ1 ; ; T: Let us parameterize the trajectory ui for the ith interval kiÿ1 ; ; ki with parameter vector iu . Based on the input parameterization, we can write the quality prediction equation at t ki as ÿ u ; ; nu : q^ jki f4 Y ki ; U ki ÿ1 ; i1
An appropriate resolution of the input parameterization for each interval depends on the length of the interval and sensitivity of the quality variables to high frequency changes during the interval. In the simplest case, the trajectory for each interval can be chosen to be constant, yielding only a single parameter. The other extreme is to parameterize it with input values at all sample times within the interval. The more the parameters, the more data one would need for the model development. Often, parameterization of very ®ne resolution is not needed. It only makes the identi®cation problem more dicult. u ; ; nu can be determined at each ki so that Now, i1 the quality constraints are met. This can be formulated as an optimization of some sort, for instance, min u
j ; j>i1
4. Control In contrast to the monitoring, batch quality control using a statistical model is still at its infancy. Most of the earlier works were oriented towards controlling continuous processes using static PCR/PLS models [6,11,2]. For semi-batch processes, Yabuki and MacGregor [16] suggested using o-line and on-line measurements to make mid-course corrections based on
13
q^Tjki q q^ jki
n X
juT j ju
14
ji1
subject to the prediction equation constraint of (13) and other constraints if needed. q and are weighting matrices, the elements of which are chosen according to the importance of respective variables. 4.2. Indirect method When the relationship between the manipulated variables and the control variables (for example between the
P. Kesavan et al. / Journal of Process Control 10 (2000) 229±236
cooking temperature and Kappa number) is strongly nonlinear, the previously developed linear model may not provide satisfactory control performance. This is especially true if the batch end-time is to be used as input. In such circumstances, it would be advantageous to use a simple nonlinear model (either fundamental or empirical) and adapt some relevant key parameters to compensate for the unknown disturbances. This can be thought of as some form of adaptive control. In this study, we propose to use the quality predictions from the statistical model for model parameter adaptation. Assume that a nonlinear model of following form is available: q g1 ; U kÿ1 ; uk
15
In the above, is a vector of model parameters that depends on (see Section 3.1). The relationship between model parameters and process parameters is generally unknown. However, from (1), we see that the quality measurements q contain information about unknown parameter . In the traditional adaptive control algorithms, the quality measurements and the manipulated variable measurements used in modifying . In the batch quality control framework, however, quality measurements are available only at the end of batch. Hence, it is not possible to account for shortterm (e.g. batch-to-batch) variations. However, if quality predictions from the PLS model were used to adapt the key model parameters, batch-to-batch variations could indeed be accounted for. For instance, assuming the invertibility of (15), an estimate of the model parameters ^ can be obtained as follows: ÿ 16 ^ jk g2 q^ jk ; U kÿ1 ; Unom k where q^ jk is the quality prediction obtained from the statistical model (with Uk Unom and Unom contains k k the nominal values for the future input moves). More generally, one can use multiple data points, that is, choose ^ jk according to min
k X ÿ
q^ ji ÿ g1 ; U iÿ1 ; Unom 2 i 2
17
i1
The control law to compute the future input moves can now be obtained by using the quality model (15) with the new set of model parameters in the following quadratic minimization problem: ÿ T ÿ min q^ jk ÿ qr q q^ jk ÿ qr UTk u Uk Uk
subject to ÿ q^ jk g1 ^ jk ; U kÿ1 ; Uk
18
19
233
Note that Uk may be parameterized with only a few parameters as before. 5. Simulation studies 5.1. Data generation A fundamental model for the batch digester described in Section 2 was developed based on the information provided in [3]. This model was used as if it were the true plant, in generating the batch digester data for the simulation study. On-line liquor measurements of EA, Li, So and Su were assumed to be taken every 5 min. Softwood was chosen as the main feed-stock. The nominal cooking temperature was 170 C and batch end time was 180 min. It was assumed that the batch temperature can be altered at the half way mark (i.e. 90 min into the cook) to a new constant value (Tmid ). Batch end time (tb ) and Tmid were taken as manipulated variables (u tb Tmid ). For the model development, 50 batches were simulated by varying the feed-stock quality, Tmid and tb , in a random manner. Varying contents of hardwood were assumed to be present in the softwood feedstock, introducing large composition changes from one batch to the next. The range of the feed-stock variation is shown in Table (1). Tmid was varied between 165 and 175 C and tb was varied between 160 and 220 min. The measurements, manipulated variables, and quality variable were all scaled to have zero mean and unit variance. The data from the 50 batches were then used to develop a PLS model relating the measurements, manipulated variables (Tmid , tb ) and ®nal pulp quality (Ka). 5.2. Modeling and control Initial simulation studies with dierent on-line measurements (EA, Li, So and Su) indicated that EA and Li had maximum correlation with ®nal kappa number. Hence, only these measurements were incorporated into the input data matrix (X). The model was developed at the half way mark. A total of 19 samples are collected at the half way mark. Hence, for the jth batch (j 1; 2; . . . ; 50, xk j EA1 j, . . . ; EA19 j, Li j, . . . ; Li19 j; tb j; Tmid j. A PLS model as discussed in Section 3 was developed using the data. A total of 6 PCs were enough to explain 99% of the variance in X Table 1 Range of normal feed-stock variations used for building PLS model Variable
Range
Chip moisture Chip size Hard-wood content
45±55% 3±4 mm 0±20%
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P. Kesavan et al. / Journal of Process Control 10 (2000) 229±236
and 98% of the variance in q. Thus, the number of variables were reduced from 40 (in X) to 6. A plot of the PCs versus the Kappa number indicated a linear trend. Hence, a linear regression model was developed between the PCs and the Kappa number. Additional models developed at later time instances of batch did not yield any signi®cant improvement in the ®nal quality prediction. Hence, the control calculation was performed only once (at the 90 min mark). Control moves were calculated by the following two methods. 5.3. Direct method For fresh batches, the PLS model was used to predict the ®nal Kappa number at the nominal batch end time. If the predicted Kappa was dierent from the target Kappa, the control law as in (14) was used to calculate the values for the manipulated variables tb and Tmid in order to achieve the target Kappa. q and were chosen as 1 and [10 1], respectively. Note that a higher weight is given to the batch end time, in order to minimize the batch scheduling and inventory problems. 5.4. Indirect method In this approach, in order to handle the nonlinearity between the temperature, batch end time and the ®nal Kappa number, a semi-empirical model developed by Chari [1] was used. Chari's model is given by Ka Ac
Ve1 fr0
20
e3 Ce2 ar0 H
where Ac , e1, e2, e3 are model parameters, Ka is the ®nal Kappa number, Vfr0 is the ratio of initial white liquor volume to dry wood weight, Car0 is the ratio of initial active alkali to dry wood weight and H is the Hfactor, which is de®ned as the area under the plot of relative deligni®cation rate versus time [7]: tb 16113 21 H e43:2ÿT273 dt
PLS model development. For parameter estimation, the logarithmic form of (20) as given below is used since this results in a linear parameter estimation problem. ÿ log Ka log Ac e1 log Vfr0 ÿ ÿ e2 log Car0 ÿ e3 log H
24
In the above equation, Ac was chosen as adjustable parameter for each batch; it is estimated on-line at time tb1 on the basis of the Kappa prediction from the PLS model (with tb and Tmid kept at their nominal values), the known values of Vfr0 and Car0 and the nominal value of H. The logarithmic form of Chari's model with the adjusted Ac is then used to compute Tmid and tb according to the objective given in (18). q and u were chosen the same as in the direct algorithm. 5.5. Results and discussion For testing the PLS model, 20 new batch data were generated with both normal and large random variations in the feed-stock in the range shown in Table 2. We included some large variations in the test data in order to test the prediction capability of the model outside the range of modeling data. Fig. 2 shows the predicted ®nal Kappa number at the nominal batch end Table 2 Range of large feed-stock variations used for testing PLS model Variable
Range
Chip moisture Chip size Hard-wood content
40±60% 3±6 mm 0±45%
0
tb1 0
e
16113 43:2ÿT273
H1 e
dt
16113 mid 273
43:2ÿT
tb tb1
e
43:2ÿT
tb ÿ tb1
16113 mid 273
dt
22 23
In the above equations simpli®cation is achieved by using the fact that Tmid is held constant after the change at time tb1 (=90). H1 is the H-factor up to time tb1 (when the change in temperature is made) and can be calculated from past batches. The parameters of Chari's model are estimated by using data that was used for the
Fig. 2. Kappa number predictions obtained with the PLS model versus the actual Kappa number.
P. Kesavan et al. / Journal of Process Control 10 (2000) 229±236
time by using the PLS model versus the true value, for dierent batches. From the ®gure we see that the model predictions are very close to the actual values. In order to test the control strategy, a Monte Carlo simulation was performed, with random variations in the initial conditions. Twenty batch runs were simulated. Fig. 3(a) shows the variations in the ®nal Kappa number without any control, with the control based on the PLS model and with the control based on the combined PLS/modi®ed Chari's model. The standard deviation (square root of variance) was reduced from 6 (without control) to 3 with the PLS model based control and to 1.24 with the combined PLS/modi®ed H-factor model based control. Fig. 3(b) and (c) show the variations in the manipulated variables (Tmid and tb ) from their nominal values (170 and 180). Note that the adaptive control strategy also results in lesser variations of the batch end time from the nominal value. This helps in preventing scheduling problems due to variable batch end times. The better performance of the combined PLS/modi®ed Chari's model based control can be attributed to better handling of the nonlinearity between the manipulated variables and the ®nal pulp quality. 6. Experimental studies 6.1. Data generation The batch digester shown in Fig. 1 was used for cooking wood chips. Two-hundred and ®fty grams of oven dry wood chips was used in each batch. Liquor to wood ratio
Fig. 3. (a) Kappa number variations obtained without control, with PLS based control strategy and with combined PLS/modi®ed H-factor based control strategy. Target Kappa number is 40. (b) Variation in the mid-batch temperature (Tmid ) with respect to the nominal value (170). (c) Variation in the batch end time (tb ) with respect to the nominal value (180).
235
was 5.5. Softwood was used for cooking. Chip size varied between 3 and 5 mm thickness, chip composition varied between 26±28% lignin and chip moisture varied between 45±55%. The temperature was ramped up to 170 C and maintained at that value. Batch end time was taken as 180 min. For the time being, data were gathered to build and test the prediction capability of a PLS model only. Hence Tmid and tb were kept at their nominal values for all batches. In the future, additional data will be generated to develop control relevant models by varying Tmid and tb around their nominal values. 6.2. Modeling Data for 30 batch runs were obtained. After an analysis of the o-line and on-line data, only 21 batches were found to be suitable for model building and testing. Since 21 batches were not sucient for us to divide into separate model-building and testing data sets, we decided to build the model using 20 batches, leaving only a single batch for testing. However, we tested all the possible choices for model-building set, producing 21 data points for model testing. On-line data consisting of EA, lignin, solids and sul®de available at 5 min intervals were used in the PLS model. A linear PLS model with 7 principal components was built relating the measurements collected up to the 90 min mark and the ®nal Kappa number. Fig. 4 shows the predictions of ®nal Kappa number by the PLS model versus the actual Kappa number. For comparison, the predictions from traditional Chari's H-factor model is also shown (the word traditional is used since we used the Chari's model without the parameter adaptation described earlier). From the ®gure we see that the PLS model is able to give better predictions because of its ability to use more on-line liquor measurements. The
Fig. 4. Comparison of the prediction performance of PLS model (*) with that obtained from traditional H-factor model (o) by using data from experimental studies.
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use of the PLS model results in a signi®cant reduction in the mean square error (MSE) for the quality prediction when compared to the Chari's model. The prediction of the PLS model is slightly o in the Kappa range of 30 because the data sets used for modeling were mostly in the range 18±25. Thus, the PLS model was forced to extrapolate beyond the range of model-building data. Use of more data around the 30 Kappa range would probably have resulted in smaller prediction error. Currently, data are being collected to develop a controlrelevant model. This model will then be used to implement the control strategies on the experimental reactor. Since the control strategy utilized is dependent on the Kappa number estimation, the estimation accuracy will normally aect the performance of the control algorithm. 7. Conclusion In this paper, a data driven approach has been developed for prediction and control of ®nal Kappa number in batch digesters. The approach made use of on-line measurements of cooking liquor during the course of batch, in the PLS framework. Manipulated variables such as the batch end time and mid-batch temperature were also incorporated into the model for control purposes. The potential of the technique for predicting and controlling the ®nal Kappa number was demonstrated by means of simulation studies. The prediction capability was also tested using experimental data. Currently additional experimental data are being obtained to test the control algorithms in real time. Acknowledgements The authors gratefully acknowledge the ®nancial and technical support of the US Department of Energy, Pulp and Paper Consortium and Auburn Pulp and Paper Research and Education Center.
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Partial least squares (PLS) based monitoring and control of batch digesters Parthasarathy Kesavan1, Jay H. Lee*, Victor Saucedo, Gopal A. Krishnagopalan Department of Chemical Engineering, Auburn University, Auburn, AL 36849-5127, USA
Abstract In this paper, a data-based control method for reducing product quality variations in batch pulp digesters is presented. Compared to the existing techniques, the new technique uses more liquor measurements in predicting the ®nal pulp quality. The liquor measurements obtained at dierent time instances during a cook are related to the ®nal pulp quality through a partial least squares (PLS) regression model. In using the PLS regression model for control, two approaches are proposed. In the ®rst approach, optimal control moves are computed directly using the PLS model, while the second approach employs a nonlinear H-factor model of which parameters are adapted using the prediction from the PLS model. The eectiveness of the prediction and control algorithms is examined through simulation studies. Experimental study is then performed on a lab-scale batch digester, to test the eectiveness of the prediction performance of the PLS model. The control algorithms will be tested on the experimental set-up in the future. # 2000 IFAC. Published by Elsevier Science Ltd. All rights reserved. Keywords: Partial least squares; Pulp digester; Quality prediction and control
1. Introduction Over the last few decades, increased global competition has stepped up the need to produce paper of uniform quality at competitive prices. This demands a reduction in the variability seen in both paper machines and pulping processes. Pulp can be produced by using either batch or continuous digesters. In this paper, we will address the issue of controlling pulp quality variations in batch digesters. Variations in the pulp quality can be attributed largely to the variations in the characteristics of wood chips used for pulping. Moisture contents of chips, chip size and chip composition can all vary signi®cantly. The most important variable in determining the pulp quality is the Kappa number, which is a measure of the residual lignin content in the pulp. The main diculty in maintaining consistent Kappa number stems from the fact that on-line Kappa number measurements are unavailable. This is because on-line sampling of pulp is infeasible. The problem is further complicated by the absence of feed-stock quality measurements. * Corresponding author, currently at School of Chemical Engineering, Purdue University, West Lafayette, IN 47907, USA. Tel.: +1765-494-4088; fax: +1-765-494-0805. E-mail address: [email protected] (J.H. Lee). 1 Currently with ABB Industrial Systems, Houston, TX 77077, USA.
The current practice consists of statistical quality control (SQC) and model based control (MBC) approaches. In the SQC approach, historical data are used to form a statistical base for the ®nal Kappa number. If the Kappa number deviations of recent cooks fall outside the statistical bounds, the cooking conditions are altered by the operator to oset the deviation. This is essentially an o-line method that cannot deal with uncorrelated, i.e. batch-to-batch, changes. Because of this, what is considered to be ``normal variation'' by SQC can be quite signi®cant. In the MBC approach, a model for the feed-stock disturbances, measured outputs, manipulated inputs and ®nal Kappa number is ®rst developed. The model is then used to predict on-line the ®nal Kappa number based on the measured outputs and to modify the cooking conditions appropriately to achieve the target Kappa number. The model can be either fundamental [15,3] or empirical [5,1]. Due to the complexity of fundamental models, current industrial practices rely almost exclusively on simple empirical or semi-empirical models. Some of these models [1,14] utilize on-line eective alkali (EA) measurements available at a particular time instant of cook (for example, at the beginning of the bulk phase), to compensate for the uncertainty in the initial conditions. However, single EA measurement alone cannot account for all the uncertainties in the feed-stock condition, and use of more on-line measurements is highly
0959-1524/00/$ - see front matter # 2000 IFAC. Published by Elsevier Science Ltd. All rights reserved. PII: S0959-1524(99)00028-1
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desired. Recently, methods for measuring concentrations of various components of the cooking liquor in real time have been developed [13]. Bene®ts of these additional measurements in fundamental model based estimation and control has already been demonstrated by Datta and Lee [3]. The main contribution of this paper is in how the online liquor measurements are utilized for better Kappa number control. We propose ways to use these measurements for control without resorting to complex fundamental models. We discuss the issues that arise in developing a regression model between the liquor measurements and the ®nal Kappa number. We also present two dierent ways to use the regression model for control purposes. In the ®rst approach, the manipulated variables (the cooking temperature and batch length) are included as inputs to the regression model and control algorithm is drawn directly from this model. In the second approach, the regression model is used to adapt parameters of an empirical model (for example, Chari's model [1]) to compensate for feed disturbances. The empirical model is then used to adjust the manipulated variables. This paper is organized as follows: in Section 2, the batch digester control problem is formulated. Section 3 deals with the development of regression model between on-line measurements, manipulated variables and ®nal quality variables. Two dierent approaches are proposed in Section 4 for using the regression model for control. The eectiveness of so developed prediction models and control algorithms are examined through simulation and experimental studies in Sections 5 and 6, respectively. Finally, some concluding remarks are made in Section 7.
feedback control is not possible. Kappa number can be measured after completion of batch, which can be used to improve only future batches. As a result, batch-to-batch variations are mostly left untouched. Recently, techniques have been developed [13] for in-situ measurements of cooking liquor, such as the concentrations of eective alkali (EA), lignin (Li), solids (So) and sul®de (Su) Ð details on the on-line liquor measurement techniques can be found in [13]. Hidden in these liquor measurements are information about the feed-stock disturbances that ultimately aect the ®nal Kappa number. The objective of this paper is to develop algorithms for converting these on-line measurements into prediction of ®nal Kappa number so that it can be controlled before the completion of batch. The manipulated variables that are considered in this work for control purposes are the cooking temperature and batch end time. 3. Prediction model In this section, we will develop a model relating the ®nal Kappa number to the measurements available during a batch and the manipulated variables. This model will then be used to predict the ®nal quality variable and to manipulate the inputs to achieve target quality.
2. Problem description Fig. 1 displays the batch digester set-up at Auburn University, which resembles typical industrial batch digester but with some additional provision to take on-line liquor measurements. Wood chips and white liquor, consisting mainly of sodium hydroxide and sodium sul®de, are fed to the digester. The temperature of the digester is raised to 170 C and maintained at that value by recirculating the liquor through a heater controlled by a temperature controller. The chemicals react with the wood to remove lignin, the binding material present in the wood, to generate pulp containing cellulose ®bers. The amount of residual lignin present in the pulp is a measure of pulp quality and is denoted by Kappa number. The control objective is to minimize the deviation of ®nal Kappa number from some target value. The main disturbances are feed-stock disturbances such as changes in the wood composition, chip size and initial moisture content. Since on-line pulp sampling is infeasible, direct
Fig. 1. Schematic diagram of the batch digester set-up and its instrumentation.
P. Kesavan et al. / Journal of Process Control 10 (2000) 229±236
q^ 0jk AY 0k BU 0kÿ1 CU0k
3.1. Model structure Let us assume the following underlying model for quality variables: q f1 ; U Tÿ1
1
231
7
where q0 q ÿ qr ; qr being the target quality. We represent the above with the notation q^ 0jk Mxk
8
In the above, q is a vector containing the quality variables at the end of a batch, contains unknown parameters that change from one batch to another (including feed-stock conditions, T process parameters, etc.), and U Tÿ1 uT0 uTTÿ1 . Here, u represents known process input variables whose paths can potentially be manipulated (most often through tracking control systems). The subscript i denotes the ith sample time. T is the total number of samples within a single batch and fi is an unknown, possibly nonlinear function representing the eect of feed-stock disturbance and manipulated variables on the ®nal quality variables. We assume that we have additional process measurements that are determined through the following relation:
0T 0T T . For conwhere M A; B; C and xk Y 0T k ; U k ; Uk venience, we will drop the superscript (0 ) from here on.
yk f2 ; U kÿ1 k
In the above, the index (j) is used to denote the data vector corresponding to the jth batch. The least squares F is the solution that minimizes kQ ÿ MXkF , where kk Frobenious norm, is given by
2
where y represents the measurements of process variables at any given sample time k, U kÿ1 T T u0 uTkÿ1 , and is the measurement error. Let
T T
Y k yT1 yk
3
Since Y k contains information about , it can be used to estimate . Let us denote an optimal estimate Ð in some sense Ð of based on Y k as ^jk f3 Y k ; U kÿ1
4
Then, substituting (4) in (1), we get the following expression for the corresponding estimate of q: q^ jk f1 f3 Y k ; U kÿ1 ; U Tÿ1
5
The ``hat'' notation (^) is used to denote an estimate. The notation jk represents the fact that all the information available at time k is utilized. We simply rewrite the above to obtain q^ jk f Y k ; U kÿ1 ; Uk
6
T where Uk uTk uTTÿ1 . Note that at time k, Uk is the set of manipulated variable moves to be implemented in the future. For pure monitoring, we assume Uk to be at the reference values; for control, Uk is to be determined by the controller. We can linearize Eq. (6) with respect to the nominal trajectory yr1 ; ; yrk and corresponding ur0 ; ; urTÿ1 to arrive at
3.2. Regression problem The problem is to identify matrix M appearing in the predictor of Eq. (8), given historical data for xk and q. Let us form the following matrices with data available from N batches: X xk 1 . . . xk j . . . xk N
9
Q q 1 . . . q j . . . q N
ÿ ÿ1 MLS QXT XXT
10
In practice, since X contains measurements and manipulated input moves made at various sample time instants during a batch, regressor vector xk is of very high dimension and its elements exhibit strong correlation. Hence, matrix (XXT ) tends to be highly illconditioned and the least squares estimator is generally a poor choice (in terms of variance, robustness, etc.). Multivariate statistical modeling techniques such as the partial least squares (PLS) and principal component regression (PCR) should alleviate this problem [4]. The multivariable statistical modeling methods utilize correlation among dierent measurements and manipulated variables, as exhibited by model-building data, in reducing the number of regression variables. The reduction in dimensionality is achieved by projecting the original variables onto a lower dimensional subspace called the principal component space. The projection of original data to the principal component space can be represented as S PX
11
where P is a projection matrix (which is a ``fat'' matrix) and S is a matrix containing the transformed variables for each batch called the principal components (PC). Now the regression problem is solved in the principal component space, i.e. using data matrix S. The predictor takes the form of
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ÿ ÿ1 q^ 0jk QST SST Pxk |{z}
12
M
Note that the number of rows in S, i.e. the number of principal components, would be, in general, signi®cantly smaller than that in X and SST will be well-conditioned due to the nature of the projection. Ideally, the number of principal components would be equal to the number of modes of variations present in the process. However, in practice, due to the inherent nonlinearity of the process and measurement noise, a few more PCs may be needed to retain the relevant information present in the data matrix. The PCs can be chosen to maximize the variance of the X data explained, as in PCR, or to maximize the covariance between X and Q, as in PLS. Since our ultimate interest here lies in the output quality prediction, it should be to one's advantage to consider the correlation with the output quality, as is done in the PLS method [4]. Several dierent techniques are available in the literature on how to decide on the number of PCs to be retained in building a regression model (see for example [8]). PCs themselves can be used for monitoring batch processes, as suggested by MacGregor and co-workers in several related papers ([9,10] and the references therein). Monitoring the PCs is useful for detecting the occurrence of disturbances. In this paper, however, we are concerned with how the disturbances aect the ®nal quality. Hence, instead of monitoring the PCs, we monitor the ®nal quality predictions derived from the regression model. If the quality prediction is signi®cantly dierent from the desired quality, the control algorithms discussed in the next section can be utilized to minimize the ®nal quality deviations. The regression model for ®nal quality prediction could be built at several instances during the batch, as more and more measurements are taken. Depending on the quality of the measurements, the ®nal quality predictions could improve as more measurements are taken. Instead of building more than one regression model to utilize the successive measurements, one could also build a single model that utilizes the measurements in a recursive manner as discussed in the paper by Russell et al. [12].
PLS models. More recently, Russell et al. [12] presented a more general approach to batch reactor control, equipped with a recursive method for quality prediction based on Kalman ®ltering. In this section we discuss two ways to use the PLSbased prediction model for control. In the ®rst approach, we use the prediction directly in calculating the manipulated input adjustments. This approach is similar to those proposed in [16] and [12]. In the second approach, we use the prediction indirectly, as a basis for adapting some key parameters of a nonlinear model. 4.1. Direct method For control, we want to manipulate the input trajectory u to control the quality. For this, let us divide [0,T) into m intervals: 0; ; k1 ; ; kmÿ1 ; ; T: Let us parameterize the trajectory ui for the ith interval kiÿ1 ; ; ki with parameter vector iu . Based on the input parameterization, we can write the quality prediction equation at t ki as ÿ u ; ; nu : q^ jki f4 Y ki ; U ki ÿ1 ; i1
An appropriate resolution of the input parameterization for each interval depends on the length of the interval and sensitivity of the quality variables to high frequency changes during the interval. In the simplest case, the trajectory for each interval can be chosen to be constant, yielding only a single parameter. The other extreme is to parameterize it with input values at all sample times within the interval. The more the parameters, the more data one would need for the model development. Often, parameterization of very ®ne resolution is not needed. It only makes the identi®cation problem more dicult. u ; ; nu can be determined at each ki so that Now, i1 the quality constraints are met. This can be formulated as an optimization of some sort, for instance, min u
j ; j>i1
4. Control In contrast to the monitoring, batch quality control using a statistical model is still at its infancy. Most of the earlier works were oriented towards controlling continuous processes using static PCR/PLS models [6,11,2]. For semi-batch processes, Yabuki and MacGregor [16] suggested using o-line and on-line measurements to make mid-course corrections based on
13
q^Tjki q q^ jki
n X
juT j ju
14
ji1
subject to the prediction equation constraint of (13) and other constraints if needed. q and are weighting matrices, the elements of which are chosen according to the importance of respective variables. 4.2. Indirect method When the relationship between the manipulated variables and the control variables (for example between the
P. Kesavan et al. / Journal of Process Control 10 (2000) 229±236
cooking temperature and Kappa number) is strongly nonlinear, the previously developed linear model may not provide satisfactory control performance. This is especially true if the batch end-time is to be used as input. In such circumstances, it would be advantageous to use a simple nonlinear model (either fundamental or empirical) and adapt some relevant key parameters to compensate for the unknown disturbances. This can be thought of as some form of adaptive control. In this study, we propose to use the quality predictions from the statistical model for model parameter adaptation. Assume that a nonlinear model of following form is available: q g1 ; U kÿ1 ; uk
15
In the above, is a vector of model parameters that depends on (see Section 3.1). The relationship between model parameters and process parameters is generally unknown. However, from (1), we see that the quality measurements q contain information about unknown parameter . In the traditional adaptive control algorithms, the quality measurements and the manipulated variable measurements used in modifying . In the batch quality control framework, however, quality measurements are available only at the end of batch. Hence, it is not possible to account for shortterm (e.g. batch-to-batch) variations. However, if quality predictions from the PLS model were used to adapt the key model parameters, batch-to-batch variations could indeed be accounted for. For instance, assuming the invertibility of (15), an estimate of the model parameters ^ can be obtained as follows: ÿ 16 ^ jk g2 q^ jk ; U kÿ1 ; Unom k where q^ jk is the quality prediction obtained from the statistical model (with Uk Unom and Unom contains k k the nominal values for the future input moves). More generally, one can use multiple data points, that is, choose ^ jk according to min
k X ÿ
q^ ji ÿ g1 ; U iÿ1 ; Unom 2 i 2
17
i1
The control law to compute the future input moves can now be obtained by using the quality model (15) with the new set of model parameters in the following quadratic minimization problem: ÿ T ÿ min q^ jk ÿ qr q q^ jk ÿ qr UTk u Uk Uk
subject to ÿ q^ jk g1 ^ jk ; U kÿ1 ; Uk
18
19
233
Note that Uk may be parameterized with only a few parameters as before. 5. Simulation studies 5.1. Data generation A fundamental model for the batch digester described in Section 2 was developed based on the information provided in [3]. This model was used as if it were the true plant, in generating the batch digester data for the simulation study. On-line liquor measurements of EA, Li, So and Su were assumed to be taken every 5 min. Softwood was chosen as the main feed-stock. The nominal cooking temperature was 170 C and batch end time was 180 min. It was assumed that the batch temperature can be altered at the half way mark (i.e. 90 min into the cook) to a new constant value (Tmid ). Batch end time (tb ) and Tmid were taken as manipulated variables (u tb Tmid ). For the model development, 50 batches were simulated by varying the feed-stock quality, Tmid and tb , in a random manner. Varying contents of hardwood were assumed to be present in the softwood feedstock, introducing large composition changes from one batch to the next. The range of the feed-stock variation is shown in Table (1). Tmid was varied between 165 and 175 C and tb was varied between 160 and 220 min. The measurements, manipulated variables, and quality variable were all scaled to have zero mean and unit variance. The data from the 50 batches were then used to develop a PLS model relating the measurements, manipulated variables (Tmid , tb ) and ®nal pulp quality (Ka). 5.2. Modeling and control Initial simulation studies with dierent on-line measurements (EA, Li, So and Su) indicated that EA and Li had maximum correlation with ®nal kappa number. Hence, only these measurements were incorporated into the input data matrix (X). The model was developed at the half way mark. A total of 19 samples are collected at the half way mark. Hence, for the jth batch (j 1; 2; . . . ; 50, xk j EA1 j, . . . ; EA19 j, Li j, . . . ; Li19 j; tb j; Tmid j. A PLS model as discussed in Section 3 was developed using the data. A total of 6 PCs were enough to explain 99% of the variance in X Table 1 Range of normal feed-stock variations used for building PLS model Variable
Range
Chip moisture Chip size Hard-wood content
45±55% 3±4 mm 0±20%
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and 98% of the variance in q. Thus, the number of variables were reduced from 40 (in X) to 6. A plot of the PCs versus the Kappa number indicated a linear trend. Hence, a linear regression model was developed between the PCs and the Kappa number. Additional models developed at later time instances of batch did not yield any signi®cant improvement in the ®nal quality prediction. Hence, the control calculation was performed only once (at the 90 min mark). Control moves were calculated by the following two methods. 5.3. Direct method For fresh batches, the PLS model was used to predict the ®nal Kappa number at the nominal batch end time. If the predicted Kappa was dierent from the target Kappa, the control law as in (14) was used to calculate the values for the manipulated variables tb and Tmid in order to achieve the target Kappa. q and were chosen as 1 and [10 1], respectively. Note that a higher weight is given to the batch end time, in order to minimize the batch scheduling and inventory problems. 5.4. Indirect method In this approach, in order to handle the nonlinearity between the temperature, batch end time and the ®nal Kappa number, a semi-empirical model developed by Chari [1] was used. Chari's model is given by Ka Ac
Ve1 fr0
20
e3 Ce2 ar0 H
where Ac , e1, e2, e3 are model parameters, Ka is the ®nal Kappa number, Vfr0 is the ratio of initial white liquor volume to dry wood weight, Car0 is the ratio of initial active alkali to dry wood weight and H is the Hfactor, which is de®ned as the area under the plot of relative deligni®cation rate versus time [7]: tb 16113 21 H e43:2ÿT273 dt
PLS model development. For parameter estimation, the logarithmic form of (20) as given below is used since this results in a linear parameter estimation problem. ÿ log Ka log Ac e1 log Vfr0 ÿ ÿ e2 log Car0 ÿ e3 log H
24
In the above equation, Ac was chosen as adjustable parameter for each batch; it is estimated on-line at time tb1 on the basis of the Kappa prediction from the PLS model (with tb and Tmid kept at their nominal values), the known values of Vfr0 and Car0 and the nominal value of H. The logarithmic form of Chari's model with the adjusted Ac is then used to compute Tmid and tb according to the objective given in (18). q and u were chosen the same as in the direct algorithm. 5.5. Results and discussion For testing the PLS model, 20 new batch data were generated with both normal and large random variations in the feed-stock in the range shown in Table 2. We included some large variations in the test data in order to test the prediction capability of the model outside the range of modeling data. Fig. 2 shows the predicted ®nal Kappa number at the nominal batch end Table 2 Range of large feed-stock variations used for testing PLS model Variable
Range
Chip moisture Chip size Hard-wood content
40±60% 3±6 mm 0±45%
0
tb1 0
e
16113 43:2ÿT273
H1 e
dt
16113 mid 273
43:2ÿT
tb tb1
e
43:2ÿT
tb ÿ tb1
16113 mid 273
dt
22 23
In the above equations simpli®cation is achieved by using the fact that Tmid is held constant after the change at time tb1 (=90). H1 is the H-factor up to time tb1 (when the change in temperature is made) and can be calculated from past batches. The parameters of Chari's model are estimated by using data that was used for the
Fig. 2. Kappa number predictions obtained with the PLS model versus the actual Kappa number.
P. Kesavan et al. / Journal of Process Control 10 (2000) 229±236
time by using the PLS model versus the true value, for dierent batches. From the ®gure we see that the model predictions are very close to the actual values. In order to test the control strategy, a Monte Carlo simulation was performed, with random variations in the initial conditions. Twenty batch runs were simulated. Fig. 3(a) shows the variations in the ®nal Kappa number without any control, with the control based on the PLS model and with the control based on the combined PLS/modi®ed Chari's model. The standard deviation (square root of variance) was reduced from 6 (without control) to 3 with the PLS model based control and to 1.24 with the combined PLS/modi®ed H-factor model based control. Fig. 3(b) and (c) show the variations in the manipulated variables (Tmid and tb ) from their nominal values (170 and 180). Note that the adaptive control strategy also results in lesser variations of the batch end time from the nominal value. This helps in preventing scheduling problems due to variable batch end times. The better performance of the combined PLS/modi®ed Chari's model based control can be attributed to better handling of the nonlinearity between the manipulated variables and the ®nal pulp quality. 6. Experimental studies 6.1. Data generation The batch digester shown in Fig. 1 was used for cooking wood chips. Two-hundred and ®fty grams of oven dry wood chips was used in each batch. Liquor to wood ratio
Fig. 3. (a) Kappa number variations obtained without control, with PLS based control strategy and with combined PLS/modi®ed H-factor based control strategy. Target Kappa number is 40. (b) Variation in the mid-batch temperature (Tmid ) with respect to the nominal value (170). (c) Variation in the batch end time (tb ) with respect to the nominal value (180).
235
was 5.5. Softwood was used for cooking. Chip size varied between 3 and 5 mm thickness, chip composition varied between 26±28% lignin and chip moisture varied between 45±55%. The temperature was ramped up to 170 C and maintained at that value. Batch end time was taken as 180 min. For the time being, data were gathered to build and test the prediction capability of a PLS model only. Hence Tmid and tb were kept at their nominal values for all batches. In the future, additional data will be generated to develop control relevant models by varying Tmid and tb around their nominal values. 6.2. Modeling Data for 30 batch runs were obtained. After an analysis of the o-line and on-line data, only 21 batches were found to be suitable for model building and testing. Since 21 batches were not sucient for us to divide into separate model-building and testing data sets, we decided to build the model using 20 batches, leaving only a single batch for testing. However, we tested all the possible choices for model-building set, producing 21 data points for model testing. On-line data consisting of EA, lignin, solids and sul®de available at 5 min intervals were used in the PLS model. A linear PLS model with 7 principal components was built relating the measurements collected up to the 90 min mark and the ®nal Kappa number. Fig. 4 shows the predictions of ®nal Kappa number by the PLS model versus the actual Kappa number. For comparison, the predictions from traditional Chari's H-factor model is also shown (the word traditional is used since we used the Chari's model without the parameter adaptation described earlier). From the ®gure we see that the PLS model is able to give better predictions because of its ability to use more on-line liquor measurements. The
Fig. 4. Comparison of the prediction performance of PLS model (*) with that obtained from traditional H-factor model (o) by using data from experimental studies.
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use of the PLS model results in a signi®cant reduction in the mean square error (MSE) for the quality prediction when compared to the Chari's model. The prediction of the PLS model is slightly o in the Kappa range of 30 because the data sets used for modeling were mostly in the range 18±25. Thus, the PLS model was forced to extrapolate beyond the range of model-building data. Use of more data around the 30 Kappa range would probably have resulted in smaller prediction error. Currently, data are being collected to develop a controlrelevant model. This model will then be used to implement the control strategies on the experimental reactor. Since the control strategy utilized is dependent on the Kappa number estimation, the estimation accuracy will normally aect the performance of the control algorithm. 7. Conclusion In this paper, a data driven approach has been developed for prediction and control of ®nal Kappa number in batch digesters. The approach made use of on-line measurements of cooking liquor during the course of batch, in the PLS framework. Manipulated variables such as the batch end time and mid-batch temperature were also incorporated into the model for control purposes. The potential of the technique for predicting and controlling the ®nal Kappa number was demonstrated by means of simulation studies. The prediction capability was also tested using experimental data. Currently additional experimental data are being obtained to test the control algorithms in real time. Acknowledgements The authors gratefully acknowledge the ®nancial and technical support of the US Department of Energy, Pulp and Paper Consortium and Auburn Pulp and Paper Research and Education Center.
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