Stage-Based Online Quality Control for Batch Processes - Industrial

A stage-based quality control scheme, which combines an online adjustment ... self-recovery method based on reinforcement learning with small data in ...
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Ind. Eng. Chem. Res. 2006, 45, 2272-2280

Stage-Based Online Quality Control for Batch Processes Ningyun Lu and Furong Gao* Department of Chemical Engineering, Hong Kong UniVersity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

A stage-based quality control scheme, which combines an online adjustment strategy with the authors’ previous works on stage partial least squares (PLS) modeling and quality prediction, is developed for within-batch control of end-product quality for batch processes. Considering the inherent time-specific nature of process trajectories to the end-product quality, a critical-to-quality-control stage is introduced for quality control and stability improvement, together with guidelines on the manipulating variable selection and no-control region. The effectiveness and feasibility of the proposed scheme are illustrated on an injection molding process. 1. Introduction Batch processes are widely used today for producing highervalue-added products to meet the rapidly changing market. Semiconductor processing, injection molding, fermentation, and most bio-processes are all batch processes in nature. Competition and demand for consistent and high-quality products have spurred the development of quality-related researches for batch processes. Quality control of batch processes is often conducted in an open-loop manner through process automation and control of key process variables, in the hope that consistent operation condition can lead to consistent end-product quality. Despite the wide use of advanced process-control schemes, quality variations still exist, because of process malfunctions, the drifting of process conditions, changes in materials, or unknown disturbances. Batch-to-batch feedback control strategies can be adopted to reduce quality variations; however, they cannot compensate for quality deviations in an evolving batch. Online quality control strategy is necessary for industries to ensure consistent and acceptable product quality. However, online quality control for batch processes is difficult to achieve, because of complicated dynamic and nonlinear process behaviors, the lack of online quality measurements, and the high-dimensional correlated process variables that cannot be independently manipulated. Significant efforts have been exerted on the development of methods for online quality prediction and control for batch processes, among which multivariate statistical models, such as principal component analysis (PCA),1 partial least squares (PLS),2 or multiway PCA/PLS,3,4 are the most popular, because they can be derived directly from historical data with little prior process knowledge but superior ability in handling high-dimensional correlated process data. A review of multivariate statistical model-based online quality prediction for batch processes has been given by the authors.5 This paper will focus on online quality control. Most online quality control methods using multivariate statistical models were concerned with continuous processes.6-9 For batch or semibatch processes, Yabuki and MacGregor10 proposed a so-called midcourse control policy for controlling the end-product quality, using both online and offline measurements available up to the midpoint of a semibatch process. This method is dependent highly on process knowledge and makes * To whom correspondence should be addressed. Tel.: +852-23587139. Fax: +852-2358-0054. E-mail: [email protected].

only one adjustment within a batch for quality control. To make more frequent corrections in a batch, Kesavan et al.11 and FloresCerrillo and MacGregor12,13 proposed PLS-based quality control methods by adjusting the trajectories of the manipulated variables. The trajectories are artificially divided into several segments with a control decision point in each segment. At each decision point, final product qualities are predicted and adjustments on the remaining segments are computed if the predicted qualities are beyond the desired specifications. However, the control decision points referenced in the aforementioned literature must be determined by deep process knowledge. A general data-based approach has been proposed by Russell et al.14 for online prediction and control of the final product quality at any point of a process in a recursive manner. The application of the aforementioned procedure to a methyl methacrylate polymerization (PMMA) process has been reported by Pan and Lee.15 A recipe-based quality improvement strategy has also been reported for a nylon-6,6 process by Kaistha et al.16 to reduce the variations in the final product quality. For many batch processes, it is common that certain quality may be only affected by certain variables in certain stages (or phases). Batch adjustment outside these specific stages cannot result in any quality improvement. Rather, it may cause control difficulties and stability problems. None of the aforementioned quality control schemes has mentioned the nature of timespecific effects of process variables on the end-product quality in their methods. However, applications are actually tested in the specific periods of batch processes. For example, the midcourse correction is only made at a time of 230 min for controlling the concerned quality in a semibatch polymerization of SBR,10 and the recursive data-based quality control method illustrated on the nylon polymerization process is also conducted in the specific time period based on process knowledge.14 This paper aims to develop a general online quality control scheme for batch processes, taking explicit advantage of the time-specific nature of batch processes. This work extends the authors’ earlier work on stage-based modeling, monitoring, and process analysis5,17 to stage-based quality control. The proposed quality control scheme has the following features: (1) It explores time-specific relationships between process variable trajectories and end-product qualities, to determine which process variables and what time periods have critical effects on the final qualities; (2) It provides accurate online estimation of end-product qualities to determine if online batch adjustment is needed;

10.1021/ie050887d CCC: $33.50 © 2006 American Chemical Society Published on Web 03/08/2006

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Figure 1. Batch process and relationship among process data.

(3) If necessary, it defines when and how online adjustment should be activated to compensate for quality deviations to achieve desired final product quality. A stage-based quality controller is designed to maintain final product quality by adjusting set points of proper variables in proper stages. The concept of critical-to-quality-control stage is introduced, together with guidelines on determination of key implementation parameters of the proposed scheme. The quality control scheme will be introduced in detail in section 3, and then will be illustrated on an injection-molding process in section 4. Finally, conclusions are drawn in the last section. 2. Nature of Batch Process Data Before moving on to the methodology, it is necessary to describe briefly the nature of batch process data. Data flow in a batch process can be systematically presented in Figure 1, where ysp is the desired end-product quality specification, x/sp is the set point of the controlled process variables x*, d is the process disturbance, x(k) is the online process measurement collected from measurable process variables, y is the end-product quality at the end of batch operation, and k is the index of sampling point within a batch. The dashed lines in Figure 1 depict the information flow about batch process data. The determination of initial set points of process controllers x/sp is made either explicitly or implicitly, in terms of the quality specifications ysp, whereas the end-product quality properties y can be determined by or estimated from either set points of controlled variables or process trajectories. Quality prediction by using the set points only has the advantage of simplicity. However, it is less accurate, compared to the method of using all online process measurements, because the end-product qualities also may vary with uncontrolled variables or process disturbances. The objective of this paper is to develop a scheme to control the end-product quality in a closed-loop manner, by adjusting the set-point profiles of process controllers x/sp, according to the online quality prediction y(k). 3. Stage-Based Online Quality Control for Batch Processes 3.1. Overview. The proposed stage-based online quality control scheme is illustrated in Figure 2. Prior to that, offline development will be necessary, including data preparation, model development for stage-based quality prediction and control, and other offline analysis (such as definitions of the critical-to-quality stages and determinations of adjustable process variables and no-control regions). The online implementation will determine the stage of the current evolving batch, and check if the current stage is a critical-to-quality stage. The corresponding stage PLS model is used for online quality prediction. If the predicted quality deviates from the desired region, an online batch adjustment algorithm is used to output new set points for the process controllers, as shown in Figure 2.

Figure 2. Procedures of the stage-PLS-based online quality-control system.

3.2. Offline Development. 3.2.1. Data Preparation. Building an appropriate reference data set is critical to the proposed databased quality control system, which mainly includes data selection to span the operating region, data alignment for uneven-length batch processes, and data preprocessing such as centering and scaling. The data-based models are generally valid only in the region spanned by the data used for model building; therefore, the reference data should carry sufficient information on process characteristics in the entire window of normal operation. Historical data from a wide range of operating conditions should be collected. In addition, designed experiments may be necessary to generate a wider range of variation in process trajectories under the normal operating conditions.18 For industrial processes with varying batch length, many methods19 are available to examine uneven-length batch data, among which the “indicator variable” method can be the first choice if there exists prior knowledge to determine a proper indicator variable. After proper data selection and alignment, the reference data set collected on a batch process typically consists of three-way process trajectories, X(I × Jx × K), and two-way quality measurements, Y(I × Jy), where I is the number of batch operations selected in the reference data set, K is the number of sampling time in each batch, Jx and Jy are the numbers of variables in each block, respectively. X is normalized as in MPLS modeling,4 that is, centered and scaled across the batch direction to focus on batchto-batch variations. Two-way quality data Y are also normalized to have zero means and unit variances. 3.2.2. Model Development. Stage-based modeling methods5,17 were proposed based on the recognition that (i) a batch process may be divided into several stages, reflected by its changing process correlation nature, and (ii) despite the fact that the process may be time varying, the correlation of its variables will be largely similar within the same stage, and the changes in the correlation can be used to indicate the changes

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of process stages. The main procedures of stage PLS modeling are summarized below. The three-way process trajectory matrix X is first cut along the time axis, resulting in K time-slice matrices, X ˜ k(I × Jx) (k ) 1, 2, ..., K), which contain batch-to-batch variations of process variables at sampling time k. PLS is then applied to {X ˜ k,Y} to reveal the time-specific correlation between process and quality variables. This time-slice PLS model can be finally represented in a compact form as Yˆ k ) X ˜ kΘ ˜ k. The regression coefficient matrix, Θ ˜ k, which contains the correlation information at time k, should remain similar in the same stage and show significant differences over different stages. The change of process correlation can be reflected by the change of the regression parameter matrix Θ ˜ k. A modified k-means clustering algorithm is adopted for dividing the K number of Θ ˜ k into clusters with different characteristics. Process stages are determined by the clustering results associated with process operating time. Suppose that the batch process is divided into C stages; then the stage PLS modeling method generates C number of independent PLS models for different stages. The representative regression parameter matrix of the PLS model for stage c is defined as the average of Θ ˜ k, i.e.,

Θ/c )

1 nstage_c

∑k Θ˜ k

(for c ) 1, ..., C; k ) 1, ..., nstage_c)

where nstage_c is the number of samples in stage c. Details about stage division and stage PLS modeling are given in ref 5. 3.2.3. Offline Analysis. The stage PLS modeling has provided a platform for analyzing the time-specific effects of process variables on the final product qualities by determining the critical-to-quality stage. The stage that has significant correlation with the end-product quality variations is defined as the criticalto-quality stage. This is implemented by measuring the goodness-of-fit of the stage PLS models, and the multiple coefficient of determination, R2, is used to evaluate the fitness of each stage of the PLS models.5 It should be mentioned that the criticalto-quality stages defined in our previous work should be interpreted as critical-to-quality-prediction stages. In this paper, the concept of critical-to-quality-control stage will be introduced. The critical-to-prediction stage that has manipulatible process variables to affect the end-product quality is defined as the critical-to-quality-control stage. The necessity to differentiate these two concepts is obvious. For example, in injection molding, the cavity pressure in the earlier phase of the plastication stage has good ability to predict the final product weight;5 however, this stage could not be used as the criticalto-weight-control stage, because cavity pressure is no longer a controlled variable during this stage, and the adjustment of other controlled variables in this stage can hardly have any effect on the product weight. Therefore, certain prior knowledge on the manipulatible process variables is required to determine the critical-to-control stages, but such knowledge can be readily available in the industry. The concept of a critical-to-control stage is important to improve quality-control effectiveness and system stability, because, as mentioned previously, batch adjustment outside of these important stages may result in poor design of the quality-control system and may even cause stability problems. In a critical-to-control stage, it is necessary to determine the proper process variables to be adjusted. The criteria of selecting manipulating variables xa are as follows: (i) the variables should and can be manipulated to affect the concerned end-product quality; (ii) the variables can be easily manipulated, so that the

batch adjustment will not overburden the low-level process control system; and (iii) the adjustment of such variables during the specific stage should have minimal interference to the following stages (that is, it is desirable to adjust the variables with time-specific effects on the final quality). Among the three rules, the first is absolutely necessary, whereas the other two are needed when several options exist, but we need to choose the better manipulating variables to achieve better performance and lower cost in designing the quality-control system. In selecting these adjustable variables, fundamental knowledge of the process control will be helpful; for example, adjustment of variables with quick dynamics is better than that with a slow response, because the former is easier to manipulate and will have faster influence on the process behavior. The no-control region for each critical-to-control stage also should be determined in the offline development phase. A nocontrol region is introduced for the following reasons. First, with advanced batch sequencing and control systems, many batches can proceed satisfactorily without the need of frequent changes of settings. Corrective actions are needed only when the predicted qualities are truly deviating from the target specifications. Second, the uncertainty of the prediction models should be taken into account. Third, too-frequent quality adjustment may reduce the efficiency of batch operation.20 The no-control region can be determined in terms of product specifications (e.g., the region between upper and lower limits around the target product specifications10,13) or by using historical normal quality data (e.g., the band of width, plus or minus one standard deviation around the target value).20 In this work, a simple control region based on product specifications will be used, as explained later in section 3.3.2. 3.3. Online Implementation. 3.3.1. Online Quality Prediction. In the proposed stage-based quality-control system, the quality predictor and controller work only in specific critical stages. The first step of online quality control is to determine the stage of the current evolving batch. This can be accomplished, for example, by checking which time period the current sampling falls in, because process stages may be represented by process operating time span in the stage PLS modeling. If the current stage is a critical-to-quality stage, the online quality prediction algorithms that had been proposed in ref 5 will be adopted and improved for the proposed online quality-control system described below. For quality variables affected only by the current stage (e.g., stage c), the current stage PLS model can be directly used for online prediction:

yˆ c(k) ) x(k)‚Θ/c

(1)

where x(k) represents the online process measurements measured at each sampling time k, yc represents the quality variables concerned in stage c (yc ) [y1, ..., yqc]T), yˆ c(k) is the online prediction of yc, Θ/c is the regression matrix of the corresponding stage PLS model, and qc is the total number of concerned quality variables in stage c. The averaged yˆ c(k) over the entire critical stage (e.g., stage c), yˆ /c is defined as the endof-stage prediction. For quality variables affected by more than one stage, without losing generality, assuming that the current stage (stage c) and a future stage (stage f) determine the same group of quality variables yc ) yf ) [y1, ..., yqc]T in a cumulative manner, online quality prediction in stage c can be formulated as

yˆ c(k) ) wc‚x(k)‚Θ/c + wf ‚ yˆ /f

(2)

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J ) min {(QComp - QLoss)2 + Qcost} / ∆xa,sp

(5)

/ / / ∆xa,sp ) xa,sp,new - xa,sp,old / / / ∆xa,sp,min e ∆xa,sp e ∆xa,sp,max

where

Figure 3. Dual-rate nature of the proposed quality-control system.

kcTq

where the model consists of two parts: the current stage’s contribution (x(k)‚Θ/c ) and future stage’s contribution (yˆ /f ). Because future process measurements are not available up to time k in stage c, the aforementioned prediction model is performed assuming that the future stage will be kept at their nominal conditions and the nominal end-of-stage quality prediction yˆ /f is used for online quality prediction. The parameters wc and wf are stage’s weight obtained using the stacked regression method.5 Online prediction in stage f is formulated as

yˆ f (k) ) wc ‚ yˆ /f + wf‚x(k)‚Θ/f

(3)

where yˆ /f is the end-of-stage prediction in stage c that is known information in stage f. For the details of the original quality prediction algorithms, please refer to the authors’ previous work.5 3.3.2. Online Batch Adjustment. Assuming that the sampling rate of online process measurements is Ts (Ts ) 1), the quality-control interval Tq is commonly selected to be multiple times of Ts. For easier interpretation of the proposed method, online process measurements x(k) in a critical-to-control stage (e.g., stage c) are double-indexed as x(kc,ki), as shown in Figure 3, where kc is the index of quality control decision points (kc ) 1, ..., Kc), and ki is the index of sampling points in stage c (ki ) 1, ..., Nc). Kc and Nc are the total numbers of decision points and sampling points, respectively, in stage c, and Nc obviously equals to TqKc. At each decision point (kc) in the critical-to-control stage (stage c), the following criterion is used to check whether the end-product quality will be outside the no-control region: T W1 yc,sp (yˆ c(kc) - yc,sp)TW1(yjc(kc) - yc,sp) > δyc,sp

(4)

where yˆ c(kc) is the averaged yˆ c(kc,ki) within a quality control interval, yˆ c(kc,ki) is the online quality prediction of yc (using the prediction model given by eq 2 or eq 3), W1 is a diagonal weighting matrix (with weights proportional to the relative importance of the concerned quality variables), and δ is a small number (e.g., 0.1%) specified to satisfy the customer’s need. The reason for using yˆ c(kc) in eq 4 is 2-fold. First, the proposed quality control system is, by nature, a dual-rate system, as shown in Figure 3. It is necessary to synchronize the rate of online quality prediction with that of online quality control. Second, the online quality prediction may be varying with time because of measurement noises and model uncertainty; therefore, the averaged value within a quality control interval can provide smoother quality predictions for the following online batch adjustment algorithm. When the condition of eq 4 is satisfied, which indicates that the end-product quality is deviating from the desired value, the change of set points of manipulating variables in the remaining period of the current critical-to-control stage is needed to compensate for the quality loss in the past, which can be obtained by solving the following objective function:

QLoss )

(yˆ c(ki) - yc,sp)TW1(yˆ c(ki) - yc,sp) ∑ k )1

(6)

i

kcTq+1

Qcomp )

∑

ki)1

(yˆ c(ki) - yc,sp)TW1(yˆ c(ki) - yc,sp)

Qcost ) (∆x/sp)TW2(∆x/sp)

(7) (8)

Qloss is the cumulated quality loss up to decision point kc caused by disturbances or other factors, which can be reflected by the online process measurements and estimated by the quality prediction model. Qcomp is the desired quality compensation with / new set points xa,new,sp of the manipulating variables in the / represents the set points in remaining period of stage c. xa,old,sp the last quality-control interval. The first term of eq 5 is obviously to minimize the difference between the future quality compensation and the past quality loss, where Qloss can be interpreted as the time-varying set point of Qcomp. The quality prediction yˆ c(ki) in eq 6 can be calculated by eq 2 or eq 3, using the available online process measurements. However, the quality prediction models eq 2 and eq 3 cannot be used to calculate yˆ c(ki) in eq 7, because the future process measurements are not available at kc. There are two solutions to this problem. One is to predict the future process measurements based on the changes introduced by the new set / points xa,sp,new and then compute the end-product quality prediction using eq 2 or eq 3. The other is to build an empirical / / model directly on xa,sp and y (y ) f(xa,sp )) in the modeling phase, using a proper regression method. The future quality / prediction is then obtained by yˆ c(ki) ) f(xa,sp,new ). The second method is adopted in the proposed scheme for its straightforwardness. Although quality prediction using only set points may be less accurate, it will not significantly affect the performance of the proposed online batch adjustment algorithm, as demonstrated in section 4. The second term of eq 5 takes into account the quality-control costs in the proposed system. The weighting matrix W2 can be determined by considering an appropriate response criterion for the manipulating variables, such as the integral of square error (ISE), the integral of absolute error (IAE), or the integral of time multiplied by the absolute error (ITAE). The variable with smaller response criterion value is commonly easier to adjust. Therefore, the weights in W2 can be set to be proportional to the response criterion values of different manipulating variables. In addition, hard constraint on the set-point adjustment, / / / ∆xa,sp,min e ∆xa,sp e ∆xa,sp,max , is also introduced in eq 5, to limit the adjustment size for smoother control. The above batch adjustment is repeated at every qualitycontrol decision point until the completion of the stage. Similar procedures are conducted in other critical-to-control stages to control their corresponding qualities. 3.3.3. Summary. The proposed stage-based online quality control scheme for batch processes can be summarized as follows.

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Figure 4. Simplified schematic of injection molding machine and its major measurements.

Model Building (1) Collect historical batches to form a training data set; (2) Divide the batch process into stages and build stage PLS models between the online process data and the end-product quality data; (3) Determine the critical-to-prediction stages and criticalto-control stages for each quality variable. (4) In each critical-to-control stage, determine the no-control region; (5) In each critical-to-control stage, select manipulating variables for the stage-concerned quality variables; (6) In each critical-to-control stage, build regression models between the set points of manipulating variables and the stageconcerned quality data. Online Quality Control (7) Collect the online process measurement; (8) Determine the current stage and the concerned quality variables; (9) Call the corresponding stage PLS model to calculate the current prediction of the end-product qualities; (10) At each decision point, if the quality prediction is outside the no-control region, calculate the new set points of the manipulating variables by solving eq 5; otherwise, go back to step (7). 4. Illustration 4.1. Injection Molding Process. Injection molding is an ideal process for the application and verification of the proposed stage-based online quality control scheme. Figure 4 shows a simplified diagram of a typical reciprocating-screw injection molding machine. As a multistage process, injection molding operates in stages, among which injection (or filling), packingholding, and cooling are the most important phases. During filling, the screw moves forward and pushes melt into the mold

Figure 5. Stage division results and critical stages in the injection molding.

cavity. When the mold is completely filled, the process then switches to the packing-holding phase, during which additional polymer is “packed” at a pressure to compensate for the material shrinkage associated with the material cooling and solidification. The packing-holding continues until the gate freezes off, which isolates the material in the mold from that in the injection unit. The process enters the cooling phase; the part in the mold continues to solidify until it is rigid enough to be ejected from the mold without damage. Concurrently with the early cooling phase, plastication happens in the barrel, where the polymer is melted and conveyed to the front of barrel by screw rotation, in preparation for the next cycle. Product weight and length control is selected as an online quality-control example in this paper for the following reasons. First, product weight and length are highly correlated. Second, product weight and length can be readily measured at the end of each batch for easy verification. Third, weight and length are good representatives of process stability and are of great commercial interest. A few literature that are concerned with only product weight control of injection molding have been reported in the past, most of which are, however, cycle-to-cycle closed-loop quality-control strategies.21-24 The proposed qualitycontrol scheme in this paper is a multivariate method, which can predict and correct product weight and length deviations simultaneously within the batch. 4.2. Offline Analysis. In ref 5, the injection molding process, under the given conditions, is divided into five major stages: filling, packing-holding, plastication I, plastication II, and cooling. The packing-holding and plastication I stages are determined to be critical-to-weight/length stages, as shown in Figure 5. At the packing-holding stage, larger pressures (nozzle pressure, hydraulic pressure, and cavity pressure) and lower temperatures (barrel temperature and mold temperature) lead to heavier products. Although the cavity and nozzle pressures at the plastication I stage also have superior prediction ability of product weight and length, this stage could not be selected as a critical-to-control stage because there is no manipulating variable that can be adjusted to affect the concerned quality variables. Thus, only the packing-holding stage is selected as the critical stage for online weight/length prediction and control. As mentioned previously, in the packing-holding stage, several pressure and temperature variables are all closely related to the final product weight and length, among which nozzle pressure, barrel temperature, and mold temperature can be selected as manipulating variables, because they are closedloop controlled in the packing stage of the injection molding machine in our laboratory. Nozzle pressure is the most preferred, because it has a much quicker dynamic response than the other two temperature variables.25-27 In addition, the two temperatures are also critical to the operation of the following plastication

Ind. Eng. Chem. Res., Vol. 45, No. 7, 2006 2277 Table 1. Operation Conditions for Training Data Sets by DOE data set

nozzle pressure (bar)

barrel temperature (°C)

mold temperature (°C)

1 2 3 4 5 6

150 450 150 450 150 450

180 180 180 180 180 180

15 15 35 35 55 55

7 8 9

300 300 300

200 200 200

15 35 55

10 11 12 13 14

150 450 150 450 150

220 220 220 220 220

15 15 35 35 55

Table 2. Other Process Settings for Injection Molding Process parameter

setting

material injection velocity injection stroke packing-holding time plastication back pressure screw rotation speed cooling time

high-density polyethylene (HDPE) 24 mm/s 38.5 mm 6s 5 bar 80 rpm 15 s

Figure 7. Online batch adjustment with improper settings of operation conditions (example I).

Figure 6. End-of-packing-stage quality prediction by stage PLS model.

and cooling stages.5 Therefore, it is ill-suited to be adjusted during packing stage. Nozzle pressure in the packing-holding stage is selected as the manipulating variable for online weight/ length control.

All batch data are generated by a dynamic simulator of injection molding process, which can cover a wide range of normal operating conditions. Only filling and packing stages are considered in the simulator, because the other stages have no significant correlation with the product weight and length. Operation conditions and relevant process settings for training data are shown in Tables 1 and 2. Eight key process variables are collected online, including injection velocity, stroke, nozzle pressure, plastication pressure, cavity pressure, cavity temperature, nozzle temperature and mold temperature. The sampling interval of the process variables is 0.02 s, whereas the quality control interval Tq is 0.1 s. The parameter δ in determining the no-control region is 0.1%. Figure 6 shows the end-of-packingstage weight/length predictions of the reference data by the stage PLS model, which are accurate enough for the following online quality control. 4.3. Online Quality Control Results. To verify the proposed stage-based online quality-control scheme, three types of abnormal test batches are intentionally simulated: improper settings of operating conditions, check-ring failure problem, and disturbance in nozzle pressure. The results and discussions are detailed as follows. 4.3.1. Case I: Improper Settings of Operating Condition. Industrial processes are usually operated over a range of conditions to produce various products with different specifications. Given the quality specifications, the process engineer should find appropriate operating conditions, under which the process can operate efficiently and safely and the final products can meet the customers’ requirements. It is likely that the process

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Figure 8. Online batch adjustment with improper settings of operation conditions (example II).

Figure 9. Online batch adjustment with a check-ring problem.

is originally set to work under improper conditions. The process cannot achieve the desired product qualities if no quality-control action is applied. In batch-to-batch quality-control strategies, batch adjustment is calculated for the next batches, not within the current batch. Obviously, the products of the first few batches may be wasted. The online quality-control scheme proposed in this paper can solve such improper setting of the operating conditions problem in a within-batch manner. It can automatically adjust the evolving batch process to suitable operating conditions, which can obviously reduce the production of off-specification products. Figures 7 and 8 show the results of online weight/length control of two test batches with improper original operating conditions. For the example shown by Figure 7, the specified product weight and length are (27 g, 117.05 mm), as marked by a pentacle. The original process settings are as follows: nozzle pressure, 150 bar; barrel temperature, 220 °C; and mold temperature, 35 °C. Product quality under these conditions will be about (26.36 g, 116.67 mm) if no corrective action is applied. According to the analysis in section 4.2, a higher nozzle pressure leads to a heavier product weight; therefore, the set point of nozzle pressure is increased during the packing-holding stage, and finally stabilized at 423 bar, as shown in Figure 7a. Figure 7b shows the online weight/length predictions during the packing-holding stage by the proposed stage PLS model. From Figure 7b, the online weight/length predictions at the beginning of packing stage are far away from the target values, because of the wrong settings of the original operating conditions. The online predicted weight/length is approaching the target as the adjusted nozzle pressure is increasing. The final product qualities

are (26.983 g, 117.049 mm), which are very similar to the desired values. Figure 8 is another example, where the original process settings are as follows: nozzle pressure, 450 bar; barrel temperature, 180 °C; and mold temperature, 35 °C. Target qualities are also (27 g, 117.05 mm), whereas the product qualities under these wrong settings will be about (27.9 g, 117.59 mm). By the proposed online quality control scheme, the setpoint profile of nozzle pressure is decreasing in this case, as shown in Figure 8a; and the online predicted weight/length is approaching to the target value, as shown in Figure 8b. The final process settings are as follows: nozzle pressure, 245 bar; barrel temperature, 180 °C; and mold temperature, 35 °C, and the final product qualities are (27.00 g, 117.067 mm). 4.3.2. Case II: Check-Ring Failure. The check-ring valve, which is a device that allows the polymer melt to flow from the screw channel to the nozzle during plastication, closes during the injection and packing-holding stages to prevent polymer backflow from the nozzle to the screw channel. When the checkring value fails to close properly, a smaller amount of material will be injected into the cavity during filling stage due to the backflow. Although the packing-holding stage can make up some shortfall in the filling, batches with check-ring problems usually have slightly lighter and smaller product. Figure 9 shows the results of online weight/length control of a test batch with check-ring problem. The operation conditions are as follows: nozzle pressure, 450 bar; barrel temperature, 180 °C; and mold temperature, 35 °C. The expected product quality parameters are (27.9 g, 117.59 mm). As explained previously, the trajectories of the nozzle pressure and correlated variables such as

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Figure 10. Online batch adjustment with a step disturbance in nozzle pressure.

hydraulic, plastication, and cavity pressures are slightly lower than the normal case. To compensate for the quality loss during filling, the new set point of nozzle pressure will be slightly higher than the normal one. In Figure 9a, the solid line shows the adjusted set-point profile and the dashed line shows the online measurements of nozzle pressure. A normal trajectory of nozzle pressure without a check-ring problem is also given by a dashed-dotted line in Figure 9a for comparison. The adjusted nozzle pressure is slightly higher than the normal one at the earlier phase of the packing-holding stage, but the final product qualities after adjustment are exactly (27.90 g, 117.59 mm). 4.3.3. Case III: Disturbance in Nozzle Pressure. In this case, a step disturbance is introduced to the nozzle pressure trajectory in the middle of the packing-holding stage to determine how the online quality adjustment algorithm acts during the remaining period to maintain the final product quality. The test batch is conducted with the following original conditions: nozzle pressure, 450 bar; barrel temperature, 180 °C; and mold temperature, 35 °C. The expected product weight under these conditions is (27.9 g, 117.59 mm). A step disturbance of nozzle pressure from 450 bar to 430 bar is added in the period of 150-225 (i.e., 3-4.5 s). The decrease in nozzle pressure will cause quality loss, about (0.012 g, 0.05 mm), if no corrective action is applied. The quality-control algorithm tries to compensate for the estimated quality loss by increasing the set point of the nozzle pressure. Figure 10a shows the adjusted set-point profile of nozzle pressure and the corresponding online measurements. Figure 10 b, c, and d shows the trajectories of the

online predicted product qualities. The final product qualities are (27.901 g, 117.591 mm). In summary, the proposed online quality-control scheme can not only compensate the quality loss occurred in the previous stages as illustrated by the first two cases, but it is also able to compensate for the quality loss caused by the fault that occurred in the current stage, as illustrated in the third case. The aforementioned results show the feasibility and validity of the proposed scheme for online quality control of batch processes. 5. Conclusions A scheme of stage-based online quality control for batch processes has been proposed by integrating the online batch adjustment algorithm with the previously developed stage partial least squares (PLS) modeling and quality-related process analysis method. In the proposed scheme, quality predictor and controller are both stage-based. The stage PLS models perform as soft sensors to provide online quality prediction. The quality controller is designed to maintain the end-product quality on target by adjusting proper manipulating variables in proper stages. The paper also provided the guidelines on how to select manipulating variables and how to determine the no-control region in each stage. Simulation results on injection molding show good feasibility of the proposed scheme. Acknowledgment This work is supported in part by the Hong Kong Research Grant Council (under Project No. 601104).

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ReceiVed for reView July 28, 2005 ReVised manuscript receiVed February 8, 2006 Accepted February 10, 2006 IE050887D