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Estimating Product Composition Profiles in Batch Distillation Via ARTICLE IN PRESS Control Engineering Practice 12 (2004) 917–929 Estimating product composition profiles in batch distillation via partial least squares regression Eliana Zamprognaa, Massimiliano Baroloa,*, Dale E. Seborgb a Dipartimento di Principi e Impianti di Ingegneria Chimica (DIPIC), Universita" di Padova, Via Marzolo, 9, 35131 Padova PD, Italy b Department of Chemical Engineering, University of California, Santa Barbara, CA 93106, USA Received 15 February 2003; accepted 24 November 2003 Abstract The properties of two multivariate regression techniques, principal component analysis and partial least squares (PLS) regression, are exploited to develop soft sensors able to estimate the product composition profiles in a simulated batch distillation process using available temperature measurements. The estimators’ performance is evaluated with respect to several issues, such as pre-processing of the calibration and validation data sets, number of measurements used as sensor inputs, presence of noise in the input measurements, and use of lagged measurements. A simple augmentation of the conventional PLS regression approach is also proposed, which is based on the development and sequential use of multiple regression models. The results prove that the PLS estimators can provide accurate composition estimations for a batch distillation process. The computational requirements are very low, which makes the estimators attractive for on-line use. r 2004 Elsevier Ltd. All rights reserved. Keywords: Batch distillation; Composition estimators; Soft sensors; Partial least squares regression; Principal component analysis 1. Introduction composition), at constant distillate composition (with variable reflux ratio), and at total reflux. A combination Batch distillation is a well-known unit operation that of these three basic modes can be used to optimize the is widely used in the fine chemistry, pharmaceutical, performance of the separation. Whatever the operating biochemical, and food industries to process small mode, proper operation of a batch column requires amounts of materials with high added value. The knowledge of products compositions during the entire success of batch distillation as a method of separation duration of the batch. Although product composition is undoubtedly due to its operational flexibility. A single can be measured on-line, it is well known that on-line batch column can separate a multicomponent mixture analyzers are complex pieces of equipment that are into several products within a single operation; con- expensive and difficult to maintain; they also entail versely, if the separation were carried out continuously, significant measurement delays, which can be detrimen- either a train of columns or a multi-pass operation tal from the control point of view (Leegwater, 1992). would be required. Also, whenever completely different Therefore, to circumvent these disadvantages, it is mixtures must be processed from day to day, the possible to estimate the product composition on-line, versatility of a batch column is unexcelled. These rather than measuring it. The use of such inferential attributes are crucial for quickly responding to a market composition estimators (or software sensors) has long demand characterised by short product lifetimes and been suggested to assist the monitoring and control of severe specification requirements. continuous distillation columns. Several applications Batch columns can be operated in three different have been reported in the literature, for both simulated ways: at constant-reflux ratio (with variable distillate and experimental columns (Joseph & Brosilow, 1978; Yu & Luyben, 1988; Lang & Gilles, 1990; Mejdell & *Corresponding author. Tel.: +39-0498275473; fax: +39- Skogestad, 1991; Baratti, Bertucco, Da Rold, & 0498275461. Morbidelli, 1995; Chien & Ogunnaike, 1997; Kano, E-mail address: [email protected] (M. Barolo). Miyazaki, Hasebe, & Hashimoto, 2000). However, the 0967-0661/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.conengprac.2003.11.005 ARTICLE IN PRESS 918 E. Zamprogna et al. / Control Engineering Practice 12 (2004) 917–929 issue of composition estimation in batch distillation computational requirements, but they may be difficult to columns has received very little attention. initialize, and suffer from very poor robustness to Quintero-Marmol, Luyben, and Georgakis (1991) process/model mismatch and to measurement noise. and Quintero-Marmol! and Luyben (1992) compared EKFs are much more robust to mismatch and noise, but the performances of a steady-state composition estima- still their performance heavily depends on the thermo- tor, a quasi-dynamic estimator (QDE), and an extended dynamic modeling of vapor–liquid equilibria; they are Luenberger observer (ELO) for a ternary batch column. also difficult to initialize and tune, and require They found that the ELO provided the best perfor- considerable computational effort for on-line use. mance. However, they noted that the observer was quite In all of the batch distillation studies cited above, the sensitive to the accuracy of assumed vapor–liquid composition estimator was obtained based on a funda- equilibria and to the assumed initial compositions; mental (i.e., first-principles) model of the process. In this moreover, the estimator’s performance rapidly degraded paper, we pursue a different approach by developing an when the tray temperature measurements (i.e., the estimator based on an empirical process model. The observer’s inputs) were affected by noise. Similar issues objective of this research is to evaluate the applicability were noted by Barolo and Berto (1998), who used the of multivariate regression techniques to develop a composition estimates generated by an ELO within a composition soft sensor for a conventional batch nonlinear strategy for composition control in a conven- rectifier. This approach is potentially very profitable, tional batch rectifier. They also observed that the because most of the disadvantages of estimators based estimator accuracy tended to degrade if the tray on a physical model can be resolved using an empirical hydraulics was taken into account and the number of estimator. In fact, a priori knowledge about vapor– trays was large. Han and Park (2001) used Luyben’s liquid equilibria behavior is not required in this latter QDE to estimate the distillate composition, and to case. Also, the estimator does not require composition control the estimated composition profile of a batch initialization, and is computationally simple, which is rectifier. desirable for on-line implementation. In order to improve the estimator’s robustness Partial least squares (PLS) regression is a widely used to process/model mismatch and measurement noise, multivariate regression technique, and its application to Barolo, Pistillo, and Trotta (2000) developed an the development of composition estimators for chemical extended Kalman filter (EKF) to reconstruct the processes has gained vast interest (Kourti & MacGre- product composition profiles of a middle-vessel batch gor, 1995; Yin, 1998; Kourti, 2002). This projection column from temperature measurements. They showed method is used to extract the information contained in that, while the robustness to measurement noise was available process data, and to project it onto to a low- generally improved with respect to an ELO, the dimensional space defined by new variables called latent estimation performance was greatly affected by the variables. Several applications of PLS regression to soft location of measurement sensors. The state vector sensor development have been reported for continuous initialization and filter ‘‘tuning’’ were more difficult distillation processes (Mejdell & Skogestad, 1991; Park than for the ELO case; moreover, the improvements in & Han, 1998; Hong, Jung, & Han, 1999; Kano et al., the estimator’s performance were obtained at the 2000; Shin, Lee, & Park, 2000), while the potential of expense of a much larger computational load. Oisiovici extending the use of this technique to batch distillation and Cruz (2000, 2001) developed an EKF to infer the has received relatively little attention. This may be due product composition of a batch rectifier, and applied it to the fact that PLS regression was originally developed within a globally linearizing control scheme to control for continuous steady-state process systems, and its operation at constant distillate composition. They extension to discontinuous processes raises some diffi- pointed out that accurate description of vapor–liquid culties. Recently, this technique has indeed been equilibria is very important for the performance of the extended to the analysis, on-line monitoring and filter. They also observed that the filter performance diagnosis of batch processes (Nomikos & MacGregor, usually improved when larger sets of secondary mea- 1995; Duchesne & MacGregor, 2000), and successful surements were used, and/or when the sampling applications have been reported (Wold, Kettaneh-Wold, frequency was increased; however, these options in- & Skagerberg, 1989; Kourti, Nomikos, & MacGregor, creased the estimator’s complexity and the computa- 1995; Zheng, McAvoy, Huang, & Chen, 2001). How- tional burden. Similar results were obtained by ever, in the large majority of these cases, the use of PLS Venkateswarlu and Avantika (2001), who also pointed regression is limited only to the estimation of the final out the difficulty in tuning the EKF covariance matrices. quality of the batch product, whereas
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