مقایسه عملکرد از موقعیت و مشخصات برآوردگرهای ترکیب برای کنترل کیفیت در تقطیر دودویی

In this study a number of control strategies have been developed for control of the overhead composition of a binary distillation column. The nonlinear wave model as presented in the literature, has been substantially modified in order to express it in variables that can easily be measured and make it more robust to feed flow and feed composition changes. The new model consists essentially of the equation for wave propagation and a static mass and energy balance across the top section of the column. Taylor series developments are used to relate the temperature on the measurement tray to the temperature and concentration on the tray where the inflection point of the concentration profile is located. The model has been incorporated in control of the overhead quality of a toluene/o-xylene benchmark column. In addition, a number of partial least squares (PLS) estimators have been developed: a nonlinear estimator for inferring the overhead composition from temperature measurements and a linear and nonlinear estimator for inferring the inflection point of the concentration profile in the column. These estimators are also used in a cascade control strategy and compared with use of the wave propagation model. Finally a control strategy consisting of a simple temperature controller and a composition controller were implemented on the simulated column. The study shows that the inferential control using PLS estimators performs equally well than control using the nonlinear wave model. In all cases the advantage of using inferential controllers is substantial compared with using single tray temperature control or composition control.

Systems with distributed parameters, such as distillation columns, exhibit dynamic characteristics that resemble traveling waves (Luyben, 1972, Marquardt, 1986, Hwang, 1991 and Hwang, 1995). Luyben (1972) pioneered a temperature profile position controller by measuring the temperature on five trays and calculating ‘between which trays a temperature in the middle of break lies’. This control strategy exhibited an increased sensitivity to feed changes. Marquardt (1986) analyzed the behavior of binary distillation columns by showing that a relationship exists between the product composition and the inflection point of the temperature profile. The idea behind the use of a profile for composition control is the fact that the shape of the profile does not necessarily have to be the same in order to guarantee a constant top (and/or bottom) composition, it only requires conformity of the profile. Betlem (2000) has also shown experimentally that in batch columns the inflection point under constant top quality control remains constant despite the fact that the bottom composition changes continually and consequently, the dominant first order time constant remains the same. Hwang, 1991 and Hwang, 1995 gave a comprehensive discussion on how the shift in sharp concentration profiles in a distillation column can be explained by nonlinear wave theory. The nonlinear wave model can be a very helpful tool for the implementation of dual composition control since it provides a fast method to infer the response of product compositions to feed composition and feed flow changes. It is, therefore, not surprising that various control applications have been reported in the literature (Gilles & Retzbach, 1980, Gilles & Retzbach, 1983, Balasubramhanya & Doyle, 1997, Balasubramhanya & Doyle, 2000, Han & Park, 1993 and Shin, Seo, Han & Park, 2000). The latter two authors implement the nonlinear wave model in a dual composition Generic Model Control framework. In all cases the authors report that the control strategy based on the nonlinear wave model outperforms all other tested control strategies. Another interesting approach to control the top and/or bottom composition in distillation columns is the use of a Partial Least Squares estimator for composition control (Mejdell & Skogestad, 1991 and Kano, Miyazaki, Hasebe & Hashimoto, 2000). Mejdell proposed three estimators for the composition, (i) an estimator using 12 weighted column temperatures, (ii) an estimator using logarithmic transformation of the composition and no weighting on the temperatures and (iii) an estimator using logarithmic transformations on temperatures and composition. Kano et al. carried out a comprehensive study of dynamic Partial Least Squares (PLS) for composition estimation and concluded that the estimation of column top and bottom quality should be based on reflux flow rate, reboiler heat duty, pressure and multiple tray temperatures. The cascade control system studied consisted of inner temperature control loops and outer inferential composition control loops. No feedback on actual composition was, however, included in the control strategy. In this study the nonlinear wave model will be revisited, the model is formulated such that it is dependent on easily measurable variables. The problem of maintaining a constant inflection point of the concentration profile is reduced to proper estimation of the vapor and liquid flow and of the concentration and temperature on the tray, where the inflection point of the concentration profile is located. It will be shown that several, relatively simple models can be developed to accomplish estimation of concentration and temperature. In addition, it will be shown that using the nonlinear wave model in a cascade composition control structure provides the advantage of fast response of the controlled variable. Two PLS models will be developed in this study, one for estimation of the inflection point of the concentration profile and one for the actual overhead column composition. The use of these inferential models in a cascade control structure will also be tested and compared with the use of the nonlinear wave model. In all cases the cascade control structure uses the actual measured concentration with a 10 min dead time as the actual feedback in order to avoid any offset in the controlled composition.

In this study the nonlinear wave model was revisited and a number of modifications were proposed. These included proper estimation of the vapor and liquid flow from a mass and enthalpy balance across the tail end of the column. Simple equations for the estimation of the concentration and temperature on the representative tray based on one temperature measurement, two temperature measurements and measurements that included temperature as well as pressure were proposed and compared. It was shown that a nonlinear profile position estimator and a nonlinear composition estimator could easily be derived from process data obtained from simulations with the detailed model. Using the inferential measurements from either the nonlinear wave model or from nonlinear PLS models in a cascade control structure, provided the benefit of improved response of the controlled composition. It was also shown that the performance of a control structure based on use of the nonlinear wave model was very similar to the performance of a control structure in which one of the nonlinear PLS models were used. The linear PLS estimator for the profile position could not be used in a control structure due to poor prediction properties. The nonlinear PLS estimators performed well, even for disturbances that were twice as large as the disturbances used for training the estimator. In all cases control structures using the nonlinear wave model or nonlinear PLS estimators outperformed a control structure in which a single tray temperature was used as an inferential variable. Using one tray temperature is insufficient to guarantee a constant top quality.