Evolutionary Operation and Control of Chromatographic Processes Deepak Nagrath, B. Wayne Bequette, and S. M. Cramer Howard P. Isermann Dept. of Chemical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180 ( ) A no®el generalized run-to-run control GR2R control strategy is presented for the optimization and control of nonlinear preparati®e chromatographic processes. The ( ) GR2R approach synergistically employs a hybrid both physical and empirical model to control chromatographic processes in the presence of sporadic and autocorrelated dis- turbances. First, parameters of the physical model through experiments are determined, and then the physical model is used to estimate initial parameters of the nonlinear ( ) empirical model Hammerstein using orthogonal forward regression. Parameters of the nonlinear empirical model are updated at the end of each run using a nonlinear recur- si®e parameter estimation method. The updated empirical model is then used in the ( ) control algorithm model predicti®e control to estimate operating conditions for the next batch. Processes operating under fixed optimal conditions are compared with those operating with GR2R control for both gradient and displacement chromatography. The ( GR2R outperforms the fixed conditions in the presence of ®arious disturbances such as ) bed capacity, column efficiency, and feed load and is an effecti®e strategy for the opti- mization and control of complex chromatographic processes. Introduction Ž . Although preparative ion-exchange chromatography IEC is widely employed for protein purification, the choice of op- Ž erating conditions has remained largely empirical Felinger . and Guiochon, 1994, 1996a,b; Luo and Hsu, 1997 , resulting in a suboptimal performance of these separation systems. Concurrent advances in both the theory of protein nonlinear IEC and the run-to-run control algorithm sets the stage for the development of optimal and robust nonlinear gradient and displacement purification processes with minimal experi- ments. Chromatographic processes also have the lack of real-time data directly related to the product quality or pro- ductivity, thus making R2R control a viable strategy. In this article we present a novel hybrid approach, general- Ž . ized run-to-run control GR2R for the optimization and con- trol of chromatographic processes. This approach synergisti- Ž cally uses a hybrid model both an empirical and a physical . Ž . model for optimization Siouffi and Phan-Tan-Luu, 2000 and control. The motivation for using both physical and em- pirical models is to complement the knowledge of physics from the physical model with the simplicity and low computa- Correspondence concerning this article should be addressed to S. M. Cramer. tional cost of the empirical model. The approach is based on the realization that the fixed parameter model based ap- proaches will not give an optimal performance due to batch- to-batch variability and disturbances. The parameters of both the empirical and physical model can be updated in the approach to drive the models close to the actual process. Ž . Run-to-Run R2R control refers to a class of statistical pro- Ž . cess r quality control SPCr SQC techniques used to improve the operation of batch processes. R2R handles batch-to-batch variations and gives a reasonably good performance com- pared to the cases where control algorithms do not learn from batch-to-batch. There are several approaches for R2R con- trol existing in the current literature. The R2R controller has two modes of operation: optimization and control. Optimiza- tion may be repeated periodically, if it is thought that addi- tional opportunity for improvement exists or if the process has changed drastically. Once the process is optimized, the R2R maintains the process at the optimum conditions in the Ž presence of disturbances fluctuations in operating parame- . ters from batch-to-batch . The most common R2R approach is the Exponential Ž . Weighted Moving Average EWMA based approach. Sachs January 2003 Vol. 49, No. 1 AIChE Journal 82