Interplay between Identification and Optimization in Run-to-run Schemes

Interplay between Identification and Optimization in Run-to-run Schemes B. Srinivasan, D. Bonvin ´ Institut d’Automatique, Ecole Polytechnique F´d´rale de Lausanne, ee CH-1015 Lausanne, Switzerland. Optimization of batch processes has received increasing attention since its provides an unified framework to improve productivity without violating constraints on safety, selectivity, reproducability, etc. Due to uncertainties (disturbances and modeling errors) that are invariably present at the industrial level, the optimal profiles have to be adjusted during implementation. The advantage of batch processes is that they are typically repeated, and this fact has been exploited in run-to-run schemes to adapt the optimal profile of the current batch based on measurements from the previous batches.One of the run-to-run schemes that has been studied widely for the adaptation of optimal profiles, and also used for on-line optimization and model-predictive control, is the following indirect approach: 1. Identify the parameters of a given model structure using measurements from the previous batches. Typically, a least-squares minimization problem is solved. 2. A numerical optimization of the refined model provides the updated optimal profile for the current batch. Such a scheme, however, has three main drawbacks: 1. There is no guarantee that the profile that is optimal for the previous batches is persistently exciting so as to uncover the model parameters that have to be identified. This problem becomes more acute as the number of parameters to be identified increases. 2. There is no synergy between the identification and optimization problems. The parameters that minimize the state evolution errors may be quite poor in predicting the cost and constraints of the optimization problem. This issue is more important in the case of large model mismatch, where the model is a reduced version of the actual plant. 3. No guarantee for convergence can be provided for this iterative scheme. The first drawback is fundamental to all model-based schemes and cannot be readily resolved. The contributions of this paper address the second and third problems: • An identification problem is proposed where the ob jective is a better prediction of the optimization cost rather than the entire state evolution. For this, from every measurement, a model of the system is used to predict the final cost. The parameters of the model are so identified as to minimize the variance of these predicitons. • Different ways in which the identification and optimization can be interlaced are analyzed. Inner-outer optimization schemes that can ensure convergence of the iterative scheme are discussed. The results will be illustrated in simulation on a semi-batch reactor example. 1

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American Control Conference, 2174-2179

 Record created 2004-11-26, last modified 2018-01-27

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