Cautious on‐line correction of batch process operation

Abstract

Most industrial batch processes are operated through open-loop application of an off-line optimized input profile, such as feed or temperature. This is because modeling accuracy is typically poor (Juba and Hamer, 19861, and direct concentration measurements that would allow to cope with the frequently encountered lack of reproducibility are rare.However, when on-line measurement information gives access to the system state, on-line reoptimization promises considerable improvement. Since industrial on-line measurements typically do not immediately reveal perfect information on the entire system state, on-line state and parameter estimators need to be used. Their estimates often contain non-negligible uncertainty due to the system state being inferred from indirect, so-called model-based measurements, which can be subject to both stochastic measurement noise and structural measurement-model mismatch.Given such estimates, it is common practice to perform on-line optimization ignoring their uncertainty. Still, this is optimal theoretically only for ideal linear systems rather than possibly strongly nonlinear batch processes. Another approach is to begin with the open-loop optimal profile and switch to on-line optimization either empirically after a given number of measurements or when estimate uncertainty is sufficiently small. This leaves the problem of finding a good compromise between waiting for good estimates and reacting sufficiently early, as sensitivity of the final operation objective to input changes usually decreases rapidly.The present contribution suggests a cautious on-line correction mechanism that replaces the switching from open-loop to closed-loop operation with a smooth transition controlled by estimate uncertainty. Its single scalar tuning parameter represents the desired degree of cautiousness or boldness with which current estimates are used for on-line correction of open-loop optimized input profiles. In the limiting cases of no information (large uncertainty) and perfect information (certainty), the corrector naturally reduces to optimal openloop and optimal feedback operation, respectively.

Efficient sampling technique for optimization under uncertainty

“…Furthermore, most industrial batch processes are operated through open-loop applications of an off-line optimized input profile, such as feed or temperature, commonly known as optimal control profiles. These profiles even if reoptimized using on-line measurements often contain nonnegligible uncertainties due to the system state being inferred from indirect, so-called model-based measurements, which can be subject to both stochastic measurement noise and structural measurement-model mismatch (Terwiesch, 1995). The need to take these uncertainties into consideration in the design and planning stage is well recognized (Reklaitis et al, 1989;Cott and Machhietto, 1989;Watzdorf et al, 1993;Mignon et al, 1995;Tsai and Chang, 1996;Ierapetritou and Pistikopoulos, 1996).…”

Dynamic optimization of bioreactors using probabilistic tendency models and Bayesian active learning

“…Hence, without biasing data gathering by increasingly improving the operating policy, bioreactor performance predictions are too uncertain and unreliable in quantitative terms to be useful for productivity optimization (Bonvin, 1998;Martínez & Wilson, 2003;Schenker & Agarwal, 1995). As a result, migration from laboratory conditions to production runs is often made with high levels of uncertainty about the degree of optimality of an operating policy (Terwiesch, 1995;Terwiesch & Agarwal, 1995). Consequently, a very conservative and sub-optimal operating policy is repeatedly applied to industrial bioreactors seeking reproducibility rather than improvement (Martínez & Wilson, 2003).…”

Design of Dynamic Experiments in Modeling for Optimization of Batch Processes

“…The best use of a model through proper handling of its inherent uncertainty is a recurrent issue in the vast literature related to optimization methods for batch processes. − There are two extreme assumptions which can be made regarding modeling uncertainty and available measurements in model-based dynamic optimization . One of the idealized situations is the perfect model assumption.…”