(700c) Optimal Design, Control and Scheduling of Multi-Product Systems Under Uncertainty: A Stochastic Back-Off Approach

Integration of design and control aims to specify the optimal design of a process while taking into account the dynamics of the system under different scenarios [1], [2]. In recent years, it has been shown that, for certain applications, process design and control decisions may also impact process scheduling [3], [4]. Although these tasks can be optimized individually, this approach is often found to be inadequate as it may result in sub-optimal or dynamically inoperable designs. Moreover, processes are subject to uncertainty and disturbances during operation thus adding an additional layer of complexity into the analysis. As a result, the explicit integration of these tasks results in the specification of overly challenging optimization problems, which are often found to be intractable due to the complex interactions between the tasks. Hence, there is a motivation to develop new frameworks that can perform optimal process integration.

The aim of this work is to present a decomposition algorithm for the optimal design, control and scheduling of multi-product systems subject to uncertainty and disturbances. The proposed decomposition framework involves the solution of a dynamic flexibility analysis followed by a dynamic feasibility analysis [5]. In the first (dynamic flexibility analysis), process design, control and scheduling decisions are sought using the expected values in the uncertain parameters and disturbances whereas in the latter (dynamic feasibility analysis), the solution obtained from the first is evaluated under stochastic realizations in the uncertain parameters and disturbances. The proposed framework assumes that the uncertain parameters and disturbances are stochastic random variables that follow specific probability distribution functions defined by the user. This a key feature considered in the present formulation since previous studies typically discretize the random uncertain variables[3], [5]. A back-off algorithm recently proposed in the literature is adopted to perform the optimal process integration under stochastic realizations process disturbances and uncertainty [6]. Back-off terms representing the variability of the process constraints due to stochastic realizations in uncertain parameters and disturbances are calculated using Monte Carlo (MC) sampling techniques. These back-off terms are updated at each iteration in the decomposition algorithm and added to each process constraint in the dynamic flexibility formulation to account for the stochastic realizations in the uncertain parameters and disturbances. The decomposition algorithm iterates in this fashion and eventually converges to a solution that can accommodate process variability due to uncertainty and disturbances. A case study involving the production of multiple products from a single equipment is examined to demonstrate the benefits and limitations of the proposed approach.

References

[1] Diangelakis N.A., Burnak. B., Katz J., Pistikopoulos E.N. Process design and control optimization: A simultaneous approach by multiparametric programming. AIChE Journal. 2017;63(8):4827–4846.

[2] Rafiei, M., Ricardez-Sandoval, L. Stochastic Back-Off Approach for Integration of Design and Control Under Uncertainty. Industrial & Engineering Chemistry Research. 2018;57(12):4351–4365.

[3] Patil B., Maia E., Ricardez-Sandoval L.A. Integration of Design, Scheduling and Control of Multi-Product Chemical Processes Under Uncertainty. AIChE Journal. 2015;61:2456-2470.

[4] Pistikopoulos, E.N., Diangelakis, N.A. Towards the integration of process design, control and scheduling: are we getting closer? Computers & Chemical Engineering. 2015;91:85–92.

[5] Koller, R., Ricardez-Sandoval, L. A Dynamic Optimization Framework for Integration of Design, Control and Scheduling of Multi-product Chemical Processes under Disturbance and Uncertainty. Computers & Chemical Engineering. 2017;106:147-159.

[6] Shi J., Biegler L.T., Hamdan I., Wassick J.M. Optimization of grade transitions in polyethylene solution polymerization process under uncertainty. Computers & Chemical Engineering. 2016;95:260–279.