(373l) A Back-Off Approach for Simultaneous Design and Control for Large-Scale Applications Using an Adaptive Search Space
The back-off approach is one of the proposed methodologies that relies on steady-state economics to initiate the search for an optimal and dynamically feasible process design.3â6 Those methods identify dynamically feasible solutions that are close to the optimal steady-state design. Recently, we have developed a back-off formulation using Power Series Expansions (PSE).5,6 The proposed back-off method focuses on searching for the optimal design and control parameters by solving a set of optimization problems using PSE functions. The idea is to search for the optimal direction in the optimization variables by solving a series of bounded PSE-based optimization problems. PSE functions represent the actual dynamic behavior of the system around a nominal condition, which is identified from previous iterations. Hence, using PSE functions instead of the actual nonlinear dynamic process model at each iteration reduces the computational costs.
In our previous work, the search space region in the PSE-based optimization problem was specified a priori.5 Selecting a constant search space for the PSE functions may undermine the convergence of the methodology since the predictions of the PSEs highly depends on the nominal conditions used to develop the corresponding PSE functions. In the current work, we propose an adaptive search space for individual PSE-optimization problems at every iteration. We designed the concept in a way that certifies the competence of the PSE functions at each iteration and adapts the search space of the optimization as the iteration proceeds in the algorithm. Metrics for estimating the residuals such as the mean of squared errors (MSE) are employed to quantify the accuracy of the PSE approximations. Search space regions identified by this method specify the boundaries of the decision variables for the PSE-based optimization problems. Finding a proper search region is a challenging task since the nonlinearity of the system at different nominal conditions may vary significantly; hence, the adaptive approach introduced in this work is attractive to deal with large-scale applications. The proposed approach was tested for the integration of design and control of the Tennessee Eastman process. The results indicate that the proposed methodology leads to more economically attractive and reliable designs while maintaining the dynamic operability of the system in the presence of multiple disturbances. Therefore, the proposed back-off methodology has the potential to identify dynamically feasible and near-optimal process designs for large-scale industrial systems.
1 Yuan, Z., Chen, B., Sin, G., and Gani, R., âState-of-the-Art and Progress in the Optimization-based Simultaneous Design and Control for Chemical Processes,â AIChE J., 58, pp. 1640â1659 (2012).
2 Ricardez-Sandoval, L. A., Budman, H. M., and Douglas, P. L., âIntegration of design and control for chemical processes: A review of the literature and some recent results,â Annu. Rev. Control, 33, pp. 158â171 (2009).
3 Kookos, I. K., and Perkins, J. D., âControl Structure Selection Based on Economics: Generalization of the Back-Off Methodology,â AIChE J., 62, pp. 3056â3064 (2016).
4 Bahri, P. A., Bandoni, J. A., Barton, G. W., and Romagnoli, J. A., âBack-off calculations in optimising control: A dynamic approach,â Comput. Chem. Eng., 19, pp. 699â708 (1995).
5 Rafiei-Shishavan, M., Mehta, S., and Ricardez-Sandoval, L. A., âSimultaneous design and control under uncertainty: A back-off approach using power series expansions,â Comput. Chem. Eng., 99, pp. 66â81 (2017).
6 Rafiei, M., and Ricardez-Sandoval, L. A., âStochastic Back-Off Approach for Integration of Design and Control Under Uncertainty,â Ind. Eng. Chem. Res., 57, pp. 4351â4365 (2018).