(434f) A Back-Off Approach for Simultaneous Design and Nonlinear Model Predictive Control of Dynamic Systems Under Uncertainty

Studies in simultaneous design and control of chemical processes have shown the importance of taking process dynamics into account at the design stage [1-3]. New approaches for optimal process design have been developed in recent decades to consider the control scheme as an integral part of the chemical process design. Traditionally, conventional feedback controllers such as PI and PID have been used for integration of design and control. The use of model-based control approaches such as Model Predictive Control (MPC) offers significant advantages over conventional feedback controllers at the expense of solving optimization problems online. Therefore, in the last years, multiple studies have explored the application of MPC for integration of design and control [4-7]. In [3], a multi-parametric MPC approach for simultaneous design and control was presented; an improvement in operating cost compared to decentralized PI controllers was suggested. In [8], a methodology that incorporates structural decisions for the selection of optimal process flowsheet and MPC-based control design was presented. In that study, structured singular value analysis was used to evaluate the process dynamic feasibility and asymptotic stability under uncertainty. Despite these studies pursuing implementations with MPC, to the best of the authors’ knowledge, there are no studies that have explored the benefits of nonlinear MPC (NMPC) for integration of process design and control.

Previous studies have illustrated the application of a back-off approach for the integration of design and control of dynamic systems under uncertainty [9,10]. That methodology focuses on the systematic search of the optimal design and control parameters by the solution of optimization problems formulated in terms of Power Series Expansion (PSE) approximations. The effect of enforcing different disturbance profiles combined with model parameter uncertainty has been analyzed for systems involving decentralized PI-based controllers. Results have shown that the back-off methodology returned economically attractive solutions obtained in shorter computational times when compared with the implementation of a formal integration approach.

In this work, we present an extension to the back-off method by the introduction of a model-based controller such as NMPC for integration of design and control under uncertainty. This novel application represents the solution of a bilevel optimization problem where the upper-level corresponds to the optimal design problem whereas the lower-level represents the NMPC formulation. These formulations are connected through the determination of design and controller tuning parameters in the upper-level model, while the control actions are computed by the lower-level optimization problem. In the proposed methodology, uncertainty in the process design parameters and disturbances are explicitly considered. In this work, we measure the largest variability to the process model constraints and in the cost function due to disturbances and uncertainty (i.e. worst-case scenario). Thereby, around this worst-case scenario, we carry out a sensitivity analysis to compute the first and second-order gradients of our model constraints and cost function. The aim is to reformulate the original bilevel optimization model into a single level optimization model in terms of PSE approximations with respect to the optimization variables. While the solution of a single-level PSE-based optimization formulation can be easily obtained, the validity region of the PSE approximation model is limited. Consequently, the PSE-based optimization formulation is solved repeatedly; each time this problem is solved, a new search direction in the optimization variables is found such that the amount of back-off is moving the design and control parameters to a new dynamically feasible and economic operating point. The proposed methodology converges at a local optimal point where no constraint violations are observed, and the cost function is minimized. The proposed methodology was used to perform the optimal design and control framework of a wastewater treatment plant. For this case study, we consider different scenarios using steps and sinusoidal disturbances profiles combined with multiple uncertain process parameters. The case study is also used to compare the performance of NMPC against a decentralized PI-based control strategy in the context of integration of design and control. The results show that the implementation of an NMPC strategy produces more economically attractive designs than those obtained by a PI-based control strategy.

References

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[9] Rafiei-Shishavan, M., Mehta, S., and Ricardez-Sandoval, L.A. Simultaneous design and control under uncertainty: A back-off approach using power series expansions, Computers & Chemical Engineering, vol. 99, p. 66–81, 2017.

[10] Rafiei, M. and Ricardez-Sandoval, L.A. Stochastic back-off approach for integration of design and control under uncertainty, Industrial & Engineering Chemistry Research, vol. 57, no. 12, p. 4351–4365, 2018