(365a) Feedback State-Space Mapping Framework for Dynamic Operability Analysis

The optimal design and control policies for chemical systems have complex impacts on each other [1]. In recent years, operability approaches have been developed to simultaneously optimize a process design (physical dimensions, material properties, etc.) while considering the controller implementation capabilities [2,3]. Dynamic operability studies extended the steady-state input-output operability analysis to dynamic systems. However, the existing operability mapping discretizes the input space by partitioning it for each input variable, so that the number of input combinations required to cover the achievable input set (AIS) grows exponentially with the number of inputs. In this work, a novel dynamic operability mapping framework based on a feedback procedure is proposed to address this challenge. This framework takes advantage of the discrete-time state-space structure of the dynamic model to reduce the number of input mapping combinations by augmenting the AIS to include the achievable output set (AOS) of the state variables from the previous time step.

The proposed dynamic operability mapping framework consists of three components: the AOS inspector, the AIS divider, and the merger of the AOS from the previous time with the AIS. Specifically, the AOS inspector evaluates if the current input-output combinations are approximately accurate to the real AOS when all input combinations are mapped to the output space. In case the AOS inspector gauges that the current AOS is not sufficiently precise, the AIS divider systematically generates more input-output combinations based on the current AOS. This feedback process is repeated until an accuracy tolerance is reached. To reduce computational effort, the merger component creates a set of bounding boxes to find the tightest overestimation of the current AOS before merging it with the AIS for the following time step mapping.

A dynamic operability analysis of a Fischer-Tropsch process is provided to demonstrate the application of the proposed framework. The Fischer-Tropsch bubble column reactor is simulated using a reduced-order model with dynamic discrepancy [4]. Monte Carlo simulations are then employed to confirm the accuracy of the proposed framework.

References

[1] A. Flores-Tlacuahuac, I.E. Grossmann, Simultaneous Cyclic Scheduling and Control of Tubular Reactors: Parallel Production Lines, Industrial & Engineering Chemistry Research. 50 (2011) 8086–8096.

[2] V. Gazzaneo, F.V. Lima, Multilayer Operability Framework for Process Design, Intensification, and Modularization of Nonlinear Energy Systems, Ind. Eng. Chem. Res. 58 (2019) 6069–6079.

[3] V. Gazzaneo, J.C. Carrasco, D.R. Vinson, F.V. Lima, Process Operability Algorithms: Past, Present, and Future Developments, Ind. Eng. Chem. Res. 59 (2020) 2457–2470.

[4] S. Dinh, J. Bohorquez, D.S. Mebane, F.V. Lima, Dynamic Discrepancy Reduced-Order Modeling and Model Predictive Control of a Fischer-Tropsch Slurry Bubble Column Reactor, In preparation (2022).