(687e) Accounting for Equipment Stress in Economic Model Predictive Control

Economic model predictive control (EMPC) uses optimization of an economics-based cost function subject to constraints including a system model to determine control actions for dynamic processes. EMPC has been explored for its potential to increase profits, reduce utility costs, and improve safety [1]. Unlike traditional control, EMPC may promote time-varying operation around a steady-state based on economic objectives. Much research has focused on methods of theoretically ensuring closed-loop stability of a process under EMPC (e.g., [2] and [3]). However, little has been done in connecting potential operating strategies under EMPC directly to process equipment considerations such as stress, strain, and displacement under various loads. Initial investigations in this direction were performed in [4] by elucidating relationships between stress in a pipe downstream of a continuous stirred tank reactor for which the manipulated inputs were computed by an EMPC. However, all calculations involving stress were performed for an equilibrium case, so that it is desirable to better understand the impacts of transient loading (e.g., by time-varying temperatures in equipment caused by time-varying fluid temperatures due to control actions computed by an EMPC) on the stress profiles in the equipment.

Motivated by the above considerations, this work examines the relationship between equipment considerations and control via the integration of a stress and strain model [5] into the EMPC algorithm. This model will be used in predicting stress under the inputs computed by the EMPC and thereby enforcing constraints directly on stress in the controller. The results of this approach in terms of profits and maximum stress reached in the material over time will be compared against the results from utilizing alternative controller methodologies (e.g., operating the process under a traditional tracking MPC with a quadratic objective function [6], an EMPC with a constraint on process temperature rather than directly on stress, and an EMPC with no constraints on temperature or stress). The impacts of controlling the process under an EMPC on equipment stress will be further analyzed through ANSYS Fluent and Mechanical simulations. The simulations will integrate an EMPC that uses a data-driven model fit from stress and strain data determined in ANSYS Mechanical and allow the effectiveness of constraining the approximate stress profiles in the EMPC to be assessed by observing the resulting stress in the equipment.

References:

[1] Ellis, M., Durand, H., Christofides, P. D. “A tutorial review of economic model predictive control methods.” Journal of Process Control. Volume 24, Issue 8, Pages 1156-1178. (2014)

[2] Angeli, D., Amrit, R., and Rawlings, J. “On Average Performance and Stability of Economic Model Predictive Control.” IEEE Transactions on Automatic Control. Volume 57, Issue 7, Pages 1615-1626. (2012)

[3] Müller, M., Angeli, D., Allgöwer, F. “Economic model predictive control with self-tuning terminal cost.” European Journal of Control. Volume 19, Issue 5, Pages 408-416. (2013)

[4] Durand, H. “On accounting for equipment control interactions in economic model predictive control via process state constraints.” Chemical Engineering Research and Design. Volume 144, Pages 63-78. 2019.

[5] Barron, R. and Barron, B. Design for Thermal Stresses. Wiley. (2012)

[6] Joe Qin, S., Badgwell, T. “A survey of industrial model predictive control technology” Control Engineering Practice. Volume 11, Issue 7, Pages 733-764. (2003)