(109c) In-Silico Nonlinear Model Predictive Control of an Industrial Air Separation Unit with Oxygen-, Nitrogen-, and Argon Production

Enabling frequent load changes in industrial processes, such as cryogenic air separation units (ASUs), motivates advanced process automation [1, 2]. In this context, promising strategies are model-based approaches, in particular nonlinear model predictive control (NMPC) [1, 2, 3], and model-free strategies, such as reinforcement learning [4, 5]. In NMPC, the prediction model may be anything between a mechanistic (first-principles) model and a purely data-driven model. The potential of NMPC with either model type has been demonstrated for small ASU types with up to two products [1, 2, 3, 6] and subsystems of ASUs with argon production [7, 8]. However, extending the control problem to include the argon purification section introduces a slow subsystem, leading to a stiff process model of very high order. The application of NMPC to this extended control problem is thus associated with additional challenges and has not yet been accomplished.

Here, we present an in-silico application of NMPC to an industrial Linde ASU with argon production. Most importantly, we use a centralized tracking NMPC to control all three products, i.e., oxygen, nitrogen, and argon, simultaneously. We implement an NMPC framework in Python and use our open-source dynamic optimization framework DyOS [9]. We develop a mechanistic model of the ASU in Modelica. Therein, the distillation columns are represented using equilibrium-based tray-to-tray (“MESH”) models. The multi-stream heat exchangers are modeled as one-dimensional spatially distributed systems. To obtain computationally efficient correlations, artificial neural networks and polynomial regression are used as surrogate models for some of the constitutive model equations, e.g., thermodynamic correlations. We investigate the closed-loop performance using a validated Linde digital twin in UniSim Design. The resulting nonlinear model is very high-dimensional, but sparse. Mathematical reformulation techniques are used to preserve sparsity of the differential-algebraic prediction model during the model compilation step. A moving horizon estimator (MHE) provides the system state based on plant measurements. Case studies show that the NMPC enables changes between 50 % and 100 % load at high load change rates. Moreover, we discuss practical challenges and solutions in the implementation of industrial NMPC, including options for computational speed-up [1, 6].

References

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[2] Adrian Caspari, Christoph Offermanns, Pascal Schäfer, Adel Mhamdi, and Alexander Mitsos. “A flexible air separation process: 2. Optimal operation using economic model predictive control”. In: AIChE Journal 65.11 (2019), p. e16721.

[3] Zhongzhou Chen, Michael A. Henson, Paul Belanger, and Lawrence Megan. “Nonlinear Model Predictive Control of High Purity Distillation Columns for Cryogenic Air Separation”. In: IEEE Transactions on Control Systems Technology 18.4 (2010), pp. 811–821.

[4] Ruiyu Qiu, Guanghui Yang, Zuhua Xu, and Zhijiang Shao. “Interval Weight State Update Approach with Deep Reinforcement Learning for Dynamic Load Change Tasks in Air Separation Processes”. In: 2024 IEEE 13th Data Driven Control and Learning Systems Conference (DDCLS) (2024), pp. 795–801.

[5] Maximilian Bloor, Ehecatl Antonio Rio Del Chanona, and Calvin Tsay. “Hierarchical RL-MPC for Demand Response Scheduling”. In: arXiv preprint (2025). url: http://arxiv.org/pdf/2502.13714v1.

[6] Jan C. Schulze, Danimir T. Doncevic, Nils Erwes, and Alexander Mitsos. “Data-Driven Model Reduction and Nonlinear Model Predictive Control of an Air Separation Unit by Applied Koopman Theory”. In: Foundations of Computer Aided Process Operations/Chemical Process Control (2023).

[7] Nicolas Blum, Valentin Krespach, Gerhard Zapp, Christian Oehse, Sebastian Rehfeldt, and Harald Klein. “Investigation of a Model–Based Deep Reinforcement Learning Controller Applied to an Air Separation Unit in a Production Environment”. In: Chemie Ingenieur Technik 93.12 (2021), pp. 1937–1948.

[8] Valentin Krespach, Nicolas Blum, Martin Pottmann, Sebastian Rehfeldt, and Harald Klein. “Improving extrapolation capabilities of a data-driven prediction model for control of an air separation unit”. In: Computers & Chemical Engineering 194 (2025), p. 108953.

[9] Adrian Caspari, Andreas M. Bremen, Johannes M.M. Faust, F. Jung, Chrysoula D. Kappatou, Susanne Sass, Yannic Vaupel, Ralf Hannemann-Tamás, Adel Mhamdi, and Alexander Mitsos. “DyOS - A Framework for Optimization of Large-Scale Differential Algebraic Equation Systems”. In: Computer Aided Chemical Engineering 46, Elsevier (2019), pp. 619–624.