Supplementary Information for FOCAPO-CPC 2027 paper submission titled: "Acquisition Functions for Gaussian Process-Based Model Predictive Control"

Carbon dioxide transport is a critical component of the carbon capture and sequestration (CCS) supply chain. Given the substantial energy requirements and dispersed locations of CCS facilities, optimizing pipeline operations is critical to minimize costs. Although CO2 in dense phase is typically favored for long-distance transport, gaseous phase transport is also a possibility for shorter distances and volumes. This study models a gaseous CO2 pipeline system. Since CO2 gas pipelines provide the benefit of line packing, owing to gas compressibility, this work leverages it to maximize throughput in the presence of disturbances. Pipeline pressures within each segment are perceived as an inventory (i.e. form of storage) and a model predictive control (MPC) formulation for optimal inventory management is implemented to maximize throughput. This study applies the formulation to pipelines arranged in series and parallel. It effectively maximizes throughput and optimally drains pipeline pressu... [more]

In this work, we propose a methodology for monitoring the performance of model predictive controllers (MPCs). A sequence of binary classification machine learning models, organized in cascade, called Cascade Machine Learning Models (CMLM), is evaluated to give a diagnosis of the control conditions. The proposed methodology was assessed using two case studies: a benchmark problem (the van de Vusse reactor under nonlinear MPC, NMPC) and a simulated industrial debutanizer column under commercial MPC. The ML models evaluated were the Random Forest and the Multilayer Perceptron. The results show that the proposed approach outperforms both a single multiclass model and traditional MPC performance monitoring methodologies, while remaining adaptable and scalable to larger applications.

Nonlinear model predictive control (NMPC) can substantially improve performance and constraint handling for (bio)chemical processes, but its adoption is still limited by the effort required to build maintainable first-principles models and to implement efficient dynamic optimization-based controllers. This paper presents GlycoPy, an open-source, equation-oriented and object-oriented Python framework that supports hierarchical model construction and integrated workflows for simulation, parameter estimation, dynamic optimization, and NMPC. The case study of the monoclonal antibody glycosylation process based on a multiscale model demonstrates the capability of GlycoPy.

Maintaining sufficient amounts of dissolved oxygen throughout a microbial cultivation is a classic control task in bioprocess engineering to avoid negative effects onto cell physiology and productivity. But traditional PID-based algorithms struggle when faced with pulsed substrate additions and the resulting sudden surge of oxygen uptake. In this work a nonlinear MPC is employed and compared to a PID setup for the cultivation of an E. coli strain exposed to intermittent feeding. Both controllers are tuned for a fast pulse response combined with efficient and robust control action. Their performance was tested in-silico with isolated feed pulses, as well as throughout a full cultivation run. Further, the effects of parameter uncertainty were investigated to assess the impact of a model-plant mismatch. The results showed that the predictive nature of the MPC is well suited for maintaining the dissolved oxygen levels above a threshold and outperforms the PID in almost all investigated sim... [more]

Within an Industry 4.0 framework, a variety of new considerations are of increasing importance, such as securing processes against cyberattacks on the control systems or utilizing advances in image processing for image-based control. These new technologies impact relationships between process design and control. In this work, we discuss some of these potential relationships, beginning with a discussion of side channel attacks and what they suggest about ways of evaluating plant design and instrumentation selection, along with controller and security schemes, particularly as more data is collected and there is a move toward an industrial Internet of Things. Next, we highlight how the 3D computer graphics software tool set Blender can be utilized to analyze a variety of considerations related to ensuring safety of plant operation and facilitating the design of assemblies with image-based sensing.

This paper proposes embedded model predictive control strategies for oil-production processes equipped with electric submersible pump (ESP) installations. The novelty of this paper is the robustness and computational performance analysis of the Robust Infinite-Horizon Model Predictive Controller (RIHMPC) and Nonlinear Model Predictive Controller (NMPC) strategies, which have not yet been documented by the oil and gas exploration and production literature. The proposed method to embed the control laws is flexible with different hardware and is based on automatic code generation, which facilitates the project workflow. Hardware-in-the-loop simulation cases were used to compare the performance of both control strategies embedded in the Teensy 4.1 microcontroller, using key indices for real applications. The results showed that the RIHMPC strategy is a very promising alternative for real-time operation in ESP-lifted oil wells, with overall performance similar to the NMPC controller, even i... [more]

Advanced control strategies, together with state-estimation methods, are frequently applied to nonlinear and complex systems. It is crucial to understand which of these are the most efficient methods for the best use of these approaches in a chemical process. In the current work, nonlinear model predictive control (NMPC) approaches were developed that considered three numerical methods: single shooting (SS), multiple shooting (MS), and orthogonal collocation (OC). Their performance was compared against the Van de Vusse reactor benchmark while considering set-point changes, unreachable set-point, disturbances, and mismatches. The results showed that the NMPC based on OC presented less computational cost than the other approaches. The extended Kalman filter (EKF), constrained extended Kalman filter (CEKF), and the moving horizon estimator (MHE) were also developed. The estimators’ performance was compared for the same benchmark by considering the computational cost and the mean squared e... [more]

The current flexibility of the energy market requires operating steam turbines that have challenging operation requirements such as variable steam conditions and higher number of startups. This article proposes an advanced control system based on the Nonlinear Model Predictive Control (NMPC) technique, which allows to speed up the start-up of steam turbines and increase the energy produced while maintaining rotor stress as a constraint variable. A soft sensor for the online calculation of rotor stress is presented together with the steam turbine control logic. Then, we present how the computational cost of the controller was contained by reducing the order of the formulation of the optimization problem, adjusting the scheduling of the optimizer routine, and tuning the parameters of the controller itself. The performance of the control system has been compared with respect to the PI Controller architecture fed by the soft sensor results and with standard pre-calculated curves. The contr... [more]

The integration and control of energy systems for power generation consists of multiple heterogeneous subsystems, such as chemical, electrochemical, and thermal, and contains challenges that arise from the multi-way interactions due to complex dynamic responses among the involved subsystems. The main motivation of this work is to design the control system for an autonomous automated and sustainable system that meets a certain power demand profile. A systematic methodology for the integration and control of a hybrid system that converts liquefied petroleum gas (LPG) to hydrogen, which is subsequently used to generate electrical power in a high-temperature fuel cell that charges a Li-Ion battery unit, is presented. An advanced nonlinear model predictive control (NMPC) framework is implemented to achieve this goal. The operational objective is the satisfaction of power demand while maintaining operation within a safe region and ensuring thermal and chemical balance. The proposed NMPC fram... [more]

The purpose of this study was to develop an integrated control strategy for multiscale crystallization processes. An image analysis method using a deep learning neural network is used to measure the fine-scale information of the crystallization process, and the mathematical statistical method is adopted to obtain the mean size of the crystal population. A feedforward neural network is subsequently trained and employed in a nonlinear model predictive control formulation to obtain the optimal profile of the manipulated variable. The effectiveness of the proposed nonlinear model predictive control method is evaluated using alum cooling crystallization experiments. Experimental results demonstrate benefits of the proposed combination of feedforward neural network and nonlinear model predictive control method for the multiscale crystallization process.