Keywords: Model Predictive Control, Optimization under Uncertainties
Abstract: This plenary talk addresses the general objective of how to control and optimize a process system based on an available model which, in general, describes the actual process behavior in an approximate way. The presence of systematic uncertainties, such as gain errors, poses challenges to model-based control and optimization systems so that without adequate compensation strategies there is permanently suboptimal behavior, such as offset. The talk is meant to guide the audience through the design principles of Model Predictive Control (MPC) systems to cope with the presence of a structural mismatch between the actual plant and the MPC model. The general goal is to asymptotically reach the optimal behavior for the actual unknown plant. The talk will be structured into two main parts. We start from the case of tracking, linear and nonlinear, MPC to build a general algorithm framework that guarantees offset-free tracking of piece-wise constant set-points in the outputs. The nominal model is augmented with integrating states, referred to as disturbances, and a combined state and disturbance observer is consequently designed. We analyze the requirements and opportunities of this disturbance observer and discuss how other approaches, commonly thought to be different, are indeed particular cases of this general approach. In the second part, we focus attention on so-called economic MPC formulations, in which the cost function is not positive-definite around the optimal equilibrium. For this novel class of MPC systems, we present the recent results on offset-free design which includes, in addition to an augmented model as in tracking MPC, a suitable first-order modifier necessary to achieve matching of the necessary conditions of optimality. Computation of such modifiers requires, in principle, knowledge of plant gradient information, and therefore we discuss implementation strategies based on available input-output measurements only. These offset-free economic MPC algorithms are closely related to Real-Time Optimization methods, and hence the necessary lines of conjunction will be drawn. Several examples of process control systems are presented. We conclude by sketching future research directions and open problems.

Keywords: Machine Learning Assisted Modeling, Manufacturing Plant Control, Fault Detection
Abstract: Chemical plants require reliable systems for pollutant abatement. These processes often operate under cyclic abatement and regeneration cycles over extended periods of time. Throughout this period, the abatement systems experience a multitude of phenomena that may degrade performance in a fashion that is challenging to predict by first-principle models. These complex phenomena offer an opportunity to leverage data-driven models. To improve their predictive ability, data driven models can be complemented with physics-based information that constrains modeling results. In this contribution, we describe a hybrid modeling approach where physics-derived features are developed to enable data-driven models to effectively predict the performance of real pollutant abatement systems in the Dow Chemical Company.

Keywords: Signal Processing, Large-Scale and Networked Systems, Fault Detection
Abstract: Oscillations are considered the most important indicator of poorly performing control loops. However, noise and other disturbances conceal these oscillations, thus making the detection task quite difficult. Furthermore, the efficiency of most detection and diagnosis techniques proposed in the literature is reduced considerably in the presence of noise. Therefore, denoising is recommended to make the detection task more straightforward. In this work, the multivariate singular spectrum analysis (MSSA) is employed to denoise the plant-wide oscillatory control loops. This approach stands in contrast to existing methods that typically focus on addressing noise in individual control loops. In order to improve the efficiency of MSSA, detrended fluctuation analysis (DFA) is incorporated to select only the significant components and eliminate the noise to provide a noise-free version of the multivariate data. The effectiveness of the proposed MSSA-DFA method has been verified using a numerical example and real industrial plant data.

Keywords: Fault Detection, Machine Learning Assisted Modeling, Adaptive and Learning Systems
Abstract: Dynamic latent variable (DLV) methods, represented by dynamic-inner principal component analysis (DiPCA), take into account the high dimensionality and auto-correlation of industrial process data to successfully extract and model the dynamic components. Meanwhile, the time-varying dynamics involved in industrial processes motivate us to explore adaptive DLV methods. In this paper, we propose a recursive DiPCA (RDiPCA) for time-varying dynamic process modeling. Specifically, a recursive autocovariance matrices updating method and the corresponding deflation method are given to achieve low computational costs. The computational efficiency is further improved by a recursive parameter initialization approach in the iterative optimization algorithm solving procedure. Finally, the effectiveness of the proposed algorithm is demonstrated with experiments on a numerical dataset and a wastewater treatment plant dataset.

Keywords: Identification Methods, Machine Learning Assisted Modeling, Data-Driven Optimization
Abstract: This paper presents an efficient approach for state estimation of post-combustion CO_2 capture plants (PCCPs) by using reduced-order neural network models. The approach involves extracting lower-dimensional feature vectors from the high-dimensional operational data of PCCPs and constructing a reduced-order process model through proper orthogonal decomposition (POD). A multi-layer perceptron (MLP) neural network is then constructed and trained to approximate the dynamics of the reduced-order process by using the low-dimensional data obtained from open-loop simulations. The proposed POD-MLP model serves as a foundation for estimating PCCP states with significantly reduced computational expenses. For state estimation, a reduced-order extended Kalman filtering scheme, grounded in the POD-MLP model, is developed. Our simulations demonstrate that the proposed POD-MLP modeling approach reduces computational complexity in comparison to the POD-only model when applied to nonlinear systems. Additionally, the proposed algorithm can accurately reconstruct the complete state information of PCCPs while markedly improving computational efficiency.

Keywords: Model Predictive Control, Identification Methods, Manufacturing Plant Control
Abstract: Fluidized bed spray agglomeration (FBSA) is an efficient particle formation process for the production of granules extensively used in the food, agricultural and pharmaceutical industry. Specifications on agglomerate properties such as the agglomerate size determine the quality of the product and can be controlled by varying different process conditions. In this contribution data-driven model predictive control (MPC) of the average agglomerate size is presented. Dynamic mode decomposition (DMD) is used to identify a linear model of the process dynamics from snapshot measurements of the particle size distribution. Using DMD as system identification technique eliminates the complex process of identifying a mechanistic process model and at the same time includes advantageous model order reduction for the MPC application. The DMD model is obtained from simulated data and validated against a second, independent, data set. Subsequently, the model is deployed in an MPC controller, which is tested in a simulation study, showing promising performance in set point tracking and disturbance rejection scenarios.

Keywords: Learning-Based Control, Adaptive and Learning Systems
Abstract: In nonlinear systems, the desired control performance is often not achieved because of changes in system characteristics. To cope with these changes, database-driven control (DD), which adjusts PID gains at each step based on data similar to current operating conditions, can be utilized. However, DD exhibits a number of problems, such as a necessity for online learning and inability to achieve the desired performance with small amounts of data. Therefore, this paper proposes methods for adjusting PID gains offline and pseudo-incrementing data from initial data. The proposed method is applicable to PID control systems over a wide range of industries. The effectiveness of the proposed method is verified through numerical example.

Keywords: Optimal Control, Plant-Wide Optimization, Power and Energy Systems
Abstract: Alkaline water electrolysis fueled by green electricity offers the promise of generating low-emission hydrogen for the envisioned energy transition. Coupling alkaline electrolysis processes to intermittent power supplies is however nontrivial, as the potential formation of explosive gas mixtures imposes strict purity requirements. This is especially crucial in low load scenarios, where gas production rates are low and foreign gas contamination can no longer be neglected. In this work we present a control structure for a stand-alone electrolysis unit which facilitates economically optimal operation under consideration of such safety constraints using only standard control elements. The proposed structure combines both objectives in the fast-acting regulatory control layer, alleviating the need for a supervisory real-time optimization layer. The performance of the control structure is attested through dynamic simulations of three different load scenarios.

Keywords: Extremum-Seeking Control, Wastewater Treatment, Data-Driven Optimization
Abstract: This study investigates an application of stabilizing extremum seeking (STAB-ESC) to model-free bioprocess productivity optimization. To this end, microbial growth in a chemostat is considered as a typical example. In contrast with the classical ESC formulation, STAB-ESC confines the measurable cost function in the argument of a periodic and bounded control function, which confers very interesting features to the control scheme in terms of sparse parameter tuning, fast convergence and robustness to measurement noise. These points are highlighted in the present study through an analysis of the Lie-bracket average dynamics and a performance comparison with a Newton-based recursive ES.

Keywords: Wastewater Treatment, Machine Learning Assisted Modeling
Abstract: Estimating or predicting the concentrations of bacteria cells is crucial for achieving better control of the operation of wastewater treatment plants. However, measuring the bacterial concentration along the influent wastewater stage to the treated effluent process is challenging as it involves lab access and trained personnel. Additionally, wastewater plants are generally nonlinear systems involving time-varying physical and biological characteristics, increasing the difficulty in estimating the bacterial concentration from a model-based approach. This paper proposes data-driven models based on four machine-learning models to estimate the bacterial cell density with a limited dataset in a wastewater treatment plant. The performance results demonstrate that the machine-learning models (i.e., K-Nearest Neighbour (kNN), Random Forest (RF), Gradient Boosting Regression (GBR), Extreme Gradient Boosting (XGB)) have the potential to estimate accurately the bacterial concentration. RF displays better bacteria estimation in the influent by 10.7% compared to GBR and 7.4% compared to XGB and kNN. Whereas for the effluent, XGB improved the estimation by 12.8%, 2.4%, 14.6% compared to GRB, RF, and kNN, respectively. Also, results show that conductivity as a single feature is the most significant parameter affecting the bacterial cell estimation in the influent stage for the four machine learning algorithms. Similarly, the chemical oxygen demand (COD) and turbidity have pronounced effects in the effluent stage. These results reveal potential signs of designing a universal data-driven model-based approach applicable for bacteria estimation at influent and effluent based on the minimum feature combinations (conductivity, COD, and turbidity).

Keywords: Wastewater Treatment, Model Predictive Control, Optimal Control
Abstract: A tube-based nonlinear model predictive controller (NMPC) is developed to regulate a continuous bioprocess of purple non-sulfur bacteria (PNSB). The controller employs a macroscopic model that exhibits significant parametric uncertainty due to the restricted availability of experimental data for parameter identification. The proposed model describes microbial protein production during PNSB growth on fructose and glucose. This work aims to assess the robustness of the proposed control strategy and compare the performance with classical NMPC. To this end, both controllers are challenged in a Monte-Carlo study, with identical disturbances in the form of parametric variations spread over 100 different scenarios. The resulting trajectories, as well as biomass and protein productivity levels, confirm the better performance of the robust tube-based controller.

Keywords: Wastewater Treatment, Model Predictive Control, Plant-Wide Optimization
Abstract: As oil fields mature, an increasing volume of water is produced alongside the oil and gas due to the injection of water to maintain reservoir pressure. The control of de-oiling hydrocyclones in produced water treatment on offshore oil and gas facilities is typically based on the pressure drop ratio (PDR). While PDR relates to the flow split in the hydrocyclone and affects the separation efficiency, it is only an indirect way to control the steady-state deoiling efficiency. When the separation facility is subjected to disturbances, e.g., changing inlet concentration or production volume, the separation efficiency changes dynamically. The PDR responds to changes in flow rate, but it cannot sense changes in inlet oil content. By deploying online oil-in-water monitors, the separation efficiency could, in principle, be measured and used for dynamic feedback. This work developed a plant model based on previously published models of PDR, separator water level, and hydrocyclone separation efficiency. A nonlinear model predictive controller is designed and placed in cascade with the existing PDR-based PI controller to optimize the hydrocyclone separation efficiency. The results indicate an increased separation efficiency and, thus, a potential reduction in discharged oil of approximately 12 percentage points.

Keywords: Wastewater Treatment
Abstract: Despite significant progress in advanced process control strategies and their performances, proportional-integral-derivative feedback (PID-FB) control remains one of the prevailing approaches in real applications. The popularity of PID controllers is attributed to their simplicity, straightforward implementation, and applicability, especially for single-input, single-output (SISO) systems. However, most industrial processes are multi-input multi-output (MIMO), with pronounced process interactions, necessitating multi-loop control. Identifying these interactions, choosing the optimal pairs of manipulated variables (MVs) and controlled variables (CVs) for MIMO control, and implementing strategies to mitigate system interactions are critical and challenging. This study investigates a multiple PID-FB loop control strategy for a UV/H2O2 photoreactor utilized to degrade polyvinyl alcohol (PVA) in an aqueous solution. The control objective is to regulate the effluent total organic carbon (TOC) and residual H2O2 concentrations (mg/L) while mitigating the impact of the inlet PVA concentration (mg/L) as a disturbance on CVs. The relative gain array (RGA) analysis is used to identify the interaction of control processes and determine the best MV/CV sets. Before controller design, the interaction between control loops is mitigated by designing the feedforward (FF) decouplers. Subsequently, PID controllers are tuned for each decoupled loop. The response of the decoupled system to setpoint trajectory and disturbance rejection affirms its excellent control performance. Additionally, the realizability of the designed decouplers is assessed. All simulations are conducted in MATLAB Simulink.

Keywords: process control; PID controller; MIMO system; decoupling; wastewater treatment; AOP; UV/H2O2; PID-FB multi-loop control; PVA; water soluble polymer

Keywords: Model Predictive Control, Learning-Based Control, Power and Energy Systems
Abstract: Tuning parameters in model predictive control (MPC) presents significant challenges, particularly when there is a notable discrepancy between the controller's predictions and the actual behavior of the closed-loop plant. This mismatch may stem from factors like substantial model-plant differences, limited prediction horizons that do not cover the entire time of interest, or unforeseen system disturbances. Such mismatches can jeopardize both performance and safety, including constraint satisfaction. Traditional methods address this issue by modifying the finite horizon cost function to better reflect the overall operational cost, learning parts of the prediction model from data, or implementing robust MPC strategies, which might be either computationally intensive or overly cautious. As an alternative, directly optimizing or learning the controller parameters to enhance closed-loop performance has been proposed. We apply Bayesian optimization for efficient learning of unknown model parameters and parameterized constraint backoff terms, aiming to improve closed-loop performance of battery fast charging. This approach establishes a hierarchical control framework where Bayesian optimization directly fine-tunes closed-loop behavior towards a global and long-term objective, while MPC handles lower-level, short-term control tasks. For lithium-ion battery fast charging, we show that the learning approach not only ensures safe operation but also maximizes closed-loop performance. This includes maintaining the battery's operation below its maximum terminal voltage and reducing charging times, all achieved using a standard nominal MPC model with a short horizon and notable initial model-plant mismatch.

Keywords: Model Predictive Control
Abstract: One challenge when using linear model predictive control (MPC) is that model mismatch and ill-conditioned gain matrices can lead to undesirable aggressive controller behavior. To address this issue, we propose improvements to an existing offline method for gain-matrix conditioning. The proposed algorithm identifies problematic manipulated variables (MVs) with correlated effects on controlled variables (CVs) and solves a constrained linear least-squares optimization problem to adjust the problematic gains. Additionally, the proposed algorithm prevents the optimizer from switching the signs of some gains and allows control practitioners to specify trusted key gains that should be held constant. We also extend the method to condition gain submatrices in scenarios where some of the CVs may temporarily be eliminated from the control problem. To illustrate the effectiveness of the proposed algorithm, we present a case study involving industrial fluidized catalytic cracking.

Keywords: Model Predictive Control, Estimation and Robust Estimation, Large-Scale and Networked Systems
Abstract: An integrated distributed moving horizon estimation (DMHE) and model predictive control (DMPC) approach is developed for complex process networks using an adaptive spectral community detection-based decomposition. The proposed approach employs the weighted graph representation of the process network model to identify optimal communities for distributed estimation and control architectures. The resulting decomposition dynamically adapts as the network transitions across different operating conditions. Consequently, adjustments are made to the integrated DMHE and DMPC architecture to optimize closed-loop performance and enhance robustness. A benchmark benzene alkylation process under various operating conditions is employed to substantiate the proposed methodology's efficacy. Simulation results demonstrate the effectiveness of the proposed method, showing improved closed-loop performance and computational efficiency compared to traditional unweighted hierarchical community detection-based decompositions.

Keywords: Model Predictive Control, Manufacturing Plant Control, Optimal Control
Abstract: Current energy market trends incentivize frequent optimal load changes, including the startup of cryogenic air separation units (ASUs), which are large electricity consumers. In this study, we assess the potential benefits of using an economic nonlinear model predictive control (ENMPC) framework for the optimal startup of ASUs in the presence of a measured process disturbance. We also considered strategies for improving the solution computational speed of the ENMPC problem. Our case study shows substantial profit recovery by the control strategy relative to offline pre-computed optimal inputs in response to the disturbance.

Keywords: Model Predictive Control, Optimal Control, Production Planning
Abstract: We address the task of allocating process inventories to maximise production and bottleneck isolation using a model predictive control (MPC) scheme. This scheme implicitly defines “set-points” for the inventories based on current operating conditions, and automatically adjusts these set-points when the operating conditions change. This problem has previously been identified as a challenge for MPC, and likely to requiring a forecast of disturbances or multi- scenario approach. In contrast, we address this challenge with an appropriate choice of the MPC objective and design of a disturbance model. The combined scheme does not require a forecast of disturbances or involve significant computational expense while allowing for the MPC to automatically correct for misidentified bottlenecks or unmeasured faults.

Keywords: Model Predictive Control, Machine Learning Assisted Modeling, Optimal Control
Abstract: Model based control approaches require an accurate and computationally fast prediction model to solve the governing equations in real time. While numerical approaches based on first principles models are accurate, the high computational cost renders them unsuitable for online estimation and model predictive control (MPC). On the other hand, the reduced order models can provide real time solutions, but there is invariably a trade-off between the accuracy and computational time. Machine learning based approaches such as physics informed neural networks (PINN) that are based on incorporating physics-based knowledge into NNs, can provide faster and accurate solutions in such scenarios. This work demonstrates the control-oriented modeling of process systems governed by ODEs and DAEs using residual PINN that is trained using neural tangent kernel update. Such PINN models can replace the conventional numerical time integration of the process dynamics and facilitate accurate and faster predictions. We present our results for setpoint tracking via MPC using the PINN model to demonstrate the capability of the proposed approach.

Keywords: Adaptive and Learning Systems, Estimation and Robust Estimation, Machine Learning Assisted Modeling
Abstract: Quality monitoring is important for biomanufacturing and often the methods used in laboratory setting don't translate well to industrial setting. In this regard, we present a non-invasive quality control method for classification of well differentiated cells from poorly differentiated ones that is scalable and can be used in online setting for adherent culture systems. The method was implemented on stage 4 of pluripotent stem cell differentiation into beta cells and we use textural analysis to extract features from phase contrast microscopic (PCM) images which were used to train our classifier that achieved an accuracy of 94.04 %. These preliminary findings show promise for its application in the area of processes monitoring in bio-reactors.

Keywords: Adaptive and Learning Systems, Machine Learning Assisted Modeling, Estimation and Robust Estimation
Abstract: State observation is necessary for feedback control but often challenging for nonlinear systems. While Kazantzis-Kravaris/Luenberger (KKL) observer gives a generic design, its model-based numerical solution is difficult. In this paper, we propose a simple method to determine a data-driven KKL observer, namely to (i) transform the measured output signals by a linear time-invariant dynamics, and (ii) reduce the dimensionality to principal components. This approach is especially suitable for systems with rich measurements and low-dimensional state space, for example, when videos can be obtained in real time. We present an application to a video of the well-known Belousov-Zhabotinsky (B-Z) reaction system with severe nonlinearity, where the data-driven KKL observer recovers an oscillatory state orbit with slow damping.

Keywords: Data-Driven Optimization, Optimization under Uncertainties
Abstract: Large-scale nonlinear optimization problems arise in a variety of applications and often exhibit some structure, which can be exploited by the use of parallel decompositions to speed up the solution. We present a general problem formulation for structured optimization problems and apply the interior point method, outlining different approaches to parallelize the step computations using the Schur complement decomposition. The use of an iterative linear solver can boost performance, given an appropriate preconditioner for the Schur complement. We present an approach to use sparse factorizations from previous solver iterations as a preconditioner, and compare it to both an L-BFGS preconditioner and direct solution.

Keywords: Learning-Based Control
Abstract: In the mining industry, flotation is a commonly used process to separate valuable minerals from waste rock in a concentrator. The rougher flotation is the first stage of the process and in Boliden AB’s concentrator at Aitik, it consists of two lines of four flotation cells each. In this paper we consider one line and the buffer tank upstream of it. Modeling this process step, and maintaining an updated model over time, is a challenge. The process itself changes over time as equipment degrades and parts are replaced. Additionally, the operating conditions in the flotation process change as the ore quality varies. We address these challenges by using reinforcement learning (RL) to design a state feedback controller for level control, without the need of an explicit process model. Using simulations, we compare the performance of the resulting controller to that of the cascade coupled PI-control structure that operates the real plant today. The RL-based controller improves the performance and shows good potential. However, convergence to an admissible control law requires careful hyper-parameter tuning. Industrial deployment thus requires further work to ensure the required reliability.

Keywords: Production Planning, Data-Driven Optimization
Abstract: Multivariate specifications for the properties of incoming raw materials are used to determine if a lot could allow reaching the desired final product quality prior to its purchase. Previous works have shown that introducing optimization of process variables in the decision framework leads to accepting a wider range of materials. However, this requires to run the optimization problem each time a new lot is not deemed acceptable if the process is operated at nominal conditions. The objective of this paper is to simplify the current method by defining a more general specification region for raw materials considering three regions: accept, accept with process optimization, and reject. The concept is demonstrated using a grinding-flotation simulator where the objective is to assess a minimal profit when processing a lot of ore. For the case study, the results obtained from a test dataset show that the accuracy of the proposed method is 92%. It gives similar results compared to the decision framework considering the optimization problem.

Keywords: Supply Chain and Enterprise Integration, Large-Scale and Networked Systems, Plant-Wide Optimization
Abstract: In the pursuit of reducing carbon emissions, the integration of renewable energy into society’s energy portfolio plays a crucial role despite challenges tied to their inherent unpredictability and seasonal variations. Hydrogen, as a mean of storing and transporting renewable energy becomes crucial in addressing these challenges. Notwithstanding its potential, the misalignment of cost-competitive hydrogen production hubs with demand centers calls for a thorough examination of global hydrogen distribution. The versatility of hydrogen transportation (e.g., pipelines, ships, trucks) and various forms like compressed hydrogen, liquid hydrogen, ammonia, and liquid organic hydrogen carriers (LOHC) adds complexity to designing an economically efficient hydrogen supply chain (HSC). Addressing previous scholarly limitations focused on existing technologies, this study advocates for a superstructure-based modeling approach for HSC that includes promising technologies. Through a case study involving a production site in the Middle East and a demand site in Texas, a dedicated HSC superstructure network is formulated, facilitating the identification of cost-effective hydrogen supply pathways using Mixed Integer Linear Programming. Ultimately, this effort aims to establish a comprehensive framework to discern the most sustainable and financially viable technologies, identifying the optimal configuration within the HSC.

Keywords: Fault Detection, Adaptive and Learning Systems
Abstract: Learning from time series data in industrial scenarios enables the detection and classification of anomalies or faults in equipment and production processes. In industrial settings, variations in production equipment parameters or raw materials lead to changes in production operating conditions, resulting in the multi-operating condition characteristics of the data and placing higher requirements on anomaly detection models. This paper introduces domain adaptation and contrastive learning methods for multi-operating condition time series data and designs an end-to-end model structure to enhance the performance of time series anomaly detection. The objective loss function incorporates the Maximum Mean Discrepancy (MMD) and contrastive loss functions. The proposed approach is validated and analyzed on a simulated dataset.

Keywords: Fault Detection, Signal Processing, Resilient, Safe, and Cyber-Secure Systems
Abstract: Nowadays, deep learning has emerged as a transformative technology in various domains, including process monitoring. Massive advanced deep learning algorithms, such as autoencoder, recurrent neural network, and convolutional neural network, have been explored in the application of chemical processes to enhance the overall monitoring performance. Nevertheless, deep learning models often imply complex structures and a huge number of parameters, leading to limited generalization ability when they are employed in industrial chemical processes. In this work, the above limitation is addressed by monitoring the representative and discriminative features extracted in the latent space by Siamese autoencoder. The reconstruction ability and discriminative information between a pair of inputs are considered in the extraction of latent features, by which better process monitoring performance can be achieved with much fewer model parameters. Case study on an industrial chemical process is investigated to demonstrate the effectiveness of the proposed method.

Keywords: Fault Detection
Abstract: Fault diagnosis is an essential field for the safe operation of chemical processes. In this paper, a self-supervised fault diagnosis method employing a tree-based deep learning model is proposed. The temporal information of multivariate time-series data is compressed with a Long Short-Term Memory structure, and the proposed method is demonstrated by performing the classification of fault types in the Tennessee Eastman process. It showed substantial performance enhancement compared to supervised learning, leveraging the feature representation obtained from unlabeled data. Notably, the tree-based characteristic of the proposed method provides interpretability of model results, illuminating the salient features of each fault type.

Keywords: Fault Detection, Identification Methods
Abstract: In complex processes, the activation of a single alarm can trigger a cascade of consequences that affect multiple interconnected components. As a result, the number of active alarms can increase rapidly. This sudden surge in alarms is often referred to as an alarm flood. Alarm floods are a common source of operational burden for operators, overwhelming them with a high volume of alarm notifications. If critical alarms are not promptly and accurately identified, decision-making processes can be undermined. This paper addresses these challenges by introducing a novel approach for identifying and prioritizing critical alarms from each alarm flood. Hidden Markov models are employed to construct a likelihood matrix that reveals the relationships among alarm variables, and identifies the most critical alarm from a directed acyclic graph. Case studies are conducted using a vinyl acetate monomer simulator to demonstrate the effectiveness of the proposed approach. The results highlight accurate identification and prioritization of critical alarms, enabling operators to focus on the most important process abnormalities.

Keywords: Fault Detection, Signal Processing, Data-Driven Optimization
Abstract: Alarm systems in industrial process control are critical for ensuring safety and efficiency, alerting operators to potential process deviations or failures. This paper introduces a novel methodology for the real-time optimization of alarm systems, particularly for distributional shifts in the process variables. Our approach is divided into two phases: the design phase, which uses historical data to establish key performance indices such as missed alarm rate and false alarm rate; and the application phase, which adapts to real-time data with initially unknown statistical properties. The case study on the process variable demonstrates the effectiveness of our method in detecting distributional shifts and enhancing alarm system performance at runtime. This study offers a significant contribution to the field of industrial alarm management, providing a scalable framework for dynamic environments.

Keywords: Fault Detection, Signal Processing, Manufacturing Modeling for Management and Control
Abstract: This paper examines the suitability of unsupervised machine learning methods for image analysis, within the innovative visual analytics framework for process monitoring, and proposes a set of performance metrics that evaluate accuracy for visual analytics. The effectiveness of the proposed method is demonstrated via a case study using real industrial data from a steam boiler.

Keywords: Extremum-Seeking Control, Optimal Control, Optimization under Uncertainties
Abstract: Within a frame of optimized performance by Extremum Seeking Control, this work conceptualizes the enzymatic hydrolysis of cellulose carried out in an isothermal stirred tank reactor of continuous operation. This reactor operation is aimed at increasing the production rate of reducing sugars in biorefineries. The basis is a batch reactor model extended to describe continuous operation, resulting in a stable process for any process condition. Based on an objective function that ponders productivity with dilution rate, it is applied an Extremum Seeking Control algorithm driven by the on-line estimation of the gradient of the control input-objective function map, improving convergence rate and enabling practical implementation.

Keywords: Optimal Control, Model Predictive Control, Manufacturing Plant Control
Abstract: Biological systems play a key role in many advanced manufacturing processes, of which many have interesting nonlinear dynamics. We investigate a continuous yeast cell manufacturing process that produces sustained oscillations in outputs under nominal conditions. Using a population balance model to perform dynamic optimization with multiple objectives and observability constraints, we quantify tradeoffs on the Pareto surface for varying the extent of process oscillations that the decision-maker deems tolerable (or desirable). Numerical optimal control design for oscillatory distributed parameter systems is discussed within the context of both dynamic optimization and on-line nonlinear model predictive control strategies.

Keywords: Optimal Control, Model Predictive Control
Abstract: Optimal control of a Hybrid Dynamical System is a difficult problem because of unknown non-differentiable points or switches in the solution of discontinuous ODEs. The optimal control problem for such hybrid dynamical system can be reformulated into a dynamic complementarity system (DCS) problem. In this paper, a moving finite element with switch detection method is implemented to ensure higher order accuracy for numerical discretization schemes such as Implicit Runge Kutta (IRK) or Orthogonal Collocation method. The DCS problem is solved using a globally convergent nonlinear complementarity solver based on active set strategy to avoid spurious stationary solutions.

Keywords: Optimal Control, Optimization under Uncertainties, Model Predictive Control
Abstract: In this paper, we present the linear-quadratic (LQ) discretization for converting continuous-time linear-quadratic optimal control problems (LQ-OCPs) with time delays to equivalent discrete-time extended LQ-OCPs. We formulate the LQ discretization as the systems of differential equations, allowing us to derive discrete equivalents through the solution of formulated differential equations systems. Three numerical methods are introduced for solving proposed differential equations systems: 1) the ordinary differential equation (ODE) method, 2) the matrix exponential method, and 3) the step-doubling method. To validate LQ discretization and proposed numerical methods, we implement the model predictive control (MPC) and test it on a simulated cement mill system. The objective function of the MPC is discretized using LQ discretization. The simulation results indicate that the LQ discretization-based MPC successfully stabilizes and controls the simulated cement mill system, ensuring the viability and effectiveness of LQ discretization.

Keywords: Optimal Control, Extremum-Seeking Control, Derivative-Free Optimization
Abstract: Online Feedback Optimization (OFO) controllers steer a system to its optimal operating point by treating optimization algorithms as auxiliary dynamic systems. Implementation of OFO controllers requires setting the parameters of the optimization algorithm that allows reaching convergence, posing a challenge because the convergence of the optimization algorithm is often decoupled from the performance of the controlled system. OFO controllers are also typically designed to ensure steady-state tracking by fixing the sampling time to be longer than the time constants of the system. In this paper, we first quantify the impact of OFO parameters and the sampling time on the tracking error and number of oscillations of the controlled system, showing that adjusting them without waiting for steady state allows good tracking. We then propose a tuning method for the sampling time of the OFO controller together with the parameters to allow tracking fast trajectories while reducing oscillations. We validate the proposed tuning approach in a pressure controller in a centrifugal compressor, tracking trajectories faster than the time needed to reach the steady state by the compressor. The results of the validation confirm that simultaneous tuning of the sampling time and the parameters of OFO yields up to 87% times better tracking performance than manual tuning based on steady state.

Keywords: Optimal Control, Optimization under Uncertainties, Learning-Based Control
Abstract: The application of proportional-integral-derivative (PID) control schemes to nonlinear multiple-input, multiple-output (MIMO) systems with time-varying uncertainty is challenging and underexplored. In this study, we formulated a deep Reinforcement Learning (RL) based PID tuning strategy with key novelty in designing an RL agent to achieve real-time adaptive MIMO PID tuning to track setpoints while considering time-varying uncertainty. We evaluated our tuning strategy on a continuous stirred-tank reactor subject to time-varying uncertainty. While conventional PID failed to track the effluent concentration setpoint and caused large errors and offsets, the proposed RL agents achieved fast and accurate setpoint tracking that significantly reduced the errors and eliminated offsets; thus, making our RL-based strategy attractive for chemical engineering applications under time-varying uncertainty.

Keywords: Resilient, Safe, and Cyber-Secure Systems, Data-Driven Optimization, Derivative-Free Optimization
Abstract: This paper introduces a model-free real-time optimization (RTO) framework based on unconstrained Bayesian optimization with embedded constraint control. The main contribution lies in demonstrating how this approach simplifies the black-box optimization problem while ensuring "always-feasible" setpoints, addressing a critical challenge in real-time optimization with unknown cost and constraints. Noting that controlling the constraint does not require detailed process models, the key idea of this paper is to control the constraints to "some" setpoint using simple feedback controllers. Bayesian optimization then computes the optimum setpoint for the constraint controllers. By searching over the setpoints for the constraint controllers, as opposed to searching directly over the RTO degrees of freedom, this paper achieves an inherently safe and practical model-free steady-state RTO scheme. In particular, this paper shows that the proposed approach can achieve zero cumulative constraint violation without relying on assumptions about the Gaussian process model used in Bayesian optimization.The effectiveness of the proposed approach is demonstrated on a benchmark Williams-Otto reactor example.

Keywords: Power and Energy Systems, Machine Learning Assisted Modeling
Abstract: In recent years, extreme electricity prices have occurred with greater frequency and magnitude. Accurately predicting extreme electricity prices is of great interests to market participants. This paper aims to forecast real-time electricity prices for the next 24 hours for the Houston load zone in Electric Reliability Council of Texas (ERCOT), targeting at providing accurate prediction of potential extreme prices. Historical energy prices from ERCOT and weather data from the National Oceanic and Atmospheric Administration (NOAA) were used. A new modeling framework that takes forecasted upper bound of exogenous variables to predict both (1) real-time prices with uncertainty using a temporal fusion transformer (TFT) model as well as (2) likelihood of having extreme prices in the forecasting horizon is proposed. Additionally, a concatenated model fusion strategy is applied as an additional step to further increase the framework's capability of accurately forecasting extreme prices. Our proposed method showed better forecasting capability with a RMSE of 35 compared to other state of the art methods such as auto-encoder long short-term memory (AE-LSTM) and PatchTST (RMSE of 49 and 42 respectively) on the same testing period. In addition, we quantified the uncertainty of the predictions leveraging the quantile output from the TFT model and found that 97% of the time, the 98th quantile of the forecasting horizon contains the actual real time price. Our proposed framework provided an accurate and robust approach for forecasting normal and extreme electricity prices that could have significant economic benefits to electricity market participants