Physics-Informed Neural Networks (PINNs) offer a promising approach for integrating first-principles modeling with data-driven methods, especially in dynamic thermal systems. This study introduces a hybrid PINN framework for a one-dimensional heating rod governed by heat transfer equations. Unlike traditional PINNs that rely on time-dependent automatic differentiation, this approach employs numerical derivatives to bypass gradient saturation and enhance robustness. The proposed model demonstrates accurate extrapolation and generalization with limited training data and is effectively used as a surrogate in a Model Predictive Control (MPC) framework for rod-tip temperature regulation. Additionally, a plan is outlined to apply physics-informed dimensionality reduction and model order reduction to improve computational efficiency and enable real-time application. The findings affirm PINNs' potential as control-oriented reduced models for thermal processes.

Reinforcement learning (RL) presents a promising alternative to model-based advanced control schemes, such as model predictive control (MPC), whose application can be limited by highly complex system models. However, incorporating constraints in RL remains challenging and formulating a suitable optimization objective is not straightforward. Reinforcement learning from human feedback (RLHF) offers an approach to derive the RL reward function from human expert preferences, enabling the incorporation of process knowledge. In this work, we present the application of RLHF to fine-tune an approximate MPC controller with suboptimal performance. We demonstrate that combining conventional reward formulations with RLHF, along with varying trajectory segment lengths for collecting human feedback, improves the control methodology for a batch bioreactor by enhancing safety and accounting for long-term effects. Furthermore, direct-preference based policy optimization (DPPO) represents a promising al... [more]

A safety-intelligent framework is presented for developing a multiple-input multiple-output (MIMO) risk-based explicit model predictive control (R-eMPC) for metal hydride storage systems (MHSS). These systems are susceptible to thermal runaway during the charging process as a result of the exothermic adsorption reaction within the metal alloy. To address this issue, deterministic and stochastic safety-intelligent control algorithms are designed and implemented by explicitly embedding a dynamic risk index (RI) or risk tolerance (() into the control law and decision-making. In closed-loop analysis, the deterministic R-eMPC regulates both core temperature and hydrogen storage capacity by forecasting fault occurrence, triggering alarms, and reducing the risk index by adjusting the optimal control actions, supply pressure and water flowrate. Meanwhile, the stochastic R-eMPC accounts for uncertainties in core temperature variation by incorporating risk tolerance through chance-constraints. W... [more]

The bioprocess industry is actively exploring technologies associated with the fourth industrial revolution, with modeling offering considerable potential for process optimization. Nevertheless, model adoption in industry remains limited. This is partly because model development continues to depend heavily on offline sampling, and because relatively few industrial applications convincingly demonstrate their practical value. This study therefore first examines the benefits of online rheology and online biomass measurements for model development and demonstrates, among other aspects, that online biomass significantly improves model fidelity. The second part examines how electricity prices affect process conditions, a key factor in production, and finds that, contrary to common practice, maximizing all operating parameters is not the most cost-effective strategy. Finally, an insilico framework for model predictive control, applied to a reactor endfill scenario, demonstrates that oxygen... [more]

This paper presents OpenAD-lib, an open-source Python framework for anaerobic digestion (AD) digital twins, unifying mechanistic models, machine learning (ML) surrogates, and model predictive control (MPC) within a modular ecosystem. OpenAD-lib addresses the critical fragmentation in AD digitalisation by bridging mechanistic and data-driven paradigms under explicit uncertainty. By integrating uncertainty-aware feedstock characterisation with robust process control, the platform enables the transition from isolated research tools to fully integrated digital twins, delivering economic and environmental value in AD systems.

Contains 341 original peer-reviewed research articles presented at the 36th European Symposium on Computer Aided Process Engineering (ESCAPE 36) in Sheffield, UK. Subject categories include CAPE in Circular Economy, CAPE in Clean Energy Systems, CAPEing with Uncertain Futures, Pharmaceutical & Biotechnological Systems, Modelling & Simulation, Concepts, Methods & Tools, Process Design, Scheduling & Optimisation, Process Control & Operation, Education, and Knowledge Transfer & Entrepreneurship.

While he was trapped in a Shell oil refinery for weeks during a 1973 plant strike, Charles R. Cutler (1936-2020) used the opportunity to try out his untested theories on a new method for controlling chemical plants on the actual refinery. They worked spectacularly, and the resulting Dynamic Matrix Control method later became a standard part of control engineering practice. However, DMC was kept a trade secret at Shell until 1980 when it was first made available to the public. This book uncovers the history behind the theory by publishing Cutler’s writings and letters, including his 1969 thesis proposal letter to Prof. Huang at the University of Houston outlining his theories, and a more developed draft paper from 1975 that was never published. Science historians and control engineers alike can trace the development of the theory over time from its earliest origins.

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]

Extended Dynamic Mode Decomposition (EDMD) and its variant, the pqEDMD, which uses a p-q-quasi norm reduction of polynomial basis functions, are attractive tools to derive linear operators approximating the dynamic behavior of nonlinear systems. This study highlights how this methodology can be applied to data-driven modeling and control of bioprocesses by discussing the selection of several ingredients of the method, such as the polynomial basis, order, data sampling, and preparation for training and testing, and ultimately, the exploitation of the model in linear model predictive control.

The paradigm shift into an era of Industry 4.0, also referred to as the fourth Industrial Revolution, has emphasized the need for intelligent networking between process equipment and industrial processes themselves. This has brought on an age of research and framework development for smart manufacturing in the name of Industry 4.0 [1]. While the physical and digital advancements towards smart manufacturing integration are substantial the inclusion of engineers themselves amongst this shift is often less considered [2]. There are educational efforts in Europe to create and implement smart manufacturing curriculum for non-traditional or adult learners already integrated in the workforce, but attention is also needed on a next generation smart manufacturing curriculum for pre-career students [3]. We, the teaching team of CHE 554: Smart Manufacturing at Purdue University, developed and implemented a curriculum geared towards the training of undergraduate, graduate, and non-traditional stud... [more]

Process control can be one of the most exciting and engaging chemical engineering undergraduate courses! This paper describes our experience transforming Chemical Process Control into Data Analytics, Optimization, and Control at the University of Notre Dame (second semester required course in the junior year). Our modern course is built around six hands-on experiments in which students practice data-centric modeling and analysis using the Arduino-based Temperature Control Lab (TCLab) hardware. We argue that state-space dynamic modeling and optimization are more critical for educating modern chemical engineers than topics such as frequency domain analysis and controller synthesis emphasized in many classical undergraduate control courses. All the course material is available online at https://ndcbe.github.io/controls.

Implementing Model Predictive Control (MPC) for large-scale nonlinear systems is often computationally challenging due to the intensive online optimization required. To address this, various reduced-order linearization techniques have been developed. The Koopman operator linearizes a nonlinear system by mapping it into an infinite-dimensional space of observables, enabling the application of linear control strategies. While Artificial Neural Networks (ANNs) can approximate the Koopman operator in a data-driven manner, training these networks becomes computationally intensive for high-dimensional systems as the lifting into a higher-dimensional observable space significantly increases data size and complexity. In this work, we propose a technique, combining Proper Orthogonal Decomposition (POD) with an efficient ANN structure to reduce the training time of ANN for large order systems. By first applying POD, we obtain a low order projection of the system. Subsequently, we train the ANN w... [more]

Wastewater treatment and resources recovery from large wastewater flowrates of the municipalities and circular bio-based economy ask for efficient control solutions. The paper presents solutions for operating the wastewater treatment plant, based on advanced process control methods aimed to merge the benefits of the cooperation between the lower-level regulatory control loops and the upper-level model predictive control strategy. The lower-level is designed to regulate the nitrification in the aerated bioreactors by controlling the Dissolved Oxygen or the ammonia concentration and to control the denitrification in the anoxic reactor by controlling the nitrates concentration. The model predictive controller either sets the setpoints of the regulatory layer or directly manipulates the air and nitrate recycle flow rates. The plant performance results obtained using the regulatory Proportional and Integral control are compared to the direct or the supervisory model predictive control outco... [more]

Maintaining operational efficiency while ensuring safety is a longstanding challenge in industrial process control, particularly in high-risk environments. This paper presents a novel Dynamic Risk-Informed Explicit Model Predictive Control (R-eMPC) framework that integrates safety and operational objectives using probabilistic constraints and real-time risk assessments. Unlike traditional approaches, this framework dynamically adjusts safety thresholds based on Bayesian updates, ensuring a balanced trade-off between reliability and efficiency. The validation of this approach is illustrated through a case study on tank level control, a safety-critical process where maintaining the liquid level within predefined safety limits is paramount. The results demonstrate the framework’s capability to optimize performance while maintaining robust safety margins. By emphasizing adaptability and computational efficiency, this research provides a scalable solution for integrating safety into real-ti... [more]

Recent advancements in machine learning and time series analysis have opened new avenues for improving predictive control in complex systems such as mineral flotation. Techniques leveraging multivariate predictive control in mineral flotation have seen significant progress in recent years. However, challenges in developing an accurate dynamic model that encapsulates both the pulp and froth phases have hindered further advancements. Now, with a readily available model containing equations that describe the physics of flotation froths, an opportunity for novel control strategies presents itself. In this study, a Gaussian Process (GP) Model Predictive Control (MPC) strategy is proposed to integrate uncertainty quantification directly into the control framework. By leveraging the probabilistic nature of GP models, this approach captures process variability and adapts dynamically to new data, ensuring continuous refinement of the GP model within the MPC strategy. Unlike previous implementat... [more]

Successful implementation of optimization-driven control techniques, such as model predictive control (MPC), is highly dependent on an accurate and detailed model of the process. As complexity in the system increases, linear approximation used in MPC may result in poor performance since a critical operating point is valid in only a small neighborhood of operation. To address this problem, this paper proposes a collaborative approach that combines linear and data-based models to predict state variables individually. The outputs of these models, along with constraints, are then incorporated into the MPC algorithm. For data-based process model, a multi-layered feed-forward network is used. Additionally, the offset-free technique is applied to eliminate steady-state errors resulting from model-process mismatch. To demonstrate the results, a binary distillation column process which is multivariable and inherently nonlinear is chosen as testbed. We compare the performance of the proposed met... [more]

One market scope of bioindustries is the production of recombinant proteins for its application in serotherapy. However, its process's monitoring and optimization present limitations. There are different approaches to optimize bioprocess performance; one is using model-based control strategies such as Model Predictive Control (MPC). Another strategy is learning-based control, such as Reinforcement Learning (RL). In this work, an RL approach was applied to maximize the production of recombinant proteins in E. coli at the induction phase using as a control variable the substrate feed flow rate (Fin). The RL model was trained using the actor-critic Twin-Delayed Deep Deterministic (TD3) Policy Gradient agent. The reward corresponded to the maximum value of protein productivity. The environment was represented with a dynamic hybrid model. The optimization was evaluated by stages of two hours to check the protein productivity performance. Afterwards, the results were compared with an MPC app... [more]

The motivation of this work is an application of a production scheduling based on Real-Time Optimization and Zone Control Nonlinear Model Predictive Controller on a liquid recovery unit of an LPG production plant. In this unit, the scheduling-relevant disturbances occur on a time scale relevant to the system dynamics; thus, we propose a novel combination of a well-known control strategies leading to a hierarchical two-layered strategy, where the lower layer employs a zone control nonlinear model predictive controller (NMPC) to define inventory setpoints while the upper layer uses real-time optimization (RTO) to determine optimal plant-wide flow rates from an economic perspective. Unlike a traditional RTO, the proposed upper-layer problem is parameterized by product demands, with a distinct optimization problem formulated for each demand scenario. Our novel approach allows for proactive mitigation of potential inventory issues by dynamically recalculating the distribution of plant produ... [more]

Process control should be one of the most exciting chemical engineering undergraduate courses! This presentation describes our experience transforming "Chemical Process Control" into "Data Analytics, Optimization, and Control" at the University of Notre Dame (required in the second semester of the junior year). In six hands-on experiments, students practice data-centric modeling and analysis using the Ardunio-based Temperature Control Lab (TCLab) hardware. The semester learning goals are:
- Develop mathematical models for dynamical systems from data and first principles using modern statistical methods;
- Predict dynamical system performance using numerical methods;
- Analyze, implement, tune, and debug feedback controllers using the hands-on laboratory;
- Formulate and solve optimization problems for decision-making;
- Demonstrate mastery of at least two of the above skills in an open-ended group project.

The goal of this presentation is to share our strategy to modernize... [more]

The growing electrification of buildings and vehicles, while a natural step towards achieving global decarbonization, poses some challenges for the electric grid in terms of power consumption. One way of addressing them is by deploying onsite, behind-the-meter resources (BTMR), such as battery energy storage and solar PV generation. The optimal design of these systems, however, is a demanding task that depends on the integration of multiple complex subsystems. In this work, the optimal integrated design and dispatch of BTMR systems for retail buildings with electric vehicle fast charging stations is addressed. A framework is proposed, combining high-fidelity simulation (of buildings, electric vehicle fast charging stations, and BTMR), predictive control strategies with closed-loop implementation, and a derivative-free design method that explores parallelization and high-performance computing. Focus is given to the design layer, highlighting the effect of parallelization on the choice o... [more]

The integrated design and control (IDC) framework is becoming increasingly important for systematic design of flexible manufacturing and energy systems. Recent advances in computing and derivative-free optimization have enabled more tractable solution methods for complex IDC problems that involve, e.g., multi-period dynamics, the presence of high-variance and non-stationarity probabilistic uncertainties, and mixed-integer control/scheduling decisions. Parallelly, developments in techno-ecological synergy (TES) have allowed co-design of industrial and environmental systems that have been shown to lead to win-win solutions in terms of the economy, ecological, and societal benefits. In this work, we propose to combine the IDC and TES frameworks to more accurately capture the real-time interactions between process systems and the surrounding natural resources (e.g., forests, watersheds). Specifically, we take advantage of (multi-scale) model predictive control to close the loop on a realis... [more]

In the regeneration mode, precise control of the Diesel Oxidation Catalyst (DOC) outlet temperature is crucial for the complete combustion of carbon Particulate Matter (PM) in the subsequent Diesel Particulate Filter (DPF) and the effective conversion of Nitrogen Oxides (NOx) in the Selective Catalytic Reduction (SCR). The temperature elevation process of the DOC involves a series of intricate physicochemical reactions characterized by high nonlinearity, substantial time delays, and uncertainties. These factors render effective and stable control of the DOC outlet temperature challenging. To address these issues, this study proposes an approach based on Long Short-Term Memory (LSTM) neural networks for Model Predictive Control (MPC), emphasizing precise control of the Diesel Oxidation Catalyst’s outlet temperature during the regeneration mode. To tackle the system’s nonlinear characteristics, LSTM is employed to construct a predictive model for the outlet temperature of the Diesel Oxid... [more]

In order to address the problem of the real-time scheduling and control of batch chemical systems, this work proposes a model predictive control method based on Petri nets. First, a method is presented to construct a batch chemical system’s timed Petri net model. Second, a control structure is designed to augment the Petri net model to control the valves. This results in timed Petri nets that formally represent the process specifications of a batch chemical system. Third, a model predictive control method is developed to schedule and control timed Petri nets, where a proposed heuristic function is utilized to perform the optimization computation. The model parameters are dynamically adjusted using online data, and both scheduling and valve control instructions are calculated in real time. Finally, a series of experiments is carried out in a beer canning plant to verify the proposed method. According to the experimental results, the scheduling and control problem can be solved in real t... [more]

This work focuses on developing and applying Encrypted Lyapunov-based Model Predictive Control (LMPC) in a nonlinear chemical process network for Ethylbenzene production. The network, governed by a nonlinear dynamic model, comprises two continuously stirred tank reactors that are connected in series and is simulated using Aspen Plus Dynamics. For enhancing system cybersecurity, the Paillier cryptosystem is employed for encryption−decryption operations in the communication channels between the sensor−controller and controller−actuator, establishing a secure network infrastructure. Cryptosystems generally require integer inputs, necessitating a quantization parameter d, for quantization of real-valued signals. We utilize the quantization parameter to quantize process measurements and control inputs before encryption. Through closed-loop simulations under the encrypted LMPC scheme, where the LMPC uses a first-principles nonlinear dynamical model, we examine the effect of the quantization... [more]

Wave energy converters are attracting attention as an energy source that can respond to climate change. In order to increase the energy efficiency of the wave energy converters, efficient power converters are also required. The efficient converters require operation at a low switching frequency, which increases the weight and volume of the passive components. Therefore, in this paper, the performance of various types of topologies is compared to select the optimal power converter for wave energy converters. In order to cope with the unbalanced operation and unbalanced load of renewable energy, in this paper, the topology of the four-leg type is analyzed centrally. In addition, the analysis was performed by applying the model predictive control that can quickly respond to the rapid energy change of wave energy. In addition, model predictive control was applied to the four-leg converter analyzed in this paper because it is suitable for application to atypical topologies. For performance... [more]