Keywords: Process control
Abstract: When presenting a talk on the control of different high-speed mechatronic systems at UCSB in 2008, a visibly upset graduate student asked the question: “So, you’re telling us that the state-space methods we’ve been learning all these years are useless?!?” I had not mentioned state-space methods once in the hourlong discussion of controlling these lightly damped systems. Their point was reinforced a few years later when a colleague working on laser interferometers for wafer scanners came into my office and said, “I want to build a Kalman filter,” to which my instantaneous reply was, “Isn’t your life hard enough already?” Being finally dragged into needing to use state-space for the first time since graduate school, I realized that the chances of using standard methods on such a mechatronic system with more than 20 flexible modes was minimal. The poor condition number and lack of physical intuition in the typical state-space formulation required rethinking the problem, leading to the biquad-state-space and bilinear state-space formulations. Besides their numerical advantages, these also have tight connections between the continuous and discrete-time states (taken at the outputs of the biquads), preserving physical intuition. This latter property required a reexamination of the dogma of discretization in control systems. At the same time, the use of state-space feedback control remains limited in industrial environments. While one can point to large scale problems with extensive design teams and the use of Model Predictive Control in the process worlds, the broad adaptation of modern methods is lacking. We suggest that several factors are at play here, including the lack of measurement infrastructure from which to create an accurate dynamic model of the system. This is compounded by the complete inscrutability of the discrete-time models for all but the simplest of systems, skewering physical intuition and therefore debugging. In this context, it is no small wonder that PIDs still rule in the process industry while PIDs plus filters are the standard in most mechatronic industries. We will discuss if the methods above give it a chance to make state-space methods accessible and practical to practicing engineers.

Keywords: Artificial intelligence and machine learning, Modeling and identification, Dynamic modelling and simulation for control and operation
Abstract: Neural Ordinary Differential Equations (Neural ODEs) represent continuous-time dynamics with neural networks, offering advancements for modeling and control tasks. However, training Neural ODEs requires solving differential equations at each epoch, leading to high computational costs. This work investigates simultaneous optimization methods as a faster training alternative. In particular, we employ a collocation-based, fully discretized formulation and use IPOPT—a solver for large-scale nonlinear optimization—to simultaneously optimize collocation coefficients and neural network parameters. Using the Van der Pol Oscillator as a case study, we demonstrate faster convergence compared to traditional training methods. Furthermore, we introduce a decomposition framework utilizing Alternating Direction Method of Multipliers (ADMM) to effectively coordinate sub-models among data batches. Our results show significant potential for (collocation-based) simultaneous Neural ODE training pipelines.

Keywords: Modeling and identification, Data mining tools
Abstract: In this work, we propose a novel martingale-based distributionally robust regression (MDRR) approach to system identification of uncertain dynamical systems. Under data uncertainty, the ridge regression offers a useful remedy, which can be interpreted as a min-max problem through the lens of distributionally robust optimization. However, ignoring the specific structural properties, RR amounts to robustifying against unrealistic perturbations with evident dynamics and thus leads to over-conservatism. By considering the Hankel structure of uncertainty and incorporating martingale constraints into the Wasserstein ambiguity set, the realistic data perturbation pattern can be effectively captured, and this helps to considerably alleviate the conservatism. The induced min-max problem is solved by a subgradient-based algorithm. Empirical results on both simulation and real-world datasets validate the effectiveness of MDRR, showcasing its out-performance over generic regression models and ease of parameter calibration.

Keywords: Modeling and identification, Artificial intelligence and machine learning
Abstract: For most process systems, knowledge of the model structure is incomplete. This missing physics must then be learned from experimental data. Recently, a combination of universal differential equations and symbolic regression has become a popular tool to discover these missing physics. Universal differential equations employ neural networks to represent missing parts of the model structure, and symbolic regression aims to make these neural networks interpretable. These machine learning techniques require high quality data to successfully recover the true model structure. To gather such informative data, a sequential experimental design technique is developed which is based on optimally discriminating between the plausible model structures suggested by symbolic regression. This technique is then applied to discovering the missing physics of a bioreactor.

Keywords: Modeling and identification, Dynamic modelling and simulation for control and operation
Abstract: Model order selection plays a crucial role in system identification. The existing model order selection methods rely on finding the balance between fitting error and model complexity. However, when the data contains large noise, the model order obtained by the existing methods may not be reliable. To resolve this issue, we present a new model order selection method based on trend error analysis. By making use of a specific property of trend extraction --- the insensitivity against noise, our method improves the accuracy of model order selection. Numerical simulation results show the effectiveness of the proposed method and outperformance over known heuristics under different noise levels.

Keywords: Modeling and identification, Dynamic modelling and simulation for control and operation, Data mining tools
Abstract: Design of experiments (DoE) helps us to obtain an accurate model using system identification. However, most DoE methods rely on asymptotic theory and assume availability of infinite data samples. To overcome this problem, Oshima et al. (2024) proposed a DoE method that evaluates the data quality using the volume of the nonasymptotic confidence region (CR) calculated using sign-perturbed sums (SPS) proposed by Csaji and Weyer (2015). This paper modifies the DoE objective function from Oshima et al. (2024) to derive a nonasymptotic counterpart of the E-optimal DoE, which minimizes the length of the longest axis of the asymptotic confidence ellipsoid. The proposed data-quality index is defined by the maximum distance from the center point to the points on the boundaries of the nonasymptotic CR. Moreover, a necessary condition for the points in the parameter space to be on the boundaries of the nonasymptotic CR obtained using the SPS method is theoretically derived. Based on this condition, an algorithm to calculate the maximum distance is proposed. The proposed nonasymptotic E-optimal DoE was validated in a numerical case study, where a 2-input, 3-output ARX system was targeted. As a result, it was shown that the nonasymptotic E-optimal DoE provides a more accurate model compared with the asymptotic E-optimal DoE.

Keywords: Sensors and soft sensors, Dynamic modelling and simulation for control and operation, Modeling and identification
Abstract: We address the problem of estimating the instantaneous reaction rates of the mass conversion taking place in an isothermal and isobaric continuous stirred tank reactor, CSTR, subject to a constant dilution rate. In addition to the estimation of the reaction rates, we also obtain an estimate of the influxes to the reactor. Our methodology requires the knowledge of the stoichiometric matrix and all the concentrations online, as well as the dilution rate. The observer is based on a generalised version of the Super-Twisting Algorithm, STA, which allows us to estimate in finite-time the unmeasured variables. The applicability of the observer is shown by a numerical simulation.

Keywords: Modeling and identification, Dynamic modelling and simulation for control and operation
Abstract: Applying model-based design of experiments to compute maximally-informative campaigns with multiple parallel runs is challenging. Herein, we develop a systematic framework for recasting an experiment design problem for model parameter precision as one of discrimination between multiple rival models with different uncertain parameter realizations. We use an algebraic upper bound on the Bayes Risk as information criterion and apply a search procedure that iterates between an effort-based optimization step followed by a gradient-based refinement step. Through the case study of a fed-batch reactor, we show that a Bayes Risk discrimination strategy can provide highly-informative experimental campaigns to improve parameter precision, while being computationally advantageous compared to conventional FIM-based design strategies and capable of handling structurally unidentifiable problems.

Keywords: Modeling and identification
Abstract: In this work, we propose a Symmetric Kullback Leibler divergence (SKLD)-based approach for optimal Design of Experiments (DOE) along with estimation of unspecified values in the design of experiments data matrix. Using SKLD as optimality criteria as opposed to various existing alphabetic optimality criteria, facilitates the incorporation of end-user desired performance of estimates. For the case when experimental noise is Gaussian and uncorrelated, the proposed approach results in a Mixed Integer Non-Linear Programming (MINLP) problem. This problem is NP-hard to solve. Hence, a novel heuristic solution strategy is also proposed which solves the proposed problem iteratively and sequentially. In particular, the MINLP problem is split into two sub-problems: (i) Non-Linear Programming (NLP) problem: to estimate optimal unspecified values, and (ii) Non-Linear Integer Programming (IP) problem: to obtain optimal DOE. These two subproblems are solved sequentially and iteratively until convergence is reached. The proposed solution strategy guarantees the decreasing behaviour of SKLD value. The efficacy of the proposed solution strategy is tested on an illustrative example and a Material synthesis problem, and performance is compared with Fedorov exchange algorithm, Forward Greedy search algorithm, and some of the popular MINLP solvers available in GAMS environment. Results demonstrate that the proposed solution approach outperforms most other methods.

Keywords: Process optimization, Model predictive control, Bio-applications
Abstract: This paper presents a novel workflow for the design of an adaptive model-based controller to optimize the time and energy consumption for plant cultivation combined with on-line analysis and estimation of model parameters based on scarce data. A non-linear model of lettuce growth is subject to sensitivity analysis of selected parameters to determine the effective sequence and time horizon of infrequent data sampling of plant physiological properties. In the designed measurement campaign, the parameter estimation is performed to update the model parameter space, improving the accuracy of plant growth predictions and control efficiency. The implementation of run-time-updated model in a predictive control framework leads to minimization of the energy-related cost and the full-growth time of the plant. Simulations show promising results in minimizing the time required to the desired plant yield.

Keywords: Process optimization, Process control, Industrial biotechnology
Abstract: We propose an Economic Model Predictive Control (EMPC) framework that is robust to model structure error. The approach integrates parameter estimation with gradient correction to improve controller performance. At each sampling time, the algorithm performs parameter estimation over past samples, followed by a gradient correction step that updates model parameters to match the gradients of the model and plant using transient measurements. To match the gradients while maintaining model accuracy, a correction term is added which ensures an upper bound on the model error. The approach is validated on a continuous penicillin production process subject to model-plant mismatch. Results demonstrate that the proposed EMPC with gradient correction drives the process closer to the true plant optimum values and achieves better convergence to optimal operating conditions than a similar EMPC without gradient correction.

Keywords: Microbial technology, Systems biology, synthetic biology, metabolic flux modeling, Industrial biotechnology
Abstract: Resource allocation models have been proven to be a highly effective tool to study the growth of microorganisms. Here, we use one such growth model describing the metabolism of a given bacterium in an artificial (e.g. biotechnological) environment. This model involves two controls, one quantifying the protein precursors allocation (i.e. the cellular internal control) and the other representing the nutrient concentration in the culture. We seek to determine the controls that maximize the resulting growth rate of cells living in this controlled environment. We first carry out a theoretical analysis of this optimal control problem (OCP) by means of the Pontryagin’s Maximum Principle (PMP). We show the bang-bang structure of the optimal control resource allocation control. We find the environmental control to follow a bang-singular-bang structure, and give an expression for its singular arc depending on the state and costate given by the PMP. We solve the OCP in fixed final time using a direct optimization method, implemented on the BOCOP software. This resolution reveals an intrinsic period of the optimal control, corresponding to the solution of the periodic OCP in free final time. Moreover, we find a singular arc of the environment coinciding with the analytical expression given before. Our study highlights the optimality of periodic, non-constant environments in maximizing bacterial growth.

Keywords: Sensors and soft sensors, Process control, Process and performance monitoring
Abstract: In this work the optimal control problem of maximizing the cell production rate in chemostat reactors by manipulating the dilution rate under possibly time–varying uncertainties in the growth rate is addressed. Considering that the cell mass distribution is not an available measurement during cultivation, three estimation problems are formulated and addressed. Based on the respective observability property of each subsystem, extended Kalman–Filters are designed for the estimation of the gradient with respect to the input, uncertainties in the growth rate and the cell mass distribution density function based on biomass measurements. Finally, the convergence of the proposed observers and optimal control strategy is tested in simulations.

Keywords: Modeling and identification, Biopharmaceutical processes, Dynamic modelling and simulation for control and operation
Abstract: Accurate dynamic models of virus infection processes are highly relevant for the optimization of vaccine production processes. However, fitting their parameters onto or even designing novel dynamic models from an existing set of biological measurement data is challenging as it is common that entire quantities are missing due to sub-optimal measurement setups. This work targets identifying virus dynamics models based on incomplete measurement data and domain knowledge. To this end, we unite sparse identification of non-linear dynamics (SINDy) with a commonly used approach to identify non-linear dynamical systems from incomplete measurements, namely an extended Kalman filter (EKF). This yields a hybrid model that is able to identify governing equations that describe the dynamic non-linear processes. The capabilities of this model are demonstrated on a set of incomplete artificial measurement data of an existing infection dynamics model.

Keywords: Biopharmaceutical processes, Fault detection, diagnosis, supervision, and safety, Artificial intelligence and machine learning
Abstract: The development of new monoclonal antibodies (mAb) is a long-lasting and expensive procedure. Digital models can be adopted to reduce research costs and accelerate timelines. During mAb development, Ambr®15 is a small-scale, multi-parallel bioreactor platform used to assess performance of different cell lines and find the most productive and stable ones. Many factors affect the culture performance variability and often determine anomalies in the experimental batches. Those anomalies are neither easy, nor fast to be identified even by expert scientists. In this work, a tool for the automatic identification of cell culture anomalies and outlier experimental batches in Ambr®15 scale is presented. The software, calibrated on historical data of the experimental batches, effectively identifies through assumption-free modeling anomalies and diagnoses the root cause of cell lines non-standard behavior, representing also the first application of these methodologies for the development of mAbs. Accordingly, it represents a tool of invaluable importance to speed-up analysis of experimental data and reduce the effort of operators, thus reducing development timeline and costs.

Keywords: Process control, Plantwide control
Abstract: We describe a control structure that is commonly used in the process industry, e.g. chemical and petrochemical industries, for switching between manipulated variables (MVs), but which has received little attention in academia. It has one controller for each MV, typically PID-controllers, that control the same process value (y) but with different manipulated variables (u1,u2) and different setpoints (r1,r2). The scheme is sometimes called “separate controllers with different setpoints”, but we suggest that a better name is “split-parallel control” (SPC), since the two controllers are placed in parallel in the block diagram, but the active control action is split between the two controllers, similar to in split-range control (SRC). SPC is an alternative to SRC, but it does have some advantages compared to SRC, including ease of implementation and the possibility to have different PID tunings for each MV. We also state some yet unresolved questions regarding the SPC structure, especially in regard to stability. Split-parallel control (SPC) uses setpoint separation to perform the switching, which is an advantage in some cases, for example, for bidirectional inventory control.

Keywords: Process control
Abstract: Late lumping controller design for distributed parameter systems presents a significant challenge. This paper extends the generic model control technique to diffusion-reaction systems governed by semilinear parabolic equations, focusing on controlling an output defined as a spatially weighted average of the system state. Both distributed and boundary control approaches are thoroughly investigated. While the design for distributed control is straightforward, boundary control necessitates the use of the extended operator concept. This concept allows to convert the boundary control problem into a pointwise one, a particular case of distributed control, which simplifies the controller design. The effectiveness of the proposed controllers in tracking and disturbance rejection is validated through numerical simulations using a case of a heated rod.

Keywords: Process control, Plantwide control, Dynamic modelling and simulation for control and operation
Abstract: This work develops a novel non-linear Proportional-Integral (PI) Averaging Level Control (ALC) algorithm designed to optimally utilize the available surge capacity in surge tanks, ensuring that the high and low alarm limits are not breached for the worst-case disturbance scenario. Building upon insights from previous studies, the proposed algorithm incorporates a tunable parameter for an acceptable flow overshoot. The algorithm's performance is compared with existing popular ALC algorithms for a single tank and a realistic methanol dehydration process. The proposed algorithm significantly outperforms these alternatives in mitigating manipulated flow variability for small to moderate disturbances while delivering comparable performance for large disturbances. The significant flow variability mitigation results in up to 8.25% reduction in energy consumption compared to conventional P-only ALC for the methanol dehydration process due to lower back-offs from the active constraint limits. The quantitative results highlight the significant potential of the proposed ALC algorithm towards efficient and sustainable process operation.

Keywords: Process control, Plantwide control
Abstract: Compact designs of combined cycle power plants based on gas turbines and steam bottoming cycle (CCGTs) are deemed as a promising technology for increasing energy efficiency and reducing greenhouse gas emissions of offshore oil and gas production facilities. The control of such systems can be challenging due to the need for operational flexibility regarding production of power and heat to satisfy the corresponding demands, and it differs from traditional onshore designs in dynamic characteristics and requirements. In this work, we propose and evaluate the performance of control structures for compact steam bottoming cycles with combined heat and power production, focusing on the solutions for satisfying heat demands and their effect on power production. The proposed control structures are based on the different prioritization of operational objectives and constraints, using simple control elements to switch between operating regions. The control structures were evaluated under different disturbances on the gas turbine loads and on the heat demand. It is shown that controlling the intermediate pressure in the steam turbine, which serves as source of steam for heat production, is necessary for achieving the heat demand objectives. We also show that sudden disturbances on the heat demand heavily impact the power production, and it is desirable that such disturbances happen on a ramp-like manner. Overall, we highlight how near-optimal operation with satisfaction of constraints can be achieved with the use of well-designed, simple control structures.

Keywords: Biopharmaceutical processes, Batch process modeling and control, Artificial intelligence and machine learning
Abstract: We introduce a novel two-level method to address systematic yield variability in biopharmaceutical batch processes. At the first level (inter-step), we utilize process-wide connectivity data to identify the specific process step where performance variability occurs. A sequential and orthogonalized partial least squares (SO-PLS) model is then developed to trace the origin of these variabilities, linking data blocks across the flowsheet and filtering correlated information. Once a critical step is identified, the second level (intra-step) employs unit-specific PLS models to capture the internal dynamics of that step, using entire batch trajectories for modeling. In collaboration with process experts, this level isolates variable trajectories that drive the systematic variability. Applied to a commercial batch process producing an active pharmaceutical ingredient (API), this method reveals that downstream yield is impacted by variability during cell culture production. Furthermore, a detailed analysis of bioreactor data identifies key manipulated variable trajectories, specifically the dosage of glucose and NH3, impacting cell culture production. Validation of process improvement hypotheses is conducted in collaboration with process experts, enhancing transparency and yielding valuable insights.

Keywords: Process optimization, Interaction between design and control, Scheduling, coordination and optimization
Abstract: This paper presents a study on the determination of the optimal steady states of an industrial electric flash clay calcination plant. Such a process is relevant in the context of sustainable cement production. By deploying electrical heating, CO2-free calcined clay can be produced, which can substitute some of the traditional limestone-based cement clinker. By using a nonlinear model of the plant, the optimization problem is formulated to minimize energy consumption, while maximizing the production rate of calcined clay and ensuring a specified quality requirement. The optimal manipulated variables, for each clay feed or power set-point, are computed as solution of the problem, and presented in the results. The numerical solution of the problem is obtained using a hybrid approach, that combines global optimization with gradient-based methods. Steady state optimization enables the development of process control and real-time optimization.

Keywords: Dynamic modelling and simulation for control and operation, Renewable energy system, Interaction between design and control
Abstract: The electrification of process heating presents an opportunity to decarbonize distillation column operations and enhance operational strategies to save energy. Conventional column configurations are adiabatic and have low thermodynamic efficiencies due to heat degradation. Further, the startup process for conventional columns is slow and has significant energy requirements for re-establishing steady state hydraulic, composition, and flow profiles. In this paper, a speculative fully diabatic distillation column configuration with modular electric stage heating is introduced. A dynamic simulation model is built from first principles using a compartmentalization approach for equilibrium stages, as well as a hierarchical modeling framework for column control and auxiliary heating. We demonstrate that this structure has exceptionally small startup times compared to conventional columns through a simulation case study considering the binary separation of an equimolar mixture of acetic acid/propanol, as well as illustrate its significant energy savings over the startup period, which can translate into grid-integrated operating strategies for electrified distillation systems.

Keywords: Artificial intelligence and machine learning, Data mining tools
Abstract: The development of new catalysts is typically carried out by performing extended experimental campaigns of dynamic experiments through high-throughput miniature reactors in which the sequence of the experiment is often managed based on the experience of the scientists and the developers. In these systems, the sequential nature of experiments introduces complex effects that may propagate to successive experimental batches at different conditions which are difficult to model and interpret. Big amounts of data are typically collected from experimental campaigns, which provide the opportunity to develop data-driven models that extract valuable information on the system. In this study, we propose a new machine-learning methodology that allows the in-depth understanding of the experiment dynamics, associated with both the experiment batch itself and the catalyst history (namely, the sequence of multiple experiments performed in different conditions of temperature, composition, etc.). In particular, multiway multivariate latent variables techniques are used to capture the dynamic within the single experimental batch and the high auto-and cross-correlation between variables, two-dimensional dynamic modelling is used to deal with the dynamics of the catalyst history and orthogonalization is used to remove information redundancy. The methodology is validated in the case study of the development of catalyst for ammonia production. We show that the model captures the correlation between variables which describe the reaction kinetics and thermodynamics within each experimental batch, as well as the influence of catalyst history, especially in terms of feed composition. Furthermore, the model captures the contributions of both the dynamics of the single experimental batches and the catalyst history, ensuring very good predictive performance on the ammonia productivity.

Keywords: Modeling and identification, Batch process modeling and control
Abstract: We present a reaction kinetics model for biodiesel production via transesterification, which is calibrated using concentration measurements from inline Raman spectroscopy. The novel application of Raman spectroscopy in biodiesel production provides real-time monitoring of key reaction species, e.g. fatty acid methyl esters, triglycerides, methanol, and glycerol. We employ an automated semi-batch reactor to perform reaction experiments. A robust offline calibration process of the Raman device allows achieving high accuracy for concentration predictions (R^2 = 0.99). Moreover, using sodium methylate as the catalyst, we address a gap in the literature where kinetic parameter values for transesterification with this catalyst are unavailable. For accurate parameter estimation, we use genetic algorithms. A global sensitivity-based estimability analysis confirms the sufficiency of the experimental data. We determine confidence intervals through Hessian matrix estimation. Our model predictions are validated against experimental data at 60~°C, demonstrating excellent agreement. These results highlight the effectiveness of integrating Raman spectroscopy for modeling reaction kinetics, hence offering promising tools and models for monitoring, optimization, and control of biodiesel production processes.

Keywords: Scheduling, coordination and optimization
Abstract: Heavy haul transportation characterized by long trains enjoys the benefits of cost-efficiency but suffers from high cost in combination process. Virtual coupling (VC) is a state-of-art train control technology that can help resolving the dilemma. In this paper, we proposed an integer programming model that schedules station operation plans, timetables and train combination schemes of heavy haul trains (HHTs) with VC at the same time. A genetic algorithm with a deep first search decode method is proposed to efficiently solve this problem on a large scale. The simulation results show that our method can effectively improve the efficiency of HHTs in real-world scenarios.