The industrial production of microalgae is an important and sustainable process, but its actual competitiveness is closely related to its optimization. The biological nature of the process hinders this task, mainly due to the high nonlinearity of the process along with its changing nature, features that make its modeling, control and optimization remarkably challenging. This paper presents an economic optimization framework aiming to enhance the operation of such systems. An Economic Model Predictive Controller is proposed, centralizing the decision making and achieving the theoretical optimal operation. Different scenarios with changing climate conditions are presented, and a comparison with the typical, non-optimized industrial process operation is established. The obtained results demonstrate that the proposed strategy can provide measurable economic improvements while maintaining stable process operation, highlighting the potential of optimization-based approaches for industrial microalgae production.

The Dividing Wall Column (DWC) offers significant potential in saving both energy- and capital cost compared to conventional distillation sequences. However, there are some issues regarding flexibility and control that require attention in reducing the risks or uncertainties in achieving the potential benefits in practical operation. This calls for control and optimization methods that rely on the available measurement data and less on simulation models. The “Perturb and Observe” method is a simple algorithm that seems suitable for this on-line optimisation task. A series of experiments have been carried out at the Kaibel-column pilot at NTNU and some key results are presented. The method is combined with a conventional control structure at the regulatory layer.

Advanced regulatory control (ARC), also known as advanced PID architectures, is a simple and robust way of controlling processes with changing and possibly conflicting constraints, where it previously was believed - at least in academia - that model-based solutions, such as MPC, were the only effective solution. To illustrate this, ARC is applied in two case studies. The first is a gas-liquid separation process, in which selectors and split-parallel control are combined to achieve bidirectional inventory control in which the throughput manipulator moves automatically to the most optimal position. The second case study is on keeping acceptable air quality (CO2-level) and temperature in a room (in this case, a barn for cows). The CO2 and temperature constraints can be conflicting, leading to a hierarchical switching network of PID controllers. Note: this is an extended version (with simulations) of paper at IFAC World Congress, August 2026, Korea.

We consider the problem of operating a battery in a home connected to the grid to minimize electricity cost, which combines an energy charge and a tiered peak power charge based on the average of the N largest daily peak powers in each billing month. With perfect foresight of loads and prices, the minimum cost is the solution of a mixed-integer linear program (MILP), which provides a lower bound on the cost of any implementable policy. We propose a model predictive control (MPC) policy that uses simple forecasts of loads and prices and solves a small MILP at each time step. Numerical experiments on one year of data from a home in Trondheim, Norway, show that the MPC policy attains a cost within 1.7% of the prescient bound, and saves close to three times as much as the best rule-based policy we consider.

A fully electrified flash vapor circulation (FVC) distillation system for methanol/water separation is investigated, with a focus on identifying suitable self-optimizing controlled variables for minimizing electric power consumption. Starting from two published schemes (CS1 and CS2), four new control structures (CS3-CS6) are developed to explain and remove the strongly asymmetric closed-loop behavior observed in the original designs. Closed-loop dynamic simulations are performed under +/- 20% step disturbances in throughput and methanol composition. Control performance is assessed using product quality deviations, energy indicators, settling time, and integrated absolute error. The results show that controlling compressor discharge pressure in CS1 and CS2 is a poor choice because it over-constrains the series pressure loop of the FVC configuration, which drives excessive recycle, asymmetric responses, and COP deterioration. Eliminating this redundant pressure constraint in CS3 restores the available degrees of freedom and yields more symmetric behavior with lower compression power. Building on self-optimizing control, CS4 and CS5 select condenser outlet conditions as controlled variables to coordinate the trade-off between pressure lift and circulating vapor flow, giving similar energy performance. Finally, CS6 adds a distillate composition controller on top of CS4 to enforce the methanol specification and avoid both under and over purification, with only longer transients due to the slower composition loop. To generalize these findings, a three-step workflow is proposed as a transferable design procedure for heat pump assisted distillation systems.

Despite its widespread use in the process industry, a theoretical basis for ratio control has been lacking. It is sometimes described as a special case of feedforward control, but this interpretation is misleading. Feedforward control requires an explicit process model, whereas ratio control does not. Instead, ratio control relies on physical insight: For systems that satisfy the scaling assumption, maintaining constant ratios between extensive variables when there are throughput changes, results in constant intensive variables. Moreover, the ratio setpoint can be generated by an outer feedback loop, again without requiring a process model. The paper further discusses practical aspects of ratio control implementation, including more advanced schemes, such as dual ratio control for handling actuator saturation and cross-limiting control.

This paper introduces the Multi-Agentic Architecture Specialised for Control (MAASC). This framework transforms general-purpose AI models into domain-specific controllers by arranging multiple specialised agents in a coordinated architecture. In MAASC, each agent is a specialisation of a general-purpose model trained to perform a distinct regulatory function, embedding control-theoretic inductive biases to guide learning. This paper demonstrates the concept through an advanced regulatory PID control (ARC) informed MAASC implementation, where neural specialisation units internalise key elements, such as gain calculation, selector logic, and split-range actuation. Within this framework, the Neuro-Controller Simple Internal Model Control (NCSIMC) is encapsulated as a specialised instance of a general-purpose ML model trained exclusively on open-loop data, in line with classical regulatory control practices. This encapsulation enables the architecture to reproduce expert-designed behaviours without requiring closed-loop training. The proposed MAASC implementation is validated through an oil artificial lift system operated by an electric submersible pump. Results show that this multi-agentic specialisation achieves regulatory performance and input constraint handling using only open-loop data, highlighting MAASC as a scalable paradigm for embedding domain expertise into AI-based control.

Recent literature shows that large language models (LLMs) are useful for general-purpose tasks yet perform poorly on specific domain ones. One reason is the difficulty of supplying narrow context to a general-purpose model and of bounding the task it is asked to perform. It is possible to hypothesise that a multi-agent reformulation under process-control principles offers a route to address those points, since control theory provides a discipline of decomposing a system into elements of contained scope, each defending one controlled variable, with conflicts resolved by structural priority: MIN/MAX selector networks for CV-CV switching and split-range (split-parallel) logic for MV-MV switching. The present work proposes such a reformulation, derived from Advanced Regulatory Control (ARC) theory. Each feedback loop in the ARC chain is mapped to one specialised LLM operator agent carrying the loop's control-theoretic context (controlled variable, setpoint, chain priority, selector kind). The chain's interaction logic (MIN/MAX selectors, override paths) is encapsulated as a single orchestrator agent. Two orchestrator variants are tested: a deterministic rule chain, and a Claude-based LLM orchestrator at a slower tier. The control principles limit each agent's task and inform how its limitations are handled. The multi-agent system inherits the safety property of the ARC chain: every constraint conflict is resolved deterministically by the orchestrator, regardless of the LLM output. Evaluated on a dairy-barn ventilation case over a 4-day mixed-season scenario, Qwen 2.5 7B Instruct operator agents running offline on a 24 GB consumer GPU at a 5-minute cadence produce auditable trajectories, each paired with an operator-voice rationale that supports a control campaign logbook.

In this work, we present a detailed model of a Haber-Bosch synthesis loop that includes catalytic beds, heat-exchangers, compressors, steam turbines, and flash separators. The model provides a function for the total electrical power consumption of the synthesis loop, which accounts for compression, refrigeration power, and power generation via steam turbines. This total power represents the cost function for optimising the Haber-Bosch synthesis loop across its full operating envelope, ranging from 10% to 120% load in terms of the hydrogen feed flow. The optimisation considers six degrees of freedom: the inlet temperatures of three reactor beds, the H2/N2-ratio in the reactor feed, separator temperature, and loop pressure. Results reveal that the loop pressure is the most important parameter, with an optimal value varying from over 220 bar at maximum load to around 110 bar at minimum load. We present a control architecture for the Haber-Bosch synthesis loop that enables load-flexible operation. We propose maintaining the reactor bed inlet temperatures and the reactor H2/N2-ratio constant across the operating envelope, as this results in a minimal increase in synthesis loop power (self-optimising variables). Maintaining constant operating parameters mitigates frequent changes in operating conditions during load-flexible operation, thereby simplifying control implementation and contributing to the longevity of critical process units. Using this strategy, we demonstrate stable and flexible operation of the Haber-Bosch synthesis loop down to 10% load, with rapid load-change rates of up to 3% per minute.

Dividing wall columns are state of the art distillation arrangements performing three separation tasks within one unit. Compared to using two conventional columns in series this saves both capital costs and energy but on the other hand it brings a higher risk of malfunction. This simulation study analyses what can go wrong during the operation of dividing wall columns. The emphasis is on the operation of the prefractionator section, that is, on the choice on the liquid and vapor splits, which is crucial for the overall performance. The resulting two-way flows between the prefractionator and main column gives a broader feasible operating range than in a conventional column arrangement. This can lead to peculiar behavior, including circulation of components around the dividing wall. This paper identifies 15 non-optimal operating regions for the prefractionator with specific internal flow patterns, characteristic temperature and composition profiles for the separation of a fairly ideal mixture of benzene, toluene and p-xylene. From these results it is possible to identify and hopefully rectify wrong choices for the liquid and vapor splits in a dividing wall column.

Standard dividing wall columns (DWC) are state-of-the-art integrated fully thermally coupled (FTC) (or Petlyuk) distillation arrangements performing several separation tasks within one unit and with a lower energy consumption and capital costs than conventional column sequences. This may require careful design and control of the internal flow rates to achieve the potential energy savings, which typically are about 30%. In particular adjusting the internal vapor split is regarded to be challenging. The Liquid-only transfer (LOT) arrangements offer alternative internal flow rate adjustments that may mitigate this challenge. In addition, its use in retrofit may enable practical cost-effective solutions. The key result in this paper is to provide analytical minimum energy expressions for the LOT arrangement which are shown to be identical to the ones for the standard DWC. Furthermore, the optimal operating region and flexibility for the internal sub-columns in the arrangements are explored and are also found to be equivalent and the available adjustment margines for the LOT draw rates and other operational variables are clarified. The results give valuable insight in the characteristics of optimal operation and can also be used to provide good initialisation values for rigorous simulations.

We describe a control structure that is commonly used in the process industry, e.g. chemical and petrochemical industries, for switching between manipulated variables (MV5), 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 (u(i)) and different setpoints (r(i)). 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. Copyright (c) 2025 The Authors.

This research aims to develop a simple regulatory controller to control a Core Annular Flow (CAF) in the oil and gas industry, focusing on transporting heavy oils. CAF is an economical method to transport viscous crude oil where less viscous liquid, typically water, is used to lubricate the pipe walls, creating an annular flow regime. However, managing the stability of CAF is challenging due to geometric variations, changes in pipeline flow direction, and emulsion formation. We used computational fluid dynamics (CFD) simulations to represent the CAF system and subsequently designed a simple control structure for the process. This process involved conducting both open-loop and closed-loop tests. The findings from the study indicate that the I controller significantly improves the system's response to disturbances in oil velocity by adeptly adjusting water velocity. This adjustment is crucial for maintaining the desired oil fraction and sustaining an annular flow pattern. An important observation was the effectiveness of the proportional gain in tracking the setpoint within annular flow regimes and the enhanced system stability achieved by increasing the integral action. The study concludes that the PI controller stabilizes operations in previously challenging conditions and expands the system's operational range.

This paper investigates the application of two distinct control structures, conventional single-layer control and cascade control, in a Core Annular Flow (CAF) system simulated through Computational Fluid Dynamics (CFD). Both control strategies were tested and carried out open-loop tests to tune the controllers following the SIMC rules. Results demonstrate that both structures, one I controller for the oil fraction and one cascade controller PI -I for the velocity ratio and the oil fraction, successfully controlled the system, each exhibiting unique behaviors and performance characteristics. The analysis highlights the strengths and limitations of each approach, where the single-layer structure with an I controller was faster to reach the setpoint and was efficient to reject disturbances. Copyright (c) 2025 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)

Ratio control and bidirectional inventory control are simple and powerful data-based strategies for feedforward control and coordination, respectively. By "data-based" it is meant that no explicit process models is needed, which simplifies implementation. The paper demonstrates the power of these simple architectures when applied to distillation columns. Copyright (c) 2025 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)

This work presents a plantwide model of a Haber-Bosch ammonia synthesis loop (HB-loop) in a PtA plant, consisting of heat exchangers, compressors, steam turbines, flash separators and catalytic reactor beds. The total electrical power utility of the HB-loop is a combination of compressor power, refrigeration power, and steam turbine power. We optimise the HB-loop operating parameters, subject to constraints for maximum reactor temperatures, compressor choke and stall, minimum steam temperature, and maximum loop pressure. The loop features six degrees of freedom (DOFs) for the optimisation: three reactor temperatures, reactor N2/H2-ratio, separator temperature, and loop pressure. The optimisation minimises the total loop power utility for a given hydrogen make-up feed flow, with the PtA load varied by ranging the hydrogen make-up feed flow from 10 % to 120 % of the nominal. Across this load range, different constraints become active, with the compressor surge limit being particularly critical at low loads, significantly increasing HB-loop power consumption. To address this, we investigate configurations with two, three, and four compressor trains operating in parallel. Reductions in total power of 55%, 74%, and 84% are achieved at reduced plant loads, with two, three, and four parallel trains, respectively. In terms of total compressor capital and operating cost, we demonstrated savings of 8.06%, 8.29%, and 7.11% in total cost after ten years of operation with two, three, and four parallel compressor trains compared to a single train configuration.

Optimizing subsea oil production systems utilizing recirculated gas lift and limited produced gas treatment capacity presents challenges. Real-time optimization (RTO) is a used method for optimizing such systems, but it is restricted by the lack of reliable sensors and the high cost of developing and updating models. As a result, the RTO is typically executed infrequently, and the optimal set points are not updated in real time, leading to suboptimal plant performance over extended periods. This study implements self-optimizing control (SOC) techniques as an alternative solution that can handle frequent disturbances and drive the plant towards near-optimal performance without requiring frequent model updates or solver use. It compares different SOC structures in recirculated gas-lifted oil production optimization, their advantages, and disadvantages. The study concludes that SOC structures are an effective and suitable alternative to RTO, particularly in large and complex systems with limited measurement capabilities, given sufficient process system knowledge is considered for SOC design. This conclusion reinforces previous research, but with a more realistic case study.

Model predictive control (MPC) allows for dealing with multivariable interactions, known future changes and dynamic satisfaction of constraints. Standard MPC has a cost function that aims at keeping selected controlled variables at constant setpoints. This work considers systems where the steady-state optimal active constraints change during operation. This situation is not handled optimally by standard MPC which uses fixed controlled variables for the unconstrained degrees of freedom. We propose a simple framework that detects the constraint changes and updates the controlled variables accordingly. The unconstrained controlled variables are chosen to be the reduced cost gradients, which when controlled to zero minimizes the steady-state economic cost. In this paper, the nullspace method for self-optimizing control is used to estimate the cost gradient using a static combination of the measurements. This estimated gradient is also used for detecting the current set of active constraints, which in particular allows for giving up constraints that were previously active. The proposed framework, here referred to as "region-based MPC'', is shown to be optimal for linear constrained systems with a quadratic economic cost function, and it allows for good economic performance in nonlinear systems in a neighborhood of the considered design points.

This work presents a simple and efficient way of estimating the steady-state cost gradient J(u) based on available uncertain measurements y. The main motivation is to control J(u) to zero in order to minimize the economic cost J. For this purpose, it is shown that the optimal cost gradient estimate for unconstrained operation is simply (J) over cap (u) = H(y(m) - y*) where H is a constant matrix, y(m) is the vector of measurements and y* is their nominally unconstrained optimal value. The derivation of the optimal H-matrix is based on existing methods for self-optimizing control and therefore the result is exact for a convex quadratic economic cost J with linear constraints and measurements. The optimality holds locally in other cases. For the constrained case, the unconstrained gradient estimate (J) over cap (u) should be multiplied by the nullspace of the active constraints and the resulting ''reduced gradient'' controlled to zero.

This article considers the problem of steady-state real-time optimization (RTO) of interconnected systems with a common constraint that couples several units, for example, a shared resource. Such problems are often studied under the context of distributed optimization, where decisions are made locally in each subsystem and are coordinated to optimize the overall performance. Here, we use a distributed feedback-optimizing control framework, where the local systems and the coordinator problems are converted into feedback control problems. This is a powerful scheme that allows us to design feedback control loops, estimate parameters locally, and provide a local fast response, allowing different closed-loop time constants for each local subsystem. This article provides a comparative study of different distributed feedback-optimizing control architectures using two case studies. The first case study considers the problem of demand response (DR) in a residential energy hub powered by a common renewable energy source and compares the different feedback-optimizing control approaches using simulations. The second case study experimentally validates and compares the different approaches using a laboratory-scale experimental rig that emulates a subsea oil production network, where the common resource is the gas lift that must be optimally allocated among the wells.