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.

This “white paper” is a concise perspective of the potential of machine learning in the process systems engineering (PSE) domain, based on a session during FIPSE 5, held in Crete, Greece, June 27–29, 2022. The session included two invited talks and three short contributed presentations followed by extensive discussions. This paper does not intend to provide a comprehensive review on the subject or a detailed exposition of the discussions; instead its aim is to distill the main points of the discussions and talks, and in doing so, highlight open problems and directions for future research. The general conclusion from the session was that machine learning can have a transformational impact on the PSE domain enabling new discoveries and innovations, but research is needed to develop domain-specific techniques for problems in molecular/material design, data analytics, optimization, and control.

Real-time optimization can play a key role for improving the performance of industrial processes, but it becomes challenging in cases where the process characteristics are uncertain, particularly when the uncertain characteristics impact safety-related constraints. In this study, we present an adaptive and explorative real-time optimization framework that can effectively learn the characteristics of an industrial refrigeration plant through externally driven changes in cooling load targets and through self-exploration. We utilize Gaussian processes (GP) to facilitate learning unknown compressor characteristics of the plant and we leverage the uncertainty quantification of the GP to drive exploration using a weighted sum term in the objective function for real-time optimization. Furthermore, the uncertainty information is used to probabilistically enforce the maximum total power consumption constraint for the compressors with high confidence at all times. Our simulated experiments demonstrate that the proposed approach safely enhances the energy efficiency of the refrigeration process, closely approximating the performance of a best-case solution that has complete information about the plant performance characteristics. We also demonstrate the impact of varying the exploration term in the solution and how the uncertainty of plant behaviour is reduced even in the absence of cooling load target changes.

Online Feedback Optimization is a method used to steer the operation of a process plant to its optimal operating point without explicitly solving a nonlinear constrained optimization problem. This is achieved by leveraging a linear plant model and feedback from measurements. However the presence of plant-model mismatch leads to suboptimal results when using this approach. Learning the plant-model mismatch enables Online Feedback Optimization to overcome this shortcoming. In this work we present a novel application of Online Feedback Optimization with online model adaptation using Gaussian process regression. We demonstrate our approach with a realistic load sharing problem in a compressor station with parametric and structural plant-model mismatch. We assume imperfect knowledge of the compressor maps and design an Online Feedback Optimization controller that minimizes the compressor station power consumption. In the evaluated scenario, imperfect knowledge of the plant leads to a 5% increase in power consumption compared to the case with perfect knowledge. We demonstrate that Online Feedback Optimization with model adaptation reduces this increase to only 0.8%, closely approximating the case of perfect knowledge of the plant, regardless of the type of mismatch.

Process and energy industries have been recognised as adopters of high levels of automation compared to other sectors. Nonetheless, human cognitive input still plays a critical role in the operation of process plants and replication of these cognitive capabilities remains a key challenge for advancing automation levels. In this paper, we provide an analysis of process and energy industries based on a scenario of reduced availability of skilled labour and increased demands for safety, sustainability, and resilience. We consider the different mechanical, sensing, situational awareness, and decision-making tasks involved in the operation of plants and map them to possible realisations of unmanned and autonomous systems. We discuss the implications of current technology capabilities and future technology development perspectives, the factors influencing the complexity of operation in process plants, and the importance of human-machine collaboration. As part of autonomous system capabilities, we consider adaptation as a key capability and we make a connection to adaptation of model-based solutions. We argue that reaching higher and wider levels of autonomy requires a rethink of the design processes for both the physical plants as well as the way automation, control, and safety solutions are conceptualised.

Devising optimal operating strategies for a compressor station relies on the knowledge of compressor characteristics. As the compressor characteristics change with time and use, it is necessary to provide accurate models of the characteristics that can be used in optimization of the operating strategy. This paper proposes a new algorithm for online learning of the characteristics of the compressors using Gaussian Processes. The performance of the new approximation is shown in a case study with three compressors. The case study shows that Gaussian Processes accurately capture the characteristics of compressors even if no knowledge about the characteristics is initially available. The results show that the flexible nature of Gaussian Processes allows them to adapt to the data online making them amenable for use in real-time optimization problems.