10:00 – Giacomo Albi: Feedback control strategies for magnetically confined fusion plasma

In this talk we address the challenge of confining high-temperature plasma in magnetic fusion devices. Our method focuses on employing instantaneous control techniques to guide the plasma within a specified spatial region. We model the process using the Vlasov-Poisson equation in a bounded domain, considering self-induced electric fields and external magnetic fields. Our control strategy incorporates real-time feedback, allowing for the direct minimization of a specified cost function within the particle interactions of the Vlasov model. Numerical simulations validate the effectiveness of our approach, demonstrating the ability of external magnetic fields to steer the plasma away from device boundaries.

 

10:30 – Coffee break

 

11:00 – Oscar Holroyd: Feedback control of thin liquid films

We propose a method to stabilise an unstable solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the system state is challenging in physical settings, so methods able to take this into account are important. The Navier-Stokes equations modelling this interfacial flow are a complex, highly nonlinear set of PDEs, so standard control theoretical results are not applicable. Instead, we chain together a hierarchy of increasingly idealised approximations, developing a control strategy for the simplified model which is shown to be successfully applicable to direct numerical simulations of the full system.

 

11:30 – Alexander Wray: Controlling Navier-Stokes via reduced order models

As in many fields, control has long been a key focus in fluid dynamics. Unfortunately, for multiphase flows (such as interfacial flows), the governing equations are the highly nonlinear Navier-Stokes equations, which must be solved on a time-evolving, non-rectilinear domain. Even for modest problem sizes, this presents a significant computational challenge. As a consequence, most inverse/control problems have only been examined in single phase contexts. For multiphase problems, the forward problem has often been treated via physics-driven reduced order modelling, but even these can be challenging to control due to issues of stiffness.

Here we resolve these issues in order to allow for control of the full Navier-Stokes equations for a multiphase system. In particular, we examine the paradigmatic case of free-surface flow down an inclined plane. The system is simulated using the open-source volume-of-fluid solver Basilisk. Control is implemented via development of an extremely high-fidelity reduced order model using a projection method akin to the Method of Weighted Residuals, and the use of a Model Predictive Control loop to control the direct numerical simulation with judicious use of the model. Actuation is achieved via imposition of a spatiotemporally varying electric potential on an electrode parallel to the substrate.

The model is investigated in detail, demonstrating a high degree of accuracy even into the short-wave regime. The control mechanism is shown to be applicable to both uniform and non-uniform target states, and the efficacy of the model predictive control loop is investigated across a wide variety of parameters.

 

12:00 – Closing, discussions, and lunch