Control of Multiphase Flow and Phase Transition via PDE Methods

Presently known as one of the most significant developments in control systems engineering, backstepping boundary control design enables the stabilization of a wide range of complex multi-physics systems governed by continuum models. During the past two decades, the approach has been proven efficient for the controlling of fluid flows and mechanical vibrations in deep oil drilling, macroscopic models of traffic dynamics, thermal dynamics involving phase transitions (Stefan problem), flexible wings of aircraft, electrochemistry in batteries and even continuum models of large scale multi-agent systems, to name a few. From a theoretical perspective, backstepping designs allow stabilization of hyperbolic and parabolic partial differential equations (PDEs), complex-valued PDEs, and PDE/nonlinear ordinary differential equation (ODE) cascade systems defined on fixed or time-varying spatial domains. I will present the application of this boundary control approach to two representative processes:

· The control of rivers and reservoirs sedimentation (governed by multiphase flow dynamics) in connection with global warming leading to drastic alteration rainfall patterns, increasing the risk of high floods, rivers ecological instability, and water scarcity.

· The control of screw extrusion-based 3D printing process where phase transition phenomena inducing moving interfaces must be controlled to guarantee a constant filament production rate.

I will conclude this talk by providing emerging research avenues related to PDE control and estimation.