147. stabilization of an underactuated transport-wave pde system

Department: Mechanical & Aerospace Engineering
Research Institute Affiliation: Center for Control Systems and Dynamics (CCSD)
Faculty Advisor(s): Miroslav Krstic

Primary Student
Name: Stephen Chen
Email: stc007@ucsd.edu
Phone: 858-534-5670
Grad Year: 2018

Abstract
We solve the problem of an underactuated coupled transport-wave system, which is physically motivated by instability phenomena seen in extreme ultraviolet (EUV) lithography. The system is first transformed into a 2+1 system of first-order hyperbolic PDEs, where two transport PDEs (only one of which is actuated) convect leftward, and one rightward, unactuated. A controller is designed to be applied at the inflow boundary of the controlled transport PDE. The backstepping method is used to determine a system of 3 PDEs, which are solved to determine the corresponding feedback control. The resulting intermediate control is then augmented using a feedforward controller. Finally, the controller is shown to exponentially stabilize the system in the spatial $mathcal{L}^2$ sense.

Industry Application Area(s)
Control Systems | Semiconductor

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