Characterization of PI feedback controller gains for interconnected ODE - hyperbolic PDE systems

Abstract

In this paper, we give explicit criteria to guarantee the robust stabilization of simple first-order transport systems coupled with finite-dimensional dynamics, using Proportional or Proportional Integral boundary output feedback controllers. Using a frequency-sweeping approach developed for Time-Delay Systems, we characterize the closed-loop stability intervals in the parameter space for several interconnected partial differential equations and ordinary differential equations configurations. The performances of the proposed boundary feedback controllers are compared with other classical approaches in simulation. The proposed methodology is a necessary step before a detailed comparison between proportional integral controllers with low computational complexity and other control approaches for infinite-dimensional systems.