Reduced Order Controller Design for Robust Output Regulation

Abstract

We study robust output regulation for parabolic partial differential equations and other infinite-dimensional linear systems with analytic semigroups. As our main results we show that robust output tracking and disturbance rejection for our class of systems can be achieved using a finite-dimensional controller and present algorithms for construction of two different internal model based robust controllers. The controller parameters are chosen based on a Galerkin approximation of the original PDE system and employ balanced truncation to reduce the orders of the controllers. In the second part of the paper we design controllers for robust output tracking and disturbance rejection for a 1D reaction-diffusion equation with boundary disturbances, a 2D diffusion-convection equation, and a 1D beam equation with Kelvin-Voigt damping.

Revised version with minor improvements and corrections. 28 pages, 9 figures. Accepted for publication in the IEEE Transactions on Automatic Control

References in corpus (2)

• Controller Design for Robust Output Regulation of Regular Linear Systems
• Robust Controllers for Regular Linear Systems with Infinite-Dimensional Exosystems

Cited by in corpus (6)

• Exponential integrators for second-order in time partial differential equations
• On Robust Regulation of PDEs: from Abstract Methods to PDE Controllers
• Finite-Dimensional Controllers for Robust Regulation of Boundary Control Systems
• Robust Output Regulation of the Linearized Boussinesq Equations with Boundary Control and Observation
• Robust Output Tracking for a Room Temperature Model with Distributed Control and Observation
• A Reduced Order Controller for Output Tracking of a Kelvin-Voigt Beam