Time-Varying Internal Models and Regulation of Unknown Harmonic Signals for Regular Linear Systems

TL;DR

This paper develops a framework for controlling regular linear systems with time-varying internal models to achieve output regulation of unknown harmonic signals, extending classical principles to nonautonomous controllers.

Contribution

It generalizes the internal model principle for time-dependent controllers with converging parameters, enabling effective disturbance rejection of unknown harmonic signals.

Findings

Successfully applied to boundary controlled heat equation

Achieves disturbance rejection without known harmonic frequencies

Demonstrates flexible integration with frequency estimation methods

Abstract

We introduce general results on well-posedness and output regulation of regular linear systems with nonautonomous controllers. We present a generalization of the internal model principle for time-dependent controllers with asymptotically converging parameters. This general result is utilised in controller design for output tracking and disturbance rejection of harmonic signals with unknown frequencies. Our controller can be flexibly combined with different frequency estimation methods. The results are illustrated in rejection of unknown harmonic disturbances for a one-dimensional boundary controlled heat equation.