Periodic Regulation of Linear Time-Delay Systems via Youla-Ku\v{c}era Parametrization

TL;DR

This paper introduces a novel method for periodic regulation of linear time-delay systems using Youla-Kuera parametrization, enabling implicit signal modeling without altering stabilizing controllers, demonstrated through simulations.

Contribution

It presents an alternative to the Internal Model Principle by augmenting existing controllers with Youla-Kuera parameters for time-delay systems.

Findings

All unstable systems can be periodically regulated.

The method simplifies tuning via linear equations.

The approach is validated through simulations.

Abstract

The paper proposes an alternative way to achieve the Internal Model Principle (IMP) in contrast to the standard way, where a model of the signal one wishes to track/reject is directly substituted into the closed-loop. The proposed alternative approach relies on an already-existing stabilizing controller, which can be further augmented with a Youla-Ku\v{c}era parameter to let it implicitly admit a model of a signal without altering its stabilizing feature. Thus, with the proposed method, the standard design steps of realizing IMP are reversed. The validity and potential of the proposed approach are demonstrated by considering three different types of time-delay systems. It is shown through simulations that all considered unstable systems, despite the infinite-dimensional closed-loop, can be straightforwardly periodically regulated by augmenting their stabilizing PI controllers. Thanks to a specifically chosen structure for the Youla-Ku\v{c}era parameter, the required tuning can be done by solving a set of linear equations.