Recovering Nominal Tracking Performance In An Asymptotic Sense For Uncertain Linear Systems

Keywords

Disturbance observer; Internal model principle; Nominal performance recovery; Robust control

Abstract

In this paper, we consider the problem of recovering a (predefined) nominal output trajectory in the presence of model uncertainty and external disturbance. In particular, whereas the nominal performance recovery (NPR) has been studied in an approximate fashion in the literature, we extend the notion of the NPR in an asymptotic sense from the perspective of the internal model principle: that is, as long as the disturbance and reference signals are generated by an exogenous system, the actual output not only is kept close to the nominal trajectory as much as desired but also asymptotically converges to the nominal one as time elapses. It is shown via the singular perturbation theory that the asymptotic NPR can be achieved for uncertain minimum-phase systems under arbitrarily large (but bounded) model uncertainty. A disturbance observer (DOB) approach is employed in the controller design, with the internal model embedded into the so-called Q-filter, which is a key component of the DOB. Simulation results for mechanical positioning systems illustrate that the asymptotic NPR can enhance robust performance of control systems.

Publication Date

1-1-2018

Publication Title

SIAM Journal on Control and Optimization

Volume

56

Issue

2

Number of Pages

700-722

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1137/17M1122657

Socpus ID

85047191314 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85047191314

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