VRFT with ARX controller model and constrained total least squares

TL;DR

This paper introduces a novel VRFT approach using constrained total least squares with ARX models to reduce bias in controller parameter estimation, demonstrated through two case studies.

Contribution

It proposes applying constrained total least squares to VRFT for ARX controllers, improving bias reduction over traditional least squares and instrumental variable methods.

Findings

CTLS improves bias reduction in VRFT estimates

The method outperforms traditional LS and IV approaches in case studies

Enhanced controller tuning accuracy demonstrated in practical scenarios

Abstract

The virtual reference feedback tuning (VRFT) is a non-iterative data-driven (DD) method employed to tune a controller's parameters aiming to achieve a prescribed closed-loop performance. In its most common formulation, the parameters of a linearly parametrized controller are estimated by solving a least squares (LS) problem, which in the presence of noise leads to a biased estimate of the controller's parameters. To eliminate this bias, an instrumental variable (IV) variant of the method is usual, at the cost of increasing significantly the estimate's variance. In the present work, we propose to apply the constrained total least squares (CTLS) solution to the VRFT problem. We formulate explicitly the VRFT solution with CTLS for controllers described by an autoregressive exogenous (ARX) model. The effectiveness of the proposed solution is illustrated by two case studies in which it is compared to the usual VRFT solutions and to another, statistically efficient, design method.