  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.
