Virtual Reference Feedback Tuning (VRFT) is a data-driven control method that identifies a parameterized controller by solving a least squares (MQ) problem, under the assumption the controller is linear in the parameters. Widely used for linear controller design, the VRFT method can be applied to estimate linear parameter-varying (LPV) controllers, also with an MQ solution. This paper analyzes the formulation and application of the VRFT method to LPV plants for the case where the controller class is underparameterized and for the case where the collected data is corrupted by noise. In the case of noisy data, the controller parameter estimation is analyzed employing the MQ solution and with the use of two instrumental variables (VI), one obtained from a new experiment on the plant, and the other obtained from the simulation of an identified plant model. The advantage of the filter usage in the underparameterized case, as well as the statistical properties of the VI estimations in the noise-corrupted data case, are confirmed by simulations.
