  Data-driven direct methods are still growing in popularity almost three
decades after they were introduced. These methods use data collected from the
process to identify optimal controller's parameters with little knowledge about
the process itself. However, most of those works focus on the problem of
reference tracking, whereas many of the problems faced in real-life are of
disturbance rejection or attenuation. Also, the vastly majority of those works
identify the parameters of linearly parametrized controllers, which amounts to
fixing the poles of the controller's transfer function. Although the
identification of the controller's poles is not prohibitive, as hinted by some
of the papers, there is little effort on presenting a data-driven solution
capable of doing so. With all that in mind, this work proposes a data-driven
approach which is able to identify the zeros and the poles of a linear
controller aiming at disturbance rejection. Two different one-step ahead
predictors are proposed, one that is linear on the parameters and another that
is non-linear. Also, two different techniques are employed to estimate the
controller parameters, the first one minimizes the quadratic norm of the
prediction error while the second one minimizes the correlation between the
prediction error and an external signal. Simulations show the effectiveness of
the proposed methods to estimate the optimal controller parameters of
restricted order controllers aiming at disturbance rejection.
