This article presents an optimal design methodology for feedforward controllers that face periodic reference/disturbance inputs. The feedforward controller is parametrised as a finite impulse response filter, and its parameters are computed to minimise the worst-case tracking error in the presence of uncertainty on the input period and the plant model. Numerical results indicate that for nonminimum-phase systems exploiting the periodic input characteristics in the feedforward controller design is worthwhile, and reveal the superiority of the developed design methodology with respect to current design approaches when period-time and/or plant uncertainty is present.