There are many control system applications where there is a requirement to track a reference signal which is periodic. Examples of this type of application include scanning systems such as those for optical surveillance or radar tracking, and industrial automation systems where robots repetitively follow set trajectories. The conventional integral compensator gives zero error at steady state by providing an infinite gain in the forward path of a control compensator. A compensator based on a digital comb filter can be used to provide infinite gain at a set of harmonically related frequencies. In this way it is possible to provide a digital comb compensator which gives zero steady-state error to a periodic input. The poles of the compensator are determined by the tracking requirement; the zeros must be designed so that the phase shift in the plant will not cause closed-loop instability. An example is given where the shaft angle of a small motor is controlled to track a periodic reference input.