A new type of servosystem called cyclic control is introduced. The control algorithm presented allows the execution of cycles defined by positions to be attained at given time instants. The cycle starts and ends at the same position and has to be repeated over and over in time. As distinct from repetitive control and learning control, where exact trajectory tracking is considered, the control problem formulated cares only for position. This allows the development of a finite-dimensional control scheme that does not need system reinitialisation at each trial since the new trial starts from the point reached at the end of the previous one. A control scheme design is explicitly addressed and an implementation on a flexible arm presented.