A servo system for any periodical signal can be realized based on the so-called repetitive control system. If a controlled plant has no direct path, the modified repetitive control system which includes a lowpass filter to assure the internal stability, is usually used. As a selection of the lowpass filter is constrained by a gain characteristic of sensitivity function, the sensitivity function must be shaped corresponding to a lowpass filter selected from a standpoint of performance. In this paper, we propose a new synthesis of repetitive control system using the Loop shaping design procedure. This procedure is one of method that can shape the sensitivity function as exepected. Furthermore, a pre-controller designed by this procedure has a structure of state feedback plus full state observer. In a case that plant is of high order, this feature makes a synthesis easy. We consider a periodical disturbance reduction problem in a plate temperature control system and confirm the validity of our method in both simulation and experiment.