Space Robotics Laboratory of Tohoku University is currently developing a series of 50-kg-class microsatellites for Earth observation. In this paper, we propose design of an attitude control system (ACS) focusing on its control algorithms and computers. This ACS will be equipped on our 4th microsatellite "RISESAT" and launched by the Epsilon rocket in 2018. The primary mission of RISESAT is multi-spectral Earth observation using a 5 m GSD High-Precision-Telescope with liquid crystal tunable filters. During an observation, RISESAT has to track a ground target with an accuracy of 0.1° and 0.008°/s attitude stability because imaging and wavelength switching take several tens of seconds in total. To solve this problem, we developed a high-speed attitude control computer and precision groundtracking algorithms. Evaluations of the algorithms were carried out by a hardware-in-the-loop simulator "MEVIμS" developed by SRL. We confirmed that the ACS and its algorithms satisfies the mission requirements under the influence of sensor noise and computation time limits.