Recently microcomputers have come into wide use in the field of control. They are used not only as monitors and or controllers in various plant control systems but also for Computer Aided Design of control systems. In this paper, authors propose a method to design the reduced order observers for the higher order systems and have digital simulation of time responses of the optimal state feedback control system using the maximum principle. And the real time optimal state feedback control system for the third order plant which is realized by an anolog computer is constructed by means of a microcomputer, A/D converter and D/A converter. Time responses of the real time control system are compared with those obtained by the digital simulation and their well coincedence is confirmed.