All physical systems are nonlinear to some degree. The examples are relay, backlash, deadzone, saturation element and so on. In the linear control system design, it is useful method to restrict the nonlinearity to the linearity of system over the operation range. It is worth noting that nonlinearities may be intentionally introduced in to a system. A simple of an intentional non-linearity is the Bang-Bang controller which uses the On-Off relay. In this paper, an angular position servosystem made of a DC servomotor controlled by a microcomputer is discribed. Authors use two methods in the design of controller. The one is linear controller designed by the optimal feedback control theory only and the other is nonlinear controller designed by On-Off relay with optimal feedback control theory. To do the real time control, the controller is designed by using 16bit personal computer and A/D.D/A converter(12bit) is used in order to convert the signal. According to this way, the results from real time control are as follows. 2) Under the On-Off controller with hysterisis the influence of disturbance is considerably smaller than the linerar controller. 3) An increase in the sampling period has a destabilizing effect. 4)In the controller performance, the response time of the On-Off controller is longer than that of the linear controller. To close, we note that the On-Off controller with hysterisis is more attractive than the linear controller in the presence of the input limit.