For a one link flexible arm control, quadratic optimal control is applied to the dynamic modilling which is derived from an assumed mode method. For the quadratic optimal control technique, the full state feedback must be obtained for closing the control loop, but because some of the states in the flexible system(e.g. the rate of change of the time dependent variables of the mode shapes) can not be directly measured, state estimator is necessary to achieve the practical implementation of the optimal controller. When disturbances and measurement noise occur, stochastic approach must be applied to estimating the states of the system. Kalman Filter is used as a stste estimator. Through the simulation, the flexible system with state estimator is compared with the flexible system assuming that all the states can be measured.