Abstarct: In recent years, using of Active Control of Vibration has been much developed. Laboratory and practical tests show that different methods of Active Control of Vibration are very effective in reduction of vibration of the structures. However, there are still many problems in these methods. One of the factors that caused the problem in these methods is existence of the delay in processing of control systems, sensors and actuators work and etc. This factor applies improper forces on the structure that can be controlled. Because of existence of the delays in the measurement of system variables, the calculations of the required control force, generation of force by the actuator and many other factors, its effect on the performance of the controller is inevitable. In this thesis, the effect of delay time on control of Euler- Bernoulli cantilever beam has been investigated. After transporting the governing equations of the beam to state space, optimal control methods are used in beam controlling. Delayed compared with the case without delay, the effects of delay on controlling are denoted. Knowing the switching stability and system specifications, by considering a calculated delay, one can reduce or eliminate the effects of the delays in the system and close performance of control system to its optimal case. Also, for the second and higher modes, non- collocation of the sensor and actuator can be modeled with a time delay. By adding this delay to the total delay of the system and according to the switching stability, performance of the system can be closed to its optimum. Also, considering to the piezoelectric governing equations, beam modes and equations, the optimal location of actuator in Euler-Bernoulli beam is obtained. This thesis has shown that the optimal control systems have an efficiency performance on structures control when the time delay of control and non- collocation of the sensor and actuator have been considered.