Industrial hydraulic systems are complex, and show nonlinear dynamic behavior because of their nature. When it is not easy to deal with the nonlinear models, hydraulic systems are usually described by linear or linearized models around operating points. In this work a nonlinear dynamic and mathematic model for the position control of a double rod hydraulic actuator was developed. Three control strategies were implemented: PID control, optimal control (LQR) and control by Feedback Linearization. For the PID control and optimal control (LQR) strategies a linearized model of the hydraulic actuator was developed around a specific operating point, contrary to the Feedback Linearization control that have a wide operation range and the nonlinear model was used. These mathematical models were represented on Simulink environment, in order to compare and analyze the response and dynamic behavior. The optimal control (LQR) shows better settling time than the PID control, both without overshoot; and the Feedback Linearization show the best dynamic performance in terms of settling time with a little overshoot and disturbance tolerance.