In this paper, a 2DOF FO PID (2 Degrees of Freedom Fractional Order Proportional Integral Derivative) controller is employed to control the angular position of the rotational load of a 2DOF rotary torsion plant. This plant comprises a DC servomotor with gear reduction device anchored to a cubic solid aluminium frame. The horizontal output shaft of the servomotor, acting as a driver, is in series with two rotary torsion loads using two flexible couplings. Every flexible load constitutes a 1DOF. The angular position of the rotary load of the plant is also controlled employing a 2DOF IO (Integer Order) PID controller. In this work, a FO PID controller is obtained from an IO PID controller replacing in the latter controller all its IO derivative and integral terms by FO terms. According to the experimental results obtained in this work, the controlled output of the 2DOF FO PID control systems presents less settling time and steady-state error compared with the controlled output of the 2DOF IO PID control system.