This work emphasizes on realization of fractional-order proportional integral derivative (FOPID) controller for a third order plant model in discrete-time domain. The realization includes three stages. The first stage deals with integer-order PID controller and FOPID controller designing in the continuous-time domain employing traditional Ziegler-Nichols (ZN) and Modified Ziegler-Nichols (MZN) method, respectively. The supremacy of the FOPID controller over traditional PID controller has been established in this stage through analyzing the relevant performance indices. In the next stage, the FOPID controller has been approximated using Oustaloup method within a finite frequency band. Finally, the discrete-time approximation of FOPID controller is accomplished in delta domain. The validation of the proposed methodology has been exemplified using simulation results. The overall controlled system appears to be robust in handling the varying plant gain.