In motion control applications, the precise regulation of Industrial Hydraulic Actuators (IHA) is essential for properly ascertaining the position of the actuator rod. This research used a Hammerstein-Wiener (HW) model to characterize the system, integrating a dead zone to account for nonlinearities and using an open-loop methodology. A grey-box modelling technique is used for estimating the discrete-time model of the system and identifying its parameters. The System Identification toolbox in MATLAB functions as the principal instrument for model estimation, using input-output data acquired via experimental procedures. The validation of the input-output data demonstrated a promising best-fit percentage of 88.21%, indicating a robust connection between the HW model and the real system. To assess the trajectory tracking efficacy of the system, Proportional-Integral-Derivative (PID) and Fractional Order PID (FOPID) controllers developed and evaluated using both simulation and experimental data based on a multi-sinusoidal trajectory. The findings indicate that the FOPID controller surpasses the traditional PID controller, producing reduced Mean Square Error (MSE) and Root Mean Square Error (RMSE) values. In simulations, the FOPID control technique enhanced MSE by 32.8% and RMSE by 18.0% relative to the PID controller, although the experimental findings indicated improvements of 31.9% and 17.5%, respectively. The results highlight the superior efficacy of the FOPID controller in improving trajectory tracking performance owing to its greater complexity and flexibility. Future research may concentrate on developing more sophisticated controllers, including intelligent or nonlinear variants, to enhance the tracking precision of the IHA system.