The ADITYA-U tokamak (R-0 = 0.75 m, a = 0.25 m) is designed to shape plasma column in both single and double null diverter configurations. It is quite well known that sustaining a shaped plasma in tokamak requires very good plasma column position control, both horizontal and vertical. An FPGA-based proportional-integral-derivative (PID) control system has been designed and operated to achieve horizontal plasma position control in ADITYA-U tokamak. The complete system has been rigorously tested with sample signals before implementing to the ADITYA-U plasma discharges. The control system is integrated and time-synchronized with the plasma discharge operation of ADITYA -U. Furthermore, the system has been trained to take appropriate actions during the disruption or plasma failure in the tokamak operation. Detailed experimental results have been obtained by the operation of the digital PID controller. The complete design, installation, operation, tuning of the system along with all the relevant testing and operating experience of the digital PID controller for real-time horizontal plasma position control is presented in the paper.