Design and Implementation of Discrete Fractional Order PID Controller for the Speed Control of DC Motor: Delta Operator-Based Approach

This paper presents a discrete delta-domain fractional-order PID (FOPID) controller, tuned using dynamic Particle Swarm Optimization (dPSO), for precise DC motor speed control. The proposed approach directly discretizes the FOPID controller in the delta domain, ensuring improved numerical stability and continuous-time-like performance even at fast sampling rates. The controller is optimized for time-domain criteria and implemented on an Atmega328P microcontroller, with comprehensive validation via both simulation and hardware-in-the-loop (HIL) experiments. Compared with the conventional z-domain FOPID and PID controllers, the delta-domain design achieved up to 60% reduction in overshoot and 40% improvement in settling time, while maintaining steady-state error below 1%. These results confirm the practical viability of advanced digital fractional-order control for real-time industrial applications.