Improved Trajectory Tracking for DC-Motors via Homogeneous PID Controller

Direct Current (DC) motors are widely used in industrial and robotic applications due to their simplicity of use and control. However, achieving high-performance control in DC motor systems is a longstanding challenge due to nonlinearities and uncertainties, parameter variations, and external disturbances (e.g., load changes and friction). This paper proposes a novel homogeneous Proportional-Integral-Derivative (hPID) control strategy specifically designed for DC motors, aimed at achieving robust and precise speed and position regulation. Unlike traditional PID controllers, the hPID controller utilizes the mathematical principles of homogeneous control theory to systematically improve the stability, robustness, response time and transient quality of the closed-loop system. A homogeneous PID architecture is developed by simply upgrading the conventional PID algorithm, in which homogeneous functions of the state scale the gains. This adaptation enhances the regulation quality of the closed-loop system. To support this methodology, a Lyapunov-based stability analysis is performed, establishing global asymptotic stability and finite-time convergence under mild assumptions of the system. Experimental results for a representative DC motor setup demonstrate the effectiveness of the proposed methodology for essential improvement of the regulation precision compared to a linear PID controller. Superior performance is discovered for time response, steady-state accuracy, and robustness. This research contributes to a theoretically sound and scalable control methodology to improve the performance and reliability of DC motor-driven systems under both structured and variable operating conditions.