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            <title xml:lang="en">Improved Trajectory Tracking for DC-Motors via Homogeneous PID Controller</title>
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                <title xml:lang="en">Improved Trajectory Tracking for DC-Motors via Homogeneous PID Controller</title>
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                <term xml:lang="en">DC-motor</term>
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              <p>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. Note to Practitioners—DC motors remain a core component in industrial automation, mobile robotics, mechatronic systems, and countless embedded applications. However, in practice, achieving high-precision speed or position control with DC motors is often difficult. Nonlinear friction, load variations, parameter drift, and unmodeled external disturbances commonly degrade performance. Conventional PID controllers—although easy to tune and implement—typically offer limited robustness under these conditions, and performance can deteriorate significantly outside nominal operating points. This study introduces a homogeneous PID (hPID) control strategy that can be implemented as a direct upgrade of a standard PID controller. Instead of using fixed gains, the hPID controller employs homogeneous functions of the system states to scale the effective control action automatically. This approach preserves the simplicity and familiar structure of classical PID control while substantially improving transient behavior, disturbance rejection, and robustness to parameter variations. For practitioners, the key message is that the hPID controller offers a practical, easily adoptable enhancement to existing PID-based control architectures. Its implementation requires simple modification to the conventional PID form, making it suitable for embedded systems, industrial drives, and robotic platforms where improved precision and resilience are needed without increasing system complexity. Therefore, this method can serve as a scalable and reliable solution to upgrade the performance of DC motor–driven systems in real-world applications</p>
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