PIV DESIGN FOR DC MOTOR POSITION CONTROL UNDER TIME DELAY USING SPECTRAL ABSCISSA OPTIMIZATION

Servo-based DC motor systems are widely employed in industrial automation and robotics due to their high precision in position control. However, the presence of time delay in feedback loops, arising from sensing, computation, and signal transmission, can significantly degrade system performance and may even lead to instability. This study proposes a delay-aware control design framework for a rotary servo-based DC motor system using a proportional-integral-velocity (PIV) controller. The proposed approach extends conventional proportional-velocity (PV) control by incorporating an integral action to eliminate steady-state errors in position tracking while preserving the favorable damping characteristics of velocity feedback. The controller design is formulated as a spectral abscissa minimization problem, where the real part of the rightmost closed-loop mode is minimized with respect to the controller parameters. Due to the nonconvex and nonsmooth nature of the problem, a derivative-free optimization strategy based on the Nelder–Mead algorithm is employed, and multiple initializations are considered to improve robustness of the solution. The closed-loop system is modeled as a delay-differential equation, and its stability properties are analyzed through spectral methods. In addition, the delay robustness of the designed controllers is systematically investigated by evaluating their performance under representative delay values. The effectiveness of the proposed approach is demonstrated through both spectral analysis and real-time experiments conducted on the Quanser SRV02 platform. The results show that the proposed PIV controller achieves stable closed-loop behavior with improved transient performance and eliminates steady-state error in position control, outperforming previously reported PV-based designs in the presence of time delay.