Disk margin based robust stability analysis of a DC motor drive

This research paper investigates optimal tuning of PID co-efficients using the Tree-Seed Algorithm. A DC motor drive with a PID controller is considered a simulation example. The step response of the DC drive with Tree-Seed algorithm-based PID controller is compared with Ziegler Nichols (closed-loop) method and Skogestad Internal Model Control. In this research, the Disk-based margins are proposed to investigate the feedback loop for robust stability against gain and phase uncertainty (i.e the gain of open-loop is increased or decreased by 50%, and the phase is by ± 270) for various values of skew, σ. The motivation for using the disk margins is the limitations of the classical margins. For the specified uncertainty, the safe uncertainty of DC motor drive with Tree-Seed Algorithm based controller is identified as 3.47 times the specified uncertainty, and the disk margins are computed as the gain variation between 9.1% and 1100% of the normal value, and the phase variation of ± 800. The analysis identifies that the optimal Disk margins are obtained for the DC motor drive (with Tree-Seed Algorithm-based PID controller) for zero skew value. Finally, it is proved from the MATLAB simulation results that the DC motor drive with Tree-Seed Algorithm-based PID controller possesses good robustness and a wide range of stability margins for the uncertainty in the feedback loop. For the validation of the proposed methodology, the experimental setup is prepared and made the comparison of simulation and experimental results for rotor speed variations for the proposed tuning method.