Optimization of Weighted Geometrical Center Method for PI and PI-PD Controllers

This study proposes an optimized approach to enhance the performance of the Weighted Geometric Center (WGC) method for stabilizing time-delay systems, which has applications in industrial process control, robotics, and high-order dynamic systems. The traditional WGC method determines controller parameters by calculating the Weighted Geometric Center of the stable region, but it often overlooks better-performing parameter pairs near the WGC point. To address this limitation, a goal function is formulated based on percentage overshoot, rise time, and settling time. The optimization process explores the vicinity of the WGC and selects controller parameters that minimize the goal function, ensuring improved performance. The proposed optimization is applied to PI and PI-PD controllers, and its effectiveness is demonstrated through multiple case studies. Simulation results indicate that the optimized method significantly improves control performance, particularly in reducing overshoot, enhancing settling time, and ensuring a more stable response compared to the conventional WGC method. For instance, the Optimized WGC method reduces overshoot by up to 15% and settling time by up to 20%. These findings highlight the practical benefits of integrating local optimization into the WGC framework for superior controller tuning in time-delay systems.