A framework for robust PID controller design: an optimization-based approach for inductive loads

This paper presents a comprehensive comparative study of proportional-integral-derivative (PID) controller tuning methodologies for inductive load applications across three representative scenarios. We systematically evaluate classical methods (Ziegler-Nichols, internal model control) against global optimization algorithms (genetic algorithm (GA), particle swarm optimization (PSO)) applied to resistor-resistor-inductor (RRL) circuit models. Results demonstrate that PSO achieves superior performance for moderate-to-slow systems, reducing settling time by 84% while completely eliminating overshoot compared to Ziegler-Nichols. The algorithm automatically discovers optimal PI controller structures, simplifying implementation. However, for ultra-fast systems (time constants < 1 ms), internal model control proves more reliable, achieving 0.84 ms settling with only 0.16% overshoot. Optimized controllers demonstrate exceptional robustness, maintaining stability under ±50% parameter variations and effectively rejecting disturbances. This research provides engineers with a scenario-based framework for method selection, moving beyond heuristic tuning to achieve previously unattainable performance levels. The findings establish optimization-based tuning as a systematic, reliable approach for high-performance control system design in industrial applications.