Hybrid Particle Swarm and Grey Wolf Optimization for Robust Feedback Control of Nonlinear Systems

This study presents a simulation-based framework for PID controller design in strongly nonlinear dynamical systems. The proposed approach avoids system linearization by directly minimizing a performance index using metaheuristic optimization. Three strategies—Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), and their hybrid combination (PSO-GWO)—were evaluated on benchmark systems including pendulum-like, Duffing-type, and nonlinear damping dynamics. The chaotic Duffing oscillator was used as a stringent test for robustness and adaptability. Results indicate that all methods successfully stabilize the systems, while the hybrid PSO-GWO achieves the fastest convergence and requires the fewest cost function evaluations, often less than 10% of standalone methods. Faster convergence may induce aggressive transients, which can be moderated by tuning the ISO (Integral of Squared Overshoot) weighting. Overall, swarm-based PID tuning proves effective and computationally efficient for nonlinear control, offering a robust trade-off between convergence speed, control performance, and algorithmic simplicity.