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), GreyWolf 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.