Horned lizard defense tactics optimization for robust FOPID control in vehicle active suspension systems

This paper introduces a novel bio-inspired optimization algorithm, the Horned Lizard Defense Tactics Algorithm (HLOA), for optimal tuning of Fractional-Order PID (FOPID) controllers in vehicle active suspension systems. The proposed HLOA simultaneously optimizes all five FOPID parameters ( \({K}ₚ,\) \({K}ᵢ\) , \({K}d\) , \(λ\) , \(μ\) ) through a weighted cost function that balances ride comfort (minimization of sprung mass acceleration) and handling stability (limitation of suspension deflection). Extensive simulations using a double‑bump road excitation model demonstrate that the HLOA‑optimized FOPID controller achieves superior performance compared to passive systems, classical PID controllers, and non‑optimized FOPID controllers. The optimized HLOA‑FOPID system reduces RMS sprung mass acceleration by 26.6% and RMS suspension deflection by 72.6% relative to the passive benchmark. Additionally, it decreases RMS sprung mass displacement and relative suspension speed by 16.2% and 73.5%, respectively. Beyond nominal performance, the controller exhibits exceptional robustness against practical parameter uncertainties: over 10 independent runs, the RMS acceleration shows a standard deviation of only 0.0011 m/s 2 , and the controller maintains ride comfort within ± 0.73% for mass variations up to ± 25% and within ± 2.33% for spring stiffness variations up to ± 30%. The HLOA algorithm demonstrates excellent convergence characteristics and solution quality with moderate computational requirements. Results indicate that the proposed approach offers a significant advancement in intelligent suspension control, providing both superior performance and practical robustness for next‑generation automotive applications.