Robust Vibration Suppression of Double-Pendulum Gantry Cranes via Integral LQR Optimized with an Improved Genetic Algorithm Incorporating Sine–Cosine Operators

The control of double-pendulum gantry cranes presents a formidable problem: conflicting objectives of rapid transit and sway suppression contend with underactuated, chaotic dynamics. While the Integral Linear Quadratic Regulator (ILQR) offers a theoretical solution for zero steady-state error, its practical efficacy relies entirely on weighting matrices that standard tuning methods fail to optimize robustly. This study aims to resolve this high-dimensional control problem to ensure stringent industrial safety limits. An Improved Genetic Algorithm (IGA) is deployed strictly as a supporting optimization tool. By hybridizing the Genetic Algorithm with deterministic Sine Cosine Algorithm (SCA) operators, this approach navigates the complex state-space to uncover optimal vibration control parameters without premature convergence. The system's robustness is systematically evaluated against standard heuristic tunings under both nominal conditions and simultaneous parametric uncertainties (variations in cable length and payload mass). Dynamically, the optimized controller eliminates transient overshoot entirely (0.00%), achieves a rapid settling time of 2.23 s, and minimizes payload residual sway to 4.16°. Statistically, a one-way ANOVA test (P < 0.001) and minimal convergence variance (0.0117) validate that the identified parameters represent a robust physical minimum rather than a localized mathematical artifact. Under simultaneous parametric variations, the controller limits worst-case sway to approximately 3.29°, maintaining a superior safety envelope. The IGA-tuned ILQR framework provides a highly robust, empirically validated control architecture. The derived weighting parameters function as practical design guidelines, effectively managing chaotic dynamics and ensuring superior sway-suppression performance regardless of operational parametric uncertainty.