Robust frequency-region control of overhead cranes with time-varying rope length

Overhead cranes with time-varying rope length are subject to nonlinear dynamics and practical implementation issues, including actuator input delays, controller gain perturbations, and external disturbances. Furthermore, the variation of rope length continuously shifts the natural frequency, making conventional full-frequency disturbance attenuation overly conservative. To address these challenges, a robust frequency-region controller (RFRC) is proposed within a Takagi–Sugeno (T–S) fuzzy framework. The nonlinear crane dynamics are first transformed into an equivalent fuzzy model, providing a unified basis for controller synthesis. Based on this formulation, the generalized Kalman–Yakubovich–Popov (GKYP) lemma is incorporated to enforce finite-frequency H ∞ performance over the dominant resonance band associated with rope-length variation. Finally, actuator input delays, controller gain perturbations, and prescribed input/output constraints are simultaneously integrated into the proposed framework, from which sufficient LMI conditions are derived for controller synthesis. Simulation results under both nominal and disturbed operating conditions demonstrate that the proposed controller achieves accurate positioning, precise rope-length tracking, effective swing suppression, and strong robustness while maintaining smooth control inputs. These results verify the effectiveness and practical applicability of the proposed RFRC for overhead crane systems with time-varying rope length.