Prescribed Performance Sway Suppression Control for Overhead Cranes under Friction and Actuator Saturation

Overhead cranes are critical material-handling systems in industrial and port logistics, where simultaneous trolley positioning and payload sway suppression are essential for operational safety and efficiency. Trolley-rail friction and actuator saturation are two practical challenges that degrade closed-loop performance and may induce instability if left untreated. This paper presents a control framework for an underactuated overhead crane based on collocated partial feedback linearization (PFL). The directly actuated trolley channel is exactly linearized using collocated PFL together with online Coulomb--viscous friction estimation based on recursive least squares (RLS). The payload sway is then regulated indirectly by shaping the exact internal dynamics through damping injection. An anti-saturation modification ensures rapid recovery from actuator limits, and a prescribed performance function (PPF), injected through the internal dynamics, enforces an explicit time-varying bound on the sway angle throughout the motion. Unlike conventional crane controllers that address these nonlinearities separately, the proposed framework integrates friction compensation, saturation recovery, and prescribed sway constraints within a unified collocated PFL formulation. A two-phase Lyapunov analysis establishes boundedness during parameter identification and asymptotic stability with constraint satisfaction thereafter. Using physical parameters of a benchmark Inteco 3D crane, simulations show the proposed PFL+PPF controller achieves a peak sway angle of 7.4o, compared with 8.9o for the PFL controller without PPF, 11.7o for a saturated LQR baseline, and 19.2o for a PD energy-shaping baseline without friction compensation, while dissipating sway energy within 4 s - the fastest among all controllers - and respecting the 9 N actuator limit throughout. Unlike the PD baseline, which exhibits a persistent friction-induced limit-cycle oscillation, all three friction-compensated controllers converge asymptotically; the saturated LQR variant without anti-saturation recovery nonetheless produces the deepest transient sway excursion, confirming the practical benefit of explicit saturation handling.