Sliding Mode Control of Non-linear Double-Pendulum Overhead Cranes with Prescribed Trolley Convergence

In actual overhead cranes, double-pendulum (DP) effect and uncertainty will inevitably occur. This study considers these effects to improve position tracking accuracy and sway regulation for perturbed DP overhead cranes. A prescribed-performance-control based sliding-mode control (SMC-PPC) scheme to regulate the sways and satisfy some transient and steady-state (TSS) performance metrics specifications on trolley tracking error. A prescribed performance function (PPF) and an error-transformation-function (ETF) are investigated so that performance metrics on trolley tracking error can be achieved. The challenge from the unavoidable friction is circumvented using a recently developed continuously differentiable friction model. The closed-loop stability is analysed using Lyapunov method. Simulation experiments show that both hook and payload TSS sways are effectively regulated and that trolley error converged into a pre-defined narrow vestigial set, having a rate of convergence of at least a preassigned value, exhibiting maximum overshoots and undershoots below some small enough pre-set values.