Prescribed Performance Sliding Mode Control and Estimation for Perturbed Double-Pendulum Cranes

Cranes suffer significantly from parameter uncertainties, frictions, unknown dynamics, and disturbances. Besides, it may be necessary to design a state estimator for an effective feedback controller design. Furthermore, the performance quality and precision of model-based controllers and state estimators rely heavily on accurate models, which may be challenging to formulate. In this study, to address the highlighted control problems and also achieve a precise level of bogie tracking error, the sliding mode control (SMC) with a novel prescribed performance function-based sliding surface is designed. Simulations have shown that the proposed control technique achieved pre-specified transient and steady-state quality metrics on the bogie tracking error where the error converged to a pre-defined small vestigial set, with a decay rate no less than the pre-assigned rate, exhibiting overshoots and undershoots less than some small-enough pre-assigned values.