Super twisting control of a parametrically excited overhead crane

The principal contribution of this note is to avoid the parametric resonance effect and attenuate the payload oscillations in an overhead-crane system subject to periodic variations in the base support. Considering an appropriate sliding output with relative degree one, we present the sliding mode control design based on the Super-Twisting Algorithm (STA), ensuring finite time convergence to the desired sliding surface for the linear periodic system with Lipschitz continuous matched and unmatched uncertainties bounded together by their gradients by known functions. The suggested approach also provides chattering phenomenon attenuation. Obtained results are verified experimentally.