On the second order sliding mode control of a parametrically excited overhead-crane

Systems with periodic coefficients are of fundamental interest because periodic variations appears in a great range of physical systems. This kind of variations are the cause of parametric resonance, by other hand, second order sliding modes, SOSM, is known to be robust to several kind of perturbations. The principal contribution of this note is the design of a SOSM controller that can avoid the parametric resonance in an under-actuated system. We tested the proposed control scheme on a laboratory crane that is exposed to parametric resonance. We present simulations and experiments.