Vibration suppression in flexible structures via the sliding-mode control approach

The authors describe the technique of sliding-mode control design for flexible structures. As in all sliding mode control approaches, the main idea is in specifying the systems constrained on the manifold in the state space where it has the desired properties. It is demonstrated that the model of flexible structures in the form of the second order partial differential equation describing longitudinal and torsional oscillations can be transformed into the system of differential-difference equations. A class of flexible structures describing bending vibrations of flexible beams with fourth order spatial partial derivatives also can be represented in the second order form by means of an integral transformation