Sliding mode control of vibration in flexible structures using estimated states

The sliding mode algorithm for control of vibration in a flexible structure has been formulated when states are estimated using an observer. A singular-value approach is used to study the robustness of this control system to observation spillover. Numerical examples are presented for a simply supported beam and a flexible tetrahedral truss. For the simply supported beam structure, the natural frequencies are well separated. To have a robust system in this case with single input and output, the desired sliding manifold and the Luenberger observer gain matrix have been found by the pole-placement method. However, to have a robust system for the flexible tetrahedral truss structure with closely lumped natural frequencies, three inputs, and three outputs, a linear quadratic method for the construction of the sliding manifold and a Kalman filter with fictitious noise for the observer design have been used.