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. 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´s 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, the linear quadratic method for the construction of the sliding manifold and the Kalman filter with fictitious noises for the observer design have been used.