A fractional-order controller for vibration suppression of uncertain structures

The problem of active control of vibration structures has attracted much attention over the past decades. A general description of the control problem of vibration systems is to design an active controller to suppress the vibrations of the system induced by external disturbances such as an earthquake. In this paper, a novel fractional-order sliding mode control is introduced to attenuate the vibrations of structures with uncertainties and disturbances. After establishing a stable fractional sliding surface, a sliding mode control law is proposed. Then, the global asymptotic stability of the closed-loop system is analytically proved using fractional Lyapunov stability theorem. Finally, the robustness and applicability of the technique are verified using two examples, including a three degree of freedom structure and a two-story shear building.