Adaptive Sliding Mode Control of a Single Degree-of-Freedom Structure with Parameter Uncertainty

This paper addresses the problem of structural control for mitigating seismic effects in the presence of structural parameter uncertainties. A linear single degree-of-freedom (DOF) structure is considered. It is supposed that mass, damping and stiffness coefficients of the structure contain uncertainty. Two different methods based on sliding mode control (SMC) are proposed. The first method uses upper bounds of the system uncertainties in the control law but in the second method a prior knowledge about the bounds of the uncertainties is not necessary and the controller adapts itself during the control procedure. Numerical simulation is used to show the efficiency of the proposed approaches. The simulation results depict that both methods cause significant reduction in the displacement and velocity of the controlled structure in comparison with the uncontrolled one. Furthermore, the magnitude of control forces reveal that implementation of the proposed methods from the viewpoint of real-world applications is feasible.