Frequency Shaped Sliding Mode Control of Magnetorheological Smart Structure Systems

This paper addresses the problem of controlling multi-degree-of-freedom (MDoF) smart structures integrated with magnetorheological (MR) devices that are subject to non-linearity and hysteresis. A fluid based device, namely the MR damper (MRD), is considered in this study, where hysteresis appears in both force-displacement and force-velocity relationships of the smart device. Such nonlinear dynamics limit the performance of the device when embedded in smart structures. The describing function (DF) technique is employed using only the displacement as input to the nonlinearity to characterize this multivalued mechanism. By incorporating the proposed model into the system dynamics, frequency shaped sliding mode control (FSSMC) is developed to achieve structural resilience and sustainability against nonlinearities, modeling uncertainties, and disturbances from dynamic loadings. Frequency response functions (FRFs) are obtained for possible analysis of system conditional assessment in the frequency domain. Simulations are reported for a three-story building model integrated with two identical current-dependent MR dampers subject to one-dimensional quake-induced vibration to investigate lateral dynamic responses, as produced by earthquakes or strong winds.