Application of adaptive sliding mode control (sigma adaption method) for an uncertain three-story benchmark structure

Abstract

This study develops the application of adaptive sliding mode control to earthquake-excited uncertain structures. Adaptive sliding mode control is useful as it only requires the boundness feature of uncertainties and disturbances to determine control gain (and not the amplitude of bounds). Moreover, the amplitude of chattering effect, the main drawback of sliding mode control, attenuates while stability and robustness are preserved. For this purpose, two adaptive-gain control algorithms are considered. In addition, a time-varying boundary layer is considered to increase the accuracy. In order to examine the feasibility of the applied method, a three-story benchmark structure is considered. Furthermore, performance indexes are used to evaluate the effectiveness of adaptive sliding mode control in comparison to sliding mode control and fuzzy sliding mode control. Comparison of the simulation results in accordance to performance indexes demonstrates that adaptive sliding mode control not only attenuates the amplitude of control effort (i.e. chattering amplitude) but also makes the control of the maximum response of the structure applying adaptive sliding mode control more convenient. It is shown that displacement and drift performance indexes of adaptive sliding mode control are equal to or less than ones of sliding mode control, while root mean square of the control effort of adaptive sliding mode control is attenuated around 50%.