A Discrete Fractional Sliding Mode Control Algorithm for Vibration Mitigation of Building Structures Considering Nonlinearities and Uncertainties

A fractional-order component is introduced and incorporated into the traditional sliding mode control (SMC) algorithm of seismically excited civil structures, leveraging its flexibility and integrity. The determination of the sliding mode surface in this paper incorporates the inclusion of a fractional-order item and subsequently derives the control force. Structural uncertainties and nonlinearities were considered to evaluate the control performance of the discrete fractional sliding mode control algorithm (DFSMC). The 40-story linear structure with the active mass damper system and the three-story nonlinear structure with the Bouc–Wen model were used as analytical models. The DFSMC algorithm exhibited an advantage over the traditional SMC algorithm in terms of control performance for linear structures. Specifically, the non-dimensional base shear criterion was reduced by 5.52% compared to the conventional SMC algorithm under the El Centro ground record. The control effectiveness of the DFSMC algorithm was further analyzed in the presence of uncertainties in the structural coefficients. The control criteria experienced a maximum decrease of 31.23% for SMC, 3.74% for SMC, 23.10% for DFSMC, 1.19% for SMC, 3.51% for SMC, and 18.03% for SMC when [Formula: see text], and [Formula: see text]. For a three-story nonlinear structure, the normalized base shear of DFSMC decreased from 2.3648 to 1.9916. It can be observed that the incorporation of parameters in the DFSMC algorithm enhances the potential for improved control performance.