An optimum fractional order calculus–based sliding mode control (OFOSMC) is proposed to suppress earthquake-induced vibrations on structures equipped with active tuned mass damper (ATMD). The proposed method features a novel integration of fractional-order sliding mode control with Linear Quadratic Regulator (LQR)–based optimization. Unlike conventional integer-order sliding mode control (SMC), the approach employs a fractional-order sliding surface, introducing an additional degree of freedom that enhances control flexibility and robustness. Furthermore, the LQR-based optimization scheme is utilized to systematically obtain optimal control parameters by minimizing a cost function that balances structural response reduction and control effort, thereby eliminating the need for heuristic tuning commonly used in existing fractional-order SMC methods. For the first time, the proposed OFOSMC strategy is applied to the control of building structures equipped with an ATMD system, offering a novel and robust method for mitigating seismic responses of structures. For this end, the design of the proposed OFOSMC strategy is implemented for a benchmark 11-story shear frame equipped with an ATMD system under an artificial earthquake record. Finally, the performance of the designed OFOSMC strategy is assessed through analyzing its ability in the reduction of the building structure’s seismic responses subjected to both near-fault and far-fault earthquake excitations. A comparative study is conducted against several existing control strategies. Comparative results demonstrate that the OFOSMC strategy exhibits superior effectiveness in mitigating the structural responses during real earthquake excitations.
Mandegar et al. (2026) studied this question.