A tuning algorithm for a sliding mode controller of buildings with ATMD

This paper proposes an automatic tuning algorithm for a sliding mode controller (SMC) based on the Ackermann's formula, that attenuates the structural vibrations of a seismically excited building equipped with an Active Tuned Mass Damper (ATMD) mounted on its top floor. The switching gain and sliding surface of the SMC are designed through the proposed tuning algorithm to suppress the structural vibrations by minimizing either the top floor displacement or the control force applied to the ATMD. Moreover, the tuning algorithm selects the SMC parameters to guarantee the following closed-loop characteristics: 1) the transient responses of the structure and the ATMD are sufficiently fast and damped; and 2) the control force, as well as the displacements and velocities of the building and ATMD are within acceptable limits under the frequency band of the earthquake excitation. The proposed SMC shows robustness against the unmodeled dynamics such as the friction of the damper. Experimental results on a reduced scale structure permits demonstrating the efficiency of the tuning algorithm for the SMC, which is compared with the traditional Linear Quadratic Regulator (LQR) and with the Optimal Sliding Mode Controller (OSMC).