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).

中文翻译：

---

基于ATMD的建筑物滑模控制器整定算法

本文提出了一种基于阿克曼公式的滑模控制器 (SMC) 自动调谐算法，该算法衰减了在其顶层安装有主动调谐质量阻尼器 (ATMD) 的地震激发建筑物的结构振动。SMC 的开关增益和滑动面是通过提出的调谐算法设计的，通过最小化顶层位移或施加到 ATMD 的控制力来抑制结构振动。此外，调谐算法选择 SMC 参数以保证以下闭环特性：1) 结构和 ATMD 的瞬态响应足够快和阻尼；2）控制力，以及建筑物和ATMD的位移和速度在地震激发频带下的可接受的范围内。所提出的 SMC 显示出对未建模动力学的鲁棒性，例如阻尼器的摩擦。缩小比例结构的实验结果证明了 SMC 调谐算法的效率，与传统的线性二次调节器 (LQR) 进行了比较。