Nonsmooth active control method for base-smart isolated structures with roller bearings
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摘要: 以滾軸支座基礎隔震結構作為受控結構研究對象, 在該隔震結構的隔震層施加主動控制裝置, 形成智能隔震體系, 以控制隔震層的位移, 提高結構的安全性. 在智能隔震結構中引入非光滑控制算法, 基于隔震層位移和速度反饋, 提出了智能隔震結構的非光滑控制算法, 進一步根據Lyapunov穩定理論, 推導了在非光滑控制下智能控制閉環系統的全局有限時間穩定性. 結合一棟六層滾軸支座基礎隔震結構, 進行了非光滑主動控制算法下和LQG主動控制算法下的地震響應控制仿真分析. 結果表明, 智能隔震結構可有效控制結構的位移, 與被動隔震結構相比較上部結構的地震響應有一定程度的減小, 同時提出的非光滑控制算法與LQG控制算法相比較具有更好的控制效果, 相比LQG控制算法通過較少的反饋量即可實現反饋控制, 且非光滑控制算法具有良好的穩定性.Abstract: In applied structural control technology, base-isolated technology has become popular due to its advantage of simple shock absorption, stable performance, and reasonable cost. Currently, base isolation is extensively applied worldwide, and its role in mitigating the seismic response of structures continues to grow. Moreover, it has been proven effective in decreasing seismic response of structures under recent strong earthquakes. However, the displacement at the isolation layer is sometimes large under strong earthquakes, which will decrease the safety of the structure and perhaps lead to the failure of the isolation layer. Therefore, in this study, the base-isolated structure with roller bearings is taken to investigate the seismic response control of structures, and the active control devices are added in the isolation layer of the isolated structure to decrease the seismic displacement at the isolation layer, so that a smart-isolated structure is formed. Nonsmooth control algorithm is introduced in the smart-isolated structure. Based on the feedback of the velocity and displacement of the isolation layer, nonsmooth control algorithm is proposed for designing the smart-isolated structure. Moreover, according to Lyapunov stable theory, the global finite time stability of intelligent control closed-loop system under nonsmooth control is deduced. A six-layer isolated structure with roller bearings is used as an example, and a simulation analysis of seismic response control is performed based on the nonsmooth active control algorithm and linear quadratic Gaussian (LQG) active control algorithm. The results show that the smart-isolated technology can effectively control seismic displacement at the isolation layer, and compared with the passive isolated technology, the superstructure seismic response is significantly decreased. Meanwhile, the results demonstrate that compared with the LQG control algorithm, the nonsmooth control algorithm has a better control effect and can implement feedback control for base-isolated structures by using fewer feedbacks. Furthermore, the nonsmooth control algorithm has great stability.
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圖 2 滾軸支座單元和滾動示意圖. (a) 滾軸支座單元; (b) 滾軸支座滾動
Figure 2. Unit and roll of roller bearing: (a) unit of roller bearing; (b) roll of roller bearing
圖 11 LK0676波作用下結構隔震層響應曲線對比. (a) LK0676波作用下隔震層位移曲線對比; (b) LK0676波作用下隔震層加速度曲線對比
Figure 11. Curve comparison of structural isolation layer response under LK0676 wave: (a) curve comparison of isolation layer displacement under LK0676 wave; (b) curve comparison of isolation layer acceleration under LK0676 wave
圖 12 LK0714波作用下結構隔震層響應曲線對比. (a) LK0714波作用下隔震層位移曲線對比; (b) LK0714波作用下隔震層加速度曲線對比
Figure 12. Curve comparison of structural isolation layer response under LK714 wave: (a) curve comparison of isolation layer displacement under LK714 wave; (b) curve comparison of isolation layer acceleration under LK714 wave
圖 13 人工波作用下結構隔震層響應曲線對比. (a) 人工波作用下隔震層位移曲線對比; (b) 人工波作用下隔震層加速度曲線
Figure 13. Curve comparison of structural isolation layer response under artificial wave: (a) curve comparison of isolation layer displacement under artificial wave; (b) curve comparison of isolation layer acceleration under artificial wave
圖 14 LK0676波作用下上部結構層間位移峰值
Figure 14. Inter-story displacement peak of superstructure under LK0676
圖 16 LK0714波作用下上部結構層間位移峰值
Figure 16. Inter-story displacement peak of superstructure under LK0714
圖 18 人工波作用下上部結構層間位移峰值
Figure 18. Inter-story displacement peak of superstructure under artificial wave
圖 20 三種波作用下結構隔震層底部剪力曲線. (a) LK0676波作用下結構隔震層底部剪力曲線; (b) LK0714波作用下結構隔震層底部剪力曲線; (c) 人工波作用下結構隔震層底部剪力曲線
Figure 20. Bottom shear force of structural isolation layer under three waves: (a) bottom shear force of structural isolation layer under; (b) bottom shear force of structural isolation layer under LK0714 wave; (c) bottom shear force of structural isolation layer under artificial wave
圖 24 基礎隔震結構和智能隔震結構復位曲線
Figure 24. Reset curve of base-isolated structure and smart-isolated structure
表 1 MATLAB模型與ETABS模型周期
Table 1. Period of MATLAB model and ETABS model
振型號 MTALB周期/s ETABS周期/s 1 1.160 1.209 2 0.436 0.422 3 0.275 0.235 4 0.218 0.182 5 0.187 0.142 6 0.180 0.116 
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表 2 三條波分別作用下的隔震層響應峰值
Table 2. Peak values of isolation layer responses under three different waves
控制策略 LK0676波 LK0714 人工波 位移/
mm速度/
(m·s-1)加速度/
(m·s-2)位移/
mm速度/
(m·s-1)加速度/
(m·s-2)位移/
mm速度/
(m·s-1)加速度/
(m·s-2)隔震 120.65 0.49 2.24 110.58 0.54 2.12 91.92 0.49 1.87 LQG 43.57 0.37 2.06 48.92 0.36 1.93 36.48 0.24 1.63 非光滑 40.10 0.32 1.48 39.56 0.27 1.59 29.44 0.21 1.25
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表 3 隔震層底部剪力峰值
Table 3. Peak value of bottom shear force in the isolation layer
控制策略 剪力峰值/(103 kN) LK0676波 LK0714波 人工波 隔震 9.602 9.098 8.029 LQG 8.910 8.317 7.107 非光滑 6.678 6.903 5.672
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