Abstract
An adaptive solution to semiactive control of cable vibration is formulated by extending the linear quadratic Gaussian (LQG) control from time domain to frequency domain. Frequency shaping is introduced via the frequency dependent weights in the cost function to address the control effectiveness and robustness. The Hilbert-Huang transform (HHT) technique is further synthesized for online tuning of the controller gain adaptively to track the cable vibration evolution, which also obviates the iterative optimal gain selection for the trade-off between control performance and energy in the conventional time domain LQG (T-LQG) control. The developed adaptive frequency-shaped LQG (AF-LQG) control is realized by collocated self-sensing magnetorheological (MR) dampers considering the nonlinear damper dynamics for force tracking control. Performance of the AF-LQG control is numerically validated on a bridge cable transversely attached with a self-sensing MR damper. The results demonstrate the adaptivity in gain tuning of the AF-LQG control to target for the dominant cable mode for vibration energy dissipation, as well as its enhanced control efficacy over the optimal passive MR damping control and the T-LQG control for different excitation modes and damper locations.
Highlights
The free span of modern cable-stayed bridges increases to exceed 1000 m, such as the Stonecutter Bridge [1], the Sutong Bridge [1, 2], and the Russky Bridge [2], which results in stay cables of over 500 m in length
Simulations of a stay cable equipped with the self-sensing MR damper are conducted to demonstrate the control performance of the developed control strategy, which is compared with that achieved by using the passive MR damping control and the T-linear quadratic Gaussian (LQG) control
An adaptive frequency-shaped LQG (AF-LQG) control strategy is developed for effectively operating self-sensing MR dampers to suppress vibration of bridge cables
Summary
The free span of modern cable-stayed bridges increases to exceed 1000 m, such as the Stonecutter Bridge [1], the Sutong Bridge [1, 2], and the Russky Bridge [2], which results in stay cables of over 500 m in length. This paper aims at presenting an adaptive control methodology for smart cable damping from the frequency domain perspective To achieve this goal, the LQG control is extended from the time domain to the frequency domain by synthesizing it with a frequency-shaped quadratic cost function [27]. The frequency-shaped LQG controller is developed to possess adaptivity in online tuning the frequency dependent weights and the controller gain based on the Hilbert-Huang transform (HHT) technique [28] to adapt to the vibration evolution. This development improves the frequency targeting capability of the controller and obviates the iterative procedure of weight selection in the T-LQG control design. Simulations of a stay cable equipped with the self-sensing MR damper are conducted to demonstrate the control performance of the developed control strategy, which is compared with that achieved by using the passive MR damping control and the T-LQG control
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