Abstract Active control of flutter of a long span cable-stayed bridge is considered in this study. The control action is provided by winglets actuated using constant/variable gain output feedback controllers. Two FE modeling schemes are adopted, namely one element cables, and multi-element cables with each stay-cable discretized into multiple elements to consider the cable vibration effect. Cable discretization results in additional closely spaced modes. Rational function approximation of flat plate flutter derivatives is considered to model aeroelastic forces on deck and winglets. The output feedback controller yields the desired winglet rotation by using vertical and torsional displacements of the deck. Controllability Gramian and response indices are used to obtain the optimal location of winglets, while the best sensor location is obtained based on a combined index. This yields around 40% increase in the stability limit with winglets covering 12% of the central span, and eight measured outputs for feedback. Response indices reduce substantially if a shift from constant to variable gain is performed at a certain wind speed. Controller design based on the one-element model, when applied to the more realistic multi-element model, results in substantially lesser response attenuation. Hence, cable vibration needs to be consider for the controller design. Keywords: Flutter, Cable-stayed bridge, Winglet, Rational function approximation, Variable gain output feedback, Cable vibration.

中文翻译：

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用输出反馈驱动小翼控制斜拉桥的颤振

摘要 本研究考虑了大跨度斜拉桥颤振的主动控制。控制动作由使用恒定/可变增益输出反馈控制器致动的小翼提供。采用两种有限元建模方案，即单单元索和多单元索，每根斜拉索离散为多个单元以考虑索振动效应。电缆离散化导致额外的紧密间隔模式。考虑平板颤振导数的有理函数近似来模拟甲板和小翼上的气动弹性力。输出反馈控制器通过使用甲板的垂直和扭转位移产生所需的小翼旋转。可控性 Gramian 和响应指数用于获得小翼的最佳位置，而最佳传感器位置是基于组合索引获得的。这使小翼覆盖中心跨度的 12% 和八个用于反馈的测量输出的稳定性极限增加了约 40%。如果在特定风速下执行从恒定增益到可变增益的转变，则响应指数会显着降低。基于单元素模型的控制器设计，当应用于更真实的多元素模型时，会导致响应衰减显着减少。因此，控制器设计需要考虑电缆振动。关键词：颤振，斜拉桥，小翼，有理函数逼近，可变增益输出反馈，索振动。如果在特定风速下执行从恒定增益到可变增益的转变，则响应指数会显着降低。基于单元素模型的控制器设计，当应用于更真实的多元素模型时，会导致响应衰减显着减少。因此，控制器设计需要考虑电缆振动。关键词：颤振，斜拉桥，小翼，有理函数逼近，可变增益输出反馈，索振动。如果在特定风速下执行从恒定增益到可变增益的转变，则响应指数会显着降低。基于单元素模型的控制器设计，当应用于更真实的多元素模型时，会导致响应衰减显着减少。因此，控制器设计需要考虑电缆振动。关键词：颤振，斜拉桥，小翼，有理函数逼近，可变增益输出反馈，索振动。