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中文摘要：
采用时滞主动控制方法对输液管道的颤振失稳进行控制，以提高输液管道系统的临界流速。首先构造时滞控制策略并建立时滞控制的偏微分方程；然后利用伽辽金法离散时滞偏微分方程将其转化为时滞微分方程组，从理论上分析时滞微分方程的稳定性，并通过Matlab Biftool软件包对时滞控制系统的特征根分布情况进行模拟，与稳定性理论分析结果相当吻合；最后通过有限差分法对时滞偏微分方程进行数值模拟，与稳定性理论分析结果基本吻合。结果表明：通过时滞主动控制输液管道的颤振，控制策略简单，而且效果较好。
英文摘要：
A novel active control technique called delayed feedback control is proposed to control the flutter in the cantilever pipe conveying fluid. It＇s motivated to increase the critical flow velocity at which a pair of pure imaginary number occurs and the system becomes unstable. Firstly, a controllable strategy, e.g. delayed feedback control, is designed so that a nonlinear partial differential equation （PDE） with delay is modeled for the controlled system under consideration. Secondly, the Galerkin method is employed to transform the delayed PDE to be a set of delayed differential equations （DDE）. The stability of the DDE is considered analytically and the Matlab Biftool package is used to simulate the distribution of eigenvalue%. The analytical result is in a good qualitative agreement with the numerical one. Finally, the finite difference method is extended to study the solutions of the nonlinear partial differential equation with delay. Such numerical computation verifies the validity of the analytical results quantitatively. The results show that the provided strategy of delayed feedback control for flutter in the cantilever pipe conveying fluid is not only valid but also easily applied to engineering structures.
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