Delayed feedback control for flutter in the pipe conveying fluid

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%s. 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.