Dynamics and optimal control of an electromagnetically actuated cantilever pipe conveying fluid

摘要

This paper deals with the problem of applying electromagnetic devices of the motional type to improve the dynamic stability of a pipe conveying air. When the flow velocity reaches a critical value, the steady equilibrium position becomes unstable, and self-excited lateral vibrations arise. In contrast, electromagnetic devices of the transformer type have been demonstrated to be highly effective in the passive stabilization of such a system, as well as the active stabilization of similar non-conservative systems with a follower force. In the present paper, we apply a pair of motional devices made of a conducting plate which is attached to the pipe and moves together with it within the perpendicular magnetic field generated by the controlled electromagnets. This motion generates eddy currents in the plates and a drag force of a viscous character. In this setting, we first investigate the possibility of designing a stabilizing control within the region of the magnetic field where every passive solution results in an unstable or conservative state. For that purpose, we determine a practical condition justifying the existence of a stabilizing control for a given set of system parameters. Later we pose and solve an optimal control problem aiming at stabilizing the system with the optimal rate of decrease of the system's energy. The solution is examined by means of numerical simulations performed within the three regions of the flow velocity: low subcritical, where the Coriolis acceleration of the conveyed fluid generates the predominate damping force; high subcritical, where the inertia of the fluid begins to dominate the dynamics of the system; and low supercritical, where unstable flutter vibrations start to arise. The effectiveness of the designed optimal controller is validated by comparisons with the corresponding passive solutions. (C) 2018 The Authors. Published by Elsevier Ltd.