Stabilization of an axially moving web via regulation of axial velocity

In this paper, a novel control algorithm for suppression of the transverse vibration of an axially moving web system is presented. The principle of the proposed control algorithm is the regulation of the axial transport velocity of an axially moving beam so as to track a profile according to which the vibration energy decays most quickly. The optimal control problem that generates the proposed profile of the axial transport velocity is solved by the conjugate gradient method. The Galerkin method is applied in order to reduce the partial differential equation describing the dynamics of the axially moving beam into a set of ordinary differential equations (ODEs). For control design purposes, these ODEs are rewritten into state-space equations. The vibration energy of the axially moving beam is represented by the quadratic form of the state variables. In the optimal control problem, the cost function modified from the vibration energy function is subjected to the constraints on the state variables, and the axial transport velocity is considered as a control input. Numerical simulations are performed to confirm the effectiveness of the proposed control algorithm.

► A control algorithm using regulation of axial velocity for suppression of the transverse vibration of an axially moving beam system is investigated.
► Galerkin method is used to obtain the dimensional discrete model of the axially moving beam system.
► A design procedure based on the conjugate gradient method is introduced to generate the proposed velocity profile.
► The proposed control algorithm provides a solution to problem of the vibration control of axially moving systems when the application of boundary control technique is impossible.