Online adaptive semi-active vibration damping of slender structures subject to moving loads

Abstract

The paper deals with the adaptive optimal semi-active control of the slender vibrating structures subjected to the moving loads. The deflection of the structure is governed by Euler-Bernoulli beam equation approximated by the system of bilinear ordinary differential equations. The damping function of the structure support is chosen as the control function. The optimal control problem consists in finding such bang-bang control function to minimize the energy as well as the vibrations of the carrying structure. Although the switched optimal control is a very efficient tool in the reduction of structure vibrations it is very sensitive with respect to changes of the speed of the traveling load. This paper deals with the development of the adaptive descent type algorithm that enables the update of the optimal controls in real time based on the measured speed of the traveling load or structure’s state. The proposed algorithm uses reference optimal controls computed for the constant speeds and the set of functions describing the sensitivity of the system dynamics with respect to the measured parameters. Numerical computations are carried out for different speed scenarios of the moving load. The obtained numerical results indicate that the proposed adaptive controller can significantly outperform the reference optimal solutions.