Optimal vibration control of beams subjected to a mass moving at constant speed

Abstract

This paper studies the optimal control of vibration of a beam excited by a moving mass. One important background of this work is vehicle-bridge interaction. As this is a time-varying system, some methods suitable for time-invariant systems are not always effective and will lead to suboptimal solutions when applied. In this particular vibration problem, the terminal time instant when the moving mass leaves the beam and the moving mass as the source of excitation are known. This particularity allows this problem to be expressed in a very simple way as a fixed terminal-time optimal control problem. In this paper the limitations of the practical implementation of the control solution are discussed in relation to different performance indices and actuation strategies. Numerical results obtained by using several control methods (time-invariant, time-variant with or without bounds on the control force) are analyzed and compared. It is shown that for particular actuator locations the use of time-varying control strategy instead of a time invariant strategy is necessary. The approach of formulating the system equation in an augmented form put forward in this paper is shown to yield accurate results at lower cost than the conventional time-dependent Riccati equation method. This approach is expected to be applicable to optimal control of vibration of other more complicated time-variant systems.