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.

Scalable distributed optimal control of vibrating modular structures

“…The linear system represents the dynamics of a wide range of smart structures that can be controlled by integrated force actuators. Apart from the typical examples of such structures, namely, bridges and slender buildings exposed to earthquake or wind forces, offshore platforms subjected to sea waves or wind turbine blades exposed to wind flow which are controlled by means of electric motors or active tuned mass systems, we can also see new emerging designs that employ piezoelectric actuators and shape memory alloys or polymer‐based artificial muscles . In the present paper, we will consider a modular cantilever beam equipped with a set of electromagnetic force actuators.…”

Dynamic Responses of an Overhead Crane’s Beam Subjected to a Moving Trolley with a Pendulum Payload

“…affected by the three different types of acceleration curves when the acceleration (deceleration) time is equal to the swing period of the payload, as shown in Figure 2. Figures 6(a)-6(c), respectively; keeping these three maximum trolley acceleration values satisfies equation (18).…”

“…It has been demonstrated that the dynamic behavior of the beam is affected by many parameters, such as the mass of the moving load [15], the load's acceleration [16,17], the load's speed [5,18], and many others. Extensive research has been done on the methods and efforts of limiting undesirable payload swing, such as an energy-based control scheme [19], input shaping technology [20], nonlinear coordination control [21], neural network control [22], fuzzy control [23], a trajectory planning method [24], and so forth.…”

Optimal vibration control of moving-mass beam systems with uncertainty

“…Such bridge-vehicle system and gunprojectile system are generally taken as beam-moving mass systems (BMSs). [1][2][3][4] Recently, more and more attention has been attracted to optimal controller design of BMSs, such as time-varying optimal controller design in vehiclebridge interaction, 5 constant gain feedback gain design in vehicle-railway system, 6 the contribution of displacement-velocity feedback controller on the BMSs, 7 the influence of Lyapunov-based boundary controller on statically indeterminate beam 8 and the usage of a proportional-integral controller on the magnetic wheelsguide rail system. 9 Due to the uncertainties of system parameters and/or input disturbances, an optimal controller should be designed as uncertain.…”