Wave-absorbing control for flexible structures with noncollocated sensors and actuators

Abstract

A control method for vibration suppression of flexible structures with noncollocated sensors and actuators is introduced. A simple expression of response of flexible structural networks is also shown. The control method is an extension of wave-absorbin g control based on the concept of disturbance propagation. Disturbance propagation in a flexible structure modeled as a distributed parameter system is treated in the frequency domain, and the usual modal expansions are not employed for modeling the system. Response of structural networks is obtained from exact solutions of Laplace-transformed equations of motion. Boundary conditions are expressed in terms of reflection/transmission of traveling waves, and controllers with noncollocated sensors and actuators are designed to suppress outgoing waves at boundaries of the structure. Responses of the controlled systems to external disturbances are analyzed through numerical examples. I. Introduction S UPPRESSION of traveling disturbances of flexible space structures becomes one of significant topics in the control problem of large space structures (LSS) in accordance with increase of size and flexibility of LSS. Disturbances applied on an LSS propagate over the structure through structural members, reflect at ends or junctions of the structure, and finally form standing waves. Control of traveling waves is required to cancel the generated disturbances in the neighborhood of each excited point before they propagate over the structure. The conventional modal approach to the vibration control is also applicable to control of traveling waves. Modal control of traveling waves, however, needs a large number of modes to describe traveling waves in a sufficient degree of accuracy and results in a controller that requires much computation. Bennighof and Meirovitch1 apply independent modal-space control (IMSC) and direct feedback control to active suppression of traveling waves in structures. Their approach requires a number of actuators as well as controlled modes, and it is demonstrated that direct feedback control is more suitable than IMSC truncated to low order for the problem in which a large number of higher modes have to be controlled. Wave-absorbing control, which results from a description of the structural response in terms of propagating elastic disturbances, is the alternative to the modal control method, and its theoretical features are more suitable for control of traveling waves than the modal approach. System model of the structures is treated as distributed parameter system in frequency domain, and the modal methods are not employed in the present analysis. The model responses are described in terms of propagating disturbances. The concept of the wave-absorbing control is applied to the control of LSS by von Flotow2'3 and von Flotow and Schafer.4 They introduce the viewpoint that the elastic response of large spacecraft structures may be aptly viewed in terms of the disturbance propagation characteristics of the structure2 and