A geometric approach to the design of remotely located vibration control systems

Abstract

Over the past three decades, a wide variety of active control methods have been proposed for controlling problematic vibration. The vast majority of approaches make the implicit assumption that sensors can be located in the region where vibration attenuation is required. For many large scale structures or where the system environment is harsh, this is either not feasible or it is prohibitively expensive. As a result, the optimal control of local vibration may lead to enhancement at remote locations. Motivated by such problems in marine system environments, this paper describes a simple geometric methodology that provides an approach for defining the design freedom available for reducing vibration both at local and remote locations. The results can be used to develop design procedures for both discrete frequency and broad-band control. Robustness to modelling error can also be treated in the same geometric framework. Validation of the approach is carried out using an experimental facility that has been developed to replicate the problems associated with rotor blade vibration.

Introduction

Vibration problems generally occur either at specific discrete frequencies, caused by periodic disturbances such as out of balance forces in rotating machines, or in a narrow band, often associated with lightly damped structural modes. For both discrete frequency (or harmonic) and narrow-band control, the design aim is to minimize the vibration at specific measured points on a structure and a number of well established design methods are available (for example Refs. [1], [2], [3], [4], [5]). The optimum solution is often based solely on information local to the actuators and implementation can, in practice, result in increased levels of vibration at remote locations. Such problems are particularly evident in large scale interconnected structures where it is neither feasible nor cost effective to provide a wide distribution of sensors and actuators. Attainment of a globally optimal solution may therefore necessitate the implementation of a locally sub-optimal one.

The work presented here was motivated by the first author's previous research in the area of vibration control for marine systems [6] and where, specifically, it is not practically viable to permanently locate sensors at all points where vibration attenuation is ultimately required. This is particularly true in ship propulsion transmission systems where propeller blade excitation at specific blade passing frequencies can lead to significant large area hull excitation causing passenger and crew discomfort, self-noise sonar interference and, in extreme cases, catastrophic fatigue failure [7], [8]. Similar problems occur in helicopter rotor systems where blade-induced vibration transmits through the fuselage which, not only compromises the reliability of on-board electronic equipment, but also leads to reduced flight envelopes [9]. Also in aerospace applications, the increasing use of lightweight and flexible structures often results in wide area flow-induced vibration that can lead to dynamic aero-elastic instabilities such as wing flutter, with the potential to cause structural failures in flight [10].

Although the issue addressed here is relevant to a wide variety of systems, it is particularly apposite for bladed power transmission systems. The active approach to vibration control of a practical rotor blade system is made particularly difficult by the harsh environment in the proximity of the blades. There are also difficulties relating to the practical implementation of actuators and sensors in rotating frames [11]. Nevertheless, a number of active and semi-active solutions have been proposed to tackle the vibration problem at source by, for example, the integration of smart materials into the blades [12], [13], [14]. However, such solutions are costly, difficult to maintain and are unproven in real operational environments. An alternative approach is to attenuate the resultant vibration by actuating within the shafting system [6], [15] but this can lead to increased excitation of the blades or elsewhere in the power train. This is tackled here by considering the generic problem of determining strategies for the attenuation of both the local and the remote vibration using only local sensing and control actions.

In the paper a number of new results are presented that define the freedom available to the designer for providing both local and remote vibration reduction and a simple, yet powerful, geometric design methodology is introduced. The efficacy of the new design methodology is illustrated using a laboratory scale test rig that has been developed to replicate the generic problems associated with the propagation of rotor blade vibration through the power train.