Optimal Control Of Structural Vibrations

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International Journal of Mechanical Sciences 50 (2008) 559–568 www.elsevier.com/locate/ijmecsci

Optimal control of structural vibrations using a mixed-mode magnetorheological fluid mount
Seung-Bok ChoiÃ, Sung-Ryong Hong, Kum-Gil Sung, Jung-Woo Sohn
Smart Structures and Systems Laboratory, Department of Mechanical Engineering, Inha University, Incheon 402-751, Republic ofKorea Received 14 June 2006; received in revised form 31 July 2007; accepted 7 August 2007 Available online 11 August 2007

Abstract In this work, a mixed-mode magnetorheological (MR) mount is proposed and applied to the vibration control of a flexible beam structure subjected to external disturbances. On the basis of non-dimensional Bingham number, an appropriate size of the MR mount isdesigned and manufactured. After experimentally evaluating the field-dependent damping force of the MR mount, a structural system consisting of a flexible beam and vibrating rigid mass is established. The governing equation of motion of the system is derived and expressed as a state space control model. A linear quadratic Gaussian (LQG) controller is then designed in order to attenuate the vibration ofthe structural system. The controller is empirically realized and control responses such as acceleration and displacement of the structural system are evaluated and presented in frequency domain. r 2007 Elsevier Ltd. All rights reserved.
Keywords: MR fluid; MR mount; Mixed-mode; Optimal control; Vibration control; Flexible structure

1. Introduction In general, a flexible structure system consistsof two components: one is a vibrating machine and the other is a supporting structure [1–3]. In order to reduce unwanted vibration of the flexible structure system, various types of mounts are adopted in passive or active control manner. The passive rubber mount, which has low damping, shows efficient vibration performance at the non-resonant and high-frequency excitation. Thus, the rubber mountis the most popular method applied for various vibrating systems. However, it cannot have a favorable performance due to small damping effect at the resonant frequency excitation. On the other hand, the passive hydraulic mount has been developed to utilize dynamic absorber effect or meet large damping requirement in the resonance of low frequency domain [1,4,5]. The hydraulic mount has highdynamic stiffness, and this may deteriorate isolation performance in the non-resonant excitation domain. Thus,

ÃCorresponding author. Tel.: +82 32 860 7319; fax: +82 32 868 1716.

E-mail address: seungbok@inha.ac.kr (S.-B. Choi). 0020-7403/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmecsci.2007.08.001

the damping and stiffness of the passive mounts are notsimultaneously controllable to meet imposed performance criteria in a wide frequency range [5]. In order to overcome the limited performance of conventional passive mounts, active or semi-active mounts utilizing electromagnetic actuator [6,7], hydraulic servo actuator [8], and piezoelectric actuator [9,10] have been developed. The active mounts are normally operated by using external energy suppliedby actuators in order to generate control forces on the system subjected to excitations. On the other hand, the semi-active mounts cannot inject mechanical energy into the structural systems. But it can adjust damping to reduce unwanted vibration of the systems. Therefore, the semi-active mounts do not destabilize the structural systems. Recently, these adjustable semi-active mounts have beendesigned by incorporating electro-rheological (ER) fluids [11–13]. Furthermore, numerous researches on semi-active dampers featuring magnetorheological (MR) fluids have been developed for the purpose of vibration attenuation of dynamic systems [14–16]. The rheological changes of ER or MR fluids are primarily observed as a significant increase of the yield

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