ABSTRACT
The dynamics and control of flexible structures have merited increasing attention in recent years, because of the large potential to generate solutions to problems in important areas such as aeronautical and space engineering, precision mechanics and robotics. State-of-the-art in this field can be found in papers such as Book (1990, 1993), and books as Meirovitch (1990). A quite interesting question is related to the attenuation and control of vibrations induced in flexible devices during structure large maneuvers, which are the target of several papers such as Warren et al. (1995), Juang et al. (1986), Gildin (1998) and Lozano and Brogliato (1992), to give a few examples. Up to now, research has not tackled most of the theoretical difficulties concerning this field, especially in robotics, where the flexible motions are avoided
– and not properly faced – by employing maneuvers of high rigidity. Nowadays, the main limitations for practical usage of flexible structures are: first, the complex modeling involved in the treatment of this kind of device, if one intends to generate a simple and satisfactory model for controller design; second, the limitations of the actuators available at the present time. Concerning the first problem, one can refer to the works of Liu and Skelton (1993) and Kajiwara and Nagamatsu (1994), who discuss some aspects involved in simultaneous modeling and control design of flexible systems. This topic has to be considered as a fundamental one: it is quite difficult, if not impossible, to control movements of a structure which has not been designed for that. Even simple aspects in the design of flexible structures must be seen from a different approach. Simo and Vu-Quoc (1986) propose the formulation of a dynamic response of a flexible beam relative to an inertial frame, which is an alternative approach to the traditional formulations, referred to as a floating frame called a “shadow beam.” O¨zguner and Barbieri (1988) compare constrained and unconstrained mode expansions for a flexible slewing arm, remarking that the constrained mode expansion yields good results only if the flexible arm and the rigid hub moments of inertia ratio is small. About the second difficulty, several methods of control of vibrations have been proposed recently, such as the extensive usage of piezoelectric materials in the construction of sensors and actuators or the employment of variable positioning weights.
