Robustness and vibrational control of adaptive structures by the useof piezoelectric sensors and actuators

Abstract

One of the main applications of smart structiires is in the vibration control of flexible structures using smart sensors and actuators. A commonly used smart sensors and actuators are piezoelectric senors and actuators. The control schemes developed so far for this application have assumed a perfect structure with out any flaws as the plant model. But in general, there are discrepancies between the mathematical model and the physical system. Such discrepancies are due to damages or flaws. The controller designed for a perfect structure can not be used for the damaged structure. The result will be a poor performance or a system instability. Hence a robust controller is required to account for flaws or damages . Here delamination is assumed to be the damage in a composite beam The effects of delaminations are considered as uncertainities. p synthesis is used to develop a robust controller. *Graduate Student, Student Member AIAA tProfessor,Member AIAA '@copyright c 1991 by the American Institute of Aeronautics and Astronautics,Inc. All rights reserved INTRODUCTION During the past several years, there has been a considerable amount of research activity to use bonded or embedded piezoceramic (or PVDF) sensors and actuators to control vibration in light weight structures. Bonded piezoceramic sensors and detection circuits can be designed such that the rate of deformation of a beam structure will result in a signal that is proportional to the difference of the slope rate a t the two ends of the transducer1. Similar results can be derived for voltage time histories as a function of the deformation rates of other types of structures. The detected signal can be conditioned by operations such as filtering, phase shift and amplification. The conditioned signals are used as inputs to bonded or embedded piezoceramic actuators to transmit energy to the structure. The objective of operations of sensing, conditioning and feed back to selected actuators is to design a vibration controller to the structure. An early application of piezoelectric transducers to active control of structures has been attributed to 01sen2 . Other reported early applications of piezoceramic transducers to vibration control, that followed Olsen's work are due to orw ward^, Forward and Liu4, Forward and Swigert5, Forward,Swigert and 0ba16,Hanagud and 0ba17~8, Crawley and ~ e L u i s @ and ~ansonl ' . Similarly, early work in the area of vibration control by using PVDF film is by Bailey and Hubbard''. Since then, there has been an explosion in the research activity on using piezoceramic transducers, PVDF films, Shape memory alloys, electrostricive transducers, voice coil actuators and electro rheological fluids to control vibrations. Jet propulsion laboratory has demonstrated the use of piezoceramic transducer in the control of vibrations in a space truss like structure. Hanagud and his colleagues have used artificial intelligence techniques to control vibrations in a time varying adaptive structures l2%l3and health monitoring of structures14. In a recent work Hanagud15 and ~ a n s o n l ~ have discussed robust vibration control by the use of piezoceramic sensors and actuators. Robustness has been addressed to account for unmodelled dynamics15116 and debonded sensors 15. However , none of the reported work has addressed the problem of robust control that is needed to account for inaccurate sensor output due to imperfections and flaws in structures. This problem has been addressed in this paper. ROBUST CONTROL PROBLEM SETTING We are considering the problem of designing a vibration controller for a flexible structure. In particular, we are focussing our attention on the problem of vibration control of layered composite beams subjected to a prescribed set of disturbances. The problem of vibration suppression is being accomplished using a set of piezoceramic sensors and actuators which are bonded to the structure a t seFigure 1: Effect of delamination on sensor sig-