%0 Journal Article
%T Experimental Verifications of Vibration Suppression for a Smart Cantilever Beam with a Modified Velocity Feedback Controller
%A Ting Zhang
%A Hong Guang Li
%A Guo Ping Cai
%A Fu Cai Li
%J Shock and Vibration
%D 2014
%R 10.1155/2014/172570
%X This paper presents various experimental verifications for the theoretical analysis results of vibration suppression to a smart flexible beam bonded with a piezoelectric actuator by a velocity feedback controller and an extended state observer (ESO). During the state feedback control (SFC) design process for the smart flexible beam with the pole placement theory, in the state feedback gain matrix, the velocity feedback gain is much more than the displacement feedback gain. For the difference between the velocity feedback gain and the displacement feedback gain, a modified velocity feedback controller is applied based on a dynamical model with the Hamilton principle to the smart beam. In addition, the feedback velocity is attained with the extended state observer and the displacement is acquired by the foil gauge on the root of the smart flexible beam. The control voltage is calculated by the designed velocity feedback gain multiplied by the feedback velocity. Through some experiment verifications for simulation results, it is indicated that the suppressed amplitude of free vibration is up to 62.13% while the attenuated magnitude of its velocity is up to 61.31%. Therefore, it is demonstrated that the modified velocity feedback control with the extended state observer is feasible to reduce free vibration. 1. Introduction In recent years, a smart system, which consists of a cantilever beam bonded with a piezoelectric actuator, has drawn much interest of many researchers [1¨C5]. At the same time, the controller designs based on positioning control and vibration suppression of the smart system have attracted wide attention around the world [6]. Especially for dynamic modeling task and vibration reduction work of a smart cantilever beam with piezoelectric materials, there have been lots of studies on suppressing vibration with a designed controller [7]. For example, a full-order model is developed using assumed model expansion and the Lagrangian approach for a flexible cantilever beam bonded with a PZT patch to control a base motion [8], a finite element model of the three-layered smart beam is utilized to reduce vibration by a velocity feedback controller [9], and the multimodal vibration suppression of a smart flexible cantilever beam with piezoceramic actuator and sensor by using a pole placement method is proposed [10]. As for adopted control law to suppress vibration of mechanical system, in the past several years, many researchers have committed to the work on vibration control of a smart beam with piezoelectric sensor and actuator by a variety of
%U http://www.hindawi.com/journals/sv/2014/172570/