%0 Journal Article
%T Adaptive Vibration Control of Piezoactuated Euler-Bernoulli Beams Using Infinite-Dimensional Lyapunov Method and High-Order Sliding-Mode Differentiation
%A Teerawat Sangpet
%A Suwat Kuntanapreeda
%A R¨¹diger Schmidt
%J Journal of Engineering
%D 2014
%I Hindawi Publishing Corporation
%R 10.1155/2014/839128
%X This paper presents an adaptive control scheme to suppress vibration of flexible beams using a collocated piezoelectric actuator-sensor configuration. A governing equation of the beams is modelled by a partial differential equation based on Euler-Bernoulli theory. Thus, the beams are infinite-dimensional systems. Whereas conventional control design techniques for infinite-dimensional systems make use of approximated finite-dimensional models, the present adaptive control law is derived based on the infinite-dimensional Lyapunov method, without using any approximated finite-dimension model. Thus, the stability of the control system is guaranteed for all vibration modes. The implementation of the control law requires a derivative of the sensor output for feedback. A high-order sliding mode differentiation technique is used to estimate the derivative. The technique features robust exact differentiation with finite-time convergence. Numerical simulation and experimental results illustrate the effectiveness of the controller. 1. Introduction Flexible structures have attracted interest because of their lighter weight compared to traditional structures. They have been widely used in aerospace applications and robotics [1¨C3]. However, the flexibility leads to vibration problems. Therefore, vibration control is needed. Over the past few decades, active vibration control has drawn more interests from researchers since it can effectively suppress the vibration [4¨C7]. Piezoelectric actuators and sensors provide an effective means of vibration suppression of flexible structures [8]. The advantages of using piezoelectric actuators and piezoelectric sensors include nanometer scale resolution, high stiffness, and fast response. Many researchers have studied the vibration suppression of flexible structures using piezoelectric actuators and piezoelectric sensors. In [9], Tavakolpour et al. proposed a self-learning vibration control strategy for flexible plate structures. A control algorithm is based on a P-type iterative learning with displacement feedback. Wang et al. [10] presented a simple control law for reducing the vibration of the flexible structure. Linear feedback control was derived using a linear matrix inequality method. Qiu et al. [11] proposed a neural network controller based on PD control with collocated piezoelectric actuator and sensor. The back-propagation algorithm was utilized for adapting the controller parameters. In [12], Sangpet et al. utilized a fractional-order control approach to improve the delay margin in the control system of a
%U http://www.hindawi.com/journals/je/2014/839128/