www.as-se.org/ccse Communications in Control Science and Engineering (CCSE) Volume 1 Issue 2, April 2013 18 Adaptive-robust Control of a Smart Beam with Support Excitation Using Piezoelectric Layers Mohammad Azadi *1 , Vahid Azadi 2 Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Fars, Iran Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran *1 mazadi@shirazu.ac.ir; 2 vahid.azd@gmail.com Abstract In this paper, vibrations of a beam with support excitation and a tip mass are suppressed using piezoelectric layers. The beam is fixed to a motion support from one end and the other end is free with an attached mass. The beam is considered as an Euler-Bernoulli beam. The governing equations of motion are derived based on the generalized function theory and Lagrange-Rayleigh-Ritz technique. An adaptive-robust control scheme is applied to control the vibrations of the beam. The mathematical modelling of the beam with control algorithm is derived and in purpose to study the effect of the amount of tip mass, size and location of the piezoelectric layers and the type of the support excitation on the beam vibrations, the system is simulated. Finally, the results of simulation are presented. Keywords Adaptive-robust Control; Smart Beam; Support Excitation; Piezoelectric Layers Introduction Vibration suppression of a cantilever beam with support motion has been the subject of much attraction in recent years. Zavodney and Nayfeh (1989) studied the non-linear response of a slender cantilever beam carrying a lumped mass to a principal parametric base excitation. They used the Euler- Bernoulli theory for a slender beam that reciprocated along the beam axis to drive the governing non-linear partial differential equation for an arbitrary position of the lumped mass. A combination of the method of multiple scales and Galerkin procedure are used by Pai and Nayfeh (1990) to analyze the non-linear response of a cantilever beam subject to lateral harmonic base exaltations. Jalili et al. (2002) have presented a non model-based controller for a flexible cantilever beam with PZT patch actuator attachment and subjected to a moving base. They used the linear formulations to drive the equation of motion. Tso et al. (2003) introduced an optimal sensing system consisting of a laser diode and a position sensitive detector, for the real-time measurement of the dynamic deflection. Foutsitzi et al. (2003) studied vibration control of a beam with bonded piezoelectric sensors and actuators. They derived the equation of motion for the beam structure by using the Hamilton's principle. They also designed a H2 robust controller and showed that the vibration can be significantly suppressed by the proposed controller. Turner (2004) investigated the non-linear vibration of a linear beam with cantilever-Hertizian contact boundary conditions. He used the method of multiple scales to analyze this problem in which it is assumed that the beam remains in contact with moving surface at all times. Sun et al. (2004) described an approach for the use of smart materials, specifically, piezoelectric materials (PZT), in control of a single-link flexible manipulator. Lin and Nien (2005) investigated modelling and vibration control of a composed cantilever beam using piezoelectric damping-model actuators/sensors. Lin and Liu (2006) presented a novel resonant fuzzy logic controller (FLC) to minimize cantilever beam vibration using collocated piezoelectric actuator/sensor pairs. An active control scheme was used to restrain vibration of a cantilever beam system by Xinke and Haimin (2007). Mahmoodi et al. (2008) studied the nonlinear vibration analysis of a directly excited cantilever beam modelled as an inextensible viscoelastic Euler-Bernoulli beam. Santillan et al. (2008) investigated Large-amplitude in-plane beam vibration using numerical simulations and a perturbation analysis applied to the dynamic elastic model. Alhazza et al. (2009) developed a simple multimode delayed- acceleration feedback controller to mitigate the vibrations of a flexible cantilever beam using a single sensor and a single piezoelectric actuator.