268 Asian Journal of Control, Vol. 9, No. 3, pp. 268-291, September 2007 Manuscript received November 16, 2004; revised April 7, 2006; accepted July 3, 2006. B. Bandyopadhyay is with the Interdisciplinary Programme in Systems and Control Engineering, ACRE Building, Indian Institute of Technology Bombay, Mumbai, India (e-mail: bij- nan@ee.iitb.ac.in). T.C. Manjunath is with the Electronics and Communications Eng. Dept., East West Institute of Technology, Bangalore, Karnataka, India (e-mail: tcmanjunath@rediffmail.com). FAULT TOLERANT CONTROL OF FLEXIBLE SMART STRUCTURES USING ROBUST DECENTRALIZED FAST OUTPUT SAMPLING FEEDBACK TECHNIQUE B. Bandyopadhyay and T.C. Manjunath ABSTRACT This paper presents the modeling, design and simulation of a Robust Decentralized Fast Output Sampling (RDFOS) feedback controller for the vibration control of a smart structure (flexible cantilever beam) when there is actuator failure. The beam is divided into 8 finite elements and the sensors / actuators are placed at finite element positions 2, 4, 6, and 8 as collocated pairs. The smart structure is modeled using the concepts of piezoelectric theory, Euler-Bernoulli beam theory, Finite Element Method (FEM) techniques and the state space techniques. Four multi-variable state-space models of the smart structure plant are obtained when there is a failure of one of the four actuators to function. The effect of failure of one of the piezo actuators to function during the vibration of the beam is observed. The tip displacements, open and closed loop responses with and without the controller are observed. For all of these models, a com- mon stabilizing state feedback gain F is obtained. A robust decentralized fast output sampling feedback gain L which realizes this state feedback gain is obtained using the LMI approach. In this designed control law, the control inputs to each actuator of the multi-model representation of the smart structure is a function of the output of that corresponding sensor only and the gain matrix has got all off-diagonal terms zero and this makes the control design a robust decentralized one. Then, the perfor- mance of the designed smart system is evaluated for Active Vibration Control (AVC). The robust decentralized FOS controller obtained by the designed method requires only constant gains and hence may be easier to implement in real time. KeyWords: Smart structure, robust decentralized fast output sampling feedback control, Euler-Bernoulli theory, finite element method, state space model, multivariable model, vibration control, linear matrix inequality. I. INTRODUCTION Vibration control of any system is always a formidable challenge for any control system designer and thus, the active vibration control becomes an important problem in structures. One of the ways to tackle this problem is to make the structure smart, adaptive and intelligent by mak- ing use of smart materials such as Piezoelectrics (PZT’s), MR Fluids, Piezoceramics, ER Fluids, Shape Memory Al- loys (SMA), PVDF, Optic fibres, etc. The need for intelli-