Fault tolerant control of flexible smart structures using robust decentralized fast output sampling feedback technique

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 common 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 performance 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.