Simulation study of active vibration control of beams supported at both ends using optimal controllers

This paper deals with the design of different optimal controllers for attenuating the vibration of beams supported at both ends, viz. fixed-fixed and fixed-roller beams which form multiple input and multiple output (MIMO) system. The beam structure consists an array of sensors and actuators, mounted in a collacated manner at the root of the beam, coupled with a controller. Finite element model of the beam is obtained using ANSYS©, and through the modal analysis eigen values and eigen vectors are extracted. The state space matrices of the beam structures are obtained by mathematical modelling which is done in MATLAB©. The simulation study is performed using three optimal controllers, viz. Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian (LQG), and H-
_∞
, governed by state feedback and output feedback control laws. To reduce the computational time, the significantly contributing modes are considered. LQR controller gain is determined by considering the quadratic cost function. LQG regulator is obtain by combining the LQR gain and Kalman gain. H-
_∞
controllers maintains the stability and robustness of the system within prescribed limits. The simulation results of these three optimal controllers are further compared and the significant finding are reported in the paper.