Vibration control is a fast-evolving topic, with research being conducted on various strategies to reduce dangerous vibration levels. Composite materials have the advantage of improved material qualities compared to metallic alloys while being low in weight. The current work primarily focuses on the design of the Linear Quadratic Gaussian (LQG) controller, Linear Quadratic Regulator (LQR) controller, and Proportional Integral Derivative (PID) controller used for the Active vibration control of Carbon/Glass epoxy reinforced composite beams, using various control techniques upon composite sandwich beams with Viscoelastic material core. The implementation of LQG controller, LQR controller, and PID controller is done using the displacement-time data obtained from the Finite Element analysis to obtain transfer function, state space representation and all other related data. From there, the necessary parameters are applied within each respective controller to check the change within amplitude and settling time using MATLAB-Simulink. Composite sandwich beams with a viscoelastic material core implanted between composite face plates have been designed, and active vibration control study has been conducted. The percentage reduction in settling time as well as vibrational amplitude has been discovered to be significant.