<p>In this research, active control and forced vibrations of a smart sandwich microbeam with a viscoelastic core and piezoelectric face sheets are investigated, in which the top and bottom layers are considered as actuator and sensor, respectively. Displacement fields and governing equations are obtained based on Timoshenko’s beam theory and modified couple stress theory (MCST). The micro sandwich is resting on Vlasov’s foundation, and a harmonic force is applied to the structure. For optimal vibration control, the equations of motion are solved in state-space form using the linear quadratic regulator (LQR) approach. The effect of the viscoelastic parameter and LQR on vibration response is illustrated. Moreover, the influence of the viscoelastic parameter, loss factor, Vlasov’s foundation, and the length-to-thickness ratio on the frequency response, and natural frequency of a smart sandwich microbeam is analyzed. The results show that Vlasov’s foundation increases the loss factor and natural frequency, especially for lower length-to-thickness ratios. For length-to-thickness ratios 2 and 10, the natural frequency of the second mode increases by about 3.4 and 2.8 times relative to the natural frequency of the first mode, respectively, while this value is 7.4 and 5 times for the natural frequency of the third mode, but the length-to-thickness ratio has no significant effect on the loss factor. Additionally, the amplitude of vibration reduces significantly in a smart sandwich microbeam using LQR.</p>