This study is devoted to analyse of free and forced vibrations and semi-active control vibrations of sandwich microbeam with Functionally Graded Materials (FGM) and viscoelastic/electrorheological (ER) core. The intended model is for top and bottom layers of functionally graded materials with power law and a core model for Viscoelastic materials with complex shear modulus. Hamilton principle is used to determine the governing Equations of motion on the sandwich microbeam based on the modified couple stress theory. Mesh less method of Radial Basis Functions (RBF) is used to calculate natural frequency and the loss factor. All the effects of length scale parameter, shear modulus and changes due to variation of the electric field on the natural frequency and loss factor have been drawn. Combination of RBF method and forward difference led to evaluation of forced vibration and deflection of microbeam for length scale parameters and different electric fields under the dynamic load have been calculated and drawn. The feedback effects are analyzed for vibration amplitudes of sandwich microbeam by using Linear Quadratic Gaussian (LQG) and optimal control method. At the end, the results are compared with papers for different viscoelastic models such as Kelvin model, Bingham plastic model and complex modulus. Manuscript profile