1. You have to select a proper power law index to distribute the materials in FGM configuration; Use homogenization scheme like Mori-Tanaka to get effective elastic properties of the constituents. This will provide you the required input to build the constitutive matrix.

2. Third order theory will provide you then the required numerical platform, where you will introduce the kinematics (strain displacement relations), interpolation scheme, loads and solver etc. Follow Prof.Reddy's paper (s), where he has reduced the field variables to only 5 for plate (like FSDT). For beam, it will reduce further.. 

3. Solve for free vibration problem of FGM beam and obtain the K, M matrices.

4.Then you can choose a appropriate controller (PID, LQR, LQG, LMS etc ) in MATLAB toolbox to perform AVC study.