In this paper, an atomic force microscope is modeled based on non-classical nonlocal theory and nonlinear vibration of the system is analyzed and controlled. In this modeling, the Hamilton principle is used to derive the governing equation of Euler-Bernoulli nanocantilever based on the Eringen nonlocal elasticity theory considering Von-Karman geometric non-linearity. In the next step, using the Galerkin method, the governing dynamics differential equation of the atomic force microscope is obtained in the presence of attractive and repulsive van der Waals forces. The governing nonlinear equation is solved by employing multiple time scales method, and primary and secondary resonance of the atomic force microscope is studied. In this regard, the frequency response and excitation amplitude curves of primary, superharmonic and subharmonic resonances are plotted for different values ​​of the nonlocal parameter. Accordingly, it is shown that primary, superharmonic and subharmonic resonances of atomic force microscope are significantly affected by the nonlocal parameter. The results show that the use of nonlocal theory is a fundamental necessity for analyzing nonlinear vibrations of the atomic force microscope. Then, in addition to dynamic analysis, the chaotic vibrations are completely controlled and removed in the nonlocal model of the atomic force microscope by designing and implementing the robust adaptive fuzzy controller. For this task, the robust adaptive fuzzy controller which is considered as a powerful method of chaos controlling is used in the nonlocal model of atomic force microscope. The obtained results are used in the design and control process of the atomic force microscope.