چكيده به لاتين
This thesis is aimed at finding out the relation between the vibration motion and control of an Atomic force microscope (AFM) piezoelectric microcantilever (MC) for free and forced vibration in the amplitude mode in the air environment. Nowadays, microrobots based on AFM are widely used as tools for studying the level of materials and displacement of particles in a nanometer scale. In fact, The MC is the most important component of AFM, performing the most vital operations. Hence, the dynamic analysis and control of the MC are mandatory to obtain optimal performance. Enhancing the optimization of this system increases the sampling rate as well as the accuracy and resolution of the obtained images. MCs with a piezoelectric layer possess higher speed and accuracy compared to conventional MCs which are simpler and less expensive.
In order to model the MC in different working environments, it should be noted that each environment has its own forces and these forces affect the behavior of the system. AFM works in three modes, tapping mode, cantact mode and non-contact mode. In a non-contact mode, the MC is close to the surface of the sample by a piezoelectric layer vibration, which results in less contact with the contact modes and less damage to the sample surface. This dissertation deals with the modeling and control of piezoelectric MC vibratory motion in the air and liquid environment in a non-contact mode. In this regard, the theory of Tymoshenko beam and the modified couplE stress theory (MCS) have been used to model the vibrational four-layer MC.
In the MC vibration modeling, the Timoshenko beam model based on the modified couple stress (MCS) theory is used. Next, using the Hamilton’s principle, the motion equations of the system are derived by considering the geometric discontinuities as a result of the piezoelectric layer and two electrode layers. These equations are solved by using the finite element method and the frequency and time responses of the system at different distances from the sample surface are obtained and compared with experimental results in both air and liquid environment. In addition, the topography of a sample surface in the noncontact mode when the MC passes through rectangular and wedge-shaped roughnesses in the first and second vibration modes has been investigated. Moreover, the fuzzy-sliding mode control, which is a robust control method, is employed due to uncertainties when modeling the system and the results are compared with those of the simple sliding mode and PID control methods. For the cases of far from the surface and close to it, the MC is excited by the piezoelectric layer and piezo stack base, respectively. The proposed fuzzy-sliding mode control can properly reduce chattering in the sliding mode control and as a result, improves the results.
Keywords – Atomic force microscope; Timoshenko beam; modified couple stress theory; finite element method; fuzzy-sliding mode control
