Multilayered non-uniform atomic force microscope piezoelectric microcantilever control and vibration analysis considering different excitation based on the modified couple stress theory.

Atomic force microscope (AFM) is one of the most powerful tools for surface scanning, force measurement, and nano-manipulation. To improve its performance, vibration and control of AFM micro-cantilever (MC) should be studied. Hysteresis, as an undesired phenomenon affecting vibration amplitude and phase, is also another important issue to be examined. In this paper, vibration analysis and control of a ZnO non-uniform multi-layered piezoelectric MC has been investigated in non-contact mode. A modified couple stress theory has been used to obtain the strain energy for modeling the MC. In order to control the amplitude, a sliding mode controller (SMC) has been utilized on AFM, due to its application in uncertain and nonlinear systems. For applying the control signal, two methods of piezo and base actuation are studied. The results are compared with proportional integral derivative (PID) control method and it is demonstrated that SMC method reduces the control input close to the surface and increases the accuracy near the surface. In addition to MC control, hysteresis amplitude and phase differences are investigated by applying the Prandtl-Ishlinskii model. Also, surface topography is studied with hysteresis. The simulations show backward phase difference and an increase in amplitude, accordingly.