Adaptive Amplitude Control of the Cantilever in the Transverse Dynamic Force Microscope

In this paper, the problem of amplitude control of the cantilever in a Transverse Dynamic Force Microscope (TDFM) is considered. The dynamics of the cantilever are initially presented as a partial differential equation which is subsequently approximated by a finite dimensional model. The unknown shear force parameters which affect the amplitude of the cantilever are estimated by an adaptive scheme. A controller which utilizes the parameter estimates of the cantilever shear force model is proposed to regulate the amplitude of the cantilever. This is achieved by an adaptive internal model based feedforward approach, using a novel estimation scheme, to create an overall feedforward model with unity gain. To counter the effect of modelling uncertainty of the cantilever, a feedback scheme senses the difference between the expected unity gain model and the actual cantilever tip position, and feeds back this error dynamically. Thus, the scheme is robust to cantilever model uncertainty and shear force changes. Numerical simulations are presented to illustrate the effectiveness of the proposed methods.